Use of B-splines to obtain accurate transient responses for feedback control systems with time delays

This paper is concerned with representing the transient time response of a closed-loop control system having pure and/or distributed time delays in terms of B-spline series. More precisely, it regards to the inversion of Laplace transforms of irrational type with the B-spline series expansion approach. The B-spline series for a time function f(t) with t greater than or equal to 0 contains first several terms in boundary splines and the remaining terms in interior B-splines. It is shown that by matching the initial conditions of the response exactly, the coefficients associated with the interior B-splines can be accurately obtained by a computationally efficient FFT-based algorithm.