Question

2. Consider a symplified servo system with tachometer, current, and position feedback, shown in Figure 2, where a = 5.x, b = 2. Y, X and Y are the last digit and second last digit of your student ID, respectively. R(3) I(s V(8) P(S) pos Kool -Keur Figure 2 a) Determine the ranges of control gains Kpos, Keur, and Kyol that can stablise the overal closed-loop system (All control gains are positive). (2.5 Marks) b) Find the steady errors for the unit-step, unit-ram, and unit-parabolic inputs if the system is stable by choosing appropriate control gains Kpos, Kcur, and Kpol. (2 Marks)

a= 5.3

b= 2.9

Answer 1

Rpos Kort RIS) a Kent ܬ stb S S ple) Transfer function P() RS) kposa Kool Koura. I stb po RIS 52 1 + Keuroa stb + Kvol-Kapa + s (St b ) kposokropo Keur. stb 1 52 Kposo kuozo Keur. a. ply R19 systb) + Keures? at kuoli keur nqs + lapos kvolo Eura kposo knoL Kuroa RS RO 93 +16+ Keuz»Q)s?+ Kyoc Keukease + kpos- Kvol Revera CS Scanned with CamScanner

(a) put a=513, b=29 on PCS R9 5.9 kpose kool. KCURY 53 +12.9+ Kuvo 5:3) s2 +5.3 Kvo! Kevy.S+ 5.3 Keur' Kuor. Kpop To find the stability apply RH - Criteria 33 + 12.9 + 5.3 Kel)s?+ 5.3 KUOL" KCURS + 5.3 KuolKewa 'kpus t 93 1 5.3 Kuoro keur 82 219 +5.3 KUY 5.3 Kvoz keur, koos st (2.9+5.3 kw) (5.3 kvor Kawo) - 5.3 Kuol Kourekpos 2.9+5.3 keur so 5.3 Kuolo eurokpos system will be stable if Ist column elements will have same sigm . and 269 +5.3 kcuo 70 and RUOLO Ker: Kposto = Keur=0.547/ 2.9+5:3 keur) 54 Kyor Kyung > Koolkork 2.9 + 5.3 Kcur > kepos :- Kpos < 0.0009 CS Scanned with CamScanner

Range of stability Keuro kpos <9x109 and Kuolto 5.3 kpos • kuolo Keur b ? R® RS 83 +12.9+503 Keur)s? +5.3 KUOL. KEURS + 5.3 Keur. KuoLikpos RS - PS .. EU 2( [- ho PCS) RES) ما Steady state coror, ess = It so RS S-a RIO RES ht Sto SORIS 5.3 kpos-Kuolo Keur $342.9+5.3 eur] 52+5.3 kvozi Keures +5.3 kr. Kuolikpos CS Scanned with CamScanner

For unit step input RO =Ys ess = dt se ys['- S70 5.3 koos. Kuol keur 33 + +(5:3 Kurt 2.97s2 + 5.3 kvol Kur's + 5.3 KUOL• Keurik ur Koos 5.3 kpos. KuoLikeur لے ] 5.3 kpos. Kyou. Keur less For unit Ramp (R = 1/2) 5.3 kp kyke $3 +15-3kc+2.9) 54+5-3ko kes +5.3 kv Kc KP at se Ygz ess - S>0 les - For unit parable la CRO = 1/53) 513 kp ku ke essa $3+k+5+5-3 kqjg+ 5.3 Kuckest :3 kvickie 11 0 8. ess CS Scanned with CamScanner