Answer Happy

(a) True or False. [8 marks] Indicate, briefly justifying your answer, whether each of the fol- lowing statements are true of false: (i) The nominal complementary sensitivity To(s) has a zero at all uncancelled zeros of Go(s). (ii) The nominal sensitivity So(s) has a zero at all uncancelled poles of Go(s). (iii) The nominal sensitivity So(s) is equal to 0 at all uncancelled zeros of Go(s). (iv) The nominal complementary sensitivity To(s) is equal to 1 at all uncancelled poles of Go(s). (b) Fill in the Blanks. [3 marks] Consider a single degree of freedom controller as shown in Figure 1. r(t) u(t) y(t) C(s) Go(s) Figure 1: Closed Loop System Complete the following statements: If the magnitude of the real part of the dominant closed-loop poles is (i) greater than the smallest real right half plane zero, then the output response to a step input will exhibit ... (ii) less than the magnitude of the largest real unstable open loop pole, then the output response to a step input will exhibit ..... (iii) greater than the magnitude of an uncancelled real stable open loop zero, then the system output response will exhibit .. (c) Brief-Essay. [7 marks] Answer the following questions: (i) With respect to closed-loop bandwidth, what can be done to improve the output re- sponses in parts (bi) to (biii) above? (ii) With respect to cancellation of open loop poles and zeros by the controller, what can be done to improve the output responses in parts (bi) to (biii) above? (iii) If a slow stable open loop pole is cancelled by the numerator of the controller, what effect will this have for input disturbances?