Adaptive Control of Hysteretic Smart Material Systems

Abstract

Smart materials exhibit nonlinearities and hysteresis when driven at field levels necessary to meet stringent performance criteria in high performance applications. This requires models and control designs that effectively compensate for the nonlinear, hysteretic field-coupled material behavior. In this dissertation, we investigate model identification using the homogenized energy model and adaptive control of hysteresis in smart hysteretic system, while the approaches are applicable to control of a wide class of ferroelectric, ferromagnetic and ferroelastic materials, we illustrate the ideas through the example of controlling a ferroelectric actuator.

We pursue the problem of hysteresis control through two complimentary approaches: linear adaptive control using an inverse compensator and nonlinear adaptive control.

Inverse control is a fundamental approach to accommodate hysteresis effect by constructing a right inverse of the hysteresis. Due to the open-loop nature of inverse control, the performance of the inverse compensation is susceptible to model uncertainties and to error introduced by inexact inverse algorithms. The objective of adaptive control is to design a controller that can adjust its behavior to tolerate uncertainties or time-varying parameters. We employ the homogenized energy model to quantify the hysteresis. On the basis of the hysteresis model, we propose an adaptive control framework by combining inverse compensation with adaptive control techniques, and investigate the parameter identification methods for the hysteresis model. We prove the asymptotic tracking property of the proposed adaptive inverse control algorithm, discuss the issue of parameters convergence and illustrate the performance of the proposed control method through simulations.

Adaptive nonlinear control is a more challenging task and has received increasing attention in recent years. The challenge addressed here is how to fuse hysteresis models with available adaptive control techniques to have the basic requirement of stability of the system. In this dissertation, an adaptive variable structure control approach, serving as an illustration, is fused with the homogenized energy model without constructing a hysteresis inverse. The global stability of the system and tracking a desire trajectory to a certain precision are achieved under certain conditions. Simulations are performed on an unstable nonlinear system. The purpose of exploring new avenues to fuse the model of hysteresis nonlinearities with the available adaptive controller designs without constructing a hysteresis inverse is achieved and illustrated with the promising simulation results. This provides a step toward the development of a general nonlinear adaptive control framework for hysteretic systems.