Plant and Controller Reduction Problems for Closed-Loop Performance

Model reduction problems which consider preserving closed-loop performance (H2, H∞, and μ) in the presence of reduction error are developed. These are formulated as weighted multiplicative error problems (for plant reduction) and weighted additive error problems (for controller reduction), with the weight function incorporating explicitly such control information as the desired sensitivity operator bound, the setpoint/disturbance spectrum, and the plant uncertainties. These problems are efficiently solved using the frequency-weighted balanced realization technique. The benefits of these reduction problems are illustrated with examples taken from the control of a binary distillation column.