The Generalized PID Controller and its Application to Control of Ultrasonic and Electric Motors

Abstract

In this paper by the use of optimal stochastic control theory we formulate a tracking problem and show those cases when their solution gives the PI, PD and PID controllers. Thus, we are avoiding heuristics and giving a systematic approach to explanation for their excellent performance. It is shown that the PI controller is optimal for a first order system, the PID controller is optimal for a 2nd order system with no zero. The same approach is applied to a general linear strictly proper system and a generalized PID controller is derived. Such controller is called here PID n-1 controller. As an example, generalized PID controllers for an ultrasonic motor and an electric DC motor are presented.