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Research Papers

Optimal Tracking Using Magnetostrictive Actuators Operating in Nonlinear and Hysteretic Regimes

[+] Author and Article Information
William S. Oates

Department of Mechanical Engineering, Florida A&M/Florida State University, Tallahassee, FL 32310-6046woates@eng.fsu.edu

Ralph C. Smith

Department of Mathematics and Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695rsmith@eos.ncsu.edu

J. Dyn. Sys., Meas., Control 131(3), 031001 (Mar 19, 2009) (11 pages) doi:10.1115/1.3072093 History: Received August 19, 2005; Revised December 01, 2008; Published March 19, 2009

Many active materials exhibit nonlinearities and hysteresis when driven at field levels necessary to meet stringent performance criteria in high performance applications. This often requires nonlinear control designs to effectively compensate for the nonlinear, hysteretic, field-coupled material behavior. In this paper, an optimal control design is developed to accurately track a reference signal using magnetostrictive transducers. The methodology can be directly extended to transducers employing piezoelectric materials or shape memory alloys due to the unified nature of the constitutive model employed in the control design. The constitutive model is based on a framework that combines energy analysis at lattice length scales with stochastic homogenization techniques to predict macroscopic material behavior. The constitutive model is incorporated into a finite element representation of the magnetostrictive transducer, which provides the framework for developing the finite-dimensional nonlinear control design. The control design includes an open loop nonlinear component computed off-line with perturbation feedback around the optimal state trajectory. Estimation of immeasurable states is achieved using a Kalman filter. It is shown that when operating in a highly nonlinear regime and as the frequency increases, significant performance enhancements are achieved relative to conventional proportional-integral control.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) Linear control design employing an inverse filter, and (b) nonlinear control design

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Figure 2

Terfenol-D transducer design used for high accuracy machining operations of cutting out-of-round objects

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Figure 3

Constitutive model prediction of the displacement versus field behavior using the homogenized energy model. A sinusoid input was applied at 100 Hz. The model is compared with the data on an Etrema Terfenol-D actuator (31).

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Figure 4

Magnetostrictive transducer with damped oscillator used to quantify loads during the machining operation. Disturbance forces along the actuator are given by Fd and the control input is u(t).

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Figure 5

Tracking control response using the nonlinear control law. (a) The controlled response and tracking error between the reference signal and controlled response (in microns). (b) The corresponding H-M constitutive behavior.

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Figure 6

Tracking control response using the PI control law. (a) The controlled response and the error between the reference signal and controlled response (in microns). (b) Corresponding H-M constitutive behavior.

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Figure 7

The effect of an initial time delay on the open loop control signal is illustrated

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Figure 8

Perturbation feedback using the estimated states from the Kalman filter: (a) measurement noise is zero, and (b) measurement noise is a random signal with an amplitude of 10 μm

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