Stability and robust position control of hysteretic systems

Position control of a wide class of hysteretic systems, which includes those described by a Preisach model, is considered. The main focus of this paper is stability, tracking and the trajectories of a hysteretic system controlled by a PI controller. The system output (not its derivative) is measured and controlled. It is shown that, for arbitrary reference signals, the closed‐loop system is bounded‐input–bounded‐output‐stable with a finite gain of one. Furthermore, the absolute value of the error decreases monotonically for a constant reference signal. In this case, provided that the desired output is within the limits of the system output, zero steady‐state error is guaranteed. A bound on the time required to achieve a specified error is obtained. Only a simple condition on the controller parameters is required. The results imply that stability and position control are guaranteed, even if large errors in the model exist. Copyright © 2009 John Wiley & Sons, Ltd.