Approximations for Z(G(s)F(s)) Adjusted for Unit Step Response via Residues

摘要

Using an approximate for zG(s)F(s) based upon the second order Runge-Kutta integrator family, a recurrence for a single real pole filter was developed. The recurrence is exact for any size time step when the input is a damped exponential with identical time constant. The unit step into a single integrator is just a special case. A residue is then introduced into the real pole filter so that the recurrence is exact for a unit step input and any size time step. (Author)