Control Relevant Model Reduction of Volterra Series Models

This paper presents a two-step method for control-relevant model reduction of Volterra series models. First, using nonlinear IMC 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 computational 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 “open-loop” predictive ability of the control-relevant model, the closed-loop performance of the reducedorder control system closely mimics that of the full order model.