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Unformatted text preview: Final Exam EEL 3657 (Spring 2003 Instructions 1. There are totally 4 problems in this exam. 2. Show all work for partial credit.
3. Assemble your work for each problem in logical order. 4. Justify your conclusion. I cannot read minds. Problem 1. (25 points) For the unity feedback system sho . below, G6) = (50035) ,
s s + _R(S) + % E(S) (3(5) 1). What is the expected percent overshoot for a unit step in‘ut? 1
2). What is the settling time for a unit step input? i 3). What is the steadystate error for an input of 5u(t), wher u(t) is a unit step ﬁmction. 4). What is the steadystate error for an input of 5tu(t), whe  u(t) is a unit step function. §§vuiknnz
The closedloop transfer function is, “)' T _ 5000
“)"s2+75s+smm from which, a)" = V5000 and 2(0),, = 75. Thus, 4' = 0.5 ‘ and %OS = e—W‘IITFXIOO = 14.01%. 4 = —§4—=0.107 second. 29‘ T‘= cub 75/2
3) , Since system is Type 1, eSS for 5u( t) is zero. i
5000 _ _5__ Q) Since KV is = 66.67, e33  Ky — 0.075. I i  Problem 2. (20 points) 1 1
1. 10 oints Consider H s =Gs , H s =Gs a,
)( p ) l() ()SZJFZS+2 () ()S2_2S+2 At a frequency of a) = 2 rad/s, G(ja)) has a magnitude of A and an angle of ¢. What are
the magnitude and angle of H I ( jw) and H 2 ( jw) at the sam‘ frequency? KeZ:
S 2). (10 points) Consider G(s)H(s) = , determine th frequency a) at which 4G(ja))H(ja)) = —l810°. = +aC'I ++a"3 =“7e,
1 [swan] .= {£479 = 2r? 0 ' . ' f .
HA2» A Lt” . “S "7 2r?" : 011/} 415:“): . _________.___._.\_—_._..— 3 w. I
I . . __ 6 J 5 _~_ ﬁm
__%__/_i ___.'__‘—.J.‘Z_—:_____._ ._..___.__._.
________.._,___._______tv_4g'~___w 4______«~_______..__~__..____ .__._.—r———— Problem 3. (20 points) 1). (10 points) Sketch the straightline Bode magnitude p101 for G(s) = 2) (10 points) Identify G(s) from the magni
shown below (G(s) has no. complex poles): dB 20 2
s2(s+2)' tude plot of th straightline Bode diagram as 1/0005 Problem 4. (35 points) The ﬁgure shown below is the blo k diagram of the servocontrol
system for one of the joints of a robot. 1). (10 points) Show the plant (“Motor and arm”) transfer ction is given by
49L (5) 0.15 Ea (s) s(s + 1)(s + 5) ' 2). (10 points) With the compensator replaced with a gain I , sketch the root locus of the
system, and specify asymptotes, breakin/breakout points. 3). (15 points) Given the compensator Gc(s) = 30(K1D + Ds) as shown in the diagram,
calculate the compensator gains K p,K D to put the dminate closedloop poles at
s = ~1i j, and sketch root locus of the compensated syste . Compensator Motor and arm r_____.. 12 lg
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This note was uploaded on 01/14/2012 for the course EEL 3657 taught by Professor Staff during the Spring '08 term at University of Central Florida.
 Spring '08
 Staff

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