Question

5. Answer the following questions regarding the block diagram of the feedback control system. Gm (1) G,(s)= K., Gm (s) = Gy(s)=1, G,(s) = 100+1. Show that the feedback control system is always stable when K. > 0. (2) G(s)=K. Gr(s)= 1817, Gp(s)=1, Gr(s)=e** Use Bode Criterion to determine K range that ensure feedback control system stable (3) Also, Use 1* Padé approximant at time delay in (2) to determine the range of 1-5$ - K at which the feedback control system becomes stable. (e** tds Ix td) (4) Discuss the effect of time delay on stability

Answer 1

Solutions can be Eauation • Characteristic's Lon'Hen aus It hon so it Goh flapim so It ke: _3_20 JOSHI TOSH! +36c20 los +1 + 3 kc 20 make Routh Array now table . 1+3K0: for stable; column of Array should always be positive 13Kc yo Key-1/ , for the conditio ' for stability - Hence kayo, always show stable system. 2. hora achthelma - kce-5.3 TOSHI -fant (10xw) - "Lox Td X 180° = -180 ° tan (10ce) – LOX 180º = -180° IiW- Wax Bax rad/ time to

. 3Kc AR= 3 kc . vit (tusj2 11+(10x163) for Stabidiig AR showd be less than to Tier, ARKI. 3Kc L! 16.33 Kch 16:33 kc<,5:44. ..A ( for the system to be stable) 3 - ist padé approximant. -tas -S e e -0.5S T+0.55 now, the characteristic Equation, will be: It hol so It heat Ciplon 20 1 + kc 11-0:55 ,3 0 (1+0.56 OS (1+0.58 ) (105+1) + 3kcC1-0155) = 0 lost1t5 $?+0.55 + OKC -1.5Kc8 20 55+ 110.5 -105 kc) 5 + 3kc+1=0 Now malce Routh Array. 5. 3 ket! 1005-105kc o

1. (10.5.-1.5kc) (3kc+!) O 30: 10.5-losko i (10.5-45k) ( 3kc+1) yo si kc ( loob 8 kc)-13 kc<7 & ke> -1/3 Range for kc for stable will be - <kc 27 bing. 4. If a system has no Crossover frauency then the system should always be stable. In presence of dead time any system can become unstable Hence we. can say that dead time is the principle source of instability in the system.
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