- 100 Consider The Continuous Time Transfer Function G S 5 10 A What Would Be A Suitable Sampling Time Among T 0 1 (55.58 KiB) Viewed 65 times
100 Consider the continuous-time transfer function G(s) = 5+10 (a) What would be a suitable sampling time, among T, = 0.001s, T, = 0.02s, and T, = 0.5s, to represent its dynamics in discrete-time. Justify your answer. [6 marks] The digital control system for the positioning of a hard-disk read/write head is shown in Fig. 22. C(:) 102 ZOH s+10 Sampler Figure Q2 The sampling time is T, = 10ms. The controller C(z) is a discrete-time Pl controller in the form C(z) = Kp+*** where Kp > 0.K;>0 (b) Derive the transfer function Ga(z) representing the discrete-time operation of the plant. [4 marks] (c) Show that the characteristic polynomial of the closed loop system is p(z)=2 +0.952(K; +Kp) – 1.905]z +0.952(K; - Kp) +0.905 [4 marks] (d) Given Kp = 0.5, find the maximum value of Ki for which the closed-loop system is stable. [5 marks] (e) Given Kp=0.5, what would be a suitable value of the integral gain among K1=0.01, K=0.05, and K = 0.2? Justify your answer. [6 marks]
Consider the continuous-time transfer function 100 G(s) $+10 (a) What would be a suitable sampling time, among T, = 0.001s, T, = 0.02s, and To 0.5s, to represent its dynamics in discrete-time. Justify your answer. [6 marks) The digital control system for the positioning of a hard-disk read/write head is shown in Fig. 22. C() ZOH 102 s +10 Sampler Figure Q2 The sampling time is T, = 10ms. The controller C(z) is a discrete-time Pl controller in the form 2+1 C(z) = Kp+K where Kp > 0, K: >0. EL