Experimental identification of spatially-interconnected parameter-invariant and LPV models for actuated beams

This paper presents an experimental case study on system identification for spatially interconnected systems, considering both parameter-invariant and parameter-varying models. Considered here is the problem of vibration control for actuated beams - beams of different lengths are each equipped with an array of collocated actuators and sensors. Here we show how a spatially-interconnected model - a lumped approximation of a distributed system that lends itself to efficient, LMI-based synthesis of distributed control - for such actuated beams can be obtained experimentally. Experimental results show that a long beam with equally distributed actuators/sensors can be satisfactorily represented by a spatially invariant model. This is not possible for a short beam due to the stronger effect of boundary conditions, whereas it is demonstrated experimentally that a spatial LPV model captures the dynamic behaviour, thus enabling the synthesis of distributed spatial LPV controllers.