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332-5solutions

# 332-5solutions - ECE 332 Homework#5 1 For each of the...

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Unformatted text preview: ECE 332 Homework #5 1) For each of the following transfer functions G (3), sketch the root locus. 1 a) s(a+1)5 2s+1 3s+1 b) L—é—Js c) T...__3 s +23+2 2) For each plant G (s) in problem 1), consider the corresponding gain compensated system. In each case, use Routh—Hurwitz methods to ﬁnd the number of open RI-IP poles in the closed-loop system as a function of the gain K. 3) Repeat problem 2), using Nyquist plots. Compare your results with those obtained in 2). 4) Consider the plant and compensator 1 2s + 2 32—1’ Gc(s)— 3+3. Investigate the effect of varying each compensator pole and zero as well as the compensator hi gh—frequency gain on stability of the closed-loop system. That is, draw the root locus corresponding to each of the following parametrized compensators. 0(3) 2 a) Gc(3) = 2% b) 616(3) = 2%}; c) GC : Kg}; (Assume K, 2, and p to be real.) For each system, determine the range of K, 2, or p for closed-loop stability. 5) Consider the plant 1 G = . a) Using the formulas for second-order systems, design a gain K so that the gain compensated closed- loop system satisﬁes the speciﬁcations i) 6531 S .5 3, ii) tab 2 2.5 rad/s, iii) Mp S 1.35. b) In MATLAB, type “k = K; hw55” to plot closed—loop frequency and step responses for the value of K obtained in part a). Verify that speciﬁcations ii) and iii) are met. EQE: H t) he? MAM 5‘\ X \A "T" (7 ‘: . 2 WWW ﬁe 53 J‘ (a \ I <ﬂ0\\'\&? ;w,r N’pﬂ My 2 ([15+5W23—(QSI‘F z “63%4/93‘3 ------- a «.657 5214?? 4;?) a (L) A a; .1: 4'“ :7" C“ ~ Q J 6 / / Q l 3 L 3 l o % 2K 9 I-§Lk o [0/ B4réi7/V S\$+»Mé§%§s~w/ vamfa WMWV3K: [I s 34 ‘ L»~ff<’ )5 + L Q; AEQ iiiii ‘3? ‘ ”L F) X : —’2)"§ ‘"~ K“ W1 BAL>Q A “l/ K j /’ if , 0 (ii if WW2 "+7 ~" ‘5 x *1 )9 > 5:: r“ N2 2 g: 2, (5‘<77)U+Li7tjﬁfﬁ<§§222‘..;2>:?“j,59/ 222112. 2 2 2:» 2 <_ -22 2 2 2 2.2 22 “Maj/27 a (H )1) )(f )1 x) v1- )9) I “W/ .3 (gig +2,+/1€5~))/()+)) ()1 ) i f )1 2” I! V " I .4 H »’ <1" 2 DC 1) ~71! Mn N E W: \I v a} “W K (gm MW; VJ ohm/w! 1:7 “/v a “‘“tm INM M 0M. L(%UJ‘QV¢ V/ l?) Closed—Loop Frequency Response 100 2.956; radians/second Closed-Loop Step Response seconds ...
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