Model reduction with a finite-interval H criterion

Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 145)


An important problem in flight control and flying qualities is the approximation of a complex high order system by a low order model. In this chapter, for a given reduced order model, we define the correlation measure between the plant and the model outputs to be the minimum of the ratio of weighted signal energy to weighted error energy. We give a criterion for the evaluation of the correlation measure in terms of minimization of a parameter occurring in a two-point boundary value problem. Once the correlation measure for a given reduced order model can be evaluated, a nonlinear programming algorithm can be used to select a model which maximizes the correlation between the plant and model outputs. The correlation index used can be regarded as an extension of the H performance criterion to the finite-interval time-varying case. However, the usual H problem seeks an optimal controller, whereas our problem is to select the reduced order model matrices which give the best correlation index. We also give an expression for the variation of the correlation owing to parameter variations and pose a robust model reduction problem. The utilization of the theory is demonstrated by means of some examples. In particular, a problem which involves the reduction of an unstable aircraft model with structural modes is worked out.


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© Springer-Verlag 1990

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