Feedback control of unstable periodic motion for brushless motor with unsteady external torque
For dynamical systems, unstable periodic motion can play an important role, such as the walking behavior for human. Due to the dynamic characteristics, unstable periodic motion is difficult to stay on its limit orbit or equilibrium even when small disturbance occurs. Therefore, it is unusual to observe unstable periodic motions in the real world applications. At some specific circumferences, design a proper controller for a dynamic system properly when the unstable periodic motion is required becomes a problem to be solved. In this paper, a brushless motor model with unsteady external torque will be investigated. The analytic bifurcation of periodic motions will be obtained through a semi-analytic approach which is called as the discrete implicit maps algorithm. Based on the node points of the periodic motions, the analytic solution for the periodic motion can be expressed with a Fourier series. The stable and unstable analytical solutions will be verified by the numerical predictions. Then a feedback controller will be designed such that the unstable periodic motion can stay on its orbit permanently. The simulation with and without controller will be compared to show the effectiveness of the controller.
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