Modern Control System Theory and Design, 2nd Edition

6.17.  ROOT-LOCUS METHOD FOR CONTROL SYSTEMS USING MATLAB [7]

In Sections 6.14–6.16, several root-locus plots were generated using the 12 rules of construction and were hand drawn. Additionally, several root-locus plots were also illustrated which were obtained using MATLAB. In this section, the reader will be shown how to obtain the root-locus diagrams very easily and accurately using MATLAB.

A.  Drawing the Root Locus if the System is Defined by a Transfer Function

The MATLAB command used for plotting the root locus is

rlocus(num,den)

The Modern Control System Theory and Design (MCSTD) Toolbox enhances the professional toolbox by not only plotting the root locus with “rlocus” but also calculating almost any point of interest on the root-locus plot directly (the professional version has only “rootfind,” a graphical method, to locate these points). The most commonly required value, K_max, can now be obtained directly using the MCSTD Toolbox.

What is left now is to understand how to create root-locus diagrams, and to practice creating them. There are many examples of creating root-locus diagrams on the MCSTD diskette (try some). Several functions exist that assist with root-locus diagrams, of which I have listed ones that I believe are important:

1. “rlocus” is described in Reference 7. This function returns/plots the root-locus response of the system. A single example is given in the text manual.
2. “rlaxis” is described in the MCSTD Toolbox. This function returns a set of data representing ...