Question

The figure below shows a block diagram of a feedback system. Both cascade clutch and forward clutch are used to obtain the best possible control. G1 and G2 have the following transfer functions: G1(s) = 8 / 1+5s , G2(s)= 7/ 1+10s

a) Suppose that a (t) = σ (t) or A (s) = 1 / s. Dimension Gr1 = K so that the residual error s e in the inner loop from A (s) to B (s) becomes less than 0.2 i.e. so that e_s < 0.2.

b) Also suppose that the disturbance v (t) is measurable. For this case, and with the value of K calculated in the a-part, design a forward link G_K (s) that gives the best interference compensation.

8 G(s)= 7 G2(s)= 1+10s 1+55 Mätbar störning V(s) GK R(s) A + B Y(s) GR2 GR1 Gi(s) G2(s) +

Answer 1

Solution:

Griven! Gisla any 8 1 * 5.5 622 (5) - It los GRI K - V AC) Required specification - es < 0.2 £ Beso Inner loop - GRI ACA) 6, () Error function = £(s) E($): ACs) - BCS Eriss ACS) - Ecs). GRI.G, (S) ACA Ecos (1 G Rio G7(6) ) = ACAD Ers) 1 + R, Gus Vs Putting values - {(3) 1 + 55 apply following lim si Ecs) which is known so as final value Theorem, so I + K. es, we for calculating steady errore ·linit lim elt) = Ve lin es - sool of kan 1+5s lim ils - Ifki 8. 1 of 5s es 7.8k. 16.2 lb for < 0.2 'I + 8.5 I of BK > py0.5 O2 k > ® 62. VES). CK W G1 G2 (67 yo + Gez 1 KG Reso Vise is under consideration Rest will be treated zero G2 When Solving inner loop- vesi GK KG, It KG, "Y V Gieoka, 1 + KG, 1 Reduced Block Diagram ves), Yos) 255) (GR KG, fora 1 + Vicino GR2 Gk koji -) 4152 VES G2(5) It kind Ves7 GR.2 (GK KG, It If KG, G2 (6) Gk KG, - CitPG) L(1+kGI) +WXzC Cirokartth., )) from part cap Kyos soilet k = 2 28 2x8 7 1 +55 15.5 VIS) 1 +105 1661-16-1-505 1 +55 [i+5.52 - GOK So GR 2 + It 16-1-5s Yes Vio J+OS 16 6x 1+5.5 +3K 4+G Ø2 (1668-17-55) for k = 2 and GR2 Yesi ។ 16 GK 17-58 + los 7 +55 +6 2016 GJ - 17-55) 3.[ 17-553]. U152 y (5) 94 ( ا 14G where 6 is 0.2.7.f..of Closed Loop , then 7 (16GX - 17-55) 7016616-17-5:5? :-:(1+109) (17+55 +211667-17-55)) 6492 for step input ess t din 6C52 5-s0 1 ess + 7 (166.6 - 17 A 7 (1668-17 J (17+2(166-17) ess 1 + Oils es ols 7 (16GK -17) 1.5. (16687177-17 for ess 2.0i2 let us take ;0,5 e 16 Gixe -173-17 5 ( 1.6 hk - 17 ) - 17 +7(1649-17) 80 GR + 10.2 Só Gle 103 + 112GK -119 0.15 де бе 1012 192 GR 2'22 = o.15 11 28.8GF - 33,3 = GR 80GR - 10.2 -0.451