A Frequency Domain Model-Order-Deduction Algorithm for Linear Systems

During the system design process engineers must choose the appropriate order of a model of a system of components, which is accomplished by determining the appropriate order of the component submodels. Several researchers have developed model-order-deduction algorithms, under the assumption that algorithms for synthesizing component submodels are available. Thus the issue of determining appropriate submodel order has been a principal topic. In previous efforts the primary means to determine model order adequacy has been to focus on the eigenvalues of the model. One algorithm, the model-order deduction algorithm (MODA), systematically increases the order of the system model until any subsequent increase results in adding system eigenvalues of magnitude outside a user-specified frequency range of interest [0, ωmax]. Another algorithm, EXTENDED-MODA, begins with the same model that MODA synthesizes and increases the order further until the |λi| ∈ [0, ωmax] settle within some specified tolerance. In this paper we develop a new algorithm, FD-MODA, that uses the convergence of the model in the frequency domain as its performance metric. The model’s frequency response is based on zeros and poles (eigenvalues) of the system model, so it provides a more comprehensive indication of model performance than just the eigenvalues. It also seems to be more meaningful in the context of frequency-domain controller design methods, e.g. H∞ optimization. FD-MODA’s use is illustrated with two examples, and its efficacy in selecting an appropriate combination of component submodels is thereby demonstrated. In addition to using a broader performance metric than previous algorithms, FD-MODA also provides visual feedback – frequency response plots – of model convergence that are more indicative of model performance than a map of pole locations in the s-plane. We thus conclude that by focusing on frequency response as a model performance metric FD-MODA provides a useful and direct means of coordinating the automated model synthesis process.