積分型最適サーボ系の構成

抄録

For designing a control system so that the output tracks a constant reference input, it is common to associate an integral compensator with the given plant and apply a stabilizing control law to the resulting augmented system. The LQ optimization technique is extensively used for the stabilization, and the obtained feedback control system has been refered to as an optimal servosystem. It is true that the servosystem is optimal to the changes of initial states or unknown constant disturbances, but not true when the reference input is changed. The objective of the present paper is to indicate this fact and provide the optimal control law which really minimizes the given performance index.
There are two types of quadratic performance indices which have been considered in the context of the design of servosystems. We deal with both in this paper, and show that the optimal control law is generally composed of not only the state feedback in the augmented system but also the feedforward from the reference input and a constant signal determined by the initial states of the system. The constant signal is not needed if we assume that the change of the reference input occurs only when the system is in steady states. In case we do not allow discontinuity of the control input, the optimal control law is realized by only the state feedback in the augmented system.