Question 1 Given the transfer function of a system as 9 G(s) = 52 + 4s +169 a) Obtain the percent overshoot (%OS), settl

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Question 1 Given The Transfer Function Of A System As 9 G S 52 4s 169 A Obtain The Percent Overshoot Os Settl 1 (45.69 KiB) Viewed 51 times

Question 1 Given The Transfer Function Of A System As 9 G S 52 4s 169 A Obtain The Percent Overshoot Os Settl 2 (73.92 KiB) Viewed 51 times

Question 1 Given the transfer function of a system as 9 G(s) = 52 + 4s +169 a) Obtain the percent overshoot (%OS), settling time (Ts), peak time (T₂), rise time (T) and plot the response if given the step input using MATLAB. b) Obtain the same percent overshoot (%OS), settling time (T), peak time (Tp) and rise time (T) by calculation. Show all your consideration. c) Discuss the validity of your MATLAB simulation and calculation (10 marks) Question 2 A unity feedback control system of a system shown in Figure 1 R(s) → K 8+5 s(s+4)(s +8s+100) Figure 1: A unity feedback control system of a system C(s)

a) For K = 500, plot the Bode diagram of the system using MATLAB and determine the values of gain margin (GM), phase margin (PM), gain cross over frequency (wo), phase cross over frequency (wpco) and the stability of the system. (6 marks, P4) b) For K= 1500, plot the Nichols diagram of the system using MATLAB and determine the values of gain margin (GM), phase margin (PM), gain cross over frequency (Wgc.), phase cross over frequency (wpco), resonant peak value (M,), resonant frequency (,), bandwidth (BW) and the stability of the system. (8 marks, P4) Discuss the effect of K for the gain margin (GM) and phase margin (PM) obtained in (a) and (b) c) $2 (4 marks, P4) d) Discuss the validity of your MATLAB simulation in (a) and calculation (refer to your solution in Question 2 of Assignment 2(a)). (2 marks, P4) Question 3 Consider the following open-loop transfer function of a system by using MATLAB 60K G(s)= S³ +68² +11s +6 a) Sketch the Nyquist plot of the system for 0 < a <∞o for K = 1 b) Determine the gain margin (GM), phase margin (PM) and stability of the system. c) Discuss the validity of the Nyquist plot by comparing your MATLAB simulation and calculation (refer to your solution in Question 2(b) of Assignment 2). Show all the related considerations i.e. the GM and PM by calculation. (10 marks, P4)