Tracking periodic signals in the presence of control saturation: a repetitive control approach

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• Joao Manoel Gomes da Silva Jr, Universidade Federal do Rio Grande do Sul
• Wednesday 23 November 2011, 14:00-15:00
• CAP Seminar Room .

If you have a question about this talk, please contact Alessandro Astolfi.

This talk addresses the problem of tracking and rejection of generic periodic signals for linear multi-input, multi-output (MIMO) systems subject to control saturation. To ensure the periodic tracking/rejection, a modified state-space repetitive control structure is considered. The basic idea of this approach consists in introducing a delay term in a pre-compensator, which leads to the generation of an infinite dimensional internal model, whose frequency response presents resonance peaks in all integer multiples of the fundamental frequency of the periodic signal. To overcome some stabilization and robustness issues, a low-pass filter is introduced in the repetitive control loop, at the expense of a tolerable (small) tracking error. However, in the presence of control saturation further conditions should be provided to ensure the ``almost perfect’’ tracking and the internal stability of the closed-loop system. In particular, the ``almost perfect tracking’’ depends directly on the the amplitude of the periodic references/disturbances as well as the initial conditions of the system. Taking this into account, a method based on linear matrix inequalities is proposed to simultaneously compute a stabilizing state feedback gain and an antiwindup gain. Provided that the references and disturbances belong to a certain admissible set, these gains guarantee that the trajectories of the closed-loop system starting in a certain ellipsoidal set contract to the linearity region of the closed-loop system, where the presence of the repetitive controller ensures the periodic tracking/rejection. We illustrate the approach by some numerical examples and the application to the control of a Uninterrupted Power Supply (UPS) system.

This talk is part of the Control and Power Seminars series.

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• Andrea Picciau's list
• CAP Seminar Room
• Control and Power Seminars

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