Adaptive Control of Hysteretic Smart Material Systems
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Date
2009-11-05
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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.
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Keywords
Smart Materials, Hysteresis, Adaptive Control
Citation
Degree
PhD
Discipline
Applied Mathematics