Robust Repetitive Model Predictive Control for Systems with Uncertain Period-Time
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Repetitive Model Predictive Control (RMPC) incorporates the idea of Repetitive Control (RC) into Model Predictive Control (MPC) to take full advantage of the constraint handling, multivariable control features of MPC in periodic processes. The RMPC achieves perfect asymptotic tracking/rejection in periodic processes, provided that the period length used in the control formulation matches the actual period of the reference/disturbance exactly. Even a small mismatch between the actual period of process and the controller period can deteriorate the RMPC performance significantly. The period mismatch occurs either from an inaccurate estimation of actual frequency of disturbance due to resolution limit or from trying to force the controller period to be an integer multiple of sampling time. An extension of RMPC called Robust Repetitive Model Predictive Control (R-RMPC) is proposed for such cases where period length cannot be predetermined accurately, or where period is not an integer multiple of sampling time. This robust RMPC borrows the idea of using weighted, multiple memory loops in RC for robustness enhancement. The modified RMPC is more robust in the sense that small changes in period length do not diminish the tracking/rejection properties by much. Simulation results show that R-RMPC achieves significant improvement over the standard RMPC in case of a slight period mismatch. The effectiveness of this Robust RMPC is demonstrated by applying it to a mechanical motion tracking machine whose function is to follow a constant trajectory while rejecting periodic disturbances of an uncertain period.