PD control of a second-order system with hysteretic actuator

In this paper, we design a proportional and derivative (PD) controller for a mass-damper-spring system interconnected with a hysteretic actuator, such as, the piezo-actuated stage. The hysteretic actuator is assumed to have a counterclockwise (CCW) input-output (I/O) dynamics (e.g. piezo-actuator) and is modeled by a Duhem operator. Based on the CCW of the hysteretic actuator, we provide sufficient conditions on the controller gains that depend on known intervals where the plant and hysteresis parameters lie such that the velocity of the linear plant converges to the origin. Robustness analysis and experimental results for tracking a constant reference velocity are also presented.