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 <i>L</i><sub>1</sub> 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.
Smart materials display coupling between electrical, magnetic, thermal and elastic behavior. Hence these materials
have inherent sensing and actuation capacities. However, the hysteresis inherent to smart materials presents
a challenge in control of these actuators/sensors. Inverse compensation is a fundamental approach to cope with
hysteresis, where one aims to cancel out the hysteresis effect by constructing a right inverse of the hysteresis. The
performance of the inverse compensation is susceptible to model uncertainties and to error introduced by inexact
inverse algorithms. We employ a mathematical model for describing hysteresis. On the basis of the hysteresis
model, a robust adaptive inverse control approach is presented, for reducing hysteresis. The asymptotic tracking
property of the adaptive inverse control algorithm is proved and the issue of parameters convergence is discussed
in terms of the reference trajectory. Moreover, suficient conditions under which parameter estimates converge
to their true values are derived. Simulations are used to examine the effectiveness of the proposed approach.