On the robustness of hysteretic second-order systems with PID: iISS approach

In this paper, we study the robustness property of a second-order linear plant controlled by a proportional, integral and derivative (PID) controller with a hysteretic actuator. The hysteretic actuator is modeled by a Duhem model that exhibits clockwise (CW) input-output (I/O) dynamics (such as the Dahl model, LuGre model and Maxwell-Slip model, which describe hysteresis phenomena in mechanical friction). Based on our main result, we provide sufficient conditions on the controller gains that depend on the plant parameters such that the origin of the plant and the state of the hysteresis is globally attractive. The robustness of the closed-loop system with respect to the measurement noise is also given, using the integral input-to-state stability (iISS) concept. The applicability of the robustness analysis in the design of state observer for such systems is shown in the simulation.