MATLAB CONTROL SYSTEM TOOLBOX 9 Guía de usuario descargar pdf (Pagina 97)

100

101

Time Delays

2-53

produces the discrete-time transfer function

Transfer function:

z^(–3) * -----------------

z^2 + 0.5 z + 0.2

Sampling time: 0.1

Notice the z^(–3) factor reflecting the three-sampling-period delay on the

input.

Mapping Discrete-Time Delays to Poles at the Origin

Since discrete-time delays are equivalent to additional poles at ,they can

be easily absorbed into the transfer function denominator or the state-space

equations. For example, the transfer function of the delayed integrator

You can specify this model either as the first-order transfer function

with a delay of two sampling periods on the input

Ts = 1; % sampling period

H1 = tf(1,[1 –1],Ts,'inputdelay',2)

or directly as a third-order transfer function:

H2 = tf(1,[1 –1 0 0],Ts) % 1/(z^3–z^2)

While these two models are mathematically equivalent, H1 is a more efficient

representation both in terms of storage and subsequent computations.

When necessary, you can map all discrete-time delays to poles at the origin

using the command

delay2z. For example,

H2 = delay2z(H1)

z 0

yk 1

+[]

[]

uk 2

–[]+=

Hz()

–

z 1–

------------=

1 z 1

–()⁄

1 2 ... 92 93 94 95 96 97 98 99 100 101 102 ... 648 649

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