Consider the system x (t) * (t) and the performance measure = J = = x...
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Consider the system x₁ (t) *₂ (t) and the performance measure = J = = x₂ (t) −4x₁(t) + 4x₂(t) + u(t) =√ [20x² (1) + 5x2 (1) + u²(1)]dt 0 ) (a) Find the eigenvalues of the open-loop system (Hint: x = Ax+ Bu. Consider u = 0 and find the eigenvalues of A). (b) Find the optimal control law u* (t). ) (c) Find the eigenvalues of the closed-loop system. Comment on the change of the eigenvalues compared with the open-loop case. (Hint: x = Ax + Bu with u = Kx. Find the eigenvalues of A + BK.) Consider the system x₁ (t) *₂ (t) and the performance measure = J = = x₂ (t) −4x₁(t) + 4x₂(t) + u(t) =√ [20x² (1) + 5x2 (1) + u²(1)]dt 0 ) (a) Find the eigenvalues of the open-loop system (Hint: x = Ax+ Bu. Consider u = 0 and find the eigenvalues of A). (b) Find the optimal control law u* (t). ) (c) Find the eigenvalues of the closed-loop system. Comment on the change of the eigenvalues compared with the open-loop case. (Hint: x = Ax + Bu with u = Kx. Find the eigenvalues of A + BK.)
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a To find the eigenvalues of the openloop system we need to consider the system without any control ... View the full answer
Related Book For
Management
ISBN: 9780730329534
6th Asia Pacific Edition
Authors: Schermerhorn, John, Davidson, Paul, Factor, Aharon, Woods, Peter, Simon, Alan, McBarron, Ellen
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