Modern Control System Theory and Design, 2nd Edition

6.20.  COMPARISON OF THE NYQUIST DIAGRAM, BODE DIAGRAM, NICHOLS CHART, AND ROOT LOCUS FOR 12 COMMONLY USED TRANSFER FUNCTIONS

As shown in this chapter, the control-system engineer can analyze linear control systems for stability by applying the following four graphical methods: the Nyquist diagram, Bode diagram, Nichols chart, and the root-locus method. How do these methods complement each other? This section helps to answer this question by comparing the methods for 12 commonly used transfer functions.

For a perspective on the various methods and how each method complements the others, Table 6.27 [32] compares the information provided by the Nyquist diagram, Bode diagram, Nichols chart, and the root-locus method for 12 commonly used transfer functions. This table defines time constants, and phsae and gain margins where applicable. For simplicity, the M and α contours that represent the magnitude and phase-angle contours have been omitted from the Nichols chart.

A comparison of these 12 transfer functions shows that these four graphical methods provide complementary information regarding control-system stability. It is important to emphasize that the stability results obtained by the four graphical methods should be checked by the Routh–Hurwitz method’s mathematical test.