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

• sysx = pade(sys,n)
  

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

• sysx = pade(sys,ni,no,nio)
  

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:

• A first-order approximation for the 1 second and 3 second delays
• A second-order approximation for the 7 second delay,

type

• pade(H,[],[],[1 1;2 1])
  

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