Specifications

pade
16-165
16pade
Purpose Compute the Padé approximation of models with time delays
Syntax [num,den] = pade(T,N)
pade(T,N)
sysx = pade(sys,N)
sysx = pade(sys,NI,NO,Nio)
Description pade approximates time delays by rational LTI models. Such approximations
are useful to model time delay effects such as transport and computation
delays within the context of continuous-time systems. The Laplace transform
of an time delay of seconds is . This exponential transfer function
is approximated by a rational transfer function using the Padé approximation
formulas [1].
[num,den] = pade(T,N) returns the Nth-order(diagonal) Padéapproximation
of the continuous-time I/O delay in transfer function form. The row
vectors
num and den contain the numerator and denominator coefficients in
descending powers of . Both are
Nth-order polynomials.
When invoked without output arguments,
pade(T,N)
plots the step and phase responses of the Nth-order Padé approximation and
compares them with the exact responses of the model with I/O delay
T.Note
that the Padé approximation has unit gain at all frequencies.
sysx = pade(sys,N) produces a delay-free approximation sysx of the
continuous delay system
sys. All delays are replaced by their Nth-order Padé
approximation. See Time Delays for details on LTI models with delays.
sysx = pade(sys,NI,NO,Nio) specifies independent approximation orders for
each input, output, and I/O delay. These approximation orders are given by the
arrays of integers
NI, NO,andNio,suchthat:
•
NI(j) is the approximation order for the j-th input channel.
•
NO(i) is the approximation order for the i-th output channel.
•
Nio(i,j) is the approximationorderfor the I/O delay from input j to output
i.
TsT–
()
exp
sT–
()
exp
s