Control-relevant model reduction problems for SISO H₂, H_∞, and μ-controller synthesis

The problem of model reduction in the context of control system design is investigated. Starting from closed-loop objectives (H₂, H_∞, and μ), equivalent weighted open-loop plant and controller reduction problems are developed. The control-relevant weight function incorporates explicitly all the important characteristics of the control problem, such as the setpoint/disturbance spectrum and the designer requirements for the sensitivity/complementary sensitivity functions, Furthermore, these control-relevant reduction problems are complemented with validation procedures that indicate rigorously the effects of the reduction problem on the desired performance objectives. A simple algorithm that uses standard regression routines is presented to solve these problems.