Approximate Method for Calculating the Time Response in Linear, Time-Varying, and Nonlinear Automatic Control Systems

Abstract

In past years many methods have been developed for calculating the time response in automatic control systems. In this paper an improved, approximate method for calculating the transient response in linear (Section 1), time-varying (Section 2), and nonlinear (Section 3) automatic control systems, is developed on the basis of previous works [1–5]. The basis of this method lies in an approximate solution of integral equations by means of special tables which are given in the Appendix. These tables enable the user to shorten the time for calculation. This method also can be useful for obtaining programs for digital computers. In each part of the paper, examples are given to illustrate the use of this method. These examples are identical to those of Boxer and Thaler [4] and facilitate a comparison of the solution method developed in the paper with their z-transform approach.