A review of non-linear structural control techniques
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paper_title: STRUCTURAL CONTROL: PAST, PRESENT, AND FUTURE

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This tutorial/survey paper: (1) provides a concise point of departure for researchers and practitioners alike wishing to assess the current state of the art in the control and monitoring of civil engineering structures; and (2) provides a link between structural control and other fields of control theory, pointing out both differences and similarities, and points out where future research and application efforts are likely to prove fruitful. The paper consists of the following sections: section 1 is an introduction; section 2 deals with passive energy dissipation; section 3 deals with active control; section 4 deals with hybrid and semiactive control systems; section 5 discusses sensors for structural control; section 6 deals with smart material systems; section 7 deals with health monitoring and damage detection; and section 8 deals with research needs. An extensive list of references is provided in the references section.
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paper_title: Dynamical interaction of an elastic system and a vibro-impact absorber

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The nonlinear two-degree-of-freedom system under consideration consists of the linear oscillator with a relatively big mass, which is an approximation of some continuous elastic system, and of the vibro-impact oscillator with a relatively small mass, which is an absorber of the linear system vibrations. Analysis of nonlinear normal vibration modes shows that a stable localized vibration mode, which provides the vibration regime appropriate for the elastic vibration absorption, exists in a large region of the system parameters. In this regime, amplitudes of vibrations of the linear system are small, simultaneously vibrations of the absorber are significant.
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paper_title: Seismic Vibration Control of Nonlinear Structures Using the Liquid Column Damper

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A design methodology for a variation of the conventional liquid column damper (LCD) (by attaching a spring connection to the LCD) as a seismic vibration control device for structures with nonlinear behavior has been proposed in this paper. The proposed method with the nonconventional damper has the advantage of being applicable to nonlinear structures having high initial stiffness (short natural period) in the linear range below yield with subsequent period lengthening in the postyield phase, where the conventional LCD would be ineffective. The reason for the lack of effectiveness is not only due to the damper parameters designed for the linear structure becoming inapplicable when the structures move to the inelastic regime but also because of the restriction imposed by the high natural period of the conventional damper on its applicability to comparatively stiff structures (for tuning). The methodology in this paper, thereby incorporating the use of a modified model of the LCD system, namely a spring-connected one, removes the requirement on the natural period of the liquid in the LCD and further, the design is based on the parameters of an equivalent linear system for the nonlinear structure. The latter has been represented by a single-degree-of-freedom system with bilinear hysteresis. A procedure for obtaining the equivalent linear system for the nonlinear structure by adopting a temporally averaged linearization technique has been outlined. A few different response parameters known to have damaging effects on structures, such as number/extent of nonlinear excursions of yield level, permanent set, decay of vibration (duration of response), in addition to the reduction in peak response has been the focus of this paper. The efficacy of the proposed method has been examined through simulation studies using recorded accelerograms.
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paper_title: Twisting of a high authority morphing structure

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A high authority shape morphing plate is examined. The design incorporates an active Kagome back-plane capable of changing the shape of a solid face by transmitting loads through a tetrahedral core. This design is known to perform effectively upon hinging. This article examines limitations on its authority when twisting is required to attain the desired shapes. The specific objective is to ascertain designs that provide the maximum edge twist subject to specified passive load. Non-linear effects, such as face wrinkling, have been probed by using a finite element method and the fidelity of the results assessed through comparison with measurements. The numerical results have been used to validate a dimensional analysis of trends in the actuation resistance of the structure with geometry, as well as the passive load capacity. The forces determined by such analysis have been combined with the failure mechanisms for all subsystems to establish the constraints. The important domains have been visualized using mechanism maps. An optimization has been used to generate load capacity maps that guide geometric design and provide actuator capacity requirements.
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paper_title: Dynamics of structures with wideband autoparametric vibration absorbers: experiment

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The dynamics of a resonantly excited thin cantilever with an active controller are investigated experimentally. The controller mimics a passive wideband absorber discussed in the accompanying theory paper. Lead-zirconate-titanate patches are bonded to both sides of the beam to actuate it, while an electromagnetic shaker drives the beam near resonance. An active controller consisting of an array of coupled controllers is developed, such that the governing equations for the controller are quadratically coupled to the resonating system. The control signal, in terms of the motion of the controllers, is quadratically nonlinear. It is shown that the slow time-scale equations of this physical system are identical in form to those for the passive wideband vibration absorber. The controller is implemented using modelling software and a controller hardware board. Two sets of experiments are performed: one with a constant excitation frequency and the other with a linearly varying excitation frequency at a slow sweep rate (non-stationary excitation). The experimental results verify the analysis presented for the passive wideband autoparametric vibration absorber. The experiments also demonstrate the effectiveness of the absorber in reducing the response amplitude of structures, and its robustness to frequency mistuning.
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paper_title: Application of passive dampers to modern helicopters

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Boeing Helicopters has been actively testing elastomeric and dampers for application on modern rotors. Damper bench tests have been performed on various damper configurations to understand their dynamic characteristics. A recently completed series of wind tunnel tests was performed on a 1/6-Froude-scale model of the Comanche bearingless main rotor system with both elastomeric and dampers. Elastomeric dampers have also been incorporated in the full-scale Model 360 articulated rotor design. This paper summarizes elastomeric and damper activities at Boeing, and discusses issues that must be considered in the design and analysis of such systems.
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paper_title: Static Aeroelastic Response of Chiral-core Airfoils

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Extensive research is being devoted to the analysis and application of cellular solids for the design of innovative structural components. The chiral geometry in particular features a unique mechanical behavior which is here exploited for the design of 2D airfoils with morphing capabilities. A coupled-physics model, comprising computational fluid dynamics and structural analyses, investigates the influence of the chiral core on the aerodynamic behavior of the airfoil. Specifically, the model predicts the static deflection of the airfoil as a result of given flow conditions. The morphing capabilities of the airfoil, here quantified as camber changes, are evaluated for various design configurations of the core.
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paper_title: Bistable composite flap for an airfoil

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A study was conducted to address the challenges associated with investigating a bistable composite flap for an airfoil. A full-scale rotor blade section with a span of 2.114 m and a chord of 0.68 m, fitted with a 1 m span flap was wind-tunnel tested up to a speed of 60 m/s with the flap moving between two stable states for various angles of attack. The blade was approximated as a NACA 24016 section with a 20% chord trailing-edge flap to simplify the analysis. The trailing-edge flap was designed to change between its stable geometries between hover and forward flight conditions for aerodynamic performance improvements. The flap was driven by an electromechanical actuator that was mounted inside the blade D-spar at the leading edge. All of the rotor blade structure remote from this bistable flap region was unmodified and assumed to be completely rigid during wind-tunnel testing.
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paper_title: VIBRATION SUPPRESSION FOR HIGH-SPEED RAILWAY BRIDGES USING TUNED MASS DAMPERS

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Abstract This paper deals with the applicability of passive tuned mass dampers (PTMDs) to suppress train-induced vibration on bridges. A railway bridge is modeled as an Euler–Bernouli beam and a train is simulated as series of moving forces, moving masses or moving suspension masses to investigate the influence of various vehicle models on the bridge features with or without PTMD. According to the train load frequency analysis, the resonant effects will occur as the modal frequencies of the bridges are close to the multiple of the impact frequency of the train load to the bridge. A single PTMD system is then designed to alter the bridge dynamic characteristics to avoid excessive vibrations. Numerical results from simply supported bridges of Taiwan High-Speed Railway (THSR) under German I.C.E., Japanese S.K.S. and French T.G.V. trains show that the proposed PTMD is a useful vibration control device in reducing bridge vertical displacements, absolute accelerations, end rotations and train accelerations during resonant speeds, as the train axle arrangement is regular. It is also found that the inner space of bridge box girder of THSR is wide and deep enough for the installation and movement of PTMD.
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paper_title: Passive Energy Dissipation Systems in Structural Engineering

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Fundamentals. Metallic Dampers. Friction Dampers. Viscoeleastic Dampers. Viscous Fluid Dampers. Tuned Mass Dampers. Tuned Liquid Dampers. Future Direction. Glossary. Indexes.
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paper_title: Truck Suspension Design to Minimize Road Damage

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The objective of the work described in this paper is to establish guidelines for the design of passive suspensions that cause minimum road damage. An efficient procedure for calculating a realistic measure of road damage (the 95th percentile aggregate fourth power force) in the frequency domain is derived. Simple models of truck vibration are then used to examine the influence of suspension parameters on this road damage criterion and to select optimal values.It is found that to minimize road damage a suspension should have stiffness about one fifth of current air suspensions and damping up to twice that typically provided. The use of an anti-roll bar allows a high roll-over threshold without increasing road damage. It is thought that optimization in the pitch-plane should exclude correlation between the axles, to ensure that the optimized suspension parameters are robust to payload and speed changes.A three-dimensional ‘whole-vehicle’ model of an air suspended articulated vehicle is validated against mea...
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paper_title: Adaptive Structures: Engineering Applications

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List of Contributors. Preface. 1 Adaptive Structures for Structural Health Monitoring (Daniel J. Inman and Benjamin L. Grisso). 1.1 Introduction. 1.2 Structural Health Monitoring. 1.3 Impedance-Based Health Monitoring. 1.4 Local Computing. 1.5 Power Analysis. 1.6 Experimental Validation. 1.7 Harvesting, Storage and Power Management. 1.8 Autonomous Self-healing. 1.9 The Way Forward: Autonomic Structural Systems for Threat Mitigation. 1.10 Summary. Acknowledgements. References. 2 Distributed Sensing for Active Control (Suk-Min Moon, Leslie P. Fowler and Robert L. Clark). 2.1 Introduction. 2.2 Description of Experimental Test Bed. 2.3 Disturbance Estimation. 2.4 Sensor Selection. 2.5 Conclusions. Acknowledgments. References. 3 Global Vibration Control Through Local Feedback (Stephen J. Elliott). 3.1 Introduction. 3.2 Centralised Control of Vibration. 3.3 Decentralised Control of Vibration. 3.4 Control of Vibration on Structures with Distributed Excitation. 3.5 Local Control in the Inner Ear. 3.6 Conclusions. Acknowledgements. References. 4 Lightweight Shape-Adaptable Airfoils: A New Challenge for an Old Dream (L.F. Campanile). 4.1 Introduction. 4.2 Otto Lilienthal and the Flying Machine as a Shape-Adaptable Structural System. 4.3 Sir George Cayley and the Task Separation Principle. 4.4 Being Lightweight: A Crucial Requirement. 4.5 Coupling Mechanism and Structure: Compliant Systems as the Basis of Lightweight Shape-Adaptable Systems. 4.6 Extending Coupling to the Actuator System: Compliant Active Systems. 4.7 A Powerful Distributed Actuator: Aerodynamics. 4.8 The Common Denominator: Mechanical Coupling. 4.9 Concluding Remarks. Acknowledgements. References. 5 Adaptive Aeroelastic Structures (Jonathan E. Cooper). 5.1 Introduction. 5.2 Adaptive Internal Structures. 5.3 Adaptive Stiffness Attachments. 5.4 Conclusions. 5.5 The Way Forward. Acknowledgements. References. 6 Adaptive Aerospace Structures with Smart Technologies - A Retrospective and Future View (Christian Boller). 6.1 Introduction. 6.2 The Past Two Decades. 6.3 Added Value to the System. 6.4 Potential for the Future. 6.5 A Reflective Summary with Conclusions. References. 7 A Summary of Several Studies with Unsymmetric Laminates (Michael W. Hyer, Marie-Laure Dano, Marc R. Schultz, Sontipee Aimmanee and Adel B. Jilani). 7.1 Introduction and Background. 7.2 Room-Temperature Shapes of Square [02/902]T Cross-Ply Laminates. 7.3 Room-Temperature Shapes of More General Unsymmetric Laminates. 7.4 Moments Required to Change Shapes of Unsymmetric Laminates. 7.5 Use of Shape Memory Alloy for Actuation. 7.6 Use of Piezoceramic Actuation. 7.7 Consideration of Small Piezoceramic Actuators. 7.8 Conclusions. References. 8 Negative Stiffness and Negative Poisson's Ratio in Materials which Undergo a Phase Transformation (T.M. Jaglinski and R.S. Lakes). 8.1 Introduction. 8.2 Experimental Methods. 8.3 Composites. 8.4 Polycrystals. 8.5 Discussion. References. 9 Recent Advances in Self-Healing Materials Systems (M.W. Keller, B.J. Blaiszik, S.R. White and N.R. Sottos). 9.1 Introduction. 9.2 Faster Healing Systems - Fatigue Loading. 9.3 Smaller Size Scales. 9.4 Alternative Materials Systems - Elastomers. 9.5 Microvascular Autonomic Composites. 9.6 Conclusions. References. 10 Adaptive Structures - Some Biological Paradigms (Julian F.V. Vincent). 10.1 Introduction. 10.2 Deployment. 10.3 Turgor-Driven Mechanisms. 10.4 Dead Plant Tissues. 10.5 Morphing and Adapting in Animals. 10.6 Sensing in Arthropods - Campaniform and Slit Sensilla. 10.7 Developing an Interface Between Biology and Engineering. 10.8 Envoi. Acknowledgements. References. Index.
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paper_title: Passive vibration suppression of flexible space structures via optimal geometric redesign

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Acomputationalframework is presented for the design of large flexible space structures with nonperiodicgeometries to achieve passive vibration suppression. The present system combines an approximationmodel management framework (AMMF) developed for evolutionary optimization algorithms (EAs) with reduced basis approximate dynamic reanalysis techniques. A coevolutionary genetic search strategy is employed to ensure that design changes ::: during the optimization iterations lead to low-rank perturbations of the structural system matrices, for which thereduced basis methods give high-quality approximations. The k-means algorithm is employed for cluster analysis ::: of the population of designs to determine design points at which exact analysis should be carried out. The fitness of ::: the designs in an EA generation is then approximated using reduced basis models constructed around the points ::: where exact analysis is carried out. Results are presented for the optimal design of a two-dimensional cantilevered ::: space structure to achieve passive vibration suppression. It is shown that significant vibration isolation of the order ::: of 50 dB over a 100-Hz bandwidth can be achieved. Further, it is demonstrated that the AMMF can potentially ::: arrive at a better design compared to conventional approaches when a constraint is imposed on the computational ::: budget available for optimization.
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paper_title: Vibration With Control

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Preface. 1. SINGLE DEGREE OF FREEDOM SYSTEMS. Introduction. Spring-Mass System. Spring-Mass-Damper System. Forced Response. Transfer Functions and Frequency Methods. Measurement and Testing. Stability. Design and Control of Vibrations. Nonlinear Vibrations. Computing and Simulation in Matlab. Chapter Notes. References. Problems. 2. LUMPED PARAMETER MODELS. Introduction. Classifications of Systems. Feedback Control Systems. Examples. Experimental Models. Influence Methods. Nonlinear Models and Equilibrium. Chapter Notes. References. Problems. 3. MATRICES AND THE FREE RESPONSE. Introduction. Eigenvalues and Eigenvectors. Natural Frequencies and Mode Shapes. Canonical Forms. Lambda Matrices. Oscillation Results. Eigenvalue Estimates. Computational Eigenvalue Problems in Matlab. Numerical Simulation of the Time Response in Matlab. Chapter Notes. References. Problems. 4. STABILITY. Introduction. Lyapunov Stability. Conservative Systems. Systems with Damping. Semidefinite Damping . Gyroscopic Systems. Damped Gyroscopic Systems. Circulatory Systems. Asymmetric Systems. Feedback Systems. Stability in the State Space. Stability Boundaries. Chapter Notes. References. Problems. 5. FORCED RESPONSE OF LUMPED PARAMETER SYSTEMS. Introduction. Response via State Space Methods. Decoupling Conditions and Modal Analysis. Response of Systems with Damping. Bounded-Input, Bounded-Output Stability. Response Bounds. Frequency Response Methods. Numerical Simulations in Matlab. Chapter Notes. References. Problems. 6. DESIGN CONSIDERATIONS. Introduction. Isolators and Absorbers. Optimization Methods. Damping Design. Design Sensitivity and Redesign. Passive and Active Control. Design Specifications. Model Reduction. Chapter Notes. References. Problems. 7. CONTROL OF VIBRATIONS. Introduction. Controllability and Observability. Eigenstructure Assignment. Optimal Control. Observers (Estimators). Realization. Reduced-Order Modeling. Modal Control in State Space. Modal Control in Physical Space. Robustness. Positive Position Feedback Control. Matlab Commands for Control Calculations. Chapter Notes. References. Problems. 8. VIBRATION MEASUREMENT. Introduction. Measurement Hardware. Digital Signal Processing. Random Signal Analysis. Modal Data Extraction (Frequency Domain). Modal Data Extraction (Time Domain). Model Identification. Model Updating. Chapter Notes. References. Problems. 9. DISTRIBUTED PARAMETER MODELS. Introduction. Vibrations of Strings. Rods and Bars. Vibration of Beams. Membranes and Plates. Layered Materials. Viscous Damping. Chapter Notes. References. Problems. 10. FORMAL METHODS OF SOLUTION. Introduction. Boundary Value Problems and Eigenfunctions. Modal Analysis of the Free Response. Modal Analysis in Damped Systems. Transform Methods. Green's Functions. Chapter Notes. References. Problems. 11. OPERATORS AND THE FREE RESPONSE. Introduction. Hilbert Spaces. Expansion Theorems. Linear Operators. Compact Operators. Theoretical Modal Analysis. Eigenvalue Estimates. Enclosure Theorems. Oscillation Theory. Chapter Notes. References. Problems. 12. FORCED RESPONSE AND CONTROL. Introduction. Response by Modal Analysis. Modal Design Criteria. Combined Dynamical Systems. Passive Control and Design. Distribution Modal Control. Nonmodal Distributed Control. State Space Control Analysis. Chapter Notes. References. Problems. 13. APPROXIMATIONS OF DISTRIBUTED PARAMETER MODELS. Introduction. Modal Truncation. Rayleigh- Ritz-Galerkin Approximations. Finite Element Method. Substructure Analysis. Truncation in the Presence of Control. Impedance Method of Truncation and Control. Chapter Notes. References. Problems. APPENDIX A: COMMENTS ON UNITS. APPENDIX B: SUPPLEMENTARY MATHEMATICS. Index.
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paper_title: OPTIMUM DESIGN OF A PASSIVE SUSPENSION SYSTEM OF A VEHICLE SUBJECTED TO ACTUAL RANDOM ROAD EXCITATIONS

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Abstract Vehicles are subjected to random excitation due to road unevenness and variable velocity. In most research work reported earlier, the response analysis for Mean Square Acceleration Response (MSAR) has been carried out by considering the power spectral density (PSD) of the road excitation as white noise, and the velocity of the vehicle as constant. However, in the present paper the PSD of the actual road excitation has been found to follow an approximately exponentially decreasing curve. Also the change in vehicle velocity has a significant effect on the values of Root Mean Square Acceleration Response (RMSAR). Therefore, in this work, the RMSAR of a vehicle dynamic system subjected to actual random road excitations is obtained so as to account for the effect of the actual PSD of road excitation and the frequent changes in vehicle velocity. The RMSAR of the vehicle is calculated for actual field excitation using the Fast Fourier Transformation (FFT) technique to obtain the PSD, by recording observations at the rear wheel. The effect of time lag due to wheelbase on the RMSAR of the vehicle is studied. For this purpose, a new ratio α(τ) has been introduced. The relationship between α(τ) and the autocorrelation has been formulated. This ratio is useful for considering the effect of time lag due to wheelbase on RMSAR. Similarly, the effect of vehicle velocity on the RMSAR is obtained. Further, from a ride comfort point of view, the values of the design variables like spring stiffness and viscous damping coefficient of the front and rear suspensions have been obtained, by minimising the RMSAR using the desired boundary values of the vertical RMSAR as specified in the chart of ISO 2631, 1985(E) [1].
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paper_title: Exploring the performance of a nonlinear tuned mass damper

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We explore the performance of a nonlinear tuned mass damper (NTMD), which is modeled as a two degree of freedom system with a cubic nonlinearity. This nonlinearity is physically derived from a geometric configuration of two pairs of springs. The springs in one pair rotate as they extend, which results in a hardening spring stiffness. The other pair provides a linear stiffness term. We perform an extensive numerical study of periodic responses of the NTMD using the numerical continuation software AUTO. In our search for optimal design parameters we mainly employ two techniques, the optimization of periodic solutions and parameter sweeps. During our investigation we discovered a family of detached resonance curves for vanishing linear spring stiffness, a feature that was missed in an earlier study. These detached resonance response curves seem to be a weakness of the NTMD when used as a passive device, because they essentially restore a main resonance peak. However, since this family is detached from the low-amplitude responses there is an opportunity for designing a semi-active device.
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paper_title: Design and demonstration of a high authority shape morphing structure

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Abstract A concept for a high authority shape morphing plate is described and demonstrated. The design incorporates an active back-plane comprising a Kagome truss, capable of changing the shape of a solid face, connected to the back-plane by means of a tetrahedral truss core. The two shape deformations to be demonstrated consist of hinging and twisting. The design is performed by a combination of analytic estimation and numerical simulation, guided by previous assessments of the Kagome configuration. It is shown that, while the structure is capable of sustaining large passive loads at low weight, the demonstrable authority is actuator-limited. The full potential of the system can only be realized by developing and incorporating superior actuators. An optimization has been used to ascertain the largest displacements achievable within the force capability of the actuators. These displacements have been demonstrated and shown to correspond with values predicted by numerical simulation. The consistency between measured and calculated responses has allowed objectives to be set for alternative materials, as well as structural and actuator enhancements.
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paper_title: Static analysis of a passive vibration isolator with quasi-zero-stiffness characteristic

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Abstract The frequency range over which a linear passive vibration isolator is effective, is often limited by the mount stiffness required to support a static load. This can be improved upon by employing nonlinear mounts incorporating negative stiffness elements configured in such a way that the dynamic stiffness is much less than the static stiffness. Such nonlinear mounts are used widely in practice, but rigorous analysis, and hence a clear understanding of their behaviour is not readily available in the literature. In this paper, a simple system comprising a vertical spring acting in parallel with two oblique springs is studied. It is shown that there is a unique relationship between the geometry and the stiffness of the springs that yields a system with zero dynamic stiffness at the static equilibrium position. The dynamic stiffness increases monotonically with displacement either side of the equilibrium position, and this is least severe when the oblique springs are inclined at an angle between approximately 48° and 57°. Finally, it is shown that the force–displacement characteristic of the system can be approximated by a cubic equation.
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paper_title: Inverse eigenvalue problems in vibration absorption : Passive modification and active control

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The abiding problem of vibration absorption has occupied engineering scientists for over a century and there remain abundant examples of the need for vibration suppression in many industries. For example, in the automotive industry the resolution of noise, vibration and harshness (NVH) problems is of extreme importance to customer satisfaction. In rotorcraft it is vital to avoid resonance close to the blade passing speed and its harmonics. An objective of the greatest importance, and extremely difficult to achieve, is the isolation of the pilot's seat in a helicopter. It is presently impossible to achieve the objectives of vibration absorption in these industries at the design stage because of limitations inherent in finite element models. Therefore, it is necessary to develop techniques whereby the dynamic of the system (possibly a car or a helicopter) can be adjusted after it has been built. There are two main approaches: structural modification by passive elements and active control. The state of art of the mathematical theory of vibration absorption is presented and illustrated for the benefit of the reader with numerous simple examples.
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paper_title: Determinate structures for wing camber control

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An investigation of truss structures for the purpose of creating a continuously variable camber trailing edge device for an aircraft wing is presented. By creating structures that are both statically and kinematically determinate and then substituting truss elements for actuators, it is possible to impose structural deflection without inducing member stress. A limited number of actuators with limited strain capabilities are located within the structure in order to achieve a target deflected shape starting from an initially symmetric profile. Two objective functions are used to achieve this: a geometric objective for which the target displacement is fixed and a shape objective for which the target displacement is dependent on the surface shape of the targeted aerofoil. The proposed shape objective function is able to offer improvements over the geometric objective by removing some of the constraints applied to the targeted structure joint locations. Four methods for selecting the location of a set of actuators are compared, namely exhaustive search, a genetic algorithm, stepwise forward selection (SFS) and incremental forward selection (IFS). Both SFS and IFS are variations of regression methods for subset selection; in each case an approach has been created to allow the imposing of upper and lower bounds on the search space. It is shown that the genetic algorithm is well suited to addressing the problem of optimally locating a set of actuators; however, regression methods, particularly IFS, can provide a rapid tool suitable for addressing large selection problems.
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paper_title: Nonlinear Vibration Control of a System with Dry Friction and Viscous Damping Using the Saturation Phenomenon

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Application of saturation to provide active nonlinear vibration control was introduced not long ago. Saturation occurs when two natural frequencies of a system with quadratic nonlinearities are in a ratio of around 2:1 and the system is excited at a frequency near its higher natural frequency. Under these conditions, there is a small upper limit for the high-frequency response and the rest of the input energy is channeled to the low-frequency mode. In this way, the vibration of one of the degrees of freedom of a coupled 2 degrees of freedom system is attenuated. In the present paper, the effect of dry friction on the response of a system that implements this vibration absorber is discussed. The system is basically a plant with a permanent magnet DC (PMDC) motor excited by a harmonic forcing term and coupled with a quadratic nonlinear controller. The absorber is built in electric circuitry and takes advantage of the saturation phenomenon. The method of multiple scales is used to find approximate solutions. Various response regimes of the closed-loop system as well as the stability of these regimes are studied and the stability boundaries are obtained. Especial attention is paid on the effect of dry friction on the stability boundaries. It is shown that while dry friction tends to shrink the stable region in some parts, it enlarges other parts of the stable region. To verify the theoretical results, they have been compared with numerical solution and good agreement between the two is observed.
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paper_title: Active and passive material optimization in a tendon-actuated morphing aircraft structure

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Continuously morphing aircraft wings are currently a focus of considerable research. Efforts are being made to achieve effective and optimal wing shape change under different flight conditions such as take off, cruise, dash, and loiter. The present research aims to achieve wing morphing by using an internal structure consisting of actuated tendons and passive struts. An important aspect of this approach is determining the optimal layout of tendons and struts. In this paper a genetic algorithm is developed to optimize the three-dimensional tendon-strut layout for a prescribed wing geometry and shape change. The method is applied to two morphing wing applications, the NASA HECS wing and NextGen TSCh wing.
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paper_title: Seismic control of a nonlinear benchmark building using smart dampers

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This paper addresses the third-generation benchmark problem on structural control, and focuses on the control of a full-scale, nonlinear, seismically excited, 20-story building. A semiactive design is developed in which magnetorheological (MR) dampers are applied to reduce the structural responses of the benchmark building. Control input determination is based on a clipped-optimal control algorithm which employs absolute acceleration feedback. A phenomenological model of an MR damper, based on a Bouc–Wen element, is employed in the analysis. The semiactive system using the MR damper is compared to the performance of an active system and an ideal semiactive system, which are based on the same nominal controller as is used in the MR damper control algorithm. The results demonstrate that the MR damper is effective, and achieves similar performance to the active and ideal semiactive system, while requiring very little power.
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paper_title: Stability of a Lyapunov controller for a semi-active structural control system with nonlinear actuator dynamics

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Abstract We investigate semi-active control for a wide class of systems with scalar nonlinear semi-active actuator dynamics and consider the problem of designing control laws that guarantee stability and provide sufficient performance. Requiring the semi-active actuator to satisfy two general conditions, we present a method for designing quickest descent controllers generated from quadratic Lyapunov functions that guarantee asymptotic stability within the operating range of the semiactive device for the zero disturbance case. For the external excitation case, bounded-input, bounded-output stability is achieved and a stable attractor (ball of ultimate boundedness) of the system is computed based on the upper bound of the disturbances. We show that our wide class of systems covers, in particular, two nonlinear actuator models from the literature. Tuning the performance of the simple Lyapunov controllers is straightforward using either modal or state penalties. Simulation results are presented which indicate that the Lyapunov control laws can be selected to provide similar decay rates as a “time-optimal” controller for a semi-actively controlled single degree of freedom structure with no external excitation.
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paper_title: Survey of Advanced Suspension Developments and Related Optimal Control Applications,

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Abstract The paper surveys applications of optimal control techniques to the design of active suspensions, starting from simple quarter-car, 1D models, which are followed by their half-car, 2D, and full-car, 3D, counterparts. While the main emphasis is on Linear-Quadratic (LQ) optimal control and active suspensions, the paper also addresses a number of related subjects including semi-active suspensions; robust, adaptive and nonlinear control aspects and some of the important practical considerations. © 1997 Elsevier Science Ltd.
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paper_title: State of the Art of Structural Control

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In recent years, considerable attention has been paid to research and development of structural control devices, with particular emphasis on alleviation of wind and seismic response of buildings and bridges. In both areas, serious efforts have been undertaken in the last two decades to develop the structural control concept into a workable technology. Full-scale implementation of active control systems have been accomplished in several structures, mainly in Japan; however, cost effectiveness and reliability considerations have limited their wide spread acceptance. Because of their mechanical simplicity, low power requirements, and large, controllable force capacity, semiactive systems provide an attractive alternative to active and hybrid control systems for structural vibration reduction. In this paper we review the recent and rapid developments in semiactive structural control and its implementation in full-scale structures.
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paper_title: Piecewise-Smooth Dynamical Systems : Theory and Applications

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This book deals with the analysis of bifurcation and chaos in nonsmooth (called piecewise smooth by the authors) dynamical systems. Some of the topics covered include: a very detailed study of discontinuity-induced bifurcations (DIBs) in nonsmooth maps and nonsmooth systems; limit-cycle bifurcations in vibro-impact systems; grazing bifurcations for periodic trajectories; the derivation of Poincare maps; the influence of chattering; and sliding mode systems. This book is a strong contribution to the field of bifurcation and chaos analysis and more generally to the field of nonsmooth dynamical systems analysis and will serve as a reference to specialists in the field.
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paper_title: Generalisation and optimisation of semi-active, on–off switching controllers for single degree-of-freedom systems

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This paper examines generalised forms of semi-active switching control in comparison to the sky-hook semi-active controller. A switching time controller is proposed and analysed, in order to determine the optimal performance, with regard to displacement transmissibility, of semi-active switching control. In addition, the model is also used to assess the optimality of the sky-hook switching conditions. An analytical solution is then derived for the optimal switching times. A generalised form of linear switching surface controller is then presented. It is demonstrated that this controller can produce near optimal performance.
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paper_title: Nonlinear blackbox modeling of MR-dampers for civil structural control

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Protecting civil engineering structures from severe impacts like strong earthquakes has demanded intensive research in the past two decades. One of the most promising devices proposed for structural protection is the magnetorheological (MR) fluid dampers. To fully explore their potentials in the real-time feedback control implementations, accurate and robust modeling of the devices is a prerequisite. This paper first proposes a general nonlinear blackbox structure to model the MR damping behavior on the displacement-velocity phase plane. Two constructive parameter estimation algorithms are subsequently developed which are based on the recent mathematical advances in wavelets and ridgelets analysis. Compared with the traditional physical modeling, this research aims at improving model numerical stability and model structure generality. The achievement of these objectives is evaluated in the modeling of an experimental MR-damper in a base-isolation structural control system.
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paper_title: Semi-active and passive control of the phase I linear base-isolated benchmark building model

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In this paper various semi-active control strategies and linear passive dampers are applied to the benchmark building model to evaluate their effectiveness in reducing response quantities of the building subject to prescribed earthquakes. These control strategies include: semi-active continuous pulse friction (SACPF) controller, semi-active discontinuous pulse friction (SADPF) controller, linear passive viscous (LPV) damper, smooth boundary layer semi-active friction (SBLSAF) controller, resetting semi-active stiffness damper (RSASD) and visco-elastic friction (VEF) damper. Both SACPF and SADPF controllers are designed by using the augmented structure-pulse filter model recently proposed. Extensive simulation results indicate that all these controllers are very effective in mitigating the base displacements. For different controllers, a reduction in the base displacement may result in an increase of other quantities, e.g. the base and superstructure shears, inter-storey drifts and floor accelerations, during some earthquakes. Average results of the performance indices J1–J5 indicate that various semi-active friction controllers, including SACPF, SADPF, SBLSAF and VEF, are most effective followed by the RSASD and the sample semi-active controller. Overall, SACPF and SADPF controllers have better capability of reducing all response quantities compared with other semi-active controllers. Copyright © 2005 John Wiley & Sons, Ltd.
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paper_title: Magneto-rheological tuned liquid column dampers (MR-TLCDs) for vibration mitigation of tall buildings: modelling and analysis of open-loop control

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A novel semi-active tuned liquid column damper using magneto-rheological fluid (MR-TLCD) is devised for wind-induced vibration mitigation of tall building structures. It combines the benefits of magneto-rheological smart materials and tuned liquid column dampers. A mathematical model of the devised MR-TLCD is first established using the parallel-plate theory, and then a method for analyzing stochastic dynamic response of building structures incorporating semi-active MR-TLCDs subjected to random wind excitation is developed by means of the equivalent linearization technique. The open-loop control effectiveness of MR-TLCDs in mitigating wind-induced structural response is studied by referring to a 50-storey high-rise residential building equipped with MR-TLCDs. The analysis results show that MR-TLCDs with optimal parameters are capable of achieving much better vibration mitigation capability than conventional TLCD system.
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paper_title: Active Control of Structures

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About the Authors. Preface. Acknowledgements. 1 Active Damping. 1.1 Introduction. 1.2 Structural Control. 1.3 Plant Description. 1.4 Equations of Structural Dynamics. 1.5 Collocated Control System. 1.6 Active Damping with Collocated System. 1.7 Decentralized Control with Collocated Pairs. 2 Active Isolation. 2.1 Introduction. 2.2 Relaxation Isolator. 2.3 Sky-hook Damper. 2.4 Force Feedback. 2.5 Six-Axis Isolator. 2.6 Vehicle Active Suspension. 2.7 Semi-Active Suspension. 3 A Comparison of Passive, Active and Hybrid Control. 3.1 Introduction. 3.2 System Description. 3.3 The Dynamic Vibration Absorber. 3.4 Active Mass Damper. 3.5 Hybrid Control. 3.6 Shear Control. 3.7 Force Actuator, Displacement Sensor. 3.8 Displacement Actuator, Force Sensor. 4 Vibration Control Methods and Devices. 4.1 Introduction. 4.2 Classification of Vibration Control Methods. 4.3 Construction of Active Dynamic Absorber. 4.4 Control Devices for Wind Excitation Control in Civil Structures. 4.5 Real Towers Using the Connected Control Method. 4.6 Application of Active Dynamic Absorber for Controlling Vibration of Single-d.o.f. Systems. 4.7 Remarks. 5 Reduced-Order Model for Structural Control. 5.1 Introduction. 5.2 Modeling of Distributed Structures. 5.3 Spillover. 5.4 The Lumped Modeling Method. 5.5 Method of Equivalent Mass Estimation. 5.6 Modeling of Tower-like Structure. 5.7 Modeling of Plate Structures. 5.8 Modeling of a Bridge Tower. 5.9 Robust Vibration Control for Neglected Higher Modes. 5.10 Conclusions. 6 Active Control of Civil Structures. 6.1 Introduction. 6.2 Classification of Structural Control for Buildings. 6.3 Modeling and Vibration Control for Tower Structures. 6.4 Active Vibration Control of Multiple Buildings Connected with Active Control Bridges in Response to Large Earthquakes. 6.5 Vibration Control for Real Triple Towers Using CCM. 6.6 Vibration Control of Bridge Towers Using a Lumped Modeling Approach. 6.7 Conclusion. References. Index.
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paper_title: Benchmark structural control problem for a seismically excited highway bridge-Part I: Phase I Problem definition

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This paper presents the problem definition of the benchmark structural control problem for the seismically excited highway bridge. The benchmark problem is based on the newly constructed 91/5 highway over-crossing in southern California. The goal of this benchmark effort is to develop a standardized model of a highway bridge using which competing control strategies, including devices, algorithms and sensors, can be evaluated comparatively. To achieve this goal, a 3D finite-element model is developed in MATLAB to represent the complex behavior of the full-scale highway over-crossing. The nonlinear behavior of center columns and isolation bearings is considered in formulating the bilinear force–deformation relationship. The effect of soil–structure interaction is considered by modeling the interaction by equivalent spring and dashpot. The ground motions are considered to be applied simultaneously in two directions. A MATLAB-based nonlinear structural analysis tool has been developed and made available for nonlinear dynamic analysis. Control devices are assumed to be installed between the deck and the end abutments of the bridge. Evaluation criteria and control constraints are specified for the design of controllers. Passive, semi-active and active devices and algorithms can be used to study the benchmark model. The participants in this benchmark study are required to define their control devices, sensors and control algorithms, evaluate and report the results of their proposed control strategies. Copyright © 2009 John Wiley & Sons, Ltd.
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paper_title: On the Isolation Properties of Semiactive Dampers

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The primary purpose of this study is to evaluate and better understand the isolation properties of semiactive suspensions. Specifically, this study will answer the question regarding why semiactive dampers are able to isolate at frequencies well below those for passive dampers, even though they do not add any energy to the system. A single suspension model is used to derive and analytically evaluate the transmissibility properties of passive and semiactive dampers. The results show that for semiactive dampers, the frequency range of isolation and the transmissibility amplitude are functions of ξ, the damping ratio. In contrast, the isolation frequency range for passive dampers is completely independent of ξ. Furthermore, the results show that for sufficiently large ξ, semiactive dampers are able to provide isolation at all frequencies. This feature is useful for many applications, particularly for sensitive machinery that cannot tolerate any overshoot in power- up or power-down, and yet must have good iso...
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paper_title: Vibration control of mechanical systems using semi-active MR-damper

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The concept of structural vibration control is to absorb vibration energy of the structure by introducing auxiliary devices. Various types of structural vibration control theories and devices have been recently developed and introduced into mechanical systems. One of such devices is damper employing controllable fluids such as ElectroRheological (ER) or MagnetoRheological (MR) fluids. MagnetoRheological (MR) materials are suspensions of fine magnetizable ferromagnetic particles in a non-magnetic medium exhibiting controllable rheological behaviour in the presence of an applied magnetic field. This paper presents the modelling of an MRfluid damper. The damper model is developed based on Newtonian shear flow and Bingham plastic shear flow models. The geometric parameters are varied to get the optimised damper characteristics. The numerical analysis is carried out to estimate the damping coefficient and damping force. The analytical results are compared with the experimental results. The results confirm that MR damper is one of the most promising new semi-active devices for structural vibration control.
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paper_title: Nonlinear vibration of shallow cables with semiactive tuned mass damper

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The nonlinear vibration of shallow cables, equipped with a semiactive control device is considered in this paper. The control device is represented by a tuned mass damper with a variable out-of-plane inclination. A suitable control algorithm is designed in order to regulate the inclination of the device and to dampen the spatial cable vibrations. Numerical simulations are conducted under free spatial oscillations through a nonlinear finite element model, solved in two different computational environments. A harmonic analysis, in the region of the primary resonance, is also performed through a control-oriented nonlinear Galerkin model, including detuning effects due to the cable slackening.
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paper_title: Semi-active control of seismic response of tall buildings with podium structure using ER/MR dampers

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A tall building with a large podium structure under earthquake excitation may suffer from a whipping effect due to the sudden change of building lateral stiffness at the top of the podium structure. This paper thus explores the possibility of using electrorheological (ER) dampers or magnetorheological (MR) dampers to connect the podium structure to the tower structure to prevent this whipping effect and to reduce the seismic response of both structures. A set of governing equations of motion for the tower–damper–podium system is first derived, in which the stiffness of the member connecting the ER/MR damper to the structures is taken into consideration. Based on the principle of instantaneous sub-optimal active control, a semi-active sub-optimal displacement control algorithm is then proposed. To demonstrate the effectiveness of semi-active control of the system under consideration, a 20-storey tower structure with a 5-storey podium structure subjected to earthquake excitation is finally selected as a numerical example. The results from the numerical example imply that, as a kind of intelligent control device, ER/MR dampers can significantly mitigate the seismic whipping effect on the tower structure and reduce the seismic responses of both the tower structure and the podium structure. Copyright © 2001 John Wiley & Sons, Ltd.
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paper_title: A semi-active stochastic optimal control strategy for nonlinear structural systems with MR dampers

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A non-clipped semi-active stochastic optimal control strategy for nonlinear structural systems with MR dampers is developed based on the stochastic averaging method and stochastic dynamical programming principle. A nonlinear stochastic control structure is first modeled as a semi-actively controlled, stochastically excited and dissipated Hamiltonian system. The control force of an MR damper is separated into passive and semi-active parts. The passive control force components, coupled in structural mode space, are incorporated in the drift coefficients by directly using the stochastic averaging method. Then the stochastic dynamical programming principle is applied to establish a dynamical programming equation, from which the semi-active optimal control law is determined and implementable by MR dampers without clipping in terms of the Bingham model. Under the condition on the control performance function given in section 3, the expressions of nonlinear and linear non-clipped semi-active optimal control force components are obtained as well as the non-clipped semi-active LQG control force, and thus the value function and semi-active nonlinear optimal control force are actually existent according to the developed strategy. An example of the controlled stochastic hysteretic column is given to illustrate the application and effectiveness of the developed semi-active optimal control strategy.
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paper_title: Semi‐active neuro‐control for base‐isolation system using magnetorheological (MR) dampers

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Vibration mitigation using smart, reliable and cost-effective mechanisms that requires small activation power is the primary objective of this paper. A semi-active controller-based neural network for base-isolation structure equipped with a magnetorheological (MR) damper is presented and evaluated. An inverse neural network model (INV-MR) is constructed to replicate the inverse dynamics of the MR damper. Next, linear quadratic Gaussian (LQG) controller is designed to produce the optimal control force. Thereafter, the LQG controller and the INV-MR models are linked to control the structure. The coupled LQG and INV-MR system was used to train a semi-active neuro-controller, designated as SA-NC, which produces the necessary control voltage that actuates the MR damper. To evaluate the proposed method, the SA-NC is compared to passive lead–rubber bearing isolation systems (LRBs). Results revealed that the SA-NC was quite effective in seismic response reduction for wide range of motions from moderate to severe seismic events compared to the passive systems. In addition, the semi-active MR damper enjoys many desirable features, such as its inherent stability, practicality and small power requirements. The effectiveness of the SA-NC is illustrated and verified using simulated response of a six-degree-of-freedom model of a base-isolated building excited by several historical earthquake records. Copyright © 2006 John Wiley & Sons, Ltd.
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paper_title: A Comparative Study and Analysis of Semi-Active Vibration-Control Systems

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Semi-active (SA) vibration-control systems are those which otherwise passively generated damping or spring forces are modulated according to a parameter tuning policy with only a small amount of control effort. SA units, as their name implies, fill the gap between purely passive and fully active vibration-control systems and offer the reliability of passive systems, yet maintain the versatility and adaptability of fully active devices. During recent years there has been considerable interest towards practical implementation of these systems for their low energy requirement and cost. This paper briefly reviews the basic theoretical concepts for SA vibration-control design and implementation, and surveys recent developments and control techniques for these systems. Some related practical applications in vehicle suspensions are also presented.
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paper_title: Dynamic modeling of large-scale magnetorheological damper systems for civil engineering applications

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Magnetorheological (MR) dampers are one of the most promising new devices for structural vibration mitigation. Because of their mechanical simplicity, high dynamic range, low power requirements, large force capacity, and robustness, these devices have been shown to mesh well with earthquake and wind engineering application demands and constraints. Quasistatic models of MR dampers have been investigated by researchers. Although useful for damper design, these models are not sufficient to describe the MR damper behavior under dynamic loading. This paper presents a new dynamic model of the overall MR damper system which is comprised of two parts: (1) a dynamic model of the power supply and (2) a dynamic model of the MR damper. Because previous studies have demonstrated that a current-driven power supply can substantially reduce the MR damper response time, this study employs a current driver to power the MR damper. The operating principles of the current driver, and an appropriate dynamic model are provided. Subsequently, MR damper force response analysis is performed, and a phenomenological model based on the Bouc-Wen model is proposed to estimate the MR damper behavior under dynamic loading. This model accommodates the MR fluid stiction phenomenon, as well as fluid inertial and shear thinning effects. Compared with other types of models based on the Bouc-Wen model, the proposed model has been shown to be more effective, especially in describing the force rolloff in the low velocity region, force overshoots when velocity changes in sign, and two clockwise hysteresis loops at the velocity extremes.
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paper_title: Nonsmooth Mechanics: Models, Dynamics and Control

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1 Distributional model of impacts.- 1.1 External percussions.- 1.2 Measure differential equations.- 1.2.1 Some properties.- 1.2.2 Additional comments.- 1.3 Systems subject to unilateral constraints.- 1.3.1 General considerations.- 1.3.2 Flows with collisions.- 1.3.3 A system theoretical geometric approach.- 1.3.4 Descriptor variable systems.- 1.4 Changes of coordinates in MDEs.- 1.4.1 From measure to Caratheodory systems.- 1.4.2 Decoupling of the impulsive effects (commutativity conditions).- 1.4.3 From measure to Filippov's differential equations: the Zhuravlev-Ivanov method.- 2 Approximating problems.- 2.1 Simple examples.- 2.1.1 From elastic to hard impact.- 2.1.2 From damped to plastic impact.- 2.1.3 The general case.- 2.2 The method of penalizing functions.- 2.2.1 The elastic rebound case.- 2.2.2 A more general case.- 2.2.3 Uniqueness of solutions.- 3 Variational principles.- 3.1 Virtual displacements principle.- 3.2 Gauss' principle.- 3.2.1 Additional comments and studies.- 3.3 Lagrange's equations.- 3.4 External impulsive forces.- 3.4.1 Example: flexible joint manipulators.- 3.5 Hamilton's principle and unilateral constraints.- 3.5.1 Introduction.- 3.5.2 Modified set of curves.- 3.5.3 Modified Lagrangian function.- 3.5.4 Additional comments and studies.- 4 Two bodies colliding.- 4.1 Dynamical equations of two rigid bodies colliding.- 4.1.1 General considerations.- 4.1.2 Relationships between real-world and generalized normal di-rections.- 4.1.3 Dynamical equations at collision times.- 4.1.4 The percussion center.- 4.2 Percussion laws.- 4.2.1 Oblique percussions with friction between two bodies.- 4.2.2 Rigid body formulation: Brach's method.- 4.2.3 Additional comments and studies.- 4.2.4 Rigid body formulation: Fremond's approach.- 4.2.5 Dynamical equations during the collision process: Darboux-Keller's shock equations.- 4.2.6 Stronge's energetical coefficient.- 4.2.7 3 dimensional shocks- Ivanov's energetical coefficient.- 4.2.8 A third energetical coefficient.- 4.2.9 Additional comments and studies.- 4.2.10 Multiple micro-collisions phenomenon: towards a global coef-ficient.- 4.2.11 Conclusion.- 4.2.12 The Thomson and Tait formula.- 4.2.13 Graphical analysis of shock dynamics.- 4.2.14 Impacts in flexible structures.- 5 Multiconstraint nonsmooth dynamics.- 5.1 Introduction. Delassus' problem.- 5.2 Multiple impacts: the striking balls examples.- 5.3 Moreau's sweeping process.- 5.3.1 General formulation.- 5.3.2 Application to mechanical systems.- 5.3.3 Existential results.- 5.3.4 Shocks with friction.- 5.4 Complementarity formulations.- 5.4.1 General introduction to LCPs and Signorini's conditions.- 5.4.2 Linear Complementarity Problems.- 5.4.3 Relationships with quadratic problems.- 5.4.4 Linear complementarity systems.- 5.4.5 Additional comments and studies.- 5.5 The Painleve's example.- 5.5.1 Lecornu's frictional catastrophes.- 5.5.2 Conclusions.- 5.5.3 Additional comments and bibliography.- 5.6 Numerical analysis.- 5.6.1 General comments.- 5.6.2 Integration of penalized problems.- 5.6.3 Specific numerical algorithms.- 6 Generalized impacts.- 6.1 The frictionless case.- 6.1.1 About "complete" Newton's rules.- 6.2 The use of the kinetic metric.- 6.2.1 The kinetic energy loss at impact.- 6.3 Simple generalized impacts.- 6.3.1 2-dimensional lamina striking a plane.- 6.3.2 Shock of a particle against a pendulum.- 6.4 Multiple generalized impacts.- 6.4.1 The rocking block problem.- 6.5 General restitution rules for multiple impacts.- 6.5.1 Introduction.- 6.5.2 The rocking block example continued.- 6.5.3 Additional comments and studies.- 6.5.4 3-balls example continued.- 6.5.5 2-balls.- 6.5.6 Additional comments and studies.- 6.5.7 Summary of the main ideas.- 6.5.8 Collisions near singularities: additional comments.- 6.6 Constraints with Amontons-Coulomb friction.- 6.6.1 Lamina with friction.- 6.7 Additional comments and studies.- 7 Stability of nonsmooth dynamical systems.- 7.1 General stability concepts.- 7.1.1 Stability of measure differential equations.- 7.1.2 Stability of mechanical systems with unilateral constraints.- 7.1.3 Passivity of the collision mapping.- 7.1.4 Stability of the discrete dynamic equations.- 7.1.5 Impact oscillators.- 7.1.6 Conclusions.- 7.2 Grazing orC-bifurcations.- 7.2.1 The stroboscopic Poincare map discontinuities.- 7.2.2 The stroboscopic Poincare map around grazing-motions...- 7.2.3 Further comments and studies.- 7.3 Stability: from compliant to rigid models.- 7.3.1 System's dynamics.- 7.3.2 Lyapunov stability analysis.- 7.3.3 Analysis of quadratic stability conditions for large stiffness values.- 7.3.4 A stiffness independent convergence analysis.- 8 Feedback control.- 8.1 Controllability properties.- 8.2 Control of complete robotic tasks.- 8.2.1 Experimental control of the transition phase.- 8.2.2 The general control problem.- 8.3 Dynamic model.- 8.3.1 A general form of the dynamical system.- 8.3.2 The closed-loop formulation of the dynamics.- 8.3.3 Definition of the solutions.- 8.4 Stability analysis framework.- 8.5 A one degree-of-freedom example.- 8.5.1 Static state feedback (weakly stable task).- 8.5.2 Towards a strongly stable closed-loop scheme.- 8.5.3 Dynamic state feedback.- 8.6ndegree-of-freedom rigid manipulators.- 8.6.1 Integrable transformed velocities.- 8.6.2 Examples.- 8.6.3 Non-integrable transformed velocities: general case.- 8.6.4 Non-integrable transformed velocities: a strongly stable scheme.- 8.7 Complementary-slackness juggling systems.- 8.7.1 Some examples.- 8.7.2 Some controllability properties.- 8.7.3 Control design.- 8.7.4 Further comments.- 8.8 Systems with dynamic backlash.- 8.9 Bipedal locomotion.- A Schwartz' distributions.- A.1 The functional approach.- A.2 The sequential approach.- A.3 Notions of convergence.- B Measures and integrals.- C Functions of bounded variation in time.- C.1 Definition and generalities.- C.2 Spaces of functions of bounded variation.- C.3 Sobolev spaces.- D Elements of convex analysis.
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paper_title: Seismic control of smart base isolated buildings with new semiactive variable damper

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A new semiactive independently variable damper, SAIVD, is developed and shown to be effective in achieving response reductions in smart base isolated buildings in near fault earthquakes. The semiactive device consists of four linear visco-elastic elements, commonly known as Kelvin-Voigt elements, arranged in a rhombus configuration. The magnitude of force in the semiactive device can be adjusted smoothly in real-time by varying the angle of the visco-elastic elements of the device or the aspect ratio of the rhombus configuration. Such a device is essentially linear, simple to construct, and does not present the difficulties commonly associated with modelling and analysing nonlinear devices (e.g. friction devices). The smooth semiactive force variation eliminates the disadvantages associated with rapid switching devices. Experimental results are presented to verify the proposed analytical model of the device. A H ∞ control algorithm is implemented in order to reduce the response of base isolated buildings with variable damping semiactive control systems in near fault earthquakes. The central idea of the control algorithm is to design a H ∞ controller for the structural system that serves as an aid in the determination of the optimum control force in the semiactive device. The relative performance of the SAIVD device is compared to a variable friction device, recently developed by the authors in a separate study, and several key aspects of performance are discussed regarding the use of the two devices for reducing the responses of smart base isolated buildings in near fault earthquakes.
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paper_title: Hierarchical semi-active control of base-isolated structures using a new inverse model of magnetorheological dampers

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Magnetorheological (MR) dampers have received special attention as semi-active devices for mitigation of structural vibrations. Because of the inherent nonlinearity of these devices, it is difficult to obtain a reasonable mathematical inverse model. This paper is concerned with two related concepts. On one hand, it presents a new inverse model of MR dampers based on the normalized Bouc-Wen model. On the other hand, it considers a hybrid seismic control system for building structures, which combines a class of passive nonlinear base isolator with a semi-active control system. In this application, the MR damper is used as a semi-active device in which the voltage is updated by a feedback control loop. The management of MR dampers is performed in a hierarchical way according to the desired control force, the actual force of the dampers and its capacity to react. The control is applied to a numerical three-dimensional benchmark problem which is used by the structural control community as a state-of-the-art model for numerical experiments of seismic control attenuation. The performance indices show that the proposed semi-active controller behaves satisfactorily.
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paper_title: Design Optimization of Quarter-car Models with Passive and Semi-active Suspensions under Random Road Excitation

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A methodology is presented for optimizing the suspension damping and stiffness parameters of nonlinear quarter-car models subjected to random road excitation. The investigation starts with car models involving passive damping with constant or dual-rate characteristics. Then, we also examine car models where the damping coefficient of the suspension is selected so that the resulting system approximates the performance of an active suspension system with sky-hook damping. For the models with semi-active or passive dual-rate dampers, the value of the equivalent suspension damping coefficient is a function of the relative velocity of the sprung mass with respect to the wheel subsystem. As a consequence, the resulting equations of motion are strongly nonlinear. For these models, appropriate methodologies are first employed for obtaining the second moment characteristics of motions resulting from roads with a random profile. This information is next utilized in the definition of a vehicle performance index, which is optimized to yield representative numerical results for the most important suspension parameters. Special attention is paid to investigating the effect of road quality as well as on examining effects related to wheel hop. Finally, a critical comparison is performed between the results obtained for vehicles with passive linear or bilinear suspension dampers and those obtained for cars with semi-active shock absorbers.
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paper_title: Vehicle Evaluation of the Performance of Magneto Rheological Dampers for Heavy Truck Suspensions

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This study is intended to complement many existing analytical studies in the area of semiactive suspensions by providing afield evaluation of semiactive magneto rheological (MR) primary suspensions for heavy trucks. A set of four controllable MR dampers are fabricated and used experimentally to test the effectiveness of a semiactive skyhook suspension on a heavy truck. In order to evaluate the performance of the semiactive suspensions, the performance of the truck equipped with the MR dampers is primarily compared with the performance of the truck equipped with the stock passive dampers. The performance of the semiactive system and the original passive system are compared for two different driving conditions. First, the truck is driven over a speed bump at approximately 8-11 kmh (5-7 mph) in order to establish a comparison between the performance of the MR and stock dampers to transient inputs at the wheels. Second, the truck is driven along a stretch of relatively straight and level highway at a constant speed of 100 kmh (62 mph) in order to compare the performance of the two types of dampers in steady state driving conditions. Acceleration data for both driving conditions are analyzed in bath time and frequency domains. The data for the speed bumps indicate that the magneto rheological dampers used (with the skyhook control policy) in this study have a small effect on the vehicle body and wheel dynamics, as compared to the passive stock dampers. The highway driving data shows that magneto rheological dampers and the skyhook control policy are effective in reducing the root mean square (RMS) of the measured acceleration at most measurement points, as compared to the stock dampers.
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paper_title: “Smart” Base Isolation Strategies Employing Magnetorheological Dampers

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One of the most successful means of protecting structures against severe seismic events is base isolation. However, optimal design of base isolation systems depends on the magnitude of the design level earthquake that is considered. The features of an isolation system designed for an El Centro-type earthquake typically will not be optimal for a Northridge-type earthquake and vice versa. To be effective during a wide range of seismic events, an isolation system must be adaptable. To demonstrate the efficacy of recently proposed ''smart'' base isolation paradigms, this paper presents the results of an experimental study of a particular adaptable, or smart, base isolation system that employs magnetorheological ~MR! dampers. The experimental structure, constructed and tested at the Structural Dynamics and Control/Earthquake Engineering Laboratory at the Univ. of Notre Dame, is a base-isolated two-degree-of-freedom building model subjected to simulated ground motion. A sponge-type MR damper is installed between the base and the ground to provide controllable damping for the system. The effectiveness of the proposed smart base isolation system is demonstrated for both far-field and near-field earthquake excitations.
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paper_title: Response Control of Full-Scale Irregular Buildings Using Magnetorheological Dampers

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This paper considers the capabilities of semiactive control systems using magnetorheological dampers when applied to numerical models of full scale asymmetric buildings. Two full scale building models exhibiting coupled lateral and torsional motions are studied. The first case considered is a nine-story building with an asymmetric structural plan. The footprint of this building is rectangular, but the asymmetry is due to the distribution of shear walls. The second case considered is an L-shaped, eight-story building with additional vertical irregularity due to setbacks. Linear, lumped-parameter models of the buildings are employed herein to evaluate the potential of the control system to effectively reduce the responses of the buildings. In each case a device placement scheme based on genetic algorithms is used to place the control devices effectively. The proposed control systems are evaluated by simulating the responses of the models due to the El Centro 1940 and the Kobe 1995 earthquakes. In the second case, simulations are conducted using two-dimensional ground motions. The performance of the proposed semiactive control systems are compared to that of both ideal active control systems and passive control systems.
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paper_title: Semiactive Control of the 20-Story Benchmark Building with Piezoelectric Friction Dampers

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A new control algorithm is proposed in this paper to control the responses of a seismically excited, nonlinear 20-story building with piezoelectric friction dampers. The passive friction damping mechanism is used for low-amplitude vibration while the active counterpart takes over for high-amplitude vibration. Both the stick and sliding phases of dampers are taken into account. To effectively mitigate the peak story drift and floor acceleration of the 20-story building, multiple dampers are placed on the 20-story building based on a sequential procedure developed for optimal performance of the dampers. Extensive simulations indicate that the proposed semiactive dampers can effectively reduce the seismic responses of the uncontrolled building with substantially less external power than its associated active dampers, for instance, 67% less under the 1940 El Centro earthquake when the passive friction force is equal to 10% of the damper capacity.
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paper_title: Vibration control of a suspension system via a magnetorheological fluid damper

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Semi-active control systems are becoming more popular because they offer both the reliability of passive systems and the versatility of active control systems without imposing heavy power demands. It has been found that magneto-rheological (MR) fluids can be designed to be very effective vibration control actuators. MR fluid damper is a semi-active control device that uses MR fluids to produce controllable damping force. The objective of this paper is to study a single-degree-of- freedom suspension system with a MR fluid damper for the purpose of vibration control. A mathematical model of MR fluid damper is adopted. The model is compared with experimental results for a prototype damper through finding suitable model parameters. In this study, a sliding mode controller is developed by considering loading uncertainty to result in a robust control system. Two kinds of excitations are inputted in order to investigate the performance of the suspension system. The vibration responses are evaluated in both time and frequency domains. Compared to the passive system, the acceleration of the sprung mass is significantly reduced for the system with a controlled MR damper. Under random excitation, the ability of the MR fluid damper to reduce both peak response and root-mean-square response is also shown.© (2000) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
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paper_title: Modeling and identification of a shear mode magnetorheological damper

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Magnetotheological (MR) dampers have emerged recently as potential devices for vibration mitigation and semi-active control in smart structures and vehicle applications. These devices are highly nonlinear and thus accurate models of these devices are important for effective simulation and control system design. In the current literature, the Bouc–Wen model is coupled with linear elements to describe these MR devices both in simulation and control. In this paper, we propose the friction Dahl model to characterize the dynamics of a shear mode MR damper. This leads to a reinterpretation of the MR damper behavior as a frictional device whose friction parameters change with the voltage. An identification technique for this new model is proposed and tested numerically using an experimentally obtained model. A good match has been observed between the model obtained from experiments and the Dahl based model of the MR device.
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paper_title: Semi-active Vibration Control Schemes for Suspension Systems Using Magnetorheological Dampers

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Three semi-active control methods are investigated for use in a suspension system using a commer- cial magnetorheological damper. The three control methods are the limited relative displacement method, the modified skyhook method, and the modified Rakheja-Sankar method. The method of averaging has been adopted to provide an analytical platform for analyzing the performance of the different control methods. The analytical results are verified using numerical simulation, and further are used to assess the efficiency of dif- ferent control methods. An experimental test bed has been developed to examine the three control methods under sinusoidal and random excitations. Both analytical and experimental results confirm that the Rakheja- Sankar control and modified skyhook control methods significantly reduce the root-mean-square response of both the acceleration and relative displacement of the sprung mass, while the limited relative displacement controller can only control the relative displacement of the suspension system.
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paper_title: Preliminary Design Procedure of MR Dampers for Controlling Seismic Response of Building Structures

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In this paper, the preliminary design procedure of magnetorheological (MR) dampers is developed for controlling the building response induced by seismic excitation. The dynamic characteristics and control effects of the modeling methods of MR dampers such as Bingham, biviscous, hysteretic biviscous, simple Bouc?Wen, Bouc?Wen with mass element, and phenomenological models are investigated. Of these models, hysteretic biviscous model which is simple and capable describing the hysteretic characteristics, is used for numerical studies. The capacity of MR damper is determined as a portion of not the building weight but the lateral restoring force. A method is proposed for optimal placement and number of MR dampers, and its effectiveness is verified by comparing it with the simplified sequential search algorithm. Numerical results indicate that the capacity, number and the placement can be reasonably determined using the proposed design procedure.
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paper_title: Benchmark Control Problems for Seismically Excited Nonlinear Buildings

paper_content:

This paper presents the problem definition and guidelines of a set of benchmark control problems for seismically excited nonlinear buildings. Focusing on three typical steel structures, 3-, 9-, and 20-story buildings designed for the SAC project for the Los Angeles, California region, the goal of this study is to provide a clear basis to evaluate the efficacy of various structural control strategies. A nonlinear evaluation model has been developed that portrays the salient features of the structural system. Evaluation criteria and control constraints are presented for the design problems. The task of each participant in this benchmark study is to define (including sensors and control algorithms), evaluate, and report on their proposed control strategies. These strategies may be either passive, active, semiactive, or a combination thereof. The benchmark control problems will then facilitate direct comparison of the relative merits of the various control strategies. To illustrate some of the design challenges, a sample control strategy employing active control with a linear quadratic Gaussian control algorithm is applied to the 20-story building.
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paper_title: Semiactive Control Strategies for MR Dampers-Comparative Study

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This paper presents the results of a study to evaluate the performance of a number of recently proposed semiactive control algorithms for use with multiple magnetorheological (MR) dampers. Various control algorithms used in recent semiactive control studies are considered including the Lyapunov controller, decentralized bang-bang controller, modulated homogeneous friction algorithm, and a clipped optimal controller. Each algorithm is formulated for use with the MR damper. Additionally, each algorithm uses measurements of the absolute acceleration and device displacements for determining the control action to ensure that the algorithms could be implemented on a physical structure. The performance of the algorithms is compared through a numerical example, and the advantages of each algorithm are discussed. The numerical example considers a six-story structure controlled with MR dampers on the lower two floors. In simulation, an El Centro earthquake is used to excite the system, and the reduction in the drif...
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paper_title: MR seat suspension for vibration control of a commercial vehicle

paper_content:

This paper presents vibration control of a commercial vehicle utilising a magnetorheological (MR) seat damper. A cylindrical type of MR seat damper is manufactured and its field-dependant damping forces are experimentally evaluated. The MR seat damper is then incorporated with a full-vehicle model in which conventional passive dampers are installed for primary and cabin suspension, respectively. After formulating the governing equations of motion of the full-vehicle model, a semi-active skyhook controller is realised by adopting a hardware-in-the-loop-simulation (HILS) methodology. Control responses such as acceleration at the driver's seat are evaluated under both bump and random road conditions.
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paper_title: FORCE FEEDBACK VERSUS ACCELERATION FEEDBACK IN ACTIVE VIBRATION ISOLATION

paper_content:

This paper compares the force feedback and acceleration feedback implementation of the sky-hook damper when it is used to isolate a flexible structure from a disturbance source. It is shown that the use of a force sensor produces always alternating poles and zeros in the open-loop transfer function between the force actuator and the force sensor, which guarantees the stability of the closed loop. On the contrary, the acceleration feedback produces alternating poles and zeros only when the flexible structure is stiff compared to the isolation system; this property is lost when the flexible modes of the sensitive payload interfere with the isolation system.
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paper_title: Semi-active control of sliding isolated bridges using MR dampers: an experimental and numerical study

paper_content:

Sliding base-isolation systems used in bridges reduce pier drifts, but at the expense of increased bearing displacements under near-source pulse-type earthquakes. It is common practice to incorporate supplemental passive non-linear dampers into the isolation system to counter increased bearing displacements. Non-linear passive dampers can certainly reduce bearing displacements, but only with increased isolation level forces and pier drifts. The semi-active controllable non-linear dampers, which can vary damping in real time, can reduce bearing displacements without further increase in forces and pier drifts; and hence deserve investigation. In this study performance of such a 'smart' sliding isolation System, used in a 1:20 scaled bridge model, employing semi-active controllable magneto-rheological (MR) dampers is investigated, analytically and experimentally, under several near-fault earthquakes. A non-linear analytical model, which incorporates the non-linearities of sliding bearings and the MR damper, is developed. A Lyapunov control algorithm for control of the MR damper is developed and implemented in shake table tests. Analytical and shake table test results are compared. It is shown that the smart MR damper reduces bearing displacements further than the passive low- and high-damping cases, while maintaining isolation level forces less than the passive high-damping case.
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paper_title: Adaptive Snubber-Type Magnetorheological Fluid-Elastomeric Helicopter Lag Damper

paper_content:

A snubber-type magnetorheological fluid-elastomeric lag damper is developed to provide adaptive lead-lag damping augmentation for a hingeless helicopter rotor. The magnetorheological fluid-elastomeric lag damper consists of a flow valve, a flexible snubber body, and a flexible center wall separating the body into two fluid chambers. Magnetorheological fluid enclosed in the snubber body can flow through two magnetorheological valves and be activated by a magnetic field in the valves. Consistent with the loading conditions for a helicopter lag damper, the magnetorheological fluid-elastomeric damper is tested under single and dual frequency excitations. The complex modulus method was used to compare the magnetorheological fluid-elastomeric device damping performance with the baseline passive Fluidlastic damper. A significant controllable damping range is observed as current is applied to the magnetorheological valve in the magnetorheological fluid-elastomeric damper. Furthermore, to account for the nonlinear hysteresis behavior ofthe magnetorheological fluid-elastomeric damper and estimate the damping force, a time-domain hydromechanical model is formulated based on lumped parameters. Model parameters are established using damper geometry, material properties, and experimental data. The model is then applied to simulate the force vs displacement response and force time history under both single and dual frequency excitations.
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paper_title: Hybrid model predictive control application towards optimal semi-active suspension

paper_content:

The optimal control problem of a quarter-car semi-active suspension has been studied in the past. Considering that a quarter-car semi-active suspension can either be modelled as a linear system with state dependent constraint on control (of actuator force) input, or a bi-linear system with a control (of variable damping coefficient) saturation, the seemingly simple problem poses several interesting questions and challenges. Does the saturated version of the optimal control law derived from the corresponding un-constrained system, i.e. “clipped-optimal”, remain optimal for the constrained case as suggested in some previous publications? Or should the optimal deviate from the “clipped-optimal” as suggested in other publications? If the optimal control law of the constrained system does deviate from its unconstrained counter-part, how different are they? What is the structure of the optimal control law? Does it retain the linear state feedback form (as the unconstrained case)? In this paper, we attempt to an...
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paper_title: Bifurcation and chaos in nonsmooth mechanical systems

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Introduction to Discontinuous ODEs Mathematical Background for Multivalued Formulations Properties of Numerical Schemes Stick-Slip Oscillator with Two Degrees of Freedom Piecewiselinear Approximations Chua Circuit with Discontinuities One DOF Mechanical System with Friction A Mechanical System with 7 DOF Triple Pendulum with Impacts Analytical Prediction of Stick-Slip Chaos and other topics.
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paper_title: OPTIMAL ACTIVE SUSPENSION DESIGN USING CONSTRAINED OPTIMIZATION

paper_content:

Abstract In a quarter-car vehicle model, optimal control schemes for an active suspension are designed using a constrained optimization procedure. The control laws obtained minimize the H 2 -norm of vehicle acceleration subject to constraints on r.m.s. values of the suspension stroke, tire deformation and actuator force. Constraints imposed on feedback coefficients define quasi-optimal control laws that show increased robustness to system parameter variations and disturbances. To impact body acceleration at frequencies near the unsprung mass mode, tire damping is introduced in the model. The optimal and quasi-optimal control schemes were partially verified on a quarter-car simulator with a random road input and the preliminary results are encouraging. The tests showed significant improvement (3–5 dB) of body acceleration response in the frequency range up to 25 Hz and increased robustness of the quasi-optimal control laws, that use lower amounts of spring cancellation.
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paper_title: Visco-hyperelastic model for filled rubbers used in vibration isolation

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The short time and cyclic behavior of filled rubbers used in vibration isolation in the frequency range 10{sup {minus}2} to 10{sup 2} rad/s is examined. A form of the free-energy function consistent with the assumption of an additive stress decomposition is employed. A constitutive law for the inelastic part of the stress is provided, in the form of an integro-differential equation, which involves the fractional order derivative of the internal variable. It is assumed that the volumetric response of the material is elastic. The elasticity of rubber is modeled following classical models (e.g., Rivlin, Ogden), extended to include compressibility. Step-by-step integration of the constitutive law is performed. Simple shear experiments are used to assess the capability of the model to capture essential response characteristics, such as stiffness reduction under cyclic loading of increasing amplitude and the variation of dissipated energy with amplitude and frequency.
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paper_title: SKYHOOK AND H(INFINITY) CONTROL OF SEMI-ACTIVE SUSPENSIONS: SOME PRACTICAL ASPECTS

paper_content:

This paper deals with single-wheel suspension car model. We aim to prove the benefits of controlled semi-active suspensions compared to passive ones. The contribution relies on H(infinity) control design to improve comfort and road holding of the car under industrial specifications, and on control validation through simulation on an exact nonlinear model of the suspension. Note that we define semi-active suspensions as control systems incorporating a parallel spring and an electronically controlled damper. However, the type of damper used in automotive industry can only dissipate energy. No additional force can be generated using external energy. The control issue is then to change, in an accurate way, the damping (friction) coefficient in real-time. This is what we call semi-active suspension. For this purpose, two control methodologies, H(infinity) and Skyhook control approaches, are developed, using a linear model of the suspension, and compared in terms of performances using industrial specifications. The performance analysis is done using the control-oriented linear model first, and then using an exact nonlinear model of the suspension incorporating the nonlinear characteristics of the suspension spring and damper. (A)
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paper_title: MAGNETORHEOLOGICAL FLUID AND ELASTOMERIC LAG DAMPER FOR HELICOPTER STABILITY AUGMENTATION

paper_content:

The feasibility of utilizing a composite magnetorheological fluid plus elastomeric (MRFE) damper is assessed. To emulate the loading conditions for a helicopter lag damper, the MRFE damper emulation was subjected to single frequency (lag/rev) and dual frequency (lag/rev and 1/rev) sinusoidal loading, and equivalent viscous damping was used to compare the MRFE damping characteristics with a conventional elastomeric damper. The preliminary MRFE damper showed nonlinear behavior: damping was reduced as displacement amplitude increased. Upon application of a magnetic field, the damping level was controlled according to a specific damping objective as a function of the excitation amplitude. Under dual frequency conditions, damping degradation at lag frequency due to 1/rev motion was also mitigated by magnetic field input to the MR damper.
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paper_title: Advanced Structural Dynamics and Active Control of Structures

paper_content:

Preface List of Symbols Chapter 1 Introduction to Structures (examples, definition, and properties) 1.1 Examples 1.1.1 A Simple Structure 1.1.2 A 2D Truss 1.1.3 A 3D Truss 1.1.4 A Beam 1.1.5 The Deep Space Network Antenna 1.1.6 The International Space Station Structure 1.2 Definition 1.3 Properties Chapter 2 Standard Models (how to describe typical structures) 2.1 Models of a Linear System 2.1.1 State-Space Representation 2.1.2 Transfer Function 2.2 Second-Order Structural Models 2.2.1 Nodal Models 2.2.2 Modal Models 2.3 State-Space Structural Models 2.3.1 Nodal Models 2.3.2 Models in Modal Coordinates 2.3.3 Modal Models Chapter 3 Special Models (how to describe less-common structures) 3.1 Models with Rigid Body Modes 3.2 Models with Accelerometers 3.2.1 State-Space Representation 3.2.2 Second-Order Representation 3.2.3 Transfer Function 3.3 Models with Actuators 3.3.1 Model with Proof-Mass Actuators 3.3.2 Model with Inertial Actuators 3.4 Models with Small Non-Proportional Damping 3.5 Generalized Model 3.5.1 State-Space Representation 3.5.2 Transfer Function 3.6 Discrete-Time Models 3.6.1 State-Space Representation 3.6.2 Transfer Function Chapter 4 Controllability and Observability (how to excite and monitor a structure) 4.1 Definition and Properties 4.1.1 Continuous-Time Systems 4.1.2 Discrete-Time Systems 4.1.3. Relationship between Continuous- and Discrete-Time Grammians 4.2 Balanced Representation 4.3 Balanced Structures with Rigid Body Modes 4.4 Input and Output Gains 4.5 Controllability and Observability of a Structural Modal Model 4.5.1 Diagonally Dominant Grammians 4.5.2 Closed-Form Grammians 4.5.3 Approximately Balanced Structure in Modal Coordinates 4.6 Controllability and Observability of a Second-Order Modal Model 4.6.1 Grammians 4.6.2 Approximately Balanced Structure in Modal Coordinates 4.7 Three Ways to Compute Hankel Singular Values 4.8 &nb
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paper_title: Vibration control of civil structures using piezoceramic smart materials : A review

paper_content:

Abstract A review is presented for vibration suppression of civil structures. Special emphasis is laid upon smart structures with piezoelectric control actuation. The last decade has seen spiraling efforts going on around the world into development of the smart structures field. The success of these smart structures is orchestrated by the materials, such as piezoceramics, shape memory alloys, controllable fluids such as magneto-rheological fluids and electro-rheological fluids, fiber-optic sensors and various other materials. Piezoceramics have been known as low-cost, lightweight, and easy-to-implement materials for active control of structural vibration. Piezoceramics are available in various forms such as rigid patch, flexible patch, stack, Macro-Fiber Composite (MFC) actuator, and piezoceramic friction dampers. Piezoelectric patch actuators can be surface bonded to high strain areas of the structure with minimal modification of the original structure or they can be embedded into such as composites structures. On the other hand, stack type actuators can be incorporated into the structures, which require high control forces and micron level displacements, with slight modifications. This paper first presents basics about piezoceramic materials, various actuation methods and types of piezoceramic actuators. Then this paper reviews research into the application of piezoceramic actuators in various civil structures such as beams, trusses, steel frames and cable-stayed bridges.
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paper_title: Inverse optimal control of nonlinear systems with structural uncertainty

paper_content:

Inverse optimal control for nonlinear systems with structural uncertainty is considered. Based on the control Lyapunov function, a theorem for the globally asymptotic stability is presented. From this a less conservative condition for the inverse optimal control is derived. The result is used to design an inverse optimal controller for a class of nonlinear systems, that improves and extends the existing results. The class of nonlinear systems considered is also enlarged. The simulation results show the effectiveness of the method.
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paper_title: Stability of a Lyapunov controller for a semi-active structural control system with nonlinear actuator dynamics

paper_content:

Abstract We investigate semi-active control for a wide class of systems with scalar nonlinear semi-active actuator dynamics and consider the problem of designing control laws that guarantee stability and provide sufficient performance. Requiring the semi-active actuator to satisfy two general conditions, we present a method for designing quickest descent controllers generated from quadratic Lyapunov functions that guarantee asymptotic stability within the operating range of the semiactive device for the zero disturbance case. For the external excitation case, bounded-input, bounded-output stability is achieved and a stable attractor (ball of ultimate boundedness) of the system is computed based on the upper bound of the disturbances. We show that our wide class of systems covers, in particular, two nonlinear actuator models from the literature. Tuning the performance of the simple Lyapunov controllers is straightforward using either modal or state penalties. Simulation results are presented which indicate that the Lyapunov control laws can be selected to provide similar decay rates as a “time-optimal” controller for a semi-actively controlled single degree of freedom structure with no external excitation.
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paper_title: Bistable composite flap for an airfoil

paper_content:

A study was conducted to address the challenges associated with investigating a bistable composite flap for an airfoil. A full-scale rotor blade section with a span of 2.114 m and a chord of 0.68 m, fitted with a 1 m span flap was wind-tunnel tested up to a speed of 60 m/s with the flap moving between two stable states for various angles of attack. The blade was approximated as a NACA 24016 section with a 20% chord trailing-edge flap to simplify the analysis. The trailing-edge flap was designed to change between its stable geometries between hover and forward flight conditions for aerodynamic performance improvements. The flap was driven by an electromechanical actuator that was mounted inside the blade D-spar at the leading edge. All of the rotor blade structure remote from this bistable flap region was unmodified and assumed to be completely rigid during wind-tunnel testing.
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paper_title: CONSTRUCTION OF AN ACTIVE SUSPENSION SYSTEM OF A QUARTER CAR MODEL USING THE CONCEPT OF SLIDING MODE CONTROL

paper_content:

This paper is concerned with the construction of an active suspension system for a quarter car model using the concept of sliding mode control. The active control is derived by the equivalent control and switching function where the sliding surface is obtained by using Linear quadratic control (LQ control) theory. The active control is generated with non-negligible time lag by using a pneumatic actuator, and the road profile is estimated by using the minimum order observer based on a linear system transformed from the exact non-linear system. The experimental result indicates that the proposed active suspension system is more effective in the vibration isolation of the car body than the linear active suspension system based on LQ control theory and the passive suspension system.
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paper_title: Nonlinear Dynamical Control Systems

paper_content:

Contents: Introduction.- Manifolds, Vectorfields, Lie Brackets, Distributions.- Controllability and Observability, Local Decompositions.- Input-Output Representations.- State Space Transformation and Feedback.- Feedback Linearization of Nonlinear Systems.- Controlled Invariant Distribution and the Disturbance Decoupling Problem.- The Input-Output Decoupling Problem: Geometric Considerations.- Local Stability and Stabilization of Nonlinear Systems.- Controlled Invariant Submanifolds and Nonlinear Zero Dynamics.- Mechanical Nonlinear Control Systems.- Controlled Invariance and Decoupling for General Nonlinear Systems.- Discrete-Time Nonlinear Control Systems.- Subject Index.
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paper_title: Spatial Control of Vibration

paper_content:

Modelling spatial norms and model reduction model correction spatial control optimal placement of actuators and sensors system identification for spatially distributed systems.
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paper_title: ACTUATOR AND SENSOR PLACEMENT FOR STRUCTURAL TESTING AND CONTROL

paper_content:

Abstract In this paper, the actuator and sensor locations of a structural test item are selected as a replacement of the disturbance inputs and the performance outputs of a real structure. The most straightforward approach is to place sensors in the areas of performance evaluation, and actuators in the areas of disturbance action. However, this solution is rarely possible due to technical and economical reasons. Therefore, the actuators and sensors need to be placed in preselected regions, and should duplicate as close as possible the disturbance action and the performance measurements. In this paper a placement problem with non-collocated actuators and disturbances, as well as non-collocated performance and sensor outputs is solved. The solution is determined by locating sensors (actuators) such that the Hankel singular value vector of a structure from actuator inputs to sensor outputs is closely correlated with the Hankel singular value vector of the structure from the disturbance inputs to performance outputs. It is shown that this approach improves additionally the cross-coupling between actuators and performance, and between disturbances and the sensors, thus improving overall closed loop performance. The method is illustrated with the determination of sensors of a truss structure, where two selected sensors replaced an original set of 36 sensors.
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paper_title: New Semi-active Multi-modal Vibration Control Using Piezoceramic Components

paper_content:

Active vibration control using piezoelectric elements has been extensively studied due to the requirement for increasingly high performances. Semi-active control, such as Synchronized Switch Damping, is an alternative technique. It consists in switching a piezoelectric element to a specific circuit synchronously with the motion of the structure, unlike active control. This method requires very low power supply, but performances remain poor in the case of broad bandwidth excitation. This article proposes a new method which is a combination of the SSDI semi-active control and technique developed for active control and has low power supply requirements. It extends semi-active control to any type of excitation, while optimizing modal damping on several targeted modes. Experimental measurements carried out on a clamped free beam are presented and a significant damping on targeted modes is demonstrated.
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paper_title: Semiactive Control of the 20-Story Benchmark Building with Piezoelectric Friction Dampers

paper_content:

A new control algorithm is proposed in this paper to control the responses of a seismically excited, nonlinear 20-story building with piezoelectric friction dampers. The passive friction damping mechanism is used for low-amplitude vibration while the active counterpart takes over for high-amplitude vibration. Both the stick and sliding phases of dampers are taken into account. To effectively mitigate the peak story drift and floor acceleration of the 20-story building, multiple dampers are placed on the 20-story building based on a sequential procedure developed for optimal performance of the dampers. Extensive simulations indicate that the proposed semiactive dampers can effectively reduce the seismic responses of the uncontrolled building with substantially less external power than its associated active dampers, for instance, 67% less under the 1940 El Centro earthquake when the passive friction force is equal to 10% of the damper capacity.
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paper_title: Vibration With Control

paper_content:

Preface. 1. SINGLE DEGREE OF FREEDOM SYSTEMS. Introduction. Spring-Mass System. Spring-Mass-Damper System. Forced Response. Transfer Functions and Frequency Methods. Measurement and Testing. Stability. Design and Control of Vibrations. Nonlinear Vibrations. Computing and Simulation in Matlab. Chapter Notes. References. Problems. 2. LUMPED PARAMETER MODELS. Introduction. Classifications of Systems. Feedback Control Systems. Examples. Experimental Models. Influence Methods. Nonlinear Models and Equilibrium. Chapter Notes. References. Problems. 3. MATRICES AND THE FREE RESPONSE. Introduction. Eigenvalues and Eigenvectors. Natural Frequencies and Mode Shapes. Canonical Forms. Lambda Matrices. Oscillation Results. Eigenvalue Estimates. Computational Eigenvalue Problems in Matlab. Numerical Simulation of the Time Response in Matlab. Chapter Notes. References. Problems. 4. STABILITY. Introduction. Lyapunov Stability. Conservative Systems. Systems with Damping. Semidefinite Damping . Gyroscopic Systems. Damped Gyroscopic Systems. Circulatory Systems. Asymmetric Systems. Feedback Systems. Stability in the State Space. Stability Boundaries. Chapter Notes. References. Problems. 5. FORCED RESPONSE OF LUMPED PARAMETER SYSTEMS. Introduction. Response via State Space Methods. Decoupling Conditions and Modal Analysis. Response of Systems with Damping. Bounded-Input, Bounded-Output Stability. Response Bounds. Frequency Response Methods. Numerical Simulations in Matlab. Chapter Notes. References. Problems. 6. DESIGN CONSIDERATIONS. Introduction. Isolators and Absorbers. Optimization Methods. Damping Design. Design Sensitivity and Redesign. Passive and Active Control. Design Specifications. Model Reduction. Chapter Notes. References. Problems. 7. CONTROL OF VIBRATIONS. Introduction. Controllability and Observability. Eigenstructure Assignment. Optimal Control. Observers (Estimators). Realization. Reduced-Order Modeling. Modal Control in State Space. Modal Control in Physical Space. Robustness. Positive Position Feedback Control. Matlab Commands for Control Calculations. Chapter Notes. References. Problems. 8. VIBRATION MEASUREMENT. Introduction. Measurement Hardware. Digital Signal Processing. Random Signal Analysis. Modal Data Extraction (Frequency Domain). Modal Data Extraction (Time Domain). Model Identification. Model Updating. Chapter Notes. References. Problems. 9. DISTRIBUTED PARAMETER MODELS. Introduction. Vibrations of Strings. Rods and Bars. Vibration of Beams. Membranes and Plates. Layered Materials. Viscous Damping. Chapter Notes. References. Problems. 10. FORMAL METHODS OF SOLUTION. Introduction. Boundary Value Problems and Eigenfunctions. Modal Analysis of the Free Response. Modal Analysis in Damped Systems. Transform Methods. Green's Functions. Chapter Notes. References. Problems. 11. OPERATORS AND THE FREE RESPONSE. Introduction. Hilbert Spaces. Expansion Theorems. Linear Operators. Compact Operators. Theoretical Modal Analysis. Eigenvalue Estimates. Enclosure Theorems. Oscillation Theory. Chapter Notes. References. Problems. 12. FORCED RESPONSE AND CONTROL. Introduction. Response by Modal Analysis. Modal Design Criteria. Combined Dynamical Systems. Passive Control and Design. Distribution Modal Control. Nonmodal Distributed Control. State Space Control Analysis. Chapter Notes. References. Problems. 13. APPROXIMATIONS OF DISTRIBUTED PARAMETER MODELS. Introduction. Modal Truncation. Rayleigh- Ritz-Galerkin Approximations. Finite Element Method. Substructure Analysis. Truncation in the Presence of Control. Impedance Method of Truncation and Control. Chapter Notes. References. Problems. APPENDIX A: COMMENTS ON UNITS. APPENDIX B: SUPPLEMENTARY MATHEMATICS. Index.
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paper_title: An Optimal Nonlinear Feedback Control Strategy for Randomly Excited Structural Systems

paper_content:

A strategy for optimal nonlinear feedback control of randomlyexcited structural systems is proposed based on the stochastic averagingmethod for quasi-Hamiltonian systems and the stochastic dynamicprogramming principle. A randomly excited structural system isformulated as a quasi-Hamiltonian system and the control forces aredivided into conservative and dissipative parts. The conservative partsare designed to change the integrability and resonance of the associatedHamiltonian system and the energy distribution among the controlledsystem. After the conservative parts are determined, the system responseis reduced to a controlled diffusion process by using the stochasticaveraging method. The dissipative parts of control forces are thenobtained from solving the stochastic dynamic programming equation. Boththe responses of uncontrolled and controlled structural systems can bepredicted analytically. Numerical results for a controlled andstochastically excited Duffing oscillator and a two-degree-of-freedomsystem with linear springs and linear and nonlinear dampings, show thatthe proposed control strategy is very effective and efficient.
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paper_title: Stable Feedback Control of Linear Distributed Parameter Systems: Time and Frequency Domain Conditions

paper_content:

Abstract Large space structures, or any mechanically flexible structures, are inherently distributed parameter systems (DPSs) whose dynamics are modeled by partial, rather than ordinary, differential equations. Such DPSs are described by operator equations on an infinite-dimensional Hilbert (or Banach) space. However, any feedback controller for such a DPS must be a finite-dimensional (and discrete-time) system to be implemented with on-line digital computers and a finite (small) number of actuators and sensors. There are many ways to synthesize such controllers; we will emphasize the Galerkin or finite-element approach. Although the overall performance of finite-dimensional controllers is important, the first consideration is their stability in closed-loop with the actual DPS. The analysis of DPSs makes use of the theory of semigroups on the infinite-dimensional state space. We will present stability bounds in both the time and frequency domains for infinite-dimensional systems. Currently, the frequency domain approach appears to yield more easily tested stability conditions than the time domain approach; however, we will show some relationships between these two methods and emphasize the role played by the DPS semigroup and its properties. It seems to us that such stability conditions are essential for the planning and successful operation of complex systems like large aerospace structures.
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paper_title: Constant-Gain Linear Feedback Control of Piecewise Linear Structural Systems via Nonlinear Normal Modes

paper_content:

We present a technique for using constant-gain linear position feedback control to implement eigen- structure assignment of n-degrees-of-freedom conservative structural systems with piecewise linear nonlin- earities. We employ three distinct control strategies which utilize methods for approximating the nonlinear normal mode (NNM) frequencies and mode shapes. First, the piecewise modal method (PMM) for approx- imating NNM frequencies is used to determine n constant actuator gains for eigenvalue (pole) placement. Secondly, eigenvalue placement is accomplished by finding an approximate single-degree-of-freedom re- duced model with one actuator gain for the mode to be controlled. The third strategy allows the frequencies and mode shapes (eigenstructure) to be placed by using a full n n matrix of actuator gains and employing the local equivalent linear stiffness method (LELSM) for approximating NNM frequencies and mode shapes. The techniques are applied to a two-degrees-of-freedom system with two distinct types of nonlinearities: a bilinear clearance nonlinearity and a symmetric deadzone nonlinearity.
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paper_title: Application of Nonlinear Control Theory to Electronically Controlled Suspensions

paper_content:

SUMMARY This paper illustrates the use of nonlinear control theory for designing electro-hydraulic active suspensions. A nonlinear, “sliding” control law is developed and compared with the linear control of a quarter-car active suspension system acting under the effects of coulomb friction. A comparison will also be made with a passive quarter-car suspension system. Simulation and experimental results show that nonlinear control performs better than PID control and improves the ride quality compared to a passive suspension.
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paper_title: Feedback control of flexible systems

paper_content:

Feedback control is developed for the class of flexible systents described by the generalized wave equation with damping. The control force distribution is provided by a number of point force actuators and the system displacements and/or their velocities are measured at various points. A feedback controller is developed for a finite number of modes of the flexible system and the controllability and observability conditions necessary for successful operation are displayed. The control and observation spillover due to the residual (uncontrolled) modes is examined and the combined effect of control and observation spillover is shown to lead to potential instabilities in the closed-loop system. Some remedies for spillover, including a straightforward phase-locked loop prefilter, are suggested to remove the instability mechanism. The concepts of this paper are illustrated by some numerical studies on the feedback control of a simply-supported Euler-Bernoulli beam with a single actuator and sensor.
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paper_title: Adaptive Control of Flexible Structures Using a Nonlinear Vibration Absorber

paper_content:

A nonlinear adaptive vibration absorber to control the vibrations offlexible structures is investigated. The absorber is based on thesaturation phenomenon associated with dynamical systems possessingquadratic nonlinearities and a two-to-one internal resonance. Thetechnique is implemented by coupling a second-order controller with thestructure through a sensor and an actuator. Energy is exchanged betweenthe structure and the controller and, near resonance, the structure'sresponse saturates to a small value.Experimental results are presented for the control of a rectangularplate and a cantilever beam using piezoelectric ceramics andmagnetostrictive alloys as actuators. The control technique isimplemented using a digital signal processing board and a modelingsoftware. The control strategy is made adaptive by incorporating anefficient frequency-measurement technique. This is validated bysuccessfully testing the control strategy for a nonconventionalproblem, where nonlinear effects hinder the application of thenonadaptive controller.
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paper_title: Automotive active suspensions Part 1: Basic principles

paper_content:

AbstractAutomotive suspension design is a compromise brought about by the conflicting demands of ride and handling. The past few years have seen the introduction of increasingly sophisticated, electronically controlled, components into automotive suspensions which redefine the boundaries of the compromise.The paper has been written in two parts. This first part reviews the compromises which are required in the design of a conventional passive suspension. It then goes on to show how those compromises can be changed by the inclusion of active components.The second part discusses the hardware employed which ranges from simple switched dampers, through semi-active dampers, and low bandwidth/soft active suspensions, to high bandwidth/stiff active suspensions. The benefits to be derived from each of the technologies will be assessed, together with their strengths and weaknesses.
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paper_title: Control System Design

paper_content:

From the Publisher: ::: A key aspect of the book is the frequent use of real world design examples drawn directly from the authors' industrial experience. These are represented by over 15 substantial case studies ranging from distillation columns to satellite tracking. The book is also liberally supported by modern teaching aids available on both an accompanying CD-ROM and Companion Website. Resources to be found there include MATLAB® routines for all examples; extensive PowerPoint lecture notes based on the book; and a totally unique Java Applet-driven "virtual laboratory" that allows readers to interact with the real-world case studies.
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paper_title: Nonlinear Systems: Analysis, Stability, and Control

paper_content:

1 Linear vs. Nonlinear.- 2 Planar Dynamical Systems.- 3 Mathematical Background.- 4 Input-Output Analysis.- 5 Lyapunov Stability Theory.- 6 Applications of Lyapunov Theory.- 7 Dynamical Systems and Bifurcations.- 8 Basics of Differential Geometry.- 9 Linearization by State Feedback.- 10 Design Examples Using Linearization.- 11 Geometric Nonlinear Control.- 12 Exterior Differential Systems in Control.- 13 New Vistas: Multi-Agent Hybrid Systems.- References.
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paper_title: Mixing Rules for the Piezoelectric Properties of Macro Fiber Composites

paper_content:

This article focuses on the modeling of structures equipped with Macro Fiber Composite (MFC) transducers. Based on the uniform field method under the plane stress assumption, we derive analytical mixing rules in order to evaluate equivalent properties for d31 and d33 MFC transducers. In particular, mixing rules are derived for the longitudinal and transverse piezoelectric coefficients of MFCs. These mixing rules are validated using finite element computations and experimental results available from the literature.
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paper_title: A class of proportional-integral sliding mode control with application to active suspension system

paper_content:

The purpose of this paper is to present a new robust strategy in controlling the active suspension system. The strategy utilized the proportional-integral sliding mode control scheme. A quarter-car model is used in the study and the performance of the controller is compared to the linear quadratic regulator and with the existing passive suspension system. A simulation study is performed to prove the effectiveness and robustness of the control approach.
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paper_title: SKYHOOK AND H(INFINITY) CONTROL OF SEMI-ACTIVE SUSPENSIONS: SOME PRACTICAL ASPECTS

paper_content:

This paper deals with single-wheel suspension car model. We aim to prove the benefits of controlled semi-active suspensions compared to passive ones. The contribution relies on H(infinity) control design to improve comfort and road holding of the car under industrial specifications, and on control validation through simulation on an exact nonlinear model of the suspension. Note that we define semi-active suspensions as control systems incorporating a parallel spring and an electronically controlled damper. However, the type of damper used in automotive industry can only dissipate energy. No additional force can be generated using external energy. The control issue is then to change, in an accurate way, the damping (friction) coefficient in real-time. This is what we call semi-active suspension. For this purpose, two control methodologies, H(infinity) and Skyhook control approaches, are developed, using a linear model of the suspension, and compared in terms of performances using industrial specifications. The performance analysis is done using the control-oriented linear model first, and then using an exact nonlinear model of the suspension incorporating the nonlinear characteristics of the suspension spring and damper. (A)
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paper_title: Adaptive Model Inversion Control of a Helicopter with Structural Load Limiting

paper_content:

An adaptive control system capable of providing consistent handling qualities throughout the operational flight envelope is a desirable feature for rotorcraft. The adaptive model inversion controller with structural load limit protection evaluated here offers the capability to adapt to changing flight conditions along with aggressive maneuvering without envelope limit violations. The controller was evaluated using a nonlinear simulation model of the UH-60 helicopter. The controller is based on a well-documented model inversion architecture with an adaptive neural network (ANN) to compensate for inversion error. The ANN was shown to improve the tracking ability of the controller at off-design point flight conditions; although at some flight conditions the controller performed well even without adaptation. The controller was modified to include a structural load-limiting algorithm to avoid exceeding prescribed limits on the longitudinal hub moment. The limiting was achieved by relating the hub moment to pitch acceleration. The acceleration limits were converted to pitch angle command limits imposed in the pitch axis command filter. Results show that the longitudinal hub moment response in aggressive maneuvers stayed within the prescribed limits for a range of operating conditions. The system was effective in avoiding the longitudinal hub moment limit without unnecessary restrictions on the aircraft performance.
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paper_title: HYBRID WAVE/MODE ACTIVE VIBRATION CONTROL

paper_content:

A hybrid approach to active vibration control is described in this paper. It combines elements of both wave and mode approaches to active control and is an attempt to improve on the performance of these approaches individually. In the proposed hybrid approach, wave control is first applied at one or more points in the structure. It is designed on the basis of the local behaviour of the structure and is intended to absorb vibrational energy, especially at higher frequencies. Then modal control is applied, being designed on the basis of the modified global equations of motion of the structure-plus-wave controller. These are now normally non-self-adjoint. Since the higher order modes are relatively well damped, hybrid control improves the model accuracy and the robustness of the system and gives better broadband vibration attenuation performance. Hybrid wave/mode active vibration control is described with specific reference to the control of a cantilever beam. The particular case considered is that of collocated, point force/sensor feedback wave control combined with modal control designed using pole placement. Numerical and experimental results are presented.
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paper_title: Adaptive positive position feedback for actively absorbing energy in acoustic cavities

paper_content:

A method for adaptive energy absorption in acoustic cavities is presented. The method is based on an adaptive scheme consisting of a self-tuning regulator that has the ability to target multiple modes with a single actuator. The inner control loop of the self-tuning regulator uses positive position feedback in series with a high- and low-pass Butterworth filters for each controlled mode. The outer loop consists of an algorithm that locates the zero frequencies of the collocated signal and uses these values to update the resonance frequency of the positive position feedback filter and the cut-off and cut-on frequencies of the Butterworth filters. Experimental results are provided that show how less than a 10 percent change in the frequencies of the acoustic modes of the experimental setup will cause a non-adaptive controller (using positive position feedback and Butterworth filters) to go unstable, but the self-tuning regulator will maintain stability and continue absorbing energy through a 20 percent change in the frequencies of the acoustic modes.
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paper_title: Positive position feedback control for large space structures

paper_content:

A new technique for vibration suppression in large space structures is investigated in laboratory experiments on a thin cantilever beam. The technique, called Positive Position Feedback (PPF), makes use of generalized displacement measurements to accomplish vibration suppression. Several features of Positive Position Feedback make it attractive for the large space structure control environment. The realization of the controller is simple and straightforward. Global stability conditions can be derived which are independent of the dynamical characteristics of the structure being controlled, i.e., all spillover is stabilizing. Furthermore, the method can be made insensitive to finite actuator dynamics, and is amenable to a strain-based sensing approach. The experiments described here control the first six bending modes of a cantilever beam, and make use of piezoelectric materials for actuators and sensors, simulating a piezoelectric active-member. Modal damping ratios as high as 20% of critical are achieved.
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paper_title: An experimental study on active tendon control of cable‐stayed bridges

paper_content:

Active tendon control of cable-stayed bridges subject to a vertical sinusoidal force is experimentally and analytically studied. Emphasis is placed on the effects of linear and non-linear internal resonances on the control (due to the presence of the cable vibration). A simple cable-supported cantilever beam is used as a model. It is found that active tendon control is very effective in vertical girder motion with small cable vibration (girder dominated motion), whereas it is not effective in verticaIlgirder motion with large cable vibration (cable dominated motion). Analytical prediction is very satisfactory except for the latter case
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paper_title: A Mixed Robust/Optimal Active Vibration Control for Uncertain Flexible Structural Systems with Nonlinear Actuators Using Genetic Algorithm

paper_content:

In this article, a mixed robust/optimal control approach is proposed to treat the active vibration control (or active vibration suppression) problems of flexible structural systems under the effects of mode truncation, linear time-varying parameter perturbations and nonlinear actuators. A new robust stability condition is derived for the flexible structural system which is controlled by an observer-based controller and is subject to mode truncation, nonlinear actuators and linear structured time-varying parameter perturbations simultaneously. Based on the robust stability constraint and the minimization of a defined H2 performance, a hybrid Taguchi-genetic algorithm (HTGA) is employed to find the optimal state feedback gain matrix and observer gain matrix for uncertain flexible structural systems. A design example of the optimal observer-based controller for a simply supported beam is given to demonstrate the combined application of the presented sufficient condition and the HTGA.
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paper_title: ACTIVE ISOLATION OF MULTIPLE STRUCTURAL WAVES ON A HELICOPTER GEARBOX SUPPORT STRUT

paper_content:

Abstract A helicopter gearbox support strut has been set up in the laboratory under realistic loading conditions to investigate the active control of longitudinal and lateral vibration transmission to a connected receiving structure. Three magnetostrictive actuators were clamped to the strut to introduce secondary vibration in the frequency range 250–1250 Hz, the control objective being to minimize the kinetic energy of vibration of the receiving structure. Using an extensive set of frequency response measurements, it was possible to predict on a linear basis the attenuation in the kinetic energy of the receiving structure at any discrete frequency in the measurement range for a wide range of conditions. Calculations based on frequency response measurements showed that with the installed steel bearings on the strut, attenuations in the kinetic energy of the receiving structure of 30–40 dB were possible over a range of frequencies between 250 and 1250 Hz. At some frequencies in this range, notably around 500 Hz and 800 Hz, the control was less effective. This was due to torsional motion of the strut which was amplified by the secondary actuators. Good control was also predicted when the primary excitation to the strut was applied laterally rather than longitudinally. Real-time active control has been implemented at discrete frequencies on the test strut and has generally confirmed the linear predictions. Attenuations in excess of 40 dB were measured in a number of cases. The tests confirmed that the active control of vibration transmission through a helicopter strut is practical at frequencies up to at least 1250 Hz.
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paper_title: Experimental Control of Flexible Structures Using Nonlinear Modal Coupling: Forced and Free Vibration

paper_content:

This paper is an experimental study of free and forced vibration suppression in a piezoceramic actuated flexible beam via the nonlinear Modal Coupling Control (MCC). The method is based on transferring the oscillatory energy from the plant to an auxiliary second order system (controller), coupled to the plant through nonlinear terms. The proposed controller produces an input that can be utilized by unidirectional actuators. Unidirectional actuators do not generate symmetric power during an application. Shape memory alloys, thrusters and cable based actuators are examples of this class of actuators. Existing control methods assume a symmetric actuation and therefore application of unidirectional actuators call for new control techniques. Current control techniques implement a bias in utilizing unidirectional actuators. However, the amount of the bias is variable and depends on the control effort. Moreover, the use of a bias changes the system equilibrium point and introduces a steady state error. The propo...
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paper_title: NONLINEAR STRUCTURAL CONTROL USING NEURAL NETWORKS

paper_content:

Recently, Ghaboussi and Joghataie presented a structural control method using neural networks, in which a neurocontroller was developed and applied for linear structural control when the response of the structure remained within the linearly elastic range. One of the advantages of the neural networks is that they can learn nonlinear as well as linear control tasks. In this paper, we study the application of the previously developed neurocontrol method in nonlinear structural control problems. First, we study the capabilities of the linearly trained neurocontrollers in nonlinear structural control. Next, we train a neurocontroller on the nonlinear data and study its capabilities. These studies are done through numerical simulations, on models of a three-story steel frame structure. The control is implemented through an actuator and tendon system in the first floor. The sensor is assumed to be a single accelerometer on the first floor. The acceleration of the first floor as well as the ground acceleration are used as feedback. In the numerical simulations we have considered the actuator dynamics and used a coupled model of the actuator-structure system. A realistic sampling period and an inherent time delay in the control loop have been used.
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paper_title: Numerical recipes in C

paper_content:

Note: Includes bibliographical references, 3 appendixes and 2 indexes.- Diskette v 2.06, 3.5''[1.44M] for IBM PC, PS/2 and compatibles [DOS] Reference Record created on 2004-09-07, modified on 2016-08-08
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paper_title: Vibration With Control

paper_content:

Preface. 1. SINGLE DEGREE OF FREEDOM SYSTEMS. Introduction. Spring-Mass System. Spring-Mass-Damper System. Forced Response. Transfer Functions and Frequency Methods. Measurement and Testing. Stability. Design and Control of Vibrations. Nonlinear Vibrations. Computing and Simulation in Matlab. Chapter Notes. References. Problems. 2. LUMPED PARAMETER MODELS. Introduction. Classifications of Systems. Feedback Control Systems. Examples. Experimental Models. Influence Methods. Nonlinear Models and Equilibrium. Chapter Notes. References. Problems. 3. MATRICES AND THE FREE RESPONSE. Introduction. Eigenvalues and Eigenvectors. Natural Frequencies and Mode Shapes. Canonical Forms. Lambda Matrices. Oscillation Results. Eigenvalue Estimates. Computational Eigenvalue Problems in Matlab. Numerical Simulation of the Time Response in Matlab. Chapter Notes. References. Problems. 4. STABILITY. Introduction. Lyapunov Stability. Conservative Systems. Systems with Damping. Semidefinite Damping . Gyroscopic Systems. Damped Gyroscopic Systems. Circulatory Systems. Asymmetric Systems. Feedback Systems. Stability in the State Space. Stability Boundaries. Chapter Notes. References. Problems. 5. FORCED RESPONSE OF LUMPED PARAMETER SYSTEMS. Introduction. Response via State Space Methods. Decoupling Conditions and Modal Analysis. Response of Systems with Damping. Bounded-Input, Bounded-Output Stability. Response Bounds. Frequency Response Methods. Numerical Simulations in Matlab. Chapter Notes. References. Problems. 6. DESIGN CONSIDERATIONS. Introduction. Isolators and Absorbers. Optimization Methods. Damping Design. Design Sensitivity and Redesign. Passive and Active Control. Design Specifications. Model Reduction. Chapter Notes. References. Problems. 7. CONTROL OF VIBRATIONS. Introduction. Controllability and Observability. Eigenstructure Assignment. Optimal Control. Observers (Estimators). Realization. Reduced-Order Modeling. Modal Control in State Space. Modal Control in Physical Space. Robustness. Positive Position Feedback Control. Matlab Commands for Control Calculations. Chapter Notes. References. Problems. 8. VIBRATION MEASUREMENT. Introduction. Measurement Hardware. Digital Signal Processing. Random Signal Analysis. Modal Data Extraction (Frequency Domain). Modal Data Extraction (Time Domain). Model Identification. Model Updating. Chapter Notes. References. Problems. 9. DISTRIBUTED PARAMETER MODELS. Introduction. Vibrations of Strings. Rods and Bars. Vibration of Beams. Membranes and Plates. Layered Materials. Viscous Damping. Chapter Notes. References. Problems. 10. FORMAL METHODS OF SOLUTION. Introduction. Boundary Value Problems and Eigenfunctions. Modal Analysis of the Free Response. Modal Analysis in Damped Systems. Transform Methods. Green's Functions. Chapter Notes. References. Problems. 11. OPERATORS AND THE FREE RESPONSE. Introduction. Hilbert Spaces. Expansion Theorems. Linear Operators. Compact Operators. Theoretical Modal Analysis. Eigenvalue Estimates. Enclosure Theorems. Oscillation Theory. Chapter Notes. References. Problems. 12. FORCED RESPONSE AND CONTROL. Introduction. Response by Modal Analysis. Modal Design Criteria. Combined Dynamical Systems. Passive Control and Design. Distribution Modal Control. Nonmodal Distributed Control. State Space Control Analysis. Chapter Notes. References. Problems. 13. APPROXIMATIONS OF DISTRIBUTED PARAMETER MODELS. Introduction. Modal Truncation. Rayleigh- Ritz-Galerkin Approximations. Finite Element Method. Substructure Analysis. Truncation in the Presence of Control. Impedance Method of Truncation and Control. Chapter Notes. References. Problems. APPENDIX A: COMMENTS ON UNITS. APPENDIX B: SUPPLEMENTARY MATHEMATICS. Index.
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paper_title: Optimal structural control using neural networks

paper_content:

An optimal control algorithm using neural networks is proposed. The controller neural network is trained by a training rule developed to minimize cost function. Both the linear structure and the nonlinear structure can be controlled by the proposed neurocontroller. A bilinear hysteretic model is used to simulate nonlinear structural behavior. Three main advantages of the neurocontroller can be summarized as follows. First, it can control a structure with unknown dynamics. Second, it can easily be applied to nonlinear structural control. Third, external disturbances can be considered in the optimal control. Examples show that structural vibration can be controlled successfully.
---
paper_title: Modelling of structural response and optimization of structural control system using neural network and genetic algorithm

paper_content:

This paper proposes an integrated approach to the modelling and optimization of structural control systems in tall buildings. In this approach, an artificial neural network is applied to model the structural dynamic responses of tall buildings subjected to strong earthquakes, and a genetic algorithm is used to optimize the design problem of structural control systems, which constitutes a mixed-discrete, nonlinear and multi-modal optimization problem. The neural network model of the structural dynamic response analysis is included in the genetic algorithm and is used as a module of the structural analysis to estimate the dynamic responses of tall buildings. A numerical example is presented in which the general regression neural network is used to model the structural response analysis. The modelling method, procedure and the numerical results are discussed. Two Los Angeles earthquake records are adopted as earthquake excitations. Copyright © 2000 John Wiley & Sons, Ltd.
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paper_title: Vibration control of piezoelectric beam-type plates with geometrically nonlinear deformation

paper_content:

Abstract This paper presents a wavelet-based approach of deformation identification and vibration control of beam-type plates with geometrically nonlinear deflection using piezoelectric sensors and actuators. The identification is performed by transferring the nonlinear equations of identifying deflection into a system of solvable nonlinear algebraic equations in terms of the measurable electric charges and currents on piezoelectric sensors. After that, a control law of negative feedback of the identified signals of deflection and velocity is employed, and the weighted residual method is chosen to determine control voltages applied on the piezoelectric actuators. Due to that the scaling function transform is like a low-pass filter which can automatically filter out high-order signals of vibration or disturbance from the measurement and the controller employed here, this control approach does not lead to the undesired phenomenon of control instability which is generated by the spilling over of high-order signals. Finally, some numerical simulations are carried out to show the efficiency of the proposed approach.
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paper_title: Active tendon control of cable‐stayed bridges: a large‐scale demonstration

paper_content:

This paper presents a strategy for active damping of cable structures, using active tendons. The first part of the paper summarizes the theoretical background: the control law is briefly presented together with the main results of an approximate linear theory which allows the prediction of closed-loop poles with a root locus technique. The second part of the paper reports on experimental results obtained with two test structures: the first one is a small size mock-up representative of a cable-stayed bridge during the construction phase. The control of the parametric vibration of passive cables due to deck vibration is demonstrated. The second one is a 30 m long mock-up built on the reaction wall of the ELSA test facility at the JRC Ispra (Italy); this test structure is used to demonstrate the practical implementation of the control strategy with hydraulic actuators. Copyright © 2001 John Wiley & Sons, Ltd.
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paper_title: Adaptive Model Inversion Control of a Helicopter with Structural Load Limiting

paper_content:

An adaptive control system capable of providing consistent handling qualities throughout the operational flight envelope is a desirable feature for rotorcraft. The adaptive model inversion controller with structural load limit protection evaluated here offers the capability to adapt to changing flight conditions along with aggressive maneuvering without envelope limit violations. The controller was evaluated using a nonlinear simulation model of the UH-60 helicopter. The controller is based on a well-documented model inversion architecture with an adaptive neural network (ANN) to compensate for inversion error. The ANN was shown to improve the tracking ability of the controller at off-design point flight conditions; although at some flight conditions the controller performed well even without adaptation. The controller was modified to include a structural load-limiting algorithm to avoid exceeding prescribed limits on the longitudinal hub moment. The limiting was achieved by relating the hub moment to pitch acceleration. The acceleration limits were converted to pitch angle command limits imposed in the pitch axis command filter. Results show that the longitudinal hub moment response in aggressive maneuvers stayed within the prescribed limits for a range of operating conditions. The system was effective in avoiding the longitudinal hub moment limit without unnecessary restrictions on the aircraft performance.
---
paper_title: Past, present and future of nonlinear system identification in structural dynamics

paper_content:

This survey paper contains a review of the past and recent developments in system identification of nonlinear dynamical structures. The objective is to present some of the popular approaches that have been proposed in the technical literature, to illustrate them using numerical and experimental applications, to highlight their assets and limitations and to identify future directions in this research area. The fundamental differences between linear and nonlinear oscillations are also detailed in a tutorial.
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paper_title: CONSTRUCTION OF AN ACTIVE SUSPENSION SYSTEM OF A QUARTER CAR MODEL USING THE CONCEPT OF SLIDING MODE CONTROL

paper_content:

This paper is concerned with the construction of an active suspension system for a quarter car model using the concept of sliding mode control. The active control is derived by the equivalent control and switching function where the sliding surface is obtained by using Linear quadratic control (LQ control) theory. The active control is generated with non-negligible time lag by using a pneumatic actuator, and the road profile is estimated by using the minimum order observer based on a linear system transformed from the exact non-linear system. The experimental result indicates that the proposed active suspension system is more effective in the vibration isolation of the car body than the linear active suspension system based on LQ control theory and the passive suspension system.
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paper_title: A modified model reference adaptive control approach for systems with noise or unmodelled dynamics

paper_content:

In this paper, a modified model reference adaptive control (MRAC) strategy is developed for use on plants with noise or unmodelled high-frequency dynamics. MRAC consists of two parts, an adaptive control part and a fixed gain control part. The adaptive algorithm uses a combination of low- and high-pass filters such that the frequency range for the adaptive part of the strategy is limited. The mechanism for noise-induced gain wind-up is demonstrated analytically, and it is shown how MRAC can be modified to eliminate this wind-up. Further to this, an additional filter is proposed to improve MRAC robustness to high-frequency unmodelled dynamics. Two test plants, one with added noise and the other with unmodelled high-frequency dynamics, are considered. Both plants exhibit unstable behaviour when controlled using standard MRAC, but, with the modified strategy, robustness is significantly improved.
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paper_title: BIFURCATIONS AND LIMIT DYNAMICS IN ADAPTIVE CONTROL SYSTEMS

paper_content:

Adaptive controllers are used in systems where one or more parameters are unknown. Such controllers are designed to stabilize the system using an estimate for the unknown parameters that is adapted automatically as part of the stabilization. One drawback in adaptive control design is the possibility that the closed-loop limit system is not stable. The worst situation is the existence of a destabilized limit system attracting a large open subset of initial conditions. These situations lie behind bad behavior of the closed-loop adaptive control system. The main issue in this paper is to identify and characterize the occurrence of such bad behavior in the adaptive stabilization of first- and second-order systems with one unknown parameter. We develop normal forms for all possible cases and find the conditions that lead to bad behavior. In this context, we discuss a number of bifurcation-like phenomena.
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paper_title: NONLINEAR STRUCTURAL CONTROL USING NEURAL NETWORKS

paper_content:

Recently, Ghaboussi and Joghataie presented a structural control method using neural networks, in which a neurocontroller was developed and applied for linear structural control when the response of the structure remained within the linearly elastic range. One of the advantages of the neural networks is that they can learn nonlinear as well as linear control tasks. In this paper, we study the application of the previously developed neurocontrol method in nonlinear structural control problems. First, we study the capabilities of the linearly trained neurocontrollers in nonlinear structural control. Next, we train a neurocontroller on the nonlinear data and study its capabilities. These studies are done through numerical simulations, on models of a three-story steel frame structure. The control is implemented through an actuator and tendon system in the first floor. The sensor is assumed to be a single accelerometer on the first floor. The acceleration of the first floor as well as the ground acceleration are used as feedback. In the numerical simulations we have considered the actuator dynamics and used a coupled model of the actuator-structure system. A realistic sampling period and an inherent time delay in the control loop have been used.
---
paper_title: Optimal structural control using neural networks

paper_content:

An optimal control algorithm using neural networks is proposed. The controller neural network is trained by a training rule developed to minimize cost function. Both the linear structure and the nonlinear structure can be controlled by the proposed neurocontroller. A bilinear hysteretic model is used to simulate nonlinear structural behavior. Three main advantages of the neurocontroller can be summarized as follows. First, it can control a structure with unknown dynamics. Second, it can easily be applied to nonlinear structural control. Third, external disturbances can be considered in the optimal control. Examples show that structural vibration can be controlled successfully.
---
paper_title: Output Feedback Variable Structure Adaptive Control of an Aeroelastic System

paper_content:

The paper presents an application of the variable structure model reference adaptive control theory to control of aeroelastic systems with structural nonlinearity. Interestingly, the design approach does not require any knowledge of the parameters of the system and the nonlinear functions, and only output feedback is used for the synthesis of the control systems. Control laws for the trajectory tracking of pitch angle and plunge displacement are derived. In the closed-loop system, the state vector asymptotically converges to the origin. Control laws are discontinuous functions of the tracking error, and modulation functions of the relays are generated on-line using bounds on uncertain functions and certain auxiliary signals. Digital simulation results are presented which show that in the closed-loop system, pitch angle and plunge displacement are smoothly regulated to zero in spite of the uncertainty and unmodeled functions in the system using only output feedback.
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paper_title: Modelling of structural response and optimization of structural control system using neural network and genetic algorithm

paper_content:

This paper proposes an integrated approach to the modelling and optimization of structural control systems in tall buildings. In this approach, an artificial neural network is applied to model the structural dynamic responses of tall buildings subjected to strong earthquakes, and a genetic algorithm is used to optimize the design problem of structural control systems, which constitutes a mixed-discrete, nonlinear and multi-modal optimization problem. The neural network model of the structural dynamic response analysis is included in the genetic algorithm and is used as a module of the structural analysis to estimate the dynamic responses of tall buildings. A numerical example is presented in which the general regression neural network is used to model the structural response analysis. The modelling method, procedure and the numerical results are discussed. Two Los Angeles earthquake records are adopted as earthquake excitations. Copyright © 2000 John Wiley & Sons, Ltd.
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paper_title: Adaptive Control of Flexible Structures Using a Nonlinear Vibration Absorber

paper_content:

A nonlinear adaptive vibration absorber to control the vibrations offlexible structures is investigated. The absorber is based on thesaturation phenomenon associated with dynamical systems possessingquadratic nonlinearities and a two-to-one internal resonance. Thetechnique is implemented by coupling a second-order controller with thestructure through a sensor and an actuator. Energy is exchanged betweenthe structure and the controller and, near resonance, the structure'sresponse saturates to a small value.Experimental results are presented for the control of a rectangularplate and a cantilever beam using piezoelectric ceramics andmagnetostrictive alloys as actuators. The control technique isimplemented using a digital signal processing board and a modelingsoftware. The control strategy is made adaptive by incorporating anefficient frequency-measurement technique. This is validated bysuccessfully testing the control strategy for a nonconventionalproblem, where nonlinear effects hinder the application of thenonadaptive controller.
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paper_title: Adaptive Feedback Linearization for the Control of a Typical Wing Section with Structural Nonlinearity

paper_content:

Earlier results by the authors showed constructions of Lie algebraic, partial feedback linearizing control methods for pitch and plunge primary control utilizing a single trailing edge actuator. In addition, a globally stable nonlinear adaptive control method was derived for a structurally nonlinear wing section with both a leading and trailing edge actuator. However, the global stability result described in a previous paper by the authors, while highly desirable, relied on the fact that the leading and trailing edge actuators rendered the system exactly feedback linearizable via Lie algebraic methods. In this paper, the authors derive an adaptive, nonlinear feedback control methodology for a structurally nonlinear typical wing section. The technique is advantageous in that the adaptive control is derived utilizing an explicit parameterization of the structural nonlinearity and a partial feedback linearizing control that is parametrically dependent is defined via Lie algebraic methods. The closed loop stability of the system is guaranteed to be stable via application of La Salle's invariance principle.
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paper_title: Nonlinear and Adaptive Control of Complex Systems

paper_content:

Preface. Notations and Definitions. 1. Faces of Complexity. 2. Nonlinear Systems: Analysis and Design Tools. 3. Speed-Gradient Method and Partial Stabilization. 4. Nonlinear control of Multivariable Systems. 5. Nonlinear Control of Mimo Systems. 6. Adaptive and Robus Control Design. 7. Decomposition of Adaptive Systems. 8. Control of Mechanical Systems. 9. Physics and Control. A. Appendix. References. Index.
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Title: A review of non-linear structural control techniques

Section 1: INTRODUCTION
Description 1: Describe the importance of controlling non-linear structural vibrations in various engineering applications and provide an overview of the paper.

Section 2: CONTROL DESIGN FOR NON-LINEAR STRUCTURAL VIBRATIONS
Description 2: Discuss the traditional methods and challenges of control design for non-linear structural vibrations, focusing on passive redesign techniques.

Section 3: SEMI-ACTIVE CONTROL
Description 3: Explain semi-active control methods and their applications, especially in civil/structural and automotive engineering, emphasizing the use of magnetorheological (MR) dampers.

Section 4: ACTIVE VIBRATION CONTROL
Description 4: Provide an introduction to active vibration control techniques and their application for low-dimensional systems, including a discussion on non-linear control techniques.

Section 5: MODAL CONTROL
Description 5: Discuss modal control, its applications for structures with multiple degrees of freedom, and the specific techniques used to achieve control objectives.

Section 6: ADAPTIVE CONTROL
Description 6: Briefly outline adaptive control techniques and their relevance to systems with significant parameter uncertainties, highlighting key literature.

Section 7: CONCLUSIONS
Description 7: Summarize the key points discussed in the paper, including the effectiveness, applications, and future potentials of passive, semi-active, and active control methods for non-linear structural dynamics.