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5.0 Active Vibration Isolation Systems

This section will assist engineers and scientists in gaining a general understanding of active vibration isolation systems, how they work, when they should be applied, and what limitations they have. Particular attention has been given to the semiconductor manufacturing industry, since many applications have arisen in this field.
5.1 History

Feedback control systems have existed for hundreds of years but have had their greatest growth in the 20th century. During World War II, very rapid advances were made as the technology was applied to defense systems. These developments continued, and even today most texts on control systems feature examples like fighter aircraft control and missile guidance systems.
Active vibration isolation systems were an extension of the electromechanical control systems developed for defense. As early as the 1950s, active vibration cancellation systems were being developed for applications like helicopter seats. Thus, active control systems specifically for vibration control have been around for over 40 years! In the precision vibration control industry, active vibration isolation systems have been available for nearly 20 years. There are many reasons why they have been slow to come into wider use.
Most active vibration isolation systems are relatively complex, costly, and often provide only marginal improvements in performance compared with conventional passive vibration isolation techniques. They are also more difficult to set up, and their support electronics often require adjustment. Nonetheless, active systems can provide function which is simply not possible with purely passive systems.
Two things have lead to the renewed interest in active vibration control systems in recent years. The first is the rapid growth of the semiconductor industry, and, second, the desire to produce more semiconductors, faster, and at a lower cost. Lithography and inspection processes usually involve positioning the silicon wafer relative to critical optical (or other) components by placing the wafer on a heavy and/or fast moving stage. As these stages scan from site to site on the wafer, they cause the whole instrument to “bounce” on the vibration isolation system. Even though the motion of the instrument may be small after such a move (a few mm), the resolution of the instrument is approaching, and in some cases going below, 1 nm. Instruments with this type of resolution are inevitably sensitive to even the smallest vibration levels. Active systems help in these cases by reducing the residual motions of an isolated payload after such stage motions occur.
The second change which has made active systems more popular has been the advancement in digital signal processing techniques. In general, an active system based on analog electronics will outperform a digitally based system. This is due to the inherent low noise and wide bandwidths available with high-performance analog electronics. (A relatively inexpensive operational amplifier can have a 30 bit equivalent resolution and a “sampling rate” of many MHz.) Analog electronics are also inexpensive. The problem with analog-based systems is that they must be manually adjusted and cannot (easily) deal with non-linear feedback or feedforward applications (see Section 5.4.3). Digital controllers have the potential to automatically adjust themselves and to deal with non-linear feedback and feedforward algorithms. This allows active systems to be more readily used in OEM applications (such as the semiconductor industry). They can also be programmed to perform a variety of tasks, automatically switch between tasks on command, and can have software upgrades which “rewire” the feedback system without lifting a soldering iron. To further the reader’s understanding of the costs and benefits of these systems, we have provided a brief introduction to the terminology and techniques of servo control systems.

5.2 Servos & Terminology

Although the terminology for active systems is fairly universal, there are some variations. The following discussion introduces the terminology used by TMC and should help you with the concepts involved in active systems. The basis for all active control systems is illustrated in Figure 16.
It contains three basic elements:
  • The block labeled “G” is called the plant, and it represents the behavior of your mechanical (or electronic, hydraulic, thermal, etc.) system before any feedback is applied. It represents a transfer function, which is the ratio of the block’s output to its input, expressed as a function of frequency. This ratio has both a magnitude and a phase and may or may not be unitless. For example, it may represent a vibration transfer function where the input (line on the left) represents ground motion and the output (line to the right) represents the motion of a table top.

Figure 16: A basic feedback loop consists of three elements: the plant, compensation, and summing junction.
  • In this case, the ratio is unitless. If the input is a force and the output a position, then the transfer function has units of (m/N). The transfer function of G has a special name: the plant transfer function. All transfer functions (G, H, the product GH, etc.) are represented by complex numbers (numbers with both real and imaginary components). At any given frequency, a complex number represents a vector in the complex plane. The length and angle of that vector represents the magnitude and phase of the transfer function.

  • The block labeled “H” is called the compensation and generally represents your servo. For a vibration isolation system, it may represent the total transfer function for a sensor which monitors the plant’s output (an accelerometer), some electronic filters, amplifiers, and, lastly, an actuator which produces a force acting on the payload. In this example, the response has a magnitude, phase, and units of (N/m). Note that the loop transfer function for the system, which is the product (GH), must be unitless. The loop transfer function is the most important quantity in the performance and stability analysis of a control system and will be discussed later.

  • The circle is a summing junction. It can have many inputs which are all summed to form one output. All inputs and the output have the same units (such as force). A plus or minus sign is printed next to each input to indicate whether it is added or subtracted. Note that the output of H is always subtracted at this junction, representing the concept of negative feedback. The output of the summing junction is sometimes referred to as the error signal or error point in the circuit.
It can be shown that the closed-loop transfer function for the system is given by Equation 16. This is perhaps the single most important relationship in control theory. The denominator 1+GH is called the characteristic equation, since the location of its roots in the complex plane determine a system’s stability. There are several other properties which are immediately obvious from the form of this equation.
First, when the loop gain (the magnitude |GH|) is much less than one, the closed-loop transfer function is just the numerator (G). For large loop gains ( |GH| >> 1), the transfer function is reduced or suppressed by the loop gain. Thus the servo has its greatest impact on the system when the loop gain is above unity gain. The frequency span between the unity gain frequencies or unity gain points is the active bandwidth for the servo. In practice, you are not allowed to make the loop gain arbitrarily high between unity gain points and still have a stable servo. In fact, there is a limit to how fast the gain can be increased near unity gain frequencies. Because of this, the loop gain for a system is usually limited by the available bandwidth.
Another obvious result from Equation 16 is that the only frequencies where the closed-loop transfer function can become large is where the magnitude of |GH| Equation 1, and its phase becomes close to 180°. As the quantity GH nears this point, its value approaches (-1), the denominator of Equation 16 becomes small, and the closed-loop response becomes large. The difference between the phase of GH and 180° at a unity gain frequency for GH is called the phase margin. The larger the phase margin, the lower the amplification at the unity gain points. It turns out, however, that larger phase margins also decrease the gain of the servo within its active bandwidth. Thus, picking the phase margin is a compromise between gain and stability at the unity gain points. Amplification at unity gain will always happen for phase margins less than 60°. Most servos are designed to have a phase margin between 20° and 40°. Amplification at a servo’s unity gain frequencies appear like new resonances in the system.
5.3 Active Vibration Cancellation

The previous section provided a qualitative picture of how servos function and introduced the broad concepts and terminology. In reality, most active vibration cancellation systems are much more complex than the simple figure shown in Figure 16. There are typically 3 to 6 degrees-of-freedom (DOF) controlled: three translational (X, Y, and Z motions), and three rotational (roll, pitch, and yaw). In addition, there may be many types of sensors in a system, such as height sensors for leveling the system and accelerometers for sensing the payload’s motions. These are combined in a system using parallel or nested servo loops. While these can be represented by block diagrams like that in Figure 16 and are analyzed using the same techniques, the details can become quite involved. There are, however, some general rules which apply to active vibration cancellation servos in particular.
Multiple Sensors. Although you can have both an accelerometer measuring a payload’s inertial motion, and a position sensor measuring its position relative to earth, you can’t use both of them at any given frequency. In other words, the active bandwidth for a position servo cannot overlap with the active bandwidth for an accelerometer servo. Intuitively, this is just saying that you cannot force the payload to track two independent sensors at the same time. This has some serious consequences.
Locking a payload to an inertial sensor (an accelerometer) makes the payload quieter; however, the accelerometer’s output contains no information about the earth’s location. Likewise, locking a payload to a position sensor will force a payload to track earth more closely – including earth’s vibrations. You cannot have a payload both track earth closely and have good vibration isolation performance! For example, if you need more vibration isolation at 1 Hz, you must increase the gain of the accelerometer portion of the servo. This means that the servo which positions the payload with respect to earth must have its gain lowered. The result is a quieter platform, but one that takes longer to move back to its nominal position when disturbed. This is discussed further in Section 5.6.
Gain Limits on Position Servos. As mentioned above, position sensors also couple ground vibration to a payload. This sets a practical limit on the unity gain frequency for a height control servo (like TMC's PEPS® Precision Electronic Positioning System). To keep from degrading the vibration isolation performance of a system, the unity gain frequency for PEPS is limited to less than 3 Hz. This in turn limits its low-frequency gain (which determines how fast the system re-levels after a disturbance). Its main advantages are more accurate positioning (up to 100 times more accurate than a mechanical valve), better damping, better high-frequency vibration isolation, and the ability to electronically “steer” the payload using feedforward inputs (discussed later). It will not improve how fast a payload will re-level.* PEPS can also be combined with TMC's PEPS-VX®System, which uses inertial payload sensors to improve vibration levels on the payload.

Structural Resonances. Another important concern in active vibration isolation systems is the presence of structural resonances in the payload. These resonances form the practical bandwidth limit for any vibration isolation servo which uses inertial sensors directly mounted to the payload. Even a fairly rigid payload will have its first resonances in the 100-500 Hz frequency range. This would be acceptable if these were well damped. In most structures, however, they are not. This limits the bandwidth of such servos to around 10-40 Hz. Though a custom-engineered servo can do better, a generic off-the-shelf active vibration cancellation system rarely does.

5.4 Types of Active Systems

Although we have alluded to “position” and “acceleration” servos, in reality these systems can take many different forms. In addition, the basic performance of the servo in Figure 16 can be augmented using feedforward. The following sections introduce the most common configurations and briefly discuss their relative merits.

Figure 17: The basic inertial feedback loop uses a payload sensor and a force actuator, such as a loudspeaker “voice coil,” to affect the feedback. Feedforward can be added to the loop at several points.

5.4.1 Inertial Feedback

By far the most popular type of active cancellation system has been the inertial feedback system, illustrated in Figure 17. Note that the pneumatic isolators have been modeled here as a simple spring. Neglecting the feedforward input and the ground motion sensor (discussed in Section 5.4.3), the feedback path consists of a seismometer, filter, and force actuator (such as a loudspeaker “voice coil”). The seismometer measures the displacement between its test mass and the isolated payload, filters that signal, then applies a force to the payload such that this displacement (X1 - X2) is constant – thereby nulling the output of the seismometer. Since the only force acting on the test mass comes from the compression of its spring, and that compression is servoed to be constant (X1 - X2 Equation 0), it follows that the test mass is actively isolated. Likewise, since the isolated payload is being forced to track the test mass, it must also be isolated from vibration. The details of this type of servo can be found in many references.**
The performance of this type of system is always limited by the bandwidth of the servo. As mentioned previously, structural resonances in the isolated payload limit the bandwidth in practical systems to 10-40 Hz (normally towards the low end of this range). This type of system is also “AC coupled” since the seismometer has no “DC” response. As a result, these servos have two unity gain frequencies – typically at 0.1 and 20 Hz. This is illustrated in greater detail in Section 5.6. As a result, the servo reaches a maximum gain of around 20-40 dB at ~2 Hz – the natural frequency of the passive spring mount for the system. The closed-loop response of the system has two new resonances at the ~0.1 and ~20 Hz unity gain frequencies. Due to the small bandwidth of these systems (only around two decades in frequency), the gain is not very high except at the natural (open-loop) resonant frequency of the payload. The high gain there completely suppresses that resonance. For this reason, it is helpful to think of these systems as inertial damping systems, which have the property of damping the system’s main resonance without degrading the vibration isolation performance. (Passive damping can also damp this resonance but significantly increases vibration feedthrough from the ground.)
5.4.2 More Bandwidth Limitations

These servos are also limited in how low their lower unity gain frequency can be pushed by noise in the inertial sensor. This is described in detail in the reference of Footnote 2. Virtually all commercial active vibration cancellation systems use geophones for their inertial sensors. These are simple, compact, and inexpensive seismometers used in geophysical exploration. They greatly outperform even high-quality piezoelectric accelerometers at frequencies of 10 Hz and below. Their noise performance, however, is not adequate to push an inertial feedback system’s bandwidth to below ~0.1 Hz. To break this barrier, one would need to use much more expensive sensors, and the total cost for a system would no longer be commercially feasible.
Another low-frequency “wall” which limits a system’s bandwidth arises when the inertial feedback technique is applied in the horizontal direction. (Note that a six degree-of-freedom [DOF] system has three “vertical” and three “horizontal” servos. Horizontal DOFs are those controlled using horizontally driving actuators – X, Y, and twist [yaw]). This is the problem of tilt to horizontal coupling. If you push a payload sideways with horizontal actuators and it tilts, the inertial sensors read the tilt as an acceleration and try to correct for it by accelerating the payload – which, of course, is the wrong thing to do. This effect is a fundamental limitation which has its roots in Einstein’s Principle of Equivalence, which states that it is impossible to distinguish between an acceleration and a uniform gravitational field (which a tilt introduces). The only solution to this problem is to not tilt a payload when you push it. This is very difficult to do, especially in geometries (like semiconductor manufacturing equipment) which are not designed to meet this requirement. Ultimately, one is forced to use a combination of horizontal and vertical actuators to affect a “pure” horizontal actuation. This becomes a “fine tuning” problem, which even at best yields marginal results. TMC prefers another solution.
Passive Horizontal Systems. Rather than use an active system to obtain an “effective” low resonant frequency, we have developed a passive isolation system capable of being tuned to as low as 0.3 Hz in the horizontal DOFs. Our CSP® (Compact Sub-Hertz Pendulum System) is not only a more reliable and cost-effective way to eliminate the isolator’s 1-2 Hz resonance, but it also provides better horizontal vibration isolation up to 100 Hz or more – far beyond what is practical for an active system. Unfortunately, such passive techniques are very difficult to implement for the vertical direction. TMC recommends the use of systems like our PEPS-VX® Active Cancellation System to damp the three “vertical” DOFs. PZT-based active systems, such as TMC’s STACIS®, use another approach which allows for active control of horizontal DOFs (see Section 5.4.4).
5.4.3 Feedforward

The performance of the inertial feedback system in Figure 17 can be improved with the addition of feedforward. In general, feedforward is much more difficult than feedback, but it does offer a way to improve the performance of a system when the feedback servo is limited in its bandwidth. There are two types of “feedforward” systems which are quite different, though they share the same name.
Vibrational Feedforward. This scheme involves the use of a ground motion sensor and is illustrated in Figure 17. Conceptually, it is fairly simple: If the earth moves up by an amount Equationz, the payload feels a force through the compression of the spring equal to KsEquationz. The ground motion sensor detects this motion, however, and applies an equal and opposite force to the payload. The forces acting on the payload “cancel,” and the payload remains unaffected. “Cancel” is in quotes because it is a greatly abused term. It implies perfect cancellation – which never happens. In real systems, you must consider how well these two forces cancel. For a variety of reasons, it is difficult to have these forces match any better than around 10%, which would result in a factor of 10 improvement in the system’s response. Matching these forces to the 1% level is practically impossible. The reasons are numerous: The sensor is usually a geophone, which does not have a “flat” frequency response. Its response must be “flattened” by a carefully matched conjugate filter. The gain of this signal must be carefully matched so the force produced by the actuator is exactly equal in magnitude to the forces caused by ground motion. These gains, and the properties of the “conjugate filter,” must remain constant to within a percent with time and temperature. Gain matching is also extremely difficult if the system’s mass distribution changes, which is common in a semiconductor equipment application. Lastly, the cancellation level is limited by the sensor’s inherent noise (noise floor).
Another limiting factor to vibrational feedforward is that it becomes a feedback system if the floor is not infinitely rigid (which it is not). This is because the actuator, in pushing on the payload, also pushes against the floor. The floor will deflect with that force, and that deflection will be detected by the sensor. If the level of the signal produced by that deflection is large enough, then an unstable feedback loop is formed.
Because of the numerous problems associated with vibrational feedforward, TMC has not pursued it. Indeed, though available from other vendors, we know of no successful commercial application of the technique. It is possible, however, with ever more sophisticated DSP controllers and algorithms, that it will be more appealing in the future. The technique which is successfully used is command feedforward.
Command Feedforward. Also shown in Figure 17, command feedforward is only useful in applications where there is a known force being applied to the payload, and a signal proportional to that force is available. Fortunately, this is the case in semiconductor manufacturing equipment where the main disturbance to the payload is a moving stage handling a wafer.
The concept here is very simple. A force is applied to the payload of a known magnitude (usually from a stage acceleration). An electronic signal proportional to that force is applied to an actuator which produces an equal and opposite force. As mentioned earlier, there is a tendency in the literature to overstate the effectiveness of this technique. Ridiculous statements claiming “total elimination” of residual payload motions are common. As in vibrational feedforward, there is a gain adjustment problem, but all issues concerning sensor noise or possible feedback paths are eliminated. This is true so long as the signal is a true command signal from (for example) the stage’s motion controller. If the signal is produced from an encoder reading the stage position, then it is possible to form an unstable feedback loop. These systems can perform very well, suppressing stage-induced payload motions by an order of magnitude or more and will be further discussed in Section 5.7.

5.4.4 PZT-Based Systems

Figure 18 shows the concept of a “quiet pier” isolator \such as TMC’s line of active isolators (Patent Nos. 5,660,255 and 5,823,307). It consists of an intermediate mass which is hard mounted to the floor through a piezoelectric transducer (PZT). A geophone is mounted to it, and its signal fed back to the PZT in a wide-bandwidth servo loop. This makes a “quiet pier” for supporting the payload to be isolated. Isolation at frequencies above the servo’s active bandwidth is provided by a Equation 20Hz elastomer mount. This elastomer also prevents piers from “talking” to each other through the payload (a payload must rest on several independent quiet piers). This system has a unique set of advantages and limitations.
The vibration isolation performance of the STACIS® system is among the best in the 0.6-20 Hz frequency range, subject to some limitations (discussed below). It also requires much less tuning than inertial feedback systems, and the elastomer mount makes the system all but completely immune to structural resonances in the payload. Alignment of the payload with external equipment (docking) is not an issue because the system is essentially “hard mounted” to the floor through the 20 Hz elastomers. The settling time is very good because the response of the system to an external force (a moving stage) is that of the 20 Hz elastomer mount. This is comparable to the best inertial feedback systems. The stiffness of the elastomer mount also makes STACIS® almost completely immune to room air currents or other forces applied directly to the payload and makes it capable of supporting very high center-of-gravity payloads.
STACIS® can support, and is always compatible with, tools incorporating any type of built-in passive or active pneumatic vibration isolation system.

Unfortunately, the PZT has a range of motion which is limited (around 20-25 Equationm). Thus the servo saturates and “unlocks” if the floor motion exceeds this peak-to-peak amplitude. Fortunately, in most environments, the floor motion never exceeds this amplitude. To obtain a good vibration isolation characteristic, the active bandwidth for the PZT servo is from ~0.6 to ~200 Hz. This high bandwidth is only possible if the isolator is supported by a very rigid floor. The isolator needs this because it depends on the intermediate mass moving an amount proportional to the PZT voltage up to a few hundred Hz. If the floor has a resonance within the active bandwidth, this may not be true. Most floors have resonances well below 200 Hz, but this is acceptable as long as the floor is massive enough for its resonance not to be significantly driven by the servo. The proper form of the floor specification becomes floor compliance, inEquationin/lbf (orEquationm/N). In general, STACIS® must be mounted directly on a concrete floor. It will work on raised floors or in welded steel frames only if the support frame is carefully designed to be very rigid. Another problem is “building sway,” the motion at the top of a building caused by wind. This is often more than 25 mm on upper floors, so the system can saturate if used in upper stories (depending on the building’s aspect ratio and construction).


Figure 18: This method involves quieting a small “intermediate mass” with a high-bandwidth servo, then mounting the main payload on that “quiet pier” with a passive 20 Hz rubber mount.

5.4.5 Exotics

There are many other types of active vibration isolation systems.

The first broad class of “alternate” active systems are the hybrids. One of these is a hybrid between a quiet pier and a simple pendulum isolator. Here, a 3-post system contains only three PZTs which control the vertical motion at each post actively (thus height, pitch, and roll motions of the payload are actively controlled). The “horizontal” DOFs are isolated using simple pendulums hanging from each 1-DOF quiet pier. This system has only about one-fifth the cost of a full-DOF quiet pier system because of the many fewer PZTs. On the other hand, the pendulum response of these systems in the horizontal direction is sometimes less than desirable.
There are also hybrids of the STACIS® /quiet pier type of system with inertial feedback systems to improve the dynamic performance of the elastomer mount. These systems have additional cost and must be tuned for each application). For more information see the STACIS® 2100 page.
5.5 Types of Applications

Broadly, there two different types of applications: vibration critical or settling time critical. These are not the same and each has different solutions. Some applications may be both, but since their solutions are not mutually exclusive, it is fair to think of both types independently. It is important to note, however, that since the solutions are independent, so are their costs. Therefore you should avoid buying an active system to reduce vibration if all you need is faster settling times, and vice-versa.
5.5.1 Vibration Critical Applications

Vibration critical applications are actually in the minority. This means the number of applications which need better vibration isolation than a passive system can provide is quite small. Passive vibration isolation systems by TMC are extremely effective at suppressing ground noise at frequencies above a few Hz. There are only two types of applications where the vibration isolation performance of a passive isolator is a problem.
First, it is possible that the level of ground noise is so high that an instrument which is functional in most environments becomes ground noise sensitive. This usually only happens in buildings with very weak floors or in tall buildings where building sway becomes an issue. This is an unusual situation, since most equipment (such as semiconductor inspection machines) usually come with a “floor spec” which vendors are very hesitant to overlook.
The second type of applications are those with the very highest degree of intrinsic sensitivity. Prime examples are atomic force and scanning tunneling microscopes (AFMs and STMs). These have atomic scale resolutions and are sensitive to the smallest payload vibrations.
In both these situations the isolation performance of passive mounts is usually adequate, except for the frequency range from about 0.7 Hz to 3 Hz where a passive mount amplifies ground motion. This is a convenient coincidence, since active systems (such as the inertial feedback scheme) are good at eliminating this resonant amplification. Again, it is important to avoid an active vibration cancellation system unless you have an application which you are sure has a vibration isolation problem that cannot be solved with passive isolators. Most semiconductor equipment today has a different issue: settling time.
5.5.2 Settling Time Critical Applications

Settling time critical applications are those where the vibration isolation performance of a passive pneumatic isolator is completely adequate, but the settling time of the isolator is insufficient. It is easy to determine if yours is such a system. If it works fine after you let the payload settle from a disturbance (stage motion), then you only have a settling time issue. (See Section 5.8). Before continuing, however, it is important to understand what is meant by “settling time.”
Settling Time. The term settling time is one of the most abused terms in the industry, primarily because it lacks a widely accepted definition. A physicist might define the settling time as the time for the energy in the system to drop by 1/e . This is a nice, model-independent definition. Unfortunately, it is not what anybody means when they use the term. The most common definition is the “time for the system to stop moving.” This is the worst of all definitions since it is non-physical, model and payload dependent, subjective, and otherwise completely inadequate. Nonetheless, it can be used with some qualifications.
In theory, a disturbed harmonic oscillator’s motion decays exponentially, which is infinitely long lived. When in the context of a vibration isolator, one could think of the time when a system “stops moving” as the time required for the RMS motion of the system to reach a constant value, where the system’s motion is dominated by the feedthrough of ground vibration. This is neither what people mean by settling time, nor is it model independent, since the “time to stop moving” depends on the magnitude of the initial disturbance and the level of ground noise. In fact, there is no definition of “settling time” as a single specification which can be used to define system performance in this context – passive or otherwise.
This is the definition used by TMC: Settling time is the time required for a payload subjected to a known input to decay below a critical acceleration level. This is an exact definition that requires three numbers: The known input is the initial acceleration of the payload immediately after the disturbance (stage motion) stops. The critical acceleration level is the maximum acceleration level the payload can tolerate and still successfully perform its function. The settling time is the time required after the disturbance for the payload’s motion to decay below the critical acceleration level. Notice that we use a critical acceleration level and not a maximum displacement. It is not displacement of a payload which corrupts a process, but acceleration, since acceleration is what introduces the internal stresses in a payload which distort the structure, stage positioning, optics, etc. Of the three numbers, this is the most critical to understand, since it fundamentally characterizes the rigidity of your instrument.
For the product specifications on this web site, the critical acceleration and input levels are unknowns. For this reason, we quote our settling time specifications as the time required for a 90% reduction in the initial oscillation amplitude.
5.6 The Problems with Inertial Feedback

Though inertial feedback systems can be used to reduce the settling time and improve vibration isolation performance, they have several significant drawbacks. As already mentioned, implementing a horizontal inertial feedback system is strongly limited by the tilt to horizontal coupling problem (Section 5.4.2). Another problem is that these systems (with the exception of PZT-based systems) have relatively poor position settling times.
Figure 19 shows the response of a payload to an external disturbance. It is based on a model of an idealized 1-DOF system and is only meant to qualitatively demonstrate the performance of a multi-DOF system. Both curves represent the same active system, except the first plots the ratio of displacement to applied force, and the second plots the ratio of acceleration to applied force, both as a function of frequency. The only difference is that the first graph has been multiplied by two powers of frequency to produce the second. The curves show, respectively, what a position sensor and an accelerometer would measure as this system was disturbed. Please note that the magnitude scales on these graphs have an arbitrary origin and are only meant for reference.



Figure 19: The curves show that the position response is dominated by a low-frequency resonance, while the acceleration response is dominated by a high-frequency peak. Note that the peak in the open-loop response is the same.
The curves show that the position response is dominated by a low-frequency resonance, while the acceleration response is dominated by a high-frequency peak. This is a counter-intuitive result, since the peak in the open-loop (purely passive) response is at the same frequency in both cases.
The good news is twofold. As promised, this system does a good job of suppressing the open-loop resonance in the system. In fact, it is even providing a substantial amount of additional isolation in the 0.5-5 Hz frequency range. The second piece of good news is that the acceleration curve is dominated by a well-damped resonance at around 20 Hz . If we assume the amplitude of the acceleration decays as:
where A0 is the initial amplitude and Equation = Q / (Equationv). If the quality factor Q is approximately 2, then Equation ≈ 32 ms. Quite good. For any payload which is sensitive to acceleration (which most are), the settling time for this system will be improved by an order of magnitude by this servo.
The problem with this system is illustrated in the first set of curves. They show the position response is dominated by a peak at ~0.1 Hz . Assuming the same Q as above, this means the decay constant t is approximately 6.5 seconds! Even though the servo has been designed with a large phase margin to get the Q down to 2, the low frequency of the peak means it takes a long time to settle in position. Although payloads are most sensitive to accelerations, there are two notable cases where a long position settling time is a problem.
First, a long position settling time in the roll or pitch DOF of a payload can look like a horizontal acceleration. This is due to Einstein’s Principle of Equivalence: As a payload tips, then the direction that gravity acts on the payload changes from purely vertical to some small angle off vertical. By principle this is identical to having a level payload which is being accelerated by an amount equal to the tip angle (in radians) x g . In other words, each mrad of tilt turns into a mg of horizontal acceleration. Many instruments, such as electron microscopes, are sensitive to this.
Another significant problem is docking the payload. This is a common process where the payload must be periodically positioned relative to an off-board object with extreme accuracy – typically 20 to 200 mm. It can take an inertial feedback system a very long time to position to this level. There are two possible solutions to this. The first is to run the servo at a lower gain setting, sacrificing some isolation performance (which may not be needed) for a better position settling time. The second approach is to turn off the servo for docking. Servos, unfortunately, do not like to be turned on and off rapidly – especially when their nominal gain is as high as the one illustrated here.

5.7 The Feedforward Option

For settling time sensitive applications, there is another option which is less expensive and avoids the problems associated with the inertial feedback method. As discussed in Section 5.4.3, command feedforward can be used to reduce the response of a payload to an external disturbance. You can use this technique with or without using the inertial feedback scheme in See Figure 17. This section deals with the latter option.

5.7.1 Feedforward Pros

There are many advantages to using a feedforward only system. Some of these are:
  • You do not spend extra money on improved vibration isolation performance which you do not need. The system is less expensive because you avoid the cost of six inertial sensors and a feedback controller.
  • The position stability of the payload is improved because it is now represented by the open-loop curves of Figure 19. There are also no issues about docking, since “turn-on transients” of the inertial feedback system are avoided. The feedforward system can remain on and the payload docked (using products like TMC’s AccuDock™) with no problems.
  • Since feedforward does not use any feedback, it is completely immune to resonances on the isolated payload.

Using adaptive controllers, the amount of feedforward can be tuned to ensure at least a factor of 10 reduction in the response of the payload to a disturbance (stage motion). This is comparable to what a well-tuned inertial feedback system can do.

5.7.2 Feedforward Cons

Despite being more robust, less expensive, and easier to setup, there are still some disadvantages to the feedforward only option. Some of these are:
  • As mentioned in Section 5.4.3, you are required to match the force capability of your disturbance (moving stage). Electromagnetic drivers which can do this can be expensive, difficult to align, have a high power consumption, and have some stray magnetic fields which can cause problems in some applications.
  • For moving X – Y stages, the feedforward problem is non-linear due to twist couplings. For example, a payload will twist clockwise if there is an X-acceleration when the stage is in the full – Y position but counterclockwise when the stage is in the full + Y position. Therefore, there are feedforward terms proportional to XŸ and Y ¨X. This requires the use of a DSP-based controller.
  • To keep the system running well, there should be a self-adaptive algorithm which keeps the gains properly adjusted. This is done by monitoring the motion of the payload and correlating it with the feedforward command inputs. This type of algorithm is non-linear and can be unstable under certain circumstances. In particular, with pure sinusoidal stage motion, stage accelerations become indistinguishable from payload tilting due to the shifting weight burden caused by the stage (the Principle of Equivalence again).
  • This method requires some work on the customer’s or stage manufacturer’s part to provide an appropriate set of command feedforward signals. These can be either analog or digital in form, but they must come from the stage motion controller.
  • The isolation from floor vibration is no better than it is for a passive system (though, as mentioned, you may not need any improvement).
5.8 When Will You Need an Active System?

Determining your need for an active isolation system varies depending on whether you have a vibration or settling time critical application. Both can be difficult, and in either case, you need to know something about your system’s susceptibility to vibrational noise.
In vibration critical applications, it is insufficient to simply ask “does my system work?” If your system does not work with passive systems, or if the performance is inadequate, then you need to identify the source of the problem. For AFM/STM type applications, it may be obvious. The raw output of the stylus is dominated by a 1.5 Hz noise and that is correlated with the payload motion, and you know your isolators have their resonance at that frequency. Other times it may be much less clear. For example, you may see a 20 Hz peak in your instrument, and that correlates with noise on the payload – but is it coming from the ground? Many HVAC systems in buildings use large fans which operate in this frequency range. If they do, they produce both acoustic noise and ground noise which are correlated with noise on the payload. So what is the source of the problem? Ground noise or acoustics? It can be impossible to tell. Keep in mind, however, that if your problem is at 20 Hz, inertial feedback active systems will not help you, since they do not have any loop gain at that frequency. PZT-based isolators like STACIS® may be the only solution in this frequency range.
Settling time critical applications are more straightforward. To determine if you need an active system (which we assume to be feedforward only), there are three steps:
  • Step one: Determine the critical acceleration level for your process (as discussed earlier in See Section 5.5.2). A simple way to do this might be to move your stage and wait different amounts of time before making a measurement. If you know how long you need to wait and know the acceleration level of the payload after the stage stops, then you can derive this number. For a new instrument, the critical acceleration level can be very difficult to determine, and you might have to rely on calculations, modeling, and estimates.
  • Step two: Estimate the initial acceleration level of the payload by multiplying your stage acceleration by the ratio of your stage mass to total isolated payload mass.
  • Step three: Compare the numbers from steps one and two. If the critical acceleration level is above the initial payload reaction, then any TMC passive system should work for you. If it is below, then you need to compare the ratio of the initial to critical acceleration levels, and use Equation 17 to determine if the system can settle fast enough.
  • If your allowed settling time is insufficient to get the attenuation you need, then you might want to try a system with higher passive damping. TMC’s MaxDamp® isolators have a decay rate up to five times faster than conventional pneumatic isolators (a Q-factor five times lower). This does sacrifice some vibration isolation but is often a good tradeoff.
  • If MaxDamp® isolators will not work, then you will need an active system (passive isolation systems have run out of free parameters to solve the problem).
There are certain extreme examples which can determine your need very quickly. For example, if your critical level is below the initial payload acceleration and you want “zero” settling time, then you need an active system. However, if the ratio of the initial to critical level is more than 10 (with “zero” time), then you will either be forced to re-design your instrument or allow for a non-zero settling time. Active systems are not panaceas – they can not solve all problems.
5.9 General Considerations

If you are designing a new system, there are several general considerations which will make your system function optimally, whether it is active or not.
You should always use four isolators to support a system (rather than three), and they should be as widely separated as possible. This dramatically improves both the tilt stability and tilt damping in a system with only a marginal cost increase. It simplifies the design of the frame connecting the isolators, reduces the frame fabrication costs, gives better access to the components under the payload, and improves the overall stiffness of the system (assuming that your instrument has a square footprint).
You should use a center-of-mass aligned system whenever possible. This means putting the plane of the payload’s center of gravity (CG) in the same plane as the moving stage’s CG, and both of these should be aligned with the effective support point for the pneumatic isolators. This greatly reduces the pitch and roll of the payload with stage motions and can reduce the cost of an active system by making it possible to use lower force capacity drivers in the vertical direction. Note that the “effective support point” for most isolators is slightly below the top of the isolator. Consult a TMC Sales Engineer for the exact location of this point for different isolation systems. A system’s performance will also be improved by designing the payload such that the isolators support roughly equal loads.
The cost of the isolation system can be reduced by several means. The moving mass should be reduced as much as possible – this reduces the forces required to decelerate it and thus reduces the cost of the magnetic actuators in the active system. You should also make the payload as rigid as possible to reduce the system’s overall susceptibility to payload accelerations. Lastly, you can increase the static mass of the system, which will improve the ratio of static to active mass and thus reduce the payload’s reactions to stage motions.

It is quite possible that all of these steps, taken together, will allow you to avoid the use of an active system entirely.

5.10 Conclusions
The challenges created by Moore’s Law*** will require improved collaboration between systems engineers, integrators, stage manufacturers, and semiconductor tool manufacturers. There also needs to be a significant improvement in the awareness of the problem. This is simply a legacy of the by-gone days where “blind integration” of systems was sufficient. System engineers need to significantly shift their design goals for systems, since the conflict with high system throughputs and vibration isolation systems are fundamental, and active systems only improve the performance of systems by a certain factor. If the methods of design are not changed, then there may be a day in the not too distant future when even active systems will not work. Then you are really out of luck, since there is no next generation technology to turn to. Indeed, TMC already sees specifications which cannot be met even with the most optimistic assumptions about active system performance.
Active systems are relatively expensive. The costs are driven by components like the magnetic or PZT actuators. Their prices are high because of the cost of their materials (rare earth NdFeB magnets or piezoelectric ceramics). The cost of power amplifiers can be high. When considering costs, it is important to realize that there is no such thing as an incremental active solution. The active system, if you need one, must match the forces generated by your stage motions. A system capable of less simply will not work.
TMC is striving to improve active isolation systems. Our goal is to make them more reliable, easier to install, maintain, and configure, and to make them self-configuring whenever possible. This will reduce system costs, engineering times, and speed the production of your systems.
TMC has a staff of Sales Engineers who can help you with any questions raised in this presentation or assist you in the design of an isolation system.
The Technical Background section of this web site was prepared with assistance from Dr. Peter G. Nelson, Manager of Research and Development for TMC.
* This is an approximate statement, since PEPS is a linear system, and mechanical valves are very non-linear. PEPS generally levels faster for small displacements and slower for large ones.
** See for example, P.G. Nelson, Rev. Sci. Instrum., 62, p.2069 (1991).
Back to 5.4.1  and Back to 5.4.2
*** Gordon Moore, co-founder of Intel Corp., has pointed out that the density of semiconductors (in terms of transistors/area) has roughly doubled every 18 months, on average, since the very earliest days of commercial semiconductor manufacturing (even 1960 or earlier!).

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