Research Papers

Experimental Implementation of a Hybrid Nonlinear Control Design for Magnetostrictive Actuators

[+] Author and Article Information
William S. Oates

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

Phillip G. Evans

Department of Mechanical Engineering, Ohio State University, Columbus, OH 43210evans.895@osu.edu

Ralph C. Smith

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

Marcelo J. Dapino

Department of Mechanical Engineering, Ohio State University, Columbus, OH 43210dapino.1@osu.edu

J. Dyn. Sys., Meas., Control 131(4), 041004 (Apr 29, 2009) (11 pages) doi:10.1115/1.3089560 History: Received August 30, 2007; Revised December 08, 2008; Published April 29, 2009

A hybrid nonlinear optimal control design is experimentally implemented on a magnetostrictive Terfenol-D actuator to illustrate enhanced tracking control at relatively high speed. The control design employs a homogenized energy model to quantify rate-dependent nonlinear and hysteretic ferromagnetic switching behavior. The homogenized energy model is incorporated into a finite-dimensional nonlinear optimal control design to directly compensate for the nonlinear and hysteretic magnetostrictive constitutive behavior of the Terfenol-D actuator. Additionally, robustness to operating uncertainties is addressed by incorporating proportional-integral (PI) perturbation feedback around the optimal open loop response. Experimental results illustrate significant improvements in tracking control in comparison to PI control. Accurate displacement tracking is achieved for sinusoidal reference displacements at frequencies up to 1 kHz using the hybrid nonlinear control design, whereas tracking errors become significant for the PI controller for frequencies equal to or greater than 500 Hz.

Copyright © 2009 by American Society of Mechanical Engineers
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Figure 1

Examples of nonlinear control designs. (a) Nonlinear inverse compensator. (b) Direct nonlinear control.

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Figure 2

Schematic of the Terfenol-D actuator used in the control experiments

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Figure 3

Magnetostrictive actuator with a damped oscillator used to quantify loads under a time varying magnetic field. Disturbance forces along the actuator are given by Fd, and the control input is u(t).

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Figure 4

Rate-dependent constitutive data and comparison to the homogenized energy model described in Sec. 3. The frequencies tested and fitted to the model were (a) 100 Hz, (b) 200 Hz, (c) 300 Hz, and (d) 500 Hz.

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Figure 5

Current-voltage behavior of the amplifier-actuator system. The data are compared with a linear and nonlinear inductor-resistor lumped circuit model discussed in Sec. 3. The frequencies correspond to the data in Fig. 4 where (a) 100 Hz, (b) 200 Hz, (c) 300 Hz, and (d) 500 Hz.

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Figure 6

Open loop frequency response for the Terfenol-D actuator in the operating regime. The input is voltage to the wound wire solenoid, and the output is the rod tip displacement.

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Figure 7

Frequency response of the PI controller in (a) and the open loop controller-actuator in the near-linear operating regime in (b)

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Figure 8

Frequency response of the closed loop controller-actuator system in the near linear operating regime

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Figure 9

Comparison of the tracking control performance using PI control, nonlinear open loop optimal control, and nonlinear open loop optimal control with PI perturbation feedback. The frequencies tested range from (a) 100 Hz, (b) 200 Hz, (c) 300 Hz, (d) 500 Hz, (e) 700 Hz, and (f) 1000 Hz. The reference displacement amplitude was 30 μm.

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Figure 10

Tracking control experimental results at 1 kHz expanded from Fig. 9 to illustrate improvements in tracking control between PI control and nonlinear optimal control

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Figure 11

Comparison of current inputs using open loop nonlinear optimal control and PI control. (a) Current input for the 500 Hz reference displacement. (b) Current input for the 1000 Hz reference displacement.



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