Control relevant model reduction of Volterra series models

This paper presents a two-~:tep method for control-relevant model reduction of Volterra series models. First, using the nonlinear I\1C design as a basis, an explicit expression relating the closed-loop performance to the open-loop modeling error is obtained. Secondly, an optimization problem that seeks to minimize the closed-loop error subject to the restriction of a reduced-order model is posed. By showing that model reduction of kernels with different degrees can be decoupled in the problem formulation, the optimization problem is simplified into a mathematically more convenient form which can be solved with significantly less computatic,nal effort. The effectiveness of the proposed method is illustrated on a polymerization reactor example where a second-order Volterra model with 85 parameters is reduced to a Hammerstein model with 3 parameters. Despite the lower ʹopen-loopʹ predictive ability of the controlrelevant model, the closed-bop performance of the reduced-order control system closely mimics that of the full order model.