Linear Parameter-varying Control for Active Vibration Isolation Systems with Stiffness Hysteresis

We consider the use of linear parameter-varying methods for the control of stiffness hysteresis in vibration isolation systems. We assume that the hysteresis model is known, and we describe it using a stiffness parameter that takes values in a compact convex set. The proposed parameter-dependent controller is continuously scheduled based on real-time measurements or estimates of the stiffness, and provides guaranteed stability and performance for the full range of stiffness variability. The method is applied to a simplified model of a microgravity vibration isolation system with an umbilical stiffness hysteresis non-linearity. Simulations show that the parameter-varying design is stable in the presence of hysteresis and that the desired isolation performance is achieved over the full range of displacements considered. The results are compared with those obtained with a fixed robust controller that considers the stiffness variability as uncertainty. We discuss robustness issues and demonstrate the effect of hysteresis model uncertainty in the implementation of the proposed control scheme.