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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 RIIP poles in the closedloop 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 closedloop 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 closedloop
stability. 5) Consider the plant
1 G = .
a) Using the formulas for secondorder 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‘
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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 ClosedLoop Step Response seconds ...
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 Fall '08
 cobb

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