Adaptive Control Design for Hysteretic Smart Systems

Ferroelectric and ferromagnetic actuators are being considered for a range of industrial, aerospace, aeronautic and biomedical applications due to their unique transduction capabilities. However, they also exhibit hysteretic and nonlinear behavior that must be accommodated in models and control designs. If uncompensated, these effects can yield reduced system performance and, in the worst case, can produce unpredictable behavior of the control system. One technique for control design is to approximately linearize the actuator dynamics using an adaptive inverse compensator that is also able to accommodate model uncertainties and error introduced by the inverse algorithm. This paper describes the design of an adaptive inverse control technique based on the homogenized energy model for hysteresis. The resulting inverse filter is incorporated in an L1 control theory to provide a robust control algorithm capable of providing high speed, high accuracy tracking in the presence of actuator hysteresis and nonlinearities. Properties of the control design are illustrated through numerical examples.