Experimental evaluation of an LPV-gain-scheduled observer for rejecting multisine disturbances with time-varying frequencies

A linear time-varying (LTV) discrete-time controller for the rejection of harmonic disturbances with time-varying frequencies on linear time-invariant (LTI) systems is proposed and validated in real-time experiments. The controller is an observer-based state feedback controller with a time-varying observer system matrix and a time-invariant state feedback gain. For the controller design, the combination of plant and disturbance is modeled as a polytopic linear parameter-varying (pLPV) system and linear matrix inequalities (LMIs) derived from quadratic stability theory and LMIs for an upper bound on the H₂ performance are used. The design guarantees closed-loop stability even for arbitrarily fast changes of the varying parameters. The controller is tested on an active noise control headset for a disturbance signal consisting of four harmonics.