Computational Alternative to a Gain Setting Procedure of Brown and Campbell

Abstract

A numerical method for setting the gain of a linear control system to obtain a specified peak closed-loop frequency response amplitude is presented. The essential computational step in the algorithm is the calculation of all positive roots of a polynomial. This step provides the set of all possible resonant frequencies. A gain constant for each of these frequencies is then found by a simple function evaluation. The possibility of multiple solutions is demonstrated by an example.