- Question 1 A Figure 1 Shows A Block Diagram Of A Unity Feedback System R S E S K C S S 38 30 S S 5 Figure 1 (48.89 KiB) Viewed 48 times
- Question 1 A Figure 1 Shows A Block Diagram Of A Unity Feedback System R S E S K C S S 38 30 S S 5 Figure 2 (69.76 KiB) Viewed 48 times
- Question 1 A Figure 1 Shows A Block Diagram Of A Unity Feedback System R S E S K C S S 38 30 S S 5 Figure 3 (57.43 KiB) Viewed 48 times
- Question 1 A Figure 1 Shows A Block Diagram Of A Unity Feedback System R S E S K C S S 38 30 S S 5 Figure 4 (66.75 KiB) Viewed 48 times
Question 1 (a) Figure 1 shows a block diagram of a unity feedback system. R(s) + E(s) K C(s) (s²+38+30) S" (s+5) Figure 1: A block diagram of a unity feedback system 1 If the system has 1/6000 error for an input of 10fu(t), determine the value of K and n to meet the specification. (4 marks, C3) IL With the value of K and n obtained in Question (a)i, determine the value of K, K, and K (3 marks, C3) II. Obtain the steady state error for the input of 5u(t), 15tu(t) and 25fu(t). (3 marks, C3)
(b) Figure 2 shows a block diagram of a unity feedback system. Find the number of closed- loop poles located in the right half-plane, left half-plane, and on the jo-axis by using Routh-Hurwitz criterion. Conclude the system stability. (10 marks, C4) R(S)- Ø 3s +6s' +5s +10s +14 C(s) Figure 2 A block diagram of a unity feedback system. 775 Question 2 (a) Consider a unity feedback system as shown in Figure 3. 5+5 R(S) K C(s) s(s+4)(s² +8s +100) Figure 3. A unity feedback system Plot the asymptotic Bode plot for the system if K = 500. From the plot, determine the gain margin (GM), phase margin (PM), gain cross over frequency (w), phase cross over frequency (w), and hence state and justify the stability of the system. (10 marks, C4) 33
An open loop transfer function of a unity feedback system is given by 60K G(s)=- s+65 +11s +6 L Sketch the Nyquist diagram for (0<<∞o) for K = 1 (7 marks, C4) 11. Determine the range of X for stability. (2 marks, C4) 111. Determine the frequency of oscillation for marginally stable (1 mark, C4) Question 3 (a) From the plot of frequency response, the data of an open loop system can be described as the tabulation in Table 1. Table 1: The data of an open loop system. w (rad/s) 0.01 0.02 0.03 0.06 0.11 0.19 0.34 0.52 GjdB 21 19.5 16.5 11.5 4 -3 -13. -19 ZG -32 -52 -76-101-125-146-160-165 Sketch the Nichols plot on the Nichols chart (3 marks, C3) Determine from the Nichols chart, the resonant peak value and the bandwidth of the closed loop system (2 marks, C3) (b)
(b) Create a table using the open loop data obtained from the bode diagram of a system shown in Figure 6 for w=0.5, 0.6, 0.7, 0.8, 1.0, 2.0, 3.0 (rad/s). From the table, plot the data on the Nichols chart and determine the parameters below: Bode Diagram Frony (r Figure 3: The Bode diagram of a system ( M Phossde V 83 11 Sketch the Nichols plot on the Nichols chart (3 marks, C3) From the plot, determine the resonant frequency (,) and the bandwidth (BW) of the closed loop system (2 marks, C3)