Control of Smart Actuators: A Viscosity Solutions Approach

Abstract

Hysteresis in smart materials hinders their wider applicability in actuators. In this report we investigate control of smart actuators through the example of controlling a commercially available magnetostrictive actuator. At low frequencies, the magnetostriction can be related to the bulk magnetization through a square law, thus control of the magnetization amounts to control of the magnetostriction. The model we use is the low dimensional Jiles-Atherton model for ferromagnetic hysteresis, which is a hybrid system. For illustrative purpose, we consider an infinite horizon control problem. The approach we take features dynamic programming and Hamilton-Jacobi equations. In particular, we show that the value function of the control problem satisfies a Hamilton-Jacobi- Bellman equation (HJB) of some hybrid form in the viscosity sense. We further prove uniqueness of solutions to the (HJB), and provide a numerical scheme to approximate the solution together with a suboptimal controller synthesis method.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2001
Accession Number
ADA439792

Entities

People

  • John Baras
  • Xiaobo Tan

Organizations

  • University of Maryland

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Actuators
  • Coefficients
  • Computational Fluid Dynamics
  • Computer Programming
  • Differential Equations
  • Domain Walls
  • Dynamic Programming
  • Dynamics
  • Equations
  • Ferromagnetic Materials
  • Hysteresis
  • Inequalities
  • Materials
  • Mathematical Models
  • Partial Differential Equations
  • Universities
  • Viscosity

Readers

  • Calculus or Mathematical Analysis
  • Materials Science and Engineering.
  • Robotics and Automation.