exam2-sol - Please show all work for partial credit(100...

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Unformatted text preview: Please show all work for partial credit. (100 points total) Problem 1. (40 points) Consider the unity feedback system shown below (H(s)=1): where GP (5) = ——§—— , (s + 2) (s + 3) 1) Find the location of the dominate poles to yield a 1.6-seconds settling time and an overshoot of 25%. K (s + a) . . . . 2) If a compensator Gc (s) = ——b— w1th a zero at —1 (1.e., a=1) 15 used to achieve the s + conditions of 1), what must the angular contribution of the compensator pole be? 3) Find the location of the compensator pole from your answer to 2), Le, b=? 4) Find the gain required to meet the requirements of 1), Le, =? i if 3068’ 7 7' ’ ’"” ” ’ " " "W . __ 4 ' 1n ( 100) C9 Cw“ ‘ Ts ‘ 25’ C= N = 0.404. Thus, (on = 6.188 rad/s and the operating 1:2 + 1n2 (%-l—OOBS- point is - 2.5 1 j5.67. Summation of angles including the compensating z pole must contribute 180° - 170.220 = -9.78°. 5.67 pc - 2.5 cm is -170.22°. Therefore, the compensator Using the geometry shown below, @‘ = tan 9.78°. Thus P — sc- 35.39. @ ' Adding the compensator pole and using -2.5 + j5.67 as the test point, K = 1049.41. Problem 2. (30 points) For the system shown below 1) Find KP, Kv, K3. 2) Find the steady-state error for an input of 50u(t), 50tu(t), and 50t2u(t), where u(t) is a unit step fimction. 3) State the system type. , Sb “on a: 7 7 75H 7 WV 7 ‘7 fl 7777”? 7777777 rm 1)(s+2) 5 G ( )= L: Q es 1+ 5(s+3) sfi+3s2 +7s+i5 s(s+1)(s+2) Therefore, Kp = 1/3; Kv = 0; and Ka = 0. @\ Far sou“), e(oo) = 1 30K}, = 37.5; For 50tu(t), 30») = co; For 50t2u(t), e(oo) = oo (3 Type 0 2(s +10) (.9 +1)(s + 2) asymptotic Bode magnitude plot for each individual factors separately, and then add them together. Mark the slopes in your diagram. We“ ; Problem 3. (30 points) For the transfer fimction G(s) = , sketch 7 {(9)1(3é21‘l) __ 10(510 + I) ; 5‘53: (54-00%1-1) _‘ 3* )CS/z'f'” dB 6‘3033 1014’ = 20:33 613:») a fit?!" ...
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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.

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exam2-sol - Please show all work for partial credit(100...

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