Internal Model Control Perspectives on Model Reduction

A frequency-domain understanding of reduced-order modelling in the control context is presented. Rearranging the classical feedback structure in terms of the equivalent Internal Model Control (IMC) structure allows the designer to incorporate the reduced model directly into the feedback compensator; furthermore, the corrupting effect of the full/reduced model mismatch on closed-loop stability and performance is expressed quantitatively in simple, physically meaningful terms. Secondly, two reduction techniques which consider the closed-loop objective are presented. Both obtain near-optimal models with respect to a user-designated closed-loop performance; the first method finds the model for a known setpoint/disturbance spectrum, the second for the L2 class of inputs. The benefits of these IMC-based approaches over the traditional philosophy of separating the tasks of reduction and control system design are illustrated.