Consider a discrete time ACC system with 1s sampling period with A-].B-[5].C. [],D=[0], K = [11],...

 

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Consider a discrete time ACC system with 1s sampling period with A-].B-[5].C. [],D=[0], K = [11], i.e. the closed-loop state-transition matrix is (A - BK). The following LHA represents above system. Find out Post 12 (x = 10, v = 5) i.e. the region/point for the given initial region/point after the application of the Post operation 12 times on the given LHA (up to 3 decimal place). Hint: Find out state progression of closed loop system after 12 iterations. lt = 0 |x| 10 |v|5 a:=-x-v x = v a = -x v v = a it = 1 lt 1 lt=1 lt: = 0 Which of the following express the SMT formula for evolution of the above ACC system for 2 iterations? , and A, B, C, D, K are discrete system matrices) (X = [], and a. C. == ( x [1]. --No.it -0) A (X-AX + BU) (It-1) AU--KX A = = (It-It+1) A (It-0) A (X-AX + BU) A (It 1) AU --KX2 A (It - 0) ([10] x[10]. =-x.lt = 0) ^ (It = It + 1)^(% = Ax + BU) ^ (It == 1)^U = -KX A (It = 0) A (It It + 1) A (X = AX + BU) A (lt == 1) AU == -KX2 A (lt = 0) ([0] x [], = X, lt = 0) ^ (lt = lt + 1) ^ (X = AX + BU) ^ (lt lt + 1)^ (X2 = AX1 + BU) d. ([-]x Consider a discrete time ACC system with 1s sampling period with A-].B-[5].C. [],D=[0], K = [11], i.e. the closed-loop state-transition matrix is (A - BK). The following LHA represents above system. Find out Post 12 (x = 10, v = 5) i.e. the region/point for the given initial region/point after the application of the Post operation 12 times on the given LHA (up to 3 decimal place). Hint: Find out state progression of closed loop system after 12 iterations. lt = 0 |x| 10 |v|5 a:=-x-v x = v a = -x v v = a it = 1 lt 1 lt=1 lt: = 0 Which of the following express the SMT formula for evolution of the above ACC system for 2 iterations? , and A, B, C, D, K are discrete system matrices) (X = [], and a. C. == ( x [1]. --No.it -0) A (X-AX + BU) (It-1) AU--KX A = = (It-It+1) A (It-0) A (X-AX + BU) A (It 1) AU --KX2 A (It - 0) ([10] x[10]. =-x.lt = 0) ^ (It = It + 1)^(% = Ax + BU) ^ (It == 1)^U = -KX A (It = 0) A (It It + 1) A (X = AX + BU) A (lt == 1) AU == -KX2 A (lt = 0) ([0] x [], = X, lt = 0) ^ (lt = lt + 1) ^ (X = AX + BU) ^ (lt lt + 1)^ (X2 = AX1 + BU) d. ([-]x