Output Regulation in Bimodal Systems With Application to Surface Tracking in the Presence of Contact Vibrations

Motivated by a class of surface tracking problems in mechanical systems subject to contact vibrations, this paper considers a regulation problem for discrete-time switched bimodal linear systems where it is desired to achieve output regulation against exogenous input signals featuring known deterministic and unknown random components. A first step in the regulator design involves constructing a set of observer-based parameterized stabilizing controllers that satisfy a sufficient regulation condition for the switched system against the known deterministic disturbance or reference signals. In the second step, an additional performance constraint is added to identify, from among the already constructed regulators, those that provide the best regulation performance against the unknown random disturbances. A corresponding regulator synthesis algorithm is developed based on iteratively solving properly formulated bilinear matrix inequalities. The proposed regulator is successfully evaluated on an experimental setup involving a switched bimodal mechanical system subject to contact vibrations, hence demonstrating the effectiveness of the proposed regulation approach.