A Method of Control System Design Based upon Partial Knowledge about Controlled Processes

Abstract

In this paper a unified method is developed which enables one to design control systems of various types in the situation that the dynamic characteristics of the controlled process are not known perfectly.The control system to be designed is to satisfy the following specifications:(a) It has zero steady-state error.(b) It has adequate damping characteristics.(c) (a) and (b) satisfied, it has a shortest rise-time.For the design, a sequence of parameters is found suitable to represent the dynamics of an element or a system. The sequence is equivalent to that of moments of the impulse response in the sense of I. F. S. (independency from the successors) which plays a fundamental role in the development.The specifications above are also reorganized into a sequence of conditions on the parameters of the control system to be designed.Owing to the I. F. S., any truncated sequences of conditions and parameters give rise to a formula to design a compensator and/or a controller based upon partial knowledge about the controlled process. The formula has a kind of matching property, so that the simpler control mode calls for as less the number of controlled process parameters known.Formulas for the PID and the I-PD control schemes are derived, and some results are demonstrated in step response curves, which show the effectiveness of the method. For an overdamped process, the response speed increases as the number of controller parameters, whereas the damping characteristics remain unchanged. Even for an unstable process, a satisfactory control system is brought about when a sufficient number of controller parameters are employed.