Question

a) Consider the control system in Figure 2(a). Determine the transient response characteristics (rise time, peak time, maximum overshoot and settling time) and the steady state error for the system. (2 marks) b) To improve the relative stability, the tachometer feedback are employed as shown in Figure 2(b). i. Determine the value Kn so that the damping ratio of the system is 0.5. (1 22 marks) ii. iii. From the result obtained in (i), evaluate the transient response characteristics (rise time, peak time, maximum overshoot and settling time) and steady state error. (1 72 marks) Sketch the output response for the both systems in Figure (a) and (b). (2 marks) State what type of the controller that can replace the tachometer feedback which can give the similar output response. Discuss your answer. (3 marks) [10 MARKS] iv. R(s) C(s) 10 s(s+ 1) R(5) C(s) 10 S +1 Kh (b)

Answer 1

(О. + 10 SI5+1) *15) ces) 10 RIS) $?+ 5+ 10 here an? - 10 wn = Sto rad /se. so 2X 9X STO=1 so 0-1580 2 To and wd = 2 wniz? stol 11-0.1580 wd 3-1249 dad i gise time tr TT – 0 I - tant (0.1580) Il ad 3:1249 ta CO9551 See TT Peak time tp = = ad 3:1249 tp I see

(iii) Peak over hool - all/st.za 0.158 x 1 ls 1-0.1582 x100 = 60.46 mos (N) Setting time 4 ts Zx wn x Jio asto ts - asee Port :- from figuze 265) CIS) 10 (5+) RIS) I + 10 + 3+1 s(t+1) S²+5+ lokks +10 10 C(s) RIS) s² + ( ! + lokn) 8+10 part i So Con= Jo It lokn) - 2x0.5 XJTO 2.162 Polen kn 0.2162

To make q=0.5 , ky is 0.9162 Paolo un = Jio Ę -0.5 od z won Ji-22 - 9.7386 so a) rise time to TT - Wd tanto.s 9.7386 to 0.9778 see. (b) peak time to T ad T 2.7386 ty- 1.147 see ITXO 5 11-0 (C) 20S Xloo = 16. 30 (d) Betting time ts = 4 4 ex un 0 5x Jio 9. . 53 see Part () 1-60 -0.1580 1.16 &=0.5 ts= 9.53

Part Two Tachometers com be Conboller replaced by proportional out outpul is proportional to input provided. It will give similar Outhul. in which