Question

BE CLEAR AND SHOW ALL WORK. DON'T COPY OTHER SOLUTIONS. WILL RATE ASAP.

Using the diagram and data below, determine a gain K to generate the desired error (Edesired). Assume the input is unit-step for both experimental and for new error. Hint: Determine the transfer function first. Edesired = 0.1 1 R K (s+a) (s+b) Control loop: K(used with data) 68 (still have to find new K)

Answer 1

Ansuer Gwen E R K (Sta) (St) We know that Gls R(S 1 RG 146(s) HCs) c(s) K here Gle)= 6+a) Catb) H 1 Tveofor fanction K K Sta) lstb RS Sta)th)4 K Leaayert 1 + 5ta)(sth (5-40) (Spi)HK

Given K 68 c6 R(S) Sta)st+68 We know that ES RS EG) RIS 1+Gs R6 1+GG EG R(S Steady State rrd ess 14-Gls) SO table input is unit step RG= Prom the u ie from the takle steody state ess=1-0.365316581

. 63οu6 L ess K G (Sta)th) 64a) (8tb) SCRS) 14 GS) ess so Α ) D.6304684 s0 => Ε 6ς Ι+ S+a)6+6) O.6304684 (+ axb 14 axb O.6304684 1.5861ι883 Σ axb Α

1.586122 3 - axb 0 586122 3 axb 6 8 axb o586128 3 l16.0167396 axb Given E desired = 0. ie ess=0.1 RG) 14 G(s Ces=Lt O.1 K 1t 3-90 Sta) (sth) >O.1 1+ (040) (046) 1 4 axb 1

> axlo +K axb => = 16 K axb 10-1 k =9xaxb > Kx(116.0167390 CANom k= (044.150 651 Value k. This is 1