Question

Question 2 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). Determine the value K, so that the damping ratio of the system is 0.5. (1 % marks) i. From the result obtained in (), evaluate the transient response characteristics (rise time, peak time, maximum overshoot and settling time) and steady state error. (1 % marks) ii. Sketch the output response for the both systems in Figure (a) and (b). (2 marks) iv. State what type of the controller that can replace the tachometer foedback which can give the similar output response. Discuss your answer. (3 marks) [10 MARKS] R(3) als) 10 $(+1) R(3) Cs) (b) Figure 2 (a) Control system: (b) Control system with tachometer feedback 6

Answer 1

Otte a Characteristics eqh L+ GO HD)= 1 + lo Y LEO SC S +12 S?+ 5 +10 compare with s² + 25 wnt wy2 = 0 Swna 2 on = 10 2 lon ܘܠܓ of a sto SO.15 - الوحمة S O dire time ts na-6 wd Wn lagi J To jTo.is we - 3012 0 = cost (8) cost cous po 'goº (180° 80-90°) x^/130 3112 Its a 0.55 see क ts 2 © nił time peak tp a wa Lepe I see T 3:12

Jio t = It lok Toka @ Tool TiF8314 R3 2:16 für S =0.5 on = To rise time trai na 6 ويد) loda wn J 1-82 = Jlo ST-0.52 Wd - 2.73 $ = last (0.5% = 1.041 tra π-1047 2-73 Tr0.76 sec peak time setting fine ų soon ts u tpa nT /wd 17/2.23 tp = 1.15 see - stlar the Mp Ostt 15. 120.52 to 127 e प 05 Po f=2.52see est ? lini SX 12 1 + G7 HCS) syo it S(5+6) livs SCS+126) +2-6 Sto s cst13.6)+10 ess for renip input 2.26 ess 0 for ünt step input Mp=0=163 RO) ONS lini SMO 10 -2.26

(iv) Response (t) نک tp-lsea ts=8 see ati to = 1:15 see ts=0.52 liv) Tachometer feed back can be replaced by proportional derivative controller which reduces transient error and improve transient performance و له