ECE-320, Practice Quiz #9 1) Consider the following state variable model []01 0() () ()11 2() 3 0 ()qt qt utyt qt⎡⎤ ⎡⎤=+⎢⎥ ⎢⎥⎣⎦ ⎣⎦= Assume state variable feedback of the form () () ()pfut G rt Kqt=− The closed loop transfer function for this system is which of the following? a) 216()(1 22)pfGGsskks−=−++ 1− b) 216()(1 )2 12pfGGsss k k=−+−+ c) 216()(1 )22pfGGsss k k=−−++1 d) 216()(1 2 12)pfGGsskks−=−−++ 2) Consider the following state variable model []12 1() () ()01 0() 1 0 ()qt qt utyt qt−⎡⎤⎡⎤=+⎢⎥⎢⎥⎣⎦⎣⎦= Assume state variable feedback of the form () () ()pfut G rt Kqt=− Is the closed loop transfer function for this system equal to 1()1pfGGssk=++ a) yes b) no 1Problems 3-6 refer to a system with state variable feedback with the transfer function 21128()( 12) ( 20)pfGGssk skk=++ +++ 3) Is this system controllable? a) Yes b) No c) impossible to determine 4) What is the approximate bandwidth of the open loop system? a) 2 Hz b) 2 rad/sec c) 2π rad/sec d) 10 Hz 5) In order for the open loop system to have a zero steady state error for a unit step input, the value of the prefilter should be a) b) 1pfG =25pfG = c) 52pfG = d) none of these 6) If we want to choose the feedback gains so the bandwidth of the system is 5 rad/sec and the second pole is 4 time further from the imaginary axis than the first pole (both are assumed to be real poles), then we should choose the gains to be a) b) c) 125, 20kk ==1225, 100kk ==1213, 87kk== d) 1213, 67kk== e) none of these Problems 7-10 refer to a system with state variable feedback that has the following transfer function 212()(1)( 2pfGGssk sk=)+−++ 7) Is the system controllable? a) Yes b) No c) impossible to determine 8) In order for the open loop system to have a zero steady state error for a unit step input, the value of the prefilter should be a) b) c) d) none of these 1pfG = 2pfG = 1pfG =− 9) Assume we use our state variable feedback to place both poles at -5. Then we should choose the gains to be a) b) c) 125, 5kk==1210, 25kk==1211, 23kk== d) 129, 27kk== e) none of these 10) Assume we use our state variable feedback to place both poles at -5. If we want a zero steady state error for a unit step input, then the prefilter gain should be a) b) c) d) 1pfG = 2pfG = 5pfG = 25pfG= e) none of these 211) A system with state variable feedback has the following transfer function 212()()pfGGsskk=− Is the system controllable? a) Yes b) No c) impossible to determine 12) Consider a plant that is unstable but is a controllable system. Is it possible to use state variable feedback to make this system stable? a) Yes b) No 3Problems 13-7 refer to the following open loop Bode plot of () ()GsHs -80-60-40-20020Magnitude (dB)10-210-1100101102-225-180-135-90-450Phase (deg)Bode DiagramFrequency (rad/sec)13) The gain crossover frequency used to determine the phase margin for this system is best estimated as a) 0 rad/sec b) 1 rad/sec c) 1.8 rad/sec d) 12 rad/sec e) 100 rad/sec 14) The phase crossover frequency for this system is best estimated as a) 0 rad/sec b) 1.8 rad/sec c) 3 rad/sec d) 30 rad/sec e) 100 rad/sec 15) The phase margin for this system is best estimated as a) b) c) d) 45o+ 45o− 135o+ 135o− 16) The gain margin for this system is best estimated as a) +12 dB b) - 12 dB c) dB d) -2 dB ∞ 17) Assuming is minimum phase, is the closed loop system stable? () ()GsHs a) Yes b) No c) impossible to determine 4Problems 18-22 refer to the following open loop Bode plot of () ()GsHs -100-50050100Magnitude (dB)10-210-1100101102-270-225-180-135-90Phase (deg)Bode DiagramFrequency (rad/sec)18) The gain crossover frequency used to determine the phase margin for this system is best estimated as a) 0 rad/sec b) 1 rad/sec c) 1.5 rad/sec d) 2 rad/sec e) 100 rad/sec 19) The phase crossover frequency for this system is best estimated as a) 0 rad/sec b) 1 rad/sec c) 1.5 rad/sec d) 2 rad/sec e) 100 rad/sec 20) The phase margin for this system is best estimated as a) b) c) d) 30o+ 30o− 60o+ 60o− 21) The gain margin for this system is best estimated as a) +5 dB b) - 5 dB c) dB d) 0 dB ∞ 22) Assuming is minimum phase, is the closed loop system stable? () ()GsHs a) Yes b) No c) impossible to determine 5Problems 23-27 refer to the following open loop Bode plot of () ()GsHs -40-30-20-1001020Magnitude (dB)10-1100101102-135-90-45045Phase (deg)Bode DiagramFrequency (rad/sec)23) The gain crossover frequency used to determine the phase margin for this system is best estimated as a) 0 rad/sec b) 5.5 rad/sec c) 7 rad/sec d) 15 rad/sec 24) The phase crossover frequency for this system is best estimated as a) 0 rad/sec b) 1 rad/sec c) 1.5 rad/sec d) 2 rad/sec e) none of these 25) The phase margin for this system is best estimated as a) b) c) d) 70o+ 70o− 135o+ 135o− 26) The gain margin for this system is best estimated as a) +5 dB b) - 5 dB c) dB d) 0 dB ∞ 27) Assuming is minimum phase, is the closed loop system stable? () ()GsHs a) Yes b) No c) impossible to determine 67 Answers: 1-b, 2-a, 3-a, 4-b, 5-c, 6-d, 7-a, 8-b, 9-c, 10-d, 11-b, 12-a, 13-c, 14-c, 15-a, 16-a, 17-a 18-d, 19-c, 20-b, 21-b, 22-b, 23-c, 24-e, 25-a, 26-c,
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