Realization of Dead-Time Using Pad^|^eacute; Approximants and Continued Fractions

Abstract

Padé approximants of exp(-sT) have been widely used to realize dead-time elements. The companion form realization, however, is numerically ill behaved, if we use a high order approximant, because coefficients of lower order terms of the monic denominator polynomial become very large. In this paper, the realization based on Cauer type continued fraction expansion is shown to be well behaved. A simple method of getting coefficients of the expansion of the Padé approximant, using the continued fraction expansion of the exponential function, is proposed. By simulation, it is shown that the ballancing of the overshoot and the undershoot is attained if we choose the degree L of the mumerator smaller 2 to 5 than the degree M of the denominator, and that the rise time is inversely proportional to L+M.