Accession Number : ADA187217

Title :   Robust Controller Design for Flexible Structures,

Corporate Author : COLORADO UNIV AT BOULDER DEPT OF ELECTRICAL AND COMPUTER ENGINEERING

Personal Author(s) : Su, Renjeng ; Arbouz, Nassim M

PDF Url : ADA187217

Report Date : Jan 1987

Pagination or Media Count : 13

Abstract : This document considers the problem of control of a beam which is moving in the x-y plane. It extends from x=0 to x=L. The left end at x=0 is clamped to an actuator which moves the beam along the v-axis. The control input is the force u(t) in y direction. While moving, the beam may vibrate. Let z(t) denote the displacement of the left from y=0, and w(t,x), the displacement of the beam from the line y=z(t) at position x and time t. Suppose a position sensor is place on the beam and the sensing output is v(t, sub 0)=z(t) + w(t,x0), where 0x sub 0L is the sensor location. We are interested in the case when the flexure w(t,x) of the beam is significant. The problem is to synthesize a feedback control law which moves the beam from one position to another in a stable manner. It is well known that when the sensor and the actuator are colocated a simple lead compensator suffices to produce a stable design. This result holds even when the beam dynamics are considered as a system with infinite zero-damping modes, and can be shown using root locus argument. This stabilization method may break down, however, when there is a positional gap between the sensor and actuator. In this case the classical compensation techniques are no longer effective. Time-domain optimization approaches based on state-space models have been applied to this problem. This article presents a case study of noncolocated beam control problem using frequency-domain optimization method proposed by Professor Kwakernaak. We emphasize the choice of the weighting functions in the cost function, and the search method which always leads to stable designs.

Descriptors :   *CONTROL THEORY, *FLEXIBLE STRUCTURES, ACTUATORS, COMPENSATION, CONTROL, DISPLACEMENT, FEEDBACK, POSITION(LOCATION), DYNAMICS, INPUT, COSTS, DETECTORS, LOCUS, SEARCHING, COMPENSATORS, STABILITY, WEIGHTING FUNCTIONS, STABILIZATION, OPTIMIZATION, TIME DOMAIN, BEAMS(STRUCTURAL)

Subject Categories : Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE