Structure-preserving model reduction for spatially interconnected systems with experimental validation on an actuated beam

A technique for model reduction of exponentially stable spatially interconnected systems is presented, where the order of the reduced model is determined by the number of truncated small generalised singular values of the structured solutions to a pair of Lyapunov inequalities. For parameter-invariant spatially interconnected systems, the technique is based on solving a pair of Lyapunov inequalities in continuous-time and -space domain with a rank constraint. Using log-det and cone complementarity methods, an improved error bound can be obtained. The approach is extended to spatially parameter-varying systems, and a balanced truncation approach using parameter-dependent Gramians is proposed to reduce the conservatism caused by the use of constant Gramians. This is done by considering two important operators, which can be used to represent multidimensional systems (temporal- and spatial-linear parameter varying interconnected systems). The results are illustrated with their application to an experimentally identified spatially interconnected model of an actuated beam; the experimentally obtained response to an excitation signal is compared with the response predicted by a reduced model.