adv ctrl 03

adv ctrl 03 - LAKEHEAD UNIVERSITY FACULTY OF ENGINEERING,...

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Unformatted text preview: LAKEHEAD UNIVERSITY FACULTY OF ENGINEERING, DEPARTMENT OF ELECTRICAL ENGINEERING FINAL EXAMINATION Engineering 4034 FA Electrical Engineering DEPARTMENT SUBJECT | COURSE NO. 1 SECTION Advanced Controls I Dr. A. Tayebi INSTRUCTOR COURSE TITLE Monday, December 8, 2003 9:00 - 12:00 noon 3 hours F.H.Rows:B,D,F,H,J I EXAM TIME DURATION ROOM EXAM DATE CLOSED BOOK ONLY NON PROGRAMMABLE CALCULATORS ALLOWED Do all your work on the sheets provided and show all your work! This examination question paper MAY NOT be taken from the examination room. STUDENTS PLEASE NOTE YOU MUST count the number of pages in this examination question paper BEFORE beginning to write, and report any discrepancy immediately to a proctor. This is page 1 of 4. December 8, 2003 Eng. 4034: Advanced Controls I—Final Examination Note: 3 marks will be given for neatness Q — 1 (8 points) Consider the system shown in figure 1. R(S) __K__ (s+lZ)(s+10) Figure 1: Feedback system a) Determine the steady-state error for a unit step input in terms of K and K1, where E(s) = R(s) — Y(s). b) Select K1 so that the steady state error is zero. 0) Let K = 24 and select K1 so that the steady state error is zero. For these values of K and K1 what is the percent overshoot and the settling time for a unit step input. Q — 2 (7 points) A feedback control system has a characteristic equation 56 + 255 + 984 + 1633 + 2432 + 323 + 16 = 0. Determine whether the system is stable, and determine the values of the roots. Q — 3 (7 points) Consider a closed loop system T(s) = 735%, with Plot the root loci as K varies from 0 to +00. Q — 4 (10 points) . _ 0(8) . ConSIder a closed loop system T(s) — 1 + G(S)H(s) , w1th 6(5) _ M.)— [1(3): 1, — s(s + 1)(s + 3) ’ Plot the root loci as K varies from 0 to +00. Determine the value of K such that the damping ratio of the dominant closed-loop poles is 0.5. Q — 5 (7 points) Consider the system _ Y(s) _ s R(s) — (s + 10)(s + 0.5) 0(5) a) Give the steady-state response y(t) for a sinusoidal input T(t) = Asin(wt). b) What is the magnitude and the phase of the output signal y(t) for w = 10rd/s? Q — 6 (8 points) Consider the following block diagram a) Simplify the block diagram and obtain the closed loop transfer function T (s) = Y(s) /R(s). 1 1 b) LetH1=H2=1,H3=K1,02=—andG1= s 3 conditions on the parameters K1 and K leading to the stability of T(s). . Give the necessary and sufficient Q — 7 (10 points) Consider the following transfer functions 10 01(3) = ‘1) 02(3) = (2) 1 03‘” = a) Sketch the asymptotic Bode diagram for the transfer functions 01, G2 and G3. b) Give the resonant frequency our and the magnitude peak MW at w = w, for the second order portion of the system G1(s). 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This note was uploaded on 02/25/2010 for the course ENGI 0000 taught by Professor All during the Spring '10 term at Lakehead.

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adv ctrl 03 - LAKEHEAD UNIVERSITY FACULTY OF ENGINEERING,...

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