TABLE OF CONTENTS In this chapter, I introduce two classical control system design methods: root locus design and Bode diagram design. Bode diagram design is also known as the frequency response design method. Both methods require a linear time-invariant plant model. In Chapter 3, I described some approaches for developing plant models suitable for use with these design methods.
In the root locus method, the designer creates a graph showing all possible values (the "locus") of the closed-loop system transfer function poles as a design parameter varies over a specified range. The poles are the values of s for which the transfer function denominator is zero. Poles may be real numbers or may appear as complex conjugate pairs. The varying design parameter is typically the controller gain.
The root locus diagram displays a portion of the complex plane and plots the closed-loop poles as the gain parameter varies. By selecting a value for the gain that places the poles within a suitable region of the complex plane, it is possible to determine the dynamic behavior of the controlled system. If a gain change alone does not result in satisfactory performance, the compensator structure must be modified to improve the closed-loop pole locations.
The root locus method is a direct, graphical approach for controller design. The MATLAB Control System Toolbox provides tools for creating root locus plots, selecting gain values, and altering compensator structures in a quick, interactive manner. In this chapter, I introduce the use of MATLAB-based tools for...
