User`s guide

3 Operations on LTI Models
3-24
Discretization of Systems with Delays
You can also use c2d to discretize SISO or MIMO continuous-time models with
time delays. If
Ts is the sampling period used for discretization:
• A delay of
tau seconds in the continuous-time model is mapped to a delay of
k sampling periods in the discretized model, where k = fix(tau/Ts).
• The residual fractional delay
tau – k*Ts is absorbed into the coefficients of
the discretized model (for the zero-order-hold and first-order-hold methods
only).
For example, to discretize the transfer f unction
using zero-order hold on the input, and a 10 Hz sampling rate, type
h = tf(10,[1 3 10],'inputdelay',0.25);
hd = c2d(h,0.1)
This produces the discrete-time transfer function
Transfer function:
0.01187 z^2 + 0.06408 z + 0.009721
z^(–2) * ----------------------------------
z^3 – 1.655 z^2 + 0.7408 z
Sampling time: 0.1
Here t he input delay in amounts to 2.5 times the sampling period of 0.1
seconds. Accordingly, the discretized model
hd inherits an input delay of two
sampling periods, as confirmed by the value o f
hd.inputdelay.Theresidual
half-perio d delay is facto red into the coef fic ient s of
hd by the discretization
algorithm.
Hs() e
0.25s–
10
s
2
3s 10++
-------------------------------
=
Hs
()