Abstract

Hysteresis widely exists in smart materials such as shape memory alloys (SMAs), piezoelectrics, magnetorheological (MR) fluids, electrorheological (ER) fluids and so on. It severely affects the applicability of such materials in actuators and sensors. In this thesis, problems of modeling and control of systems with hysteresic SMAs actuators are studied. The approaches are also applicable to control of a wide class of smart actuators. Hysteresis exhibited by SMAs actuators is rate-independent when the input frequency is low, and can be modeled by a classical Preisach model or a KP model. The classical Preisach hysteresis model is a foundation of other hysteresis models. In this thesis, traditional methods are explained in advance to identify and implement the classical Preisach model. Due to the extremely large amount of computation involved in the methods, a new form of the Preisach model, linearly parameterized Preisach model, is introduced, and then an effective method to implement the model is presented. The KP model is a more effective operator to describe the Preisach class of hysteresis than the Preisach model. The relationship between the two models is revealed to verify the effectiveness of the KP model. Also, a linearly parameterized KP model is proposed. For both of the Preisach hysteresis model and the KP hysteresis model, algorithms of inverse hysteresis operators are developed, and simulations for modeling and inverse compensation are conducted. Since the Preisach model and the KP model can only describe hysteresis which has saturation states and reverse curves with zero initial slopes, a novel hysteresis model is defined to overcome these shortcomings. The newly defined hysteresis model is a low dimensional hysteresis model and can describe hysteresis which has revertible linear parts and reverse curves with non-zero initial slopes. The problems for controlling systems with input hysteresis have been pursued along three different paths: inverse compensation, gradient adaptive control and robust adaptive control for linear and nonlinear systems. Control schemes of open-loop inverse compensation and gradient adaptive inverse compensation for the Preisach hysteresis model are explored to eliminate the effects of the hysteresis when the output of the hysteretic actuator is measurable. Usually hysteresis of smart actuator in systems is not exactly known, but it can be approximately modeled via the linearly parameterized KP model. For a known linear system preceded by an unknown actuator hysteresis, a model reference control scheme combining with an adaptive inverse compensation is designed for tracking control of the systems. While an unknown linear system preceded by an unknown actuator hysteresis, a model reference adaptive control scheme together with an adaptive inverse compensation is developed for tracking control of the system. Simulations for both cases have been performed to illustrate the control methods. Finally, when hysteresis of smart actuator in systems has a non-measurable output and is modeled via the KP model or the newly defined model, a novel robust adaptive control configuration is presented for tracking control of systems. The analysis for the stability and the convergence of the control systems is conducted. Simulations are performed to verify the effectiveness of the novel control method.