The stability equation method for obtaining reduced order Pade models may approximate the nondominant poles of the system, thus giving bad approximations. A modified method is given that overcomes the above drawback.

Improved Padé approximants using stability equation method

The Routh-Pade approximation problem relating to the construction of a stable reduced-order (rth-order) approximant Gr(s) for a given stable high-order (nth-order) transfer function G(s), so as to fully retain the first r time moments/Markov parameters of G(s) as well as to minimise the errors between a few subsequent time moments/Markov parameters of G(s) and those of Gr(s), is revisited. For the solution of this problem, a novel computer-aided method based on the well known Luus-Jaakola algorithm is proposed.

Obtaining Routh-Pade approximants using Luus-Jaakola algorithm

This work describes a novel method for the reduction of S1SO continuous models. The proposed method, the least squares Pade (LS-Pade) method, provides reduced models which incorporate some information about the original model over the mid-frequency range. Consequently, the present method gives better results than the classical Pade and most of the related methods for a very small additional cost

The least squares Padé method for model reduction

A computer-aided method for obtaining a reduced-order approximant of a given (stable) single-input single-output system based on the minimisation of integral squared error (ISE) pertaining to a unit-step input is presented. Both the numerator and denominator coefficients of the model are treated as free parameters in the process of optimisation. The method has a built-in stability-preserving feature. The problem of formulating the ISE is circumvented by introducing a set of equality constraints.

Optimal Routh approximants through integral squared error minimisation: computer-aided approach

Obtaining Routh-Pade approximants using the Luus-Jaakola algorithm

The letter highlights the significance of matching the terms of expansions around several points including s=0 and s=∞ in realising improved overall time-response approximation.

N. Ashoor

Papers

Remarks on system simplification under consideration of time responses