Accuracy Considerations of the Equivalent Linearization Technique for the Analysis of a Non-Linear Control System with a Gaussian Random Input

Abstract

In this paper, the accuracy of the results which can be obtained by the linearization technique of a non-linear control system with a Gaussian random input is investigated. Presence of non-linearity in the control system destroys the Gaussian nature of the response signals. In the linearization technique, therefore, assumption of the Gaussian input for the non-linear element is approximate. The accuracy analysis is restricted to consideration of the cumulants of the second and the fourth order of the input to the non-linear element. This results from the consideration that a linear element with a memory tends to make non-Gaussian signals more nearly Gaussian. A simple control system with a Gaussian input is analyzed as an example. It is concluded that the equivalent linearization technique is accurate enough for engineering purposes.