Creating and Manipulating Models | ![]() ![]() |
Padé Approximation of Time Delays
The function pade
computes rational approximations of time delays in continuous-time LTI models. The syntax is
where sys
is a continuous-time model with delays, and the integer n
specifies the Padé approximation order. The resulting LTI model sysx
is of the same type as sys
, but is delay free.
For models with multiple delays or a mix of input, output, and I/O delays, you can use the syntax
where the vectors ni
and no
, and the matrix nio
specify independent approximation orders for each input, output, and I/O delay, respectively. Set ni=[]
if there are no input delays, and similarly for no
and nio
.
For example, consider the Distillation Column Example. The two-input, two-output transfer function in this example is
To compute a Padé approximation of H(s) using:
where H
is the TF representation of defined in the distillation column example. This command produces a rational transfer function.
Transfer function from input "R" to output... -12.8 s + 25.6 Xd: --------------------- 16.7 s^2 + 34.4 s + 2 6.6 s^2 - 5.657 s + 1.616 Xb: --------------------------------------- 10.9 s^3 + 10.34 s^2 + 3.527 s + 0.2449 Transfer function from input "S" to output... 18.9 s - 12.6 Xd: ---------------------- 21 s^2 + 15 s + 0.6667 19.4 s - 12.93 Xb: -------------------------- 14.4 s^2 + 10.6 s + 0.6667
![]() | Retrieving Information About Delays | Simulink Block for LTI Systems | ![]() |