Performance of a Gain-Saturated Control System and the Numerical Analysis of the Indicial Response

Abstract

It is generally impossible to obtain the exact response of nonlinear control systems by the integral method. It is necessary, therefore, to use the approximate methods such as perturbation, iteration or others, when we intend to study the systems by the analytical method. The solution will be represented by infinite series, and the first several terms will afford an approximate solution. Then, the convergency of the solution and the accuracy of the approximate solution must be estimated, being compared with the numerical solution, which has a significant meaning in the theoretical study of nonlinear control systems. The author devised a modified Runge-Kutta method. He proved that the mcdified method is less troublesome in calculation with better accuracy than the conventional method in the illustrative analysis of the indicial response of gain-saturated second order servomechanism. He believes that the modified method will be superior to the conventional one in the general nonlinear gain systems or, moreover, in the general nonlinear control systems.