
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 xy 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 vaxis. 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 zerodamping 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. Timedomain optimization approaches based on statespace models have been applied to this problem. This article presents a case study of noncolocated beam control problem using frequencydomain 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