ECE-320, Practice Quiz #7 1) For the 2x2 matrix , the inverse of this matrix, abPcd⎡⎤=⎢⎣⎦⎥1P−, is which of the following: a) 11abPcdad bc−⎡⎤=⎢−⎣⎦⎥ b) 11dbPcaad bc−⎡⎤=⎢⎥−⎣⎦ c) 11dbPcaad bc−−⎡⎤=⎢⎥−−⎣⎦ d) 11dbPcaad bc−−⎡⎤=⎢⎥−+⎣⎦ e) 11dbPcaad bc−⎡⎤=⎢⎥+⎣⎦ f) none of these 2) For the following state variable model 10 0() () ()12 1() [1 2] ()qt qt utyt qt⎡⎤ ⎡⎤=+⎢⎥ ⎢⎥⎣⎦ ⎣⎦= The poles of the system are at a) -1 and -3 b) -2 and -2 c) 1 and 3 d) 0 and 1 e) 1 and 2 13) For the following state variable model 01 0() () ()12 1() [1 2] ()qt qt utyt qt⎡⎤⎡⎤=+⎢⎥⎢⎥−−⎣⎦⎣⎦= The poles of the system are at a) -1 and -2 b) -1 and -1 c) 1 and 3 d) 0 and 1 e) 1 and 2 4) For the following state variable model 11 0() () ()13 1() [1 2] ()qt qt utyt qt−−⎡⎤⎡⎤=+⎢⎥⎢⎥−⎣⎦⎣⎦= The poles of the system are at a) -1 and -3 b) -2 and -2 c) 1 and 3 d) 0 and 1 e) -1 and -2 25) 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−=−−++ 36) 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 45 7) A system with state variable feedback has the closed loop transfer function 21128()( 12) ( 20)pfGGssk skk=++ +++ Is this system controllable? a) Yes b) No c) impossible to determine 8) A system with state variable feedback has the closed loop transfer function 212()(1)( 2pfGGssk sk=)+−++ Is the system controllable? a) Yes b) No c) impossible to determine 9) A system with state variable feedback has the closed loop transfer function 212()()pfGGsskk=− Is the system controllable? a) Yes b) No c) impossible to determine 10) 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 Answers: 1-c, 2-e, 3-b, 4-b, 5-b, 6-a, 7-a, 8-a, 9-b,
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