On The Choice Of State Feedback Gain Multi-input Multi-output Control Systems
Résumé: It is well known from control theory that in multi-input multi-output systems the state feedback gain used to set the closed loop poles at certain desired locations is not unique. The main objective of this project is to take advantage of this non-unicity, and design a state-feedback controller, using general form transformation, with a feedback gain meeting the following criteria: - Small system feedback gain to minimize the control energy. - The best time response characterization. - System with good robustness. Our application consists of simulating the dynamics of a helicopter at hover using Matlab software. The initial condition response of some systems and some eigenvalues trajectories are plotted. The time response characteristics, gain magnitudes, matrix measures and the condition number of each system are computed. The relative change of each eigenvalue is provided to study how the eigenvalues are affected by small perturbations. All these results are then compared to select the best state-feedback gain matrix satisfying the required criteria mentioned above. The comparison showed that the system performance is considerably affected by both the choice of the input sequence and the arrangement of the eigenvalues in the desired matrix.
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