Distributed identification and control of spatially interconnected systems with application to an actuated beam

This paper presents a case study on modelling and control of spatially interconnected systems. Considered is a vibration control problem, with experimental results on a flexible beam that is equipped with an array of piezo sensors and actuators. The sensor–actuator array induces a spatial discretization of the beam into an array of interconnected subsystems. Models are experimentally identified that have the structure of spatially interconnected systems. Based on the identified models, distributed control schemes are designed by solving a linear matrix inequality (LMI) problem that has the size of a single subsystem. Modelling and control is considered for both spatially invariant and spatially varying systems; in the latter case the system is represented as linear parameter-varying (LPV) system that is scheduled not over time but over space. Simulation and experimental closed-loop results demonstrate the practicality and efficiency of the underlying framework.