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

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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?!" ...
View Full Document

## 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.

### Page1 / 4

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online