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1 ECE-320, Practice Quiz #5 1) For the 2x2 matrix abPcd, the inverse of this matrix, 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 1 0 0( ) ( ) ( )1 2 1( ) [1 2] ( )q t q t u ty t q t 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 22 3) For the following state variable model 0 1 0( ) ( ) ( )1 2 1( ) [1 2] ( )q t q t u ty t q t 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 1 1 0( ) ( ) ( )1 3 1( ) [1 2] ( )q t q t u ty t q t 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 -23 5) Consider the following state variable model 0 1 0( ) ( ) ( )1 1 2( ) 3 0 ( )q t q t u ty t q t Assume state variable feedback of the form ( ) ( ) ( )pfu t G r t Kq t The closed loop transfer function for this system is which of the following? a) 216()(1 212 )pfGGsskks b) 216()(1 ) 2 12pfGGss s k k c) 216()(1 ) 2 12pfGGss s k k d) 216()(1 212 )pfGGsskks 4 6) Consider the following state variable model 1 2 1( ) ( ) ( )0 1 0( ) 1 0 ( )q t q t u ty t q t Assume state variable feedback of the form ( ) ( ) ( )pfu t G r t Kq t Is the closed loop transfer function for this system equal to 1()1pfGGssk a) yes b) no5 7) A system with state variable feedback has the closed loop transfer function 21 1 28()( 12) ( 20)pfGGss k s k k 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) ( 2)pfGGss k s k 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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