LPV Control for Robust Attenuation of Non-stationary Sinusoidal Disturbances with Measurable Frequencies

Abstract

Attenuation of sinusoidal disturbances with uncertain and arbitrarily time-varying, yet online measurable frequencies is considered. The disturbances are modeled as the outputs of an autonomous exogenous system, whose system matrix depends on some uncertain parameters and is skew-symmetric for all admissible parameter values. A procedure is then developed for the synthesis of an observer-based controller that uses the online measurements of the uncertain parameters to guarantee a desired level of attenuation at steady-state in the face of all admissible parameter variations. The controller is scheduled by the measurements of the uncertain parameters as well as the matrix-valued outputs of a unit that is also scheduled on the uncertain parameters. The synthesis procedure is based on solving a convex optimization problem in which the variables are subject to a set of parameter-dependent matrix inequality constraints, which can be relaxed into finitely many linear matrix inequalities. The procedure also provides options for improving the transient response.