Q1. A discrete time control system is shown in Figure 1. Its digital controller has a...

 

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Q1. A discrete time control system is shown in Figure 1. Its digital controller has a transfer function Gc(z), a Zero Order Hold (ZOH) and analogue plant G(s). It is known that the sampling period T-4 sec. The digital controller is P controller type with Gc(z) = k and the analogue plant transfer function G, (s) = .answer the following questions: 10 s(0.1s+1) a. b. C. d. e. f. r(k) + Determine the transfer function for ZOH and G₂ (s) which is known as GHP(Z). [5 marks] Determine the open loop transfer function of the system. [1 marks] Draw the root locus of this system. The break-away point of the root locus is located at z=0.34 and the break-in point of the root locus is at z= -0.95. Based on your r locus plot, is this system fully stable, partially stable or total unstable? [6 marks] [2 marks] Determine the characteristic equation of the system. Apply Jury's test on the characteristic equation of the system and determine the range of gain K in which the system is stable. [6 marks] How will the system stability be affected when you increase/decrease the sampling period T, explain briefly how will it affect the root locus? [5 marks] - T=4 S Gc ZOH Figure 1 G(s) c(k) Q1. A discrete time control system is shown in Figure 1. Its digital controller has a transfer function Gc(z), a Zero Order Hold (ZOH) and analogue plant G(s). It is known that the sampling period T-4 sec. The digital controller is P controller type with Gc(z) = k and the analogue plant transfer function G, (s) = .answer the following questions: 10 s(0.1s+1) a. b. C. d. e. f. r(k) + Determine the transfer function for ZOH and G₂ (s) which is known as GHP(Z). [5 marks] Determine the open loop transfer function of the system. [1 marks] Draw the root locus of this system. The break-away point of the root locus is located at z=0.34 and the break-in point of the root locus is at z= -0.95. Based on your r locus plot, is this system fully stable, partially stable or total unstable? [6 marks] [2 marks] Determine the characteristic equation of the system. Apply Jury's test on the characteristic equation of the system and determine the range of gain K in which the system is stable. [6 marks] How will the system stability be affected when you increase/decrease the sampling period T, explain briefly how will it affect the root locus? [5 marks] - T=4 S Gc ZOH Figure 1 G(s) c(k)

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