5 - Analysis

Abstract

This chapter describes the methods for analyzing the behavior of control systems with a change in their characteristics. The methods for analysis are root locus plots, Bode plots, and Nyquist plots. The root locus plot gives a pictorial representation of the functioning of the poles in a system. The chapter illustrates a number of methods through which a system's tested response to a sine wave can be used for control system design and examines how those relate to the root locus plot. By using these tools, a variety of controllers and techniques that can be used for system design are presented. A root locus plot indicates all the possible locations for the poles of a system's transfer function as some parameter is varied. This property is directly useful in three ways: (1) to find the correct parameters for a chosen controller, (2) to determine if a system will remain stable as plant parameters change, and (3) to investigate particular types of controllers for their suitability in solving the problem at hand. A Bode plot shows a system's phase and gain as separate quantities, plotted along the frequency axis. A Nyquist plot uses the same data as a Bode plot but discards the frequency axis to the track traced by the systems frequency response on the complex plane. The Nyquist plot allows the gain and phase margins of the system, as well as the systems peak increase in sensitivity to be seen. As none of the mentioned methods is complete, a combination of these methods in controller design should be practiced.