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.
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