Chapter 7. Frequency-Response Analysis

The objective of this chapter is to develop frequency response techniques for control system analysis and design. After studying this chapter, the reader should be able to do the following:

• Substitute s = jw, and find Bode or Nyquist plots for a transfer function

• Given a Bode plot, construct a Nyquist plot

• Understand the concepts of "all-pass" and "nonminimum phase"

• Understand the effect of gains, time constants, RHP zeros, and time delays on amplitude ratios and phase angles

• Find the gain and phase margins for a given process and controller

• Tune a controller to achieve a given gain or phase margin

• Determine the amount of dead time or gain uncertainty that can be tolerated before a closed-loop system becomes unstable

• Compare the robustness of PI and PID controller tuning techniques

The major sections of this chapter are as follows:

7.1 Motivation

7.2 Bode and Nyquist Plots

7.3 Effect of Process Parameters on Bode and Nyquist Plots

7.4 Closed-Loop Stability Concepts

7.5 Bode and Nyquist Stability

7.6 Robustness

7.7 MATLAB Control Toolbox: Bode and Nyquist Functions

7.8 Summary