Distributed Control of Spatially-Interconnected Parameter-Invariant and LPV Models for Actuated Beams

This paper presents a case study on distributed controller design for spatially-invariant and linear parameter-varying (LPV) models. To apply recently proposed state-space-based synthesis conditions, the experimentally identified input/output models are realized in terms of multidimensional state space representations, both for spatially-invariant and LPV models. Inheriting the interconnected structure of the plant, a spatially-invariant distributed controller is synthesized for a spatially-invariant model, and a spatial LPV controller for a spatially-varying model using constant Lyapunov functions. Considered here is vibration control of an actuated beam, equipped with an array of collocated piezo actuators and sensors. Experimental results show that vibrations at the dominant modes are effectively attenuated for both cases.