Modification of Equivalent Gains Based on the Probability Density Function of the Response of Nonlinear Control Systems Subject to a Gaussian Random Input

Abstract

Recognizing that the probability distribution of input signal to the nonlinear element in a closed loop control system is not a Gaussian, the authors present, in this paper, a more precise evaluation of equivalent gains of various nonlinear elements in control systems subject to a Gaussian random input. The conception with respect to the Markov random process in statistics is introduced and the justification for assuming the response of a nonlinear control system as being a Gaussian process is considered in detail. The equivalent gains obtained in the previous papers are modified from the results of evaluating the probability distribution of the response of nonlinear control systems. Moreover, the statistical linearization technique is theoretically checked for the various important cases. The authors find that the results of these evaluations agree with the experimental results sufficiently.