`padecoef`

Coefficients of a Pade approximation of a time delay.

Syntax

[num, den] = padecoef(T)

First-order Pade approximation of the delay exp(-T*s).

[num, den] = padecoef(T, N)

Approximation of order N.

Description

A pure delay exp(-T*s) is not a rational function, so control tools replace it by a ratio of polynomials that matches the delay's Taylor series up to a given order. padecoef returns that ratio as two coefficient vectors.

For N = 1 the result is (1 - T*s/2) / (1 + T*s/2), scaled to a monic denominator. The approximation is accurate at low frequency and has unit gain at all frequencies; higher N extends the range of good accuracy.

Input arguments

T: Length of the time delay, a non-negative scalar.
N: Order of the approximation (default 1).

Output arguments

num: Numerator coefficients in descending powers of s.
den: Denominator coefficients in descending powers of s.

Example

Second-order approximation of a 1 s delay

[num, den] = padecoef(1, 2)

Output

num = 1×3

     1    -6    12
den = 1×3

     1     6    12

padecoef