User`s guide

Time Delays
2-55
channel delays. The resulting model has a minimum number of delays. When
this minimization takes place:
• All orpartof theI/O delaymatrixis absorbedinto the input andoutputdelay
vectors. This minimizes the total number of I/O delays.
• The input delays are transferred to output delays (or vice-versa), so as to
minimize the overall number of input and output channel delays.
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 o f input, output, and I/O delays, y ou
can use the syntax
sysx = pade(sys,ni,no,nio)
where the vectors ni and no,andthematrixnio specify independent
approximation orders for each input, output, and I/O delay, respectively. Set
ni=[] if there are no input delays, and similarly f or no and nio.
For example, consider the “Distillation Column Example” on page 2-47. 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,
Hs()
12.8e
1s–
16.7e 1+
------------------------
18.9 e
3s–
–
21.0s 1+
-------------------------
6.6e
7s–
10.9s 1+
------------------------
19.4 e
3s–
–
14.4s 1+
-------------------------
=