A Study on Static Compensation in the Galerkin Approximation Method for a class of Distributed Systems

Abstract

To achieve a reasonable controller design for a distributed parameter system, a low order finite dimensional approximation model is indispensable which adequately reflects principal characteristics of the plant.
In this paper we consider an approximation scheme, based on the Galerkin criterion, for linear stable timeinvarient distributed parameter systems. First, we illustrate the construction of the model via the Galerkin method employing a trial function with a force term. Next, we show that the static error of the model can be compensated and reduced to zero by using a function from steady-state step response in the force term, and that the reduced order finite dimensional model has frequency response which is consistent with the original one in a wider range.
A numerical study for an example shows the merit of the scheme in terms of the error plot in frequency domain. We demonstrate the feasibility by considering the achievable control performance in designing a compensator based on the model with the static compensation.