Question

Problem (2) The open loop transfer function of a feedback system is given by к H (s) = 10 G(s) = ------ - s (s +1) (0.2 s+ 1) Design a controller such that the closed loop system will have a settling time less than 1.0 sec. and a percentage overshoot (PO) less than 5%. Draw the root locus plots of the uncompensated and compensated systems using Matlab.

Answer 1

The zero must be placed at od from sd a = 444 Ton[78.9160934.7386 G.S) - (x + 4-7 sgk goin ů formed using magnitude a lk (5+4.7384)x50_ 1 The ni tende a s(s+1)(5+5)/ Ps=-4445 - k=0.14 Root locus & Root locus G H = 50k 5ok SCS+1) (5+5) v poles at s= 0,-1,-5 and ( at S= 0,-1,-5 and Do Zevos n=3 en dm =0) no Zeros so the no of branches one k= nom " The pole ot =-5 terminate infinity at mg the Real axis the locus between oond t break at break point and move along the angle of Asumproby () A = 180(2k+") k = 0,1,2 -> $ -601800, 300° nm (iv) The centroid is.- TA. & Epolers- & geros 1. TA = [0+1+5) -, nm 3-0

13) The and Ronge it k of stobility G(S) =0 for 't å given by Routh 17 5612 - s(s+i) @ +5) = 0 s3 #689 +55 +50k = 0 311 56. 7 5 Sok for stable system 30-gole zo en 150 30-50k OY KL0.6 the imagine any axis Gossing point ů 65 450k =o 8= t 2.2365] The breck point is dk to where, * = -s($t1) S+5) (vi) 1 Eo 125+5) = 0 -> 5=-0.47,- 3.5 25 of locus is between o ondt, s=-0.47 is the the The breck root point. locus is down below +2.23611 360 ? oik? 2.2361)