A model-free tuning method for proportional-multi-resonant controllers

Resonant controllers are widely used in applications involving reference tracking and disturbance rejection of periodic signals. The controller design is typically performed by a trial-and-error approach or by means of time and resource-consuming analytic methods that require an accurate plant model, intricated mathematics and sophisticated tools. In this paper, we propose an easily implementable, model-free method for tuning a proportional-multi-resonant controller applicable to general linear time-invariant causal plants. Just like the Ziegler-Nichols methods, the proposed methodology consist in identifying one specific point of the plant's frequency response -- which is easily obtained in a relay with adjustable phase experiment -- and then designing the controller with simple tuning formulas and tables. The method is analyzed in detail for three examples, showing its practical appeal and wide applicability.