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This paper presents design and implementation of model predictive control with repetitive control for periodic signal tracking and constraint handling of fast sampled-data systems. An internal model based discrete time repetitive control law is integrated with the model predictive controller and the original problem is then transformed to a quadratic programming problem to deal with the given constraints. This heavy computational control was implemented on a piezo-actuated system at a 10 kHz sampling rate. The experimental results demonstrate the feasibility and effectiveness of the proposed approach for asymptotic error tracking of periodic reference profiles with constraint handling.