Order reduction for closed-loop systems

Order reduction specifically tailored to dynamic components within a closed- loop system is considered. A simple computational method is proposed that promotes closed-loop stability and performance and directly treats unstable poles in the reduction. The reduction procedure is an extension of the frequency-weighted internally balanced approach, but is capable of approximating unstable components. The weighting strategies used are obtained directly from Nyquist Stability Theory. Multivariable loop shaping techniques yield controller designs which desensitize the closed-loop system to variations of the plant\u27s frequency response at frequencies outside the crossover region of the open-loop system. Order reduction must exploit the desensitizing aspects of feedback which generally means a good frequency response approximation is required, the accuracy of which varies with frequency and is dependent on the existing/purposed closed-loop system. Under these guidelines, a uniform approach is presented for approximating both stable and unstable components of a closed-loop system when (i) all the other components of the closed-loop system are known, and the more difficult, more common situation when (ii) all the other components of the closed-loop system are not known, e.g. plant reduction for the purpose of reduced-order controller synthesis