A Graphical Method for the Evaluation of the Statistical Responses of Non-Linear Control Systems to a Stationary Random Signal Considering Random Noise

Abstract

This paper describes a graphical method for the analysis of automatic control systems containing a non-linear element of zero-memory type with stationary random inputs. The starting point of the analysis is the use of the statistical equivalent gain of the non-linear element for the input, by which the non-linear feedback control system reduces to an equivalent linear one. When the input to the non-linear feedback control system consists of a random noise and a random signal and if these are statistically independent of each other, we can use two different equivalent gains of the non-linear element which can be found by the “R.M.S.-Error Criterion” for each one of these. Then the non-linear system may be treated as an equivalent linear feedback control system with random noise or with random signal. It is easy, therefore, to find the responses of the non-linear feedback control system to such inputs. In the special case when the system input is only a sinusoidal wave, this method reduces to the “describing-function” method. In order to illustrate the procedure of the graphical analysis in detail, we considered three control systems as numerical examples. As for the results we were able to investigate the effects of random noise on the harmonic response of the non-linear control system and the jump phenomenon which can be seen in the relation curve between the variance of the random signal and the one of the system response.