Modern Control System Theory and Design, 2nd Edition

6.22.  WHAT IS THE “BEST” STABILITY ANALYSIS TECHNIQUE? GUIDELINES FOR USING THE ANALYSIS TECHNIQUES PRESENTED

We have presented the following methods in this chapter for analyzing linear control systems: Routh–Hurwitz method, Nyquist diagram, Bode diagram, Nichols chart, and the root-locus method. Which of these stability analyses methods presented is the “best” to use? This is a logical question to ask at this point in the presentation of this chapter. For a particular application, one of these methods may be better than the others. However, in general, each method presented in this chapter complements the other. In general, there is no “best” method. The reader should regard all of the methods presented in this chapter as control-system analysis tools that can be used. The practicing control-system engineer should not restrict himself or herself to one method.

Guidelines are presented here for selecting the best method for particular cases [32]. For systems of first or second order, all of the methods presented reveal about the same amount of information, and they are of similar complexity. For systems from about the third to seventh order, there are two primary approaches, and these two approaches complement each other. One approach uses the Bode-diagram method in conjunction with the Nichols chart. The Routh–Hurwitz method can be used as a quick check. The other method uses the root locus. Using the first approach, the control-system engineer can determine relative stability ...