MATLAB CONTROL SYSTEM TOOLBOX 9 Podręcznik Użytkownika Pobierz pdf (Strona 128)

100

101

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–

3s 10++

-------------------------------

()

1 2 ... 123 124 125 126 127 128 129 130 131 132 133 ... 648 649

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