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Repetitive controllers (RCs) are linear control structures based on the internal model principle. This control strategy is known for its ability to control periodic reference signals, even if these signals have many harmonic components. Despite being a solution that results in a good performance, several parameters of the repetitive controller need to be correctly tuned to guarantee its stability. Among these parameters, one that has high impact on the system performance and stability is the finite impulse response (FIR) filter, which is usually used to increase the stability domain of RC-based controllers. In this context, this paper presents a complete tutorial for designing the zero-phase FIR filter, which is often used to stabilize control systems that use RC-based controllers. In addition, this paper presents a Matlab® application developed for performing the stability analysis of RC systems and designing its FIR filter. Simulation and experimental results of a shunt active power filter are used to validate the algorithm and the Matlab® application.

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