Simple technique for root locus plotting

Abstract

We present a simple technique for calculating and plotting the root locus of a linear control system. Although several programs are commercially available for this purpose, and remarks on this subject can be found in dedicated texts, a complete description of the program code is desirable to provide the designer with versatility and deeper insight. This report describes our technique and includes complete program codes. In this technique, the roots of the system's characteristic function are found by providing a single, unique guess value to be used in a first derivative search algorithm in order to calculate the unknown set of roots. Similarly to other techniques, the root locus is found by calculating the system's set of roots as the gain varies in the range of interest. The resolution obtained depends on the sampling rate of the gain parameter. The technique is suitable for any programming language and there is basically no limit on the root order of the system. To illustrate the technique a four-pole order system is analyzed. Then, to improve the response of the system a lead compensation network is added.. The usefulness of the technique is illustrated by comparing the time response of the compensated network over the uncompensated one.