In force-controlled experiments, Eq. 1, Eq. 2 and Eq. 4 can be transformed in state space form, using the change of variables x 1 ( t ) = u ( t ) , x ˙ ˙ 1 ( t ) = u ˙ ˙ ( t ) = x 2 ( t ) , x ˙ ˙ 2 ( t ) = u ¨ ¨ ( t ) and x 3 ( t ) = z ( t ) as: