A motor modelled by G(S) = 8 +4 is controlled by an analogue compensator 2s + 1 D(S) = K where the gain K is a positive

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A Motor Modelled By G S 8 4 Is Controlled By An Analogue Compensator 2s 1 D S K Where The Gain K Is A Positive 1 (58.7 KiB) Viewed 56 times

A motor modelled by G(S) = 8 +4 is controlled by an analogue compensator 2s + 1 D(S) = K where the gain K is a positive constant. The control system is to be implemented digitally with a sampling period T = 0.2 seconds. 5 +3 (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() 2-0.45 [6 marks] (6) Use the pole-zero mapping method to show that a digital approximation to the analogue compensator D() is given by 1.5(2-0.90) Da(z) = K 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 (2)/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-es 8 Y(2) T = 0.2 D.(2) Compensator S ZOH Motor G.(2) Figure 4.1