Port condensation of Volterra transfer functions with cross-products

Abstract

Port-based dynamic models are frequently used in the description of physical devices from an energy perspective. Port-based models group pairs of input and output variables into ports. A port in a physical model describes a process for energy transformation into, or out of, the system modeled. In complex multi-port models, it is desirable to eliminate some unused ports to decrease model complexity or to protect proprietary internal design details. Condensation is a procedure to remove unused, zero input, model ports from a model while retaining all other ports with full model input–output accuracy for those retained ports. The condensation of port-based linear models represented as transfer function matrices was treated in Radcliffe and Motato (J Dyn Syst Meas Control 131:021003–0210010, 2009). The condensation of port-based nonlinear models without cross-products and represented as Volterra models was developed in Motato and Radcliffe (Proceedings of the ASME dynamic systems control conference, Hollywood, USA, 2009). This work extends the condensation process for port-based Volterra dynamic models including cross-products of output port variables.