A Study of Periodic Solutions of Typical Relay Servo System

릴레이 제어기구 조기해법에 관한 연구

A relay servo, one of the nonlinear sytsems, is inherently compact compared to a linear system for an equivalent control problem. The power element or actuator is not adjusted proportionally in accordance with an error signals but rather is switched abruptly between several discrete conditions. Usually switched conditions are off, full, forward or full reverse. The relay system is a particularly simple and compact one, but probably more effort has been expended on its analysis and design than on all other systems together. Early studies in the art were made by Goldfarb, austin, Oppelt and Kochenburger on the describing function method, which can be used as an approximate check on the stability of the system. The describing function method is based on the assumption that any periodic wave could be approximated as a fundamental one in wide ranges of practical applications. A relay servo system usually operates on a limit cycle condition as the loop gain increases. The stability analysis compensation or any improvement effort based on the describing function method sometimes may present considerable discrepancies on physically realized practical systems. An approach to exact periodic solutions of a relay servo system is much important for the analysis, design and system improvement. This paper dells with periodic solutions of a relay servo system on the basis of describing function and generalized chopper wave form which is composed of infinite number of harmonic series. Various ways of graphical representation were attempted to get periodic solutions, some of which have shown its validity in rapid approach to exact solutions and also in judgement of system behavior.

본논문은 릴레이 제어기구의 안정도해석과 종합성능판별의 기초가 되는 리미트사이클진동의 주기해를 정확하고도 신속하게 얻을 수 있는 방법을 개발한 것으로서 특히 궤적법은 동종의 릴레이에 대해서는 특서정수의 변화에 대해서 직각대응시킬 수 있고, 주기해를 정확하게, 그리고 신속하게 직속할 수 있는 장점을 지닌다. 이제까지 다루워 왔던 describing 함수해석법과도 비교하여 그의 부정확성과 불편성 동종릴레이 특성정수변화에 대한 비적응성도 검토하여 궤적법의 우월을 명시하였다.