Abstract
Though the state of the system with time-delay is infinite demensional, only a finite number of data can be handled in a practical calculation of the feedback control variable. Thus a problem of approximating an infinite dimensional state vector by a finite dimensional one, which preserves, in some sense, the essential information on the state, becomes important. In other words, it is a problem of the best approximation of a system with time-delay by a lumped parameter system. In this paper, the approximation of this sort by applying the method of weighted residuals is discusses. In order to measure the goodness of approximation, the location of eigenvalues and the shape of transient responses of the approximated lumped parameter system are compared to those of the original system with time-delay. From the numerical analysis on the several typical examples, it is shown that the method of weighted residuals gives results superior to those given by a commonly used simple difference method of the same approximation degree.
