Question

Di sturbance Plant po-Gain pes) ses41) Le1oses-1p Ystom PO-GAin: Des)- kt Kps La): Determine Th ualues t Ko,p tram danping hatio (Y = 0-1) and Stedy state eral (esso-8) fnn wit step distatace (ule)-) C6):0se the rate maintenance of Ko,kp troun la) Wlen the value of Kp is chang ng Sketch the root-locus

Answer 1

a) Given unit step disturbonce input (uct) 1) w DLS) EptKD S Take at a time one ioput Block diagram Red roon So REO plant Weuct) Distur bancet sCst1) Gain -DLS) Trans fer functon TF (t535 -Ctpttos) SCS+1) T.F = SCST1) Kp+kps 1 TF= S4 SCEDTI) tep esς 40.3 Given onv O Compare with 1KD ; RWDE1+ kp toy un it step in pd ess- I+ kp SSE Calculate tor unity feed bact system, Convert given system into unity feedbock System

W-TtT Weutt) w-T T SCS+1) Disturbante T T DIS WEut Disturbance t GCS) ニ Now s CHED) kp- O+o+p kp- Kp Ep-i ess= 1 1+ kp kp -11 kp-I Given ess o8 Kp -1z 0.8Kf 8-0フ kp kp -ogKp Kp 6-2 Kp 5 Ko 1.4 kp ニ2.13 kp 5

open loop TP= Kp+ kos take Kp-5 SCst1) 5+ KpS kp= 2.13 SEST1) 5+ 2.13CS) 2.13 SestI) Stst1) kC S+ 2.347) open Loop Tf SCST) No of poles 2 No.0f zevos Poles> zeor No.0f Root locas Boanches NdPla 2 No.of asmptodes Na P-2) (2q+1) 1S asymptodes 2 9 90,1 -2) - Angle of E 186 kpz0 KDFO RLB b.568 o -A -42-2.34 7 -1

4 or Break in and Byeat awoy point d.s from , 1+ open loop TF o y - S) diff crantiate with espect to S2.347 S on both Sidet and equate to zee (2S+リ (s+2.347)- CsY+s) C+) dko d s +2 347) ast 4694s + 2.34 2. 347 0 (4.6.9 4) Break auny potnt O 5 68 ercae in point =4.12s