control.matlab.pade

control.matlab.pade(T, n=1, numdeg=None)[source]

Create a linear system that approximates a delay.

Return the numerator and denominator coefficients of the Pade approximation.

Parameters

  • T (number) – time delay

  • n (positive integer) – degree of denominator of approximation

  • numdeg (integer, or None (the default)) – If numdeg is None, numerator degree equals denominator degree. If numdeg >= 0, specifies degree of numerator. If numdeg < 0, numerator degree is n+numdeg.

Returns

num, den – Polynomial coefficients of the delay model, in descending powers of s.

Return type

array

Notes

Based on:

  1. Algorithm 11.3.1 in Golub and van Loan, “Matrix Computation” 3rd. Ed. pp. 572-574

  2. M. Vajta, “Some remarks on Padé-approximations”, 3rd TEMPUS-INTCOM Symposium

Examples

>>> delay = 1
>>> num, den = ct.pade(delay, 3)
>>> num, den
([-1.0, 12.0, -60.0, 120.0], [1.0, 12.0, 60.0, 120.0])

>>> num, den = ct.pade(delay, 3, -2)
>>> num, den
([-6.0, 24.0], [1.0, 6.0, 18.0, 24.0])