### 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:

- “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.
- “rlaxis” is described in the MCSTD Toolbox. This function returns a set of data representing ...