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.
Descriptors:
Subject Categories:
- Numerical Mathematics
- Electricity and Magnetism
- Fluid Mechanics