Chapter 14 - Control theory: Graphical techniques

Abstract

The root locus, Bode plots, and Nyquist plots techniques are graphical methods for understanding the performance of closed-loop control systems. The root locus is a graphical procedure for determining the poles of a closed-loop system given the poles and zeros of a forward-loop system. It is a graphical technique used to qualitatively describe the performance of a closed-loop system as various parameters are changed. The root locus provides stability, accuracy, sensitivity, and transient information, and is useful for system analysis and design. Graphically, the locus is the set of paths in the complex plane traced by the closed-loop poles as the root locus gain is varied from zero to infinity. A Bode plot is the representation of the magnitude and phase of the open-loop transfer function of a system, where the frequency vector co-contains only positive frequencies. They can be approximated as straight lines, simplifying the method. The Nyquist criterion relates the stability of a closed-loop system to the open-loop frequency response and open-loop pole location. Consequently, knowledge of the open-loop system's frequency response gives information regarding the stability of the closed-loop system. In the root locus technique, the input is of the form of step, impulse, and ramp. However, for frequency response (Bode and Nyquist plots), sinusoidal inputs are considered.