control.pade

control.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 of the given order.

Parameters

Tnumber: Time. delay
npositive integer: Degree of denominator of approximation.
numdeginteger, 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, denndarray: Polynomial coefficients of the delay model, in descending powers of s.

Notes

Based on [1] and [2].

References

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])