Control System Toolbox 8.4

Introduction to the Control System Toolbox - 5 - Converting Between Continuous and Discrete Models

In this demo, we'll use the Control System Toolbox to convert between continuous-time and discrete-time systems. We'll use several of the conversion methods the toolbox supports:

Contents

Introduction

This diagram the conversion process we will be discussing.

GSC2DConversions_aux(1); % Draw Diagram

Figure 1: Continuous/Discrete Conversions.

Performing Continuous/Discrete Conversions

The function C2D converts TF, ZPK, and SS models from continuous time to discrete time equivalents. Conversely, the function D2C converts these models from discrete time to continuous time equivalents.

We'll use these commands to perform basic zero-order hold conversions:

sysd = c2d(sysc,Ts); % Ts = sampling period in seconds

sysc = d2c(sysd);

We can specify alternative conversion methods with an extra string input

sysd = c2d(sysc,Ts,Method);

sysc = d2c(sysd,Method);

where Method can be 'zoh', 'foh', 'tustin', 'prewarp', or 'matched'.

GSC2DConversions_aux(2); % Draw Diagram

Figure 2: Continuous/Discrete Conversions

Example: Making a Continuous-to-Discrete Conversion

In this code example, we'll discretize a continuous-time model with a 0.1 second sampling time as follows:

sysc = tf([1 0.5 100],[1 5 100]) % Create continuous transfer-function

 
Transfer function:
s^2 + 0.5 s + 100
-----------------
 s^2 + 5 s + 100
 

sysd = c2d(sysc,0.1)    % Uses zero-order hold 
                        % to discretize the continuous system

 
Transfer function:
z^2 - 1.181 z + 0.9047
-----------------------
z^2 - 0.8828 z + 0.6065
 
Sampling time: 0.1

You can compare the step responses of these systems using the step function:

step(sysc,'b',sysd,'r')

Figure 3: Step Response of continuous and discrete verions of a system

Additional Information

For more information on feedback control design with the Control System Toolbox, see the Control System Toolbox product information page.

From here you can download a free 30-day trial, read the documentation and user stories, request more information, and get pricing information. See these additional demos of Control System Toolbox functionality: