User`s guide

Time Delays
2-45
Time Delays
Using the ioDelayMatrix, InputDelay,andOutputDelay properties of LTI
objects,youcanspecifydelaysinbothcontinuous-anddiscrete-timeLTI
models. Wit h these properties, you can, for example, represent:
• LTI models with independent delays for each input/output pair. For
example, the continuous-time model with transfer function
• State-space models with delayed inputs and/or d elayed outputs. For
example,
where is the t ime delay between the input and the state vector ,
and is the time delay between and the output .
You can assig n the delay properties
ioDelayMatrix, InputDelay,and
OutputDelay either when first creating your model with the tf, zpk, ss,orfrd
construct ors , or later with theset command(see“LTIPropertiesandMethods”
on page 2-4 for details).
Supported Functionality
Most analysis commands support time delays, including:
• All time a nd frequency response comma nds
• Conversions between model t ypes
• Continuous-to-discrete conversions (
c2d)
• Horiz on tal and ve r tical concatenation
• Series , parallel, a nd feedback inte rconne ctio ns of d is cre te -t ime mode ls with
delays
Hs()
e
0.1s–
2
s
---
e
0.3s–
s 1+
s 10+
---------------
10 e
0.2s–
s 1–
s 5+
------------
=
x
·
t() Ax t() Bu t τ–()+=
yt() Cx t θ–()Du t θτ+()–()+=
τ
ut
()
xt
()
θ
xt
()
yt
()