CONTROL OF LINEAR SYSTEMS WITH LARGE TIME DELAYS IN THE CONTROL

摘要

This study was motivated by the attitude-control problem from earth of a satellite in deep space. The main feature of this control problem is the presence of a large time delay in the control function due to the long times required to transmit the control signals. Time delays in the control function also arise in many other types of control problems, and thus the attitude-control problem is merely used to illustrate the influence which time delay has upon system behavior. It is assumed that the time delay is constant in magnitude and identical in magnitude for each component of the control vector. Linear systems are considered through¬out this paper, but it is pointed out that much of what is said applies to non-linear systems as well.nThe most common effect of a time delay in the control is the degrad¬ation of the system behavior with respect to its delay-free behavior. This is demonstrated by considering a second-order problem with bounded control. This degradation in system performance is due primarily to the inherent uncontrollability of systems with control delays in the time interval [to, to + td] where to is the initial time and td is the magnitude of the time delay. A theorem to this effect is presented.