The limit cycle, which is frequently observed in a nonlinear feedback system, gives us very useful information as to the dynamic characteristics of the system. This paper examines the identification problem of control system dynamics using the information of limit cycle. The following methods are proposed
(1) A method to determine the characteristics of a controlled object which contains a nonlinearity: In this method, a closed loop is formed so that the output of the object is negatively fed back to its input through a relay in order to generate a limit cycle. The frequency characteristic of the linear part of the object and the input-output relation of its nonlinearity can be determined from amplitude and frequency of the limit cycle by using describing function method. This method can be applied if the linear part has low-pass frequency characteristic, and the nonlinearity is such that its describing function depends only on the amplitude of the input and is insensitive to its frequency.
(2) A method to estimate the performance indexes of a linear feedback control system: In this method, a nonlinear device which has suitable describing function is added to the system in order to generate a limit cycle. Various indexes of the performance of a linear feedback control system (e. g. gain margin, phase margin, resonant frequency and so on) can be easily estimated by this method.
Experimental verification is given for each of these methods. Moreover, it is also shown that these methods are still applicable when there is small disturbance in the object to be measured.

View full abstract