NORTH- HOLLAND Effects of Time Delays on the Stability of Collocated and Noncollocated Point Control of Discrete Dynamic Structural Systems Ravi Kumar Department of Civil Engineering University of Southern Cali]ornia Los Angeles, California 90089-2531 Transmitted by F. E. Udwadia ABSTRACT The effects of time delays on collocated as well as noncollocated point control of discrete dynamic systems have been examined. Controllers of proportional- integral-derivative (PID) type have been considered. Analytical estimates of time delays to maintain/obtain stability for small gains have been given. Several new results dealing with the effect of time delays on collocated and noncollocated control designs are obtained. It is shown that undamped structural systems cannot be stabilized with pure velocity (or integral) feedback without time delays while using a controller which is not collocated with the sensor when the mass matrix is diagonal. However, with the appropriate choice of time delays for certain classes of commonly occurring structural systems, stable noncollocated control can be achieved. Analytical results providing the upper bound on the controller's gain necessary for stability have been presented. The theoretical results obtained are illustrated and verified with numerical examples. 1. INTRODUCTION Many structural systems are spatially distributed and are modeled by linear matrix differential equations. In the field of active control, it is a general notion that direct velocity feedback control for such multi-degree- of-freedom (MDOF) systems when using collocated sensors and actuators results in the damping out of all modes of vibration with no spillover ef- fects [1, 2]. However, in practical feedback control systems (a) direct state feedback is not possible because of the involved dynamics of the sensor and the actuator; and, (b) the collocation of the sensor with the actuator (or APPLIED MATHEMATICS AND COMPUTATION 70:215-232 (1995) (~) Elsevier Science Inc., 1995 0096-3003/95/$9.50 655 Avenue of the Americas, New York, NY 10010 SSDI 0096-3003(94)00107-F