Accession Number:

ADA439792

Title:

Control of Smart Actuators: A Viscosity Solutions Approach

Descriptive Note:

Technical rept.

Corporate Author:

MARYLAND UNIV COLLEGE PARK DEPT OF ELECTRICAL AND COMPUTER ENGINEERING

Personal Author(s):

Report Date:

2001-01-01

Pagination or Media Count:

28.0

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.

Subject Categories:

  • Numerical Mathematics
  • Electricity and Magnetism
  • Fluid Mechanics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE