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A motor modelled by 8 S + 4 G(S) is controlled by an analogue compensator 2s +1 D(s) = K s +3 where the gain K is a positive constant. The control system is to be implemented digitally with a sampling period T = 0.2 seconds. (a) Show that the corresponding z-transfer function of the DC motor preceded by a zero order hold (ZOH) is given by 1.10 Ga(z) = 2-0.45 [6 marks] (b) Use the pole-zero mapping method to show that a digital approximation to the analogue compensator D(s) is given by Da(z) = K- 1.5(z - 0.90) 2-0.55 [6 marks] (c) The digital implementation of the control system is given in Figure 4.1. Find the closed loop transfer function Y(z)/R(2). Then, use the Jury stability test to determine the range of K such that the closed loop system is stable. Further, determine the steady state output in response to the unit step signal. [8 marks] R(2) 1 - e-st Y(2) Da(z) Compensator 8 S +4 S ZOH Motor G4(2) Figure 4.1