Control System Toolbox 8.4

Creating Discrete-Time Models

This demo shows how to create discrete-time linear models using the tf, zpk, ss, and frd commands.

Contents

Specifying Discrete-Time Models

Control System Toolbox™ lets you create both continuous-time and discrete-time models. The syntax for creating discrete-time models is similar to that for continuous-time models, except that you must also provide a sampling time (sampling interval in seconds).

For example, to specify the discrete-time transfer function:

with sampling period Ts = 0.1 s, type:

num = [ 1  -1 ];
den = [ 1  -1.85  0.9 ];
H = tf(num,den,0.1)

Transfer function:
      z - 1
------------------
z^2 - 1.85 z + 0.9

Sampling time: 0.1

or equivalently:

z = tf('z',0.1);
H = (z - 1) / (z^2 - 1.85*z + 0.9);

Similarly, to specify the discrete-time state-space model:

with sampling period Ts = 0.1 s, type:

sys = ss(.5,1,.2,0,0.1);

Recognizing Discrete-Time Systems

There are several ways to determine if your LTI model is discrete:

For example, for the transfer function H specified above,

H.Ts

ans =

    0.1000

isdt(H)

ans =

     1

You can also spot discrete-time systems by looking for the following traits:

The following plots show these characteristic traits:

step(H)

bode(H), grid