Closed-loop position control of Preisach hystereses

We discuss closed-loop control of hysteretic systems having Preisach representations. We apply dissipativity methods, the key component of which is the determination of an appropriate supply rate. The concept of cyclo-dissipation is used to identify a new supply rate for Preisach hystereses and dissipativity with respect to this supply rate is shown. The result is useful in the design of output feedback controllers, and complements a previous result using feedback of the output derivative. We consider the specific example of a shape memory alloy actuator and identify a class of controllers which provide stability of position feedback with current as the control variable. This demonstrates one way in which system dynamics that couple with hysteresis can be included in controller design.