Question

Question 4: Consider the following system: 0.01 a) Describe the response to a unit step input for K 0.01 and K-0.1 and determine the value of K for a non-oscillatory minimum response time. b) If we let K-1, what will be the value of the steady state error of this system in response to a unit step input? c) If we now replace the "proportional controller" (the box with the K in it) with a proportional integral (PI) controller, with a transfer function of 1+1/s, what will be the steady state error? d) If we now use a proportional derivative controller, with a transfer function of l+s, what will be the steady state error?

Answer 1

[book 9 CCS) look 2 Asts + 10k Co-o RCS) Pro S +45+3 + 100K (0-01) 0 Given unit step input Sub (K = 0.0) in eq for k=ool 0 [nie=utt)] & C(s) = 1 87 45+3 + 106 loob (0.01) c(s) = +AS+50 =>(65) = 5 82 +4542-01D » roots are abt 16² dac - za = - 4 + VG24x1x301 - = -1.005, -2.99 -1.005 1 →-2-995-3 = (099 = SHBCS 7) = 4 + Britishing = V + klote) + Sautez? S+3 Scanned with CamScanner

-|Cit)= §.ult) Pķe ult)+ sie tych) ¢ from Given unit step input fork=001 Iritsault)] R15 = 005)_ 100(0:1) $4+45+3 + 100(0.1) (0-01) 008) = 10 S +45 +3-1 =) S = -44 V 43 4x 3-1 2 - S = -1.05,-2694 = s(s+105) [5+2194) = (18)= - 10 A + B 5* st1.05 + c S+2.94 0.05) (2+94) + (1:05) (-1-05+299) + 6 0 16-24 057 42.9476-2-94 4:05) S+lnos s+2.94 = 3.25 + 65.03) + 1-799 st1-os : Star014 Jelt)= 3.28.44) -5.03.21.05t +1.79970947 Scanned with CamScanner

b Güven, k=1 & asked to find free less forundlzlpinpot ? - steady state error should be calculated only fero Unity feedback supleme. so, add twoo Joops with love " Ove Rist SC 100 +43+3+1 RIS) 100 -CCS) s?+45+4 -100 G(5) = _100 2+45-96 Given, Ilp1ult) Adult) egs = A \+ Кр > Kp = .60) 100 = -1.04 kp = Lt 8+ 100 S +45-96 o +6-96 1-1-04 Scanned with CamScanner

R(8 ta 824313 (9 100 (5+1) S(82+45+3)+(con cos(s+D SOOD 100 S+1) scsh+as+3)+(5+1) - 100%s +) →G(S) = 1000st) SCS748 +3)--998-99 - Given, input in ult) ess=fo Itkp & Kp = Lt G(S) = lt 100ls+1). np 570 Sto S(8745+3) -998-99 - # 100 (+1) SE-1.01 0-0-99 less = =-99 SO Scanned with CamScanner

(P+D] 34+45+3 0.01 RIS _CCS! 100(S ) St4s+3 + 10oCoreD CAS) RIS) 10o CS+) STAS+3+(145) - 10015+) +GS) = 100(+1) S +45+3 -993-99 - Given, Input is ult) --> gs 1+kp Kp = Lt Ges) - Lt 100 (5+1) sto sta513-993-99 Rp 100 oto+3-0-99 = -.041 - Tess = the = -24 1 .041 Scanned with CamScanner