Question

Figure 6 shows a feedback control system for which G(s) = 6 (s + 1)3 J' and K(s) is the transfer function of a compensator. (a) Sketch the Nyquist diagram of G(s) evaluating the real-axis intercepts and their corre- sponding frequencies. [10 marks] (b) Show that the closed-loop system will oscillate at frequency w = V3 rad s-1 when the closed-loop gain is K = ? (5 marks] (c) Design a proportional-derivative compensator K(s) that leaves the steady-state loop gain unaltered and ensures that the gain margin of G(s) K(s) is infinite. Draw a rough sketch of the corresponding Nyquist diagram of G(s)K(s). Hint: Consider using a proportional-derivative compensator that cancels an open-loop pole. [5 marks] r(s)+ e(s) K(s) GS) Figure 6

Please explain part b and C in detail.

Answer 1

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