Nonlinear Control of Systems Preceded by Preisach Hysteresis Description: A Prescribed Adaptive Control Approach

When systems are preceded by hysteresis nonlinearities, many controller strategies have been developed with various hysteresis models, especially in the past decade. Among the hysteresis models, the Preisach model has a very general and well-established mathematical structure. However, designs of controllers that guarantee the closed-loop stability of nonlinear systems having the Preisach hysteresis representation are still a challenging issue in the literature. In this paper, we will attempt to demonstrate a solution in which a stable controller can be designed for nonlinear systems that couple with Preisach hysteresis model. The key is that by utilizing the so-called Preisach plane, the Preisach model is reexpressed into a control-oriented form, in which the input signal is explicitly expressed. It is then possible to fuse available control techniques with the Preisach model designing stable controllers. As an illustration to show the advantage of the developed control-oriented form, a prescribed adaptive control approach is adopted to ensure the transient and steady-state performance of the tracking error. The effectiveness of the control scheme is validated by the experimental results.