Consider the LQR problem for the system and the performance index *1 = x2, * =...
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Consider the LQR problem for the system and the performance index *1 = x2, *₂ = 2x₁ - x₂ + u J 1 = [² [ 2² (0) + 12 +²7(0) + 1/201² (19)] α6 dt (a) Find the entries of the matrix P and the gains of the optimal controller. (b) Solve the problem for the finite-time horizon of tf = 15sec, i.e., the new cost function is J 115 [ 2300) + 1/ 130(0) + + 0² (19)] de dt For this problem, the matrix P is time-varying (see handout on LQR-proofs) and you need to solve the differential Riccatti equation (backwards in time). Plot the entries of the P matrix and compare them with the constant values obtained in part (a). Note that the controller gains will be time-varying in this time. Consider the LQR problem for the system and the performance index *1 = x2, *₂ = 2x₁ - x₂ + u J 1 = [² [ 2² (0) + 12 +²7(0) + 1/201² (19)] α6 dt (a) Find the entries of the matrix P and the gains of the optimal controller. (b) Solve the problem for the finite-time horizon of tf = 15sec, i.e., the new cost function is J 115 [ 2300) + 1/ 130(0) + + 0² (19)] de dt For this problem, the matrix P is time-varying (see handout on LQR-proofs) and you need to solve the differential Riccatti equation (backwards in time). Plot the entries of the P matrix and compare them with the constant values obtained in part (a). Note that the controller gains will be time-varying in this time.
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Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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