Computation of optimal reduced-order models with time delay

Abstract

This paper considers the problem of optimally approximating high-order transfer functions by low-order ones with a time delay. The performance index used for optimization is the integral of squared error (ISE) between the unit-step responses of the reduced-order and original transfer functions. To facilitate using gradient-based methods to search optimal model parameters, an effective numerical method is adapted for evaluating the ISE and its gradient with respect to parameters. The method is based on using Parseval's identify and the variable transformation ▪, such that the accurate evaluation of ISE involving time delay is performed via solving a first-order differential equation. In determining the optimal denominator polynomial for the reduced-order transfer function, the Routh stability parameters rather than the polynomial coefficients are searched. Such a substitution avoids the effort of stability check at each iteration of parameter search.