On the robust control of systems preceded by Coleman-Hodgdon hysteresis

When the systems preceded by unknown hysteresis nonlinearities, the existence of the unknown hysteresis will degrade the system performance. The main task is to develop a control approach to mitigate effects caused by these unknown hysteresis nonlinearities. In this paper, a special case of the Duhem model, the Coleman-Hodgdon hysteresis model, is employed to describe the unknown hysteresis nonlinearities. By exploring the characteristics of the Coleman-Hodgdon hysteresis model, a sliding mode control is proposed as an illustration to show the method of mitigating the effects caused by the unknown hysteresis nonlinearities without constructing a hysteresis inverse. The proposed control approach ensures the asymptotically stability of the system and the error dynamics toward the switching surface. The effectiveness of the proposed control approach is demonstrated through simulation example.