Robust Controller Design for Flexible Structures,
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 0<x sub 0<L 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1987
- Accession Number
- ADA187217
Entities
People
- Nassim M. Arbouz
- Renjeng Su
Organizations
- University of Colorado Boulder