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ECTE942 ECTE942 COMPUTER CONTROLLED SYSTEMS
创建日期：2024-04-12 16:25:09
标签： ECTE942
ECTE942 COMPUTER CONTROLLED SYSTEMS

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ECTE942 

 Family name School of Electrical, Computer and Telecommunications Engineering 

ECTE942 COMPUTER CONTROLLED SYSTEMS 

Exam duration 3 hours 15 minutes. Materials allowed Drawing instruments and calculators approved by the Board of Studies. Directions to students Part A - five (5) questions - attempt all questions. Use a separate booklet to record your answers. Part B - four (4) questions - attempt all questions. Use the spaces provided on the examination paper to record your answers. Backs of pages may be used for working out only. Marks for questions are indicated, allow appropriate time. Make sure your answers are CLEAR and READABLE. Other information The examination paper is printed on ONE SIDE ONLY. CANDIDATES SHOULD NOTE THAT QUESTIONS ARE TO BE ANSWERED AS WRITTEN - NO CONSULTATION (INDIVIDUAL OR GROUP) ON QUESTIONS WILL BE GIVEN. ANY ASSUMPTIONS MADE SHOULD BE RECORDED WITH YOUR ANSWER. EXAMINATION PAPERS MUST BE WRITTEN IN INK. PAPERS WRITTEN IN PENCIL WILL NOT BE MARKED. This exam paper and booklet must not be removed from the exam venue Student to complete ECTE942 - Spring Session 2008 Page 2 of 11 PART A – USE THE EXAMINATION BOOKLET PROVIDED TO RECORD YOUR ANSWERS - [50 Marks in Total] QUESTION 1A - (10 MARKS) For the following system: (a) Find out the close loop pulse transfer function )( )( zR zY ; (b) If 2 1)( + = s sG , system sampling time is T, find the discrete plant model G(z) with ZOH; (c) If 1 )( + = s ssH , find out the close loop pulse transfer function. Given Z transform table ECTE942 - Spring Session 2008 Page 3 of 11 QUESTION 2A - (10 MARKS) The following transfer function is a lead network designed to add about 60˚ phase lead at ω1=3 rad/s 11.0 1)( + + = s ssH , the sampling time of the system is 0.25s. (a) Approximate the network with forward rectangular rule (b) Approximate the network with zero-pole matching method (c) Compare the frequency response of continuous system and two approximations at ω1=3 rad/s QUESTION 3A - (10 MARKS) Let's assume that you have a system with the feedback configuration as shown below. (a) Write the sensitivity function S(s) of the system. Explain the meaning of S(s). (b) If the transfer function of the plant, P(s), is given by: P(s) = 5/(s + 3), determine the closed loop DC gain when the proportional controller C(s) is Kp=7. (c) Determine the sensitivity of the closed loop DC gain to changes in the DC gain of P(s). (d) Using the sensitivity, estimate the change in the closed loop DC gain when the DC gain of P(s) increases by 6%. ECTE942 - Spring Session 2008 Page 4 of 11 QUESTION 4A - (10 MARKS) (a) Derive the discrete-time system corresponding to the following continuous-time system when ZOH circuit is used. The sampling time of the system h=1. [ ] )(01)( )( 1 0 )( 01 10)( txty tutx dt tdx = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ +⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − = (b) Find the controllability matrix Wc of the discrete-time system. (c) Find the pulse transfer function of the discrete-time system. (d) Find the controllable canonical form of the discrete-time system. QUESTION 5A - (10 MARKS) Given the system [ ]01, 2 0 , 01 21 : )()( )()()1( =⎥ ⎦ ⎤ ⎢ ⎣ ⎡ =Γ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ =Φ = Γ+Φ=+ CWhere kCxky kukxkx (a) Determine the state feedback controller L so that the characteristic polynomial of the system is 1.06.02 ++ zz . (b) Design a deadbeat full state observer K. (c) Draw the block diagram of complete system including the state feedback controller and state estimator. ECTE942 - Spring Session 2008 Page 5 of 11 PART B – USE THE SPACES PROVIDED ON THIS PAPER FOR YOUR ANSWERS - BACKS OF PAGES MAY BE USED FOR WORKING OUT ONLY - [50 Marks in Total] QUESTION 1B - (15 marks) Consider the ARMA model having unknown parameters a and b: y(k)+ay(k-1)=bu(k-3)+e(k) (a) Write down the plant model for k=3, 4, ..., N. (b) Rewrite the equations in the matrix form, y=Fp+e y = F = p = e = ECTE942 - Spring Session 2008 Page 6 of 11 QUESTION 1B (cont.) (c) Estimate the plant parameters using the output and input data: Y=[y(1) y(2) … y(6)]=[2 1.5 1 -1.5 -3 -2] U=[u(0) u(1) u(2) u(3) u(4) u(5) u(6)]=[-2 -2 -2 1 1 1 1] Estimated parameters ECTE942 - Spring Session 2008 Page 7 of 11 QUESTION 2B – (5 marks) Design the 3-step-ahead predictor for the following ARMA model. y(k+3)+2y(k+2)+3y(k+1)=4u(k)+3u(k-1)+u(k-3) Predictor: ECTE942 - Spring Session 2008 Page 8 of 11 QUESTION 3B - (10 marks) Consider the nonlinear and time-varying system y(k)+4y(k-1)+5y(k-3)=0.1[3+sin(10k)][u(k-2)]3 (a) Given the desired output y*(k) design a d-step-ahead controller. d-step-ahead controller: ECTE942 - Spring Session 2008 Page 9 of 11 QUESTION 3B (cont.) (b) Is the closed-loop system stable? Why? ECTE942 - Spring Session 2008 Page 10 of 11 QUESTION 4B - (20 marks) Consider the ARMA model y(k+1)+0.1y(k-1)=4u(k)-5u(k-1) (a) Given the weighting h=6 and the desired output y*(k). Design a weighted d-step-ahead controller for the ARMA model. Weighted d-step-ahead controller: ECTE942 - Spring Session 2008 Page 11 of 11 QUESTION 4B (cont.) (b) Determine the closed-loop transfer operator H(q-1) such that: y(k)=H(q-1)y*(k)

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关键词一 关键词二 关键词三 关键词四 关键词五 和法规和的发更好的风格和 ECON 615 FINC 612 CSC148 COMP 639 ACCT 203 ACCT 211 PSYC 101 MTH2009 COMP52315 PSYCO 432 statistics MATH4063 11 xxx 1 MA1MSP MAST30028 MATH3888 CS341 EEE30002 ES2F5 MCD4160 CC0933 ECON 1101 MCHM3001 CHEM3118 COMMGMT 2511 COMP41280 STAT 631 24T1 IRE379 SENG365 ECON433 FIT3139 MATH4602 LING5621M FINS5516 ECON3208 MN2177 L2 SM EEET1415 Finance DS4023 COMP3004 7CCSMRTS K1S5B6 Stat230 CSCI4211 CSI2132 ECON30130 MAS6100 ENVS222 COM2107 INFO1112 STAT 4004 FIT2100 comp2022 COMP4691 Physics 307 Econ 659 probability CSCI316 fir29 CSCI203 COMP3160 COMP6714 INFO1113 Physics 7B Physics Photonics S203031 STAT2005 COMP90015 CSCI 2110 CSCC46 Information CSC477 COMP4650 Statistical COMP 346 COMP1017 ELEC340 MATH1007 Programming function STAT 244 CS 134 Java cse13s Math 108A FW20 ECON3389 CSE 130 Science 331 COMP9020 engineering COSC 445 CSE 5523 GAME2012 visualization MATH 235 Math 370 CSC343 COGS 108 EE524 COMP10200 STAT 416 3FK4 MSCI 311 ECON6113 ACC40700 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