Robust rejection of sinusoids in stable nonlinearly perturbed unmodelled linear systems: Theory and application to servo

Assuming no knowledge of closed-loop dynamics other than being that of a stable nonlinearly perturbed linear system and the forward path gain at the frequency of interest being known and non-zero, a control approach is proposed that rejects a sinusoidal disturbance of known frequency from the system output. The approach consists in partitioning the feedback path of a stable closed-loop system into two weighted paths and inserting between them a loop containing an internal model based filter. The approach is supported by two theorems ascertaining internal stability, that guarantee the rejection of the unwanted sinusoid under the augmentation proposed, with no closed-loop stability loss. The efficacy of the approach is demonstrated through simulations on a model of a servo system consisting of a beam with an electro-hydraulic actuator attached at one end and a mass at the other, and through experiments on the corresponding physical testbed. Robustness of the approach is briefly discussed. A relative non-intrusiveness of the augmentation procedure, a virtual lack of a modeling necessity, and simplicity of estimating the unaugmented forward path gain via experiment on the stable closed-loop system make the approach proposed well suited for industrial use.