Control System Toolbox 8.4

Introduction to the Control System Toolbox - 3 - Connecting Linear Time-Invariant (LTI) Models

In this demo, we'll use the Control System Toolbox to create linear time-invariant (LTI) models. The Control System Toolbox provides a number of functions for building complex networks of models. These include functions to perform:

Contents

Connecting Models

Let's start by looking at some of the connecting schemes we can set up using the Control Systems Toolbox.

Figure 1: Various connecting schemes that you can set up.

Series Connections

We can connect models H1 and h3 in series using:

H = series(H1,h3);

A series connection is equivalent to the product of the models:

H = h3 * H1;

Figure 2: Series connection.

Parallel Connection

We can connect models H1 and h3 in parallel using:

H = parallel(H1,h3);

A parallel connection is equivalent to the sum of the models:

H = h3 + H1;

Figure 3: Parallel connection.

Feedback Connection

We can connect models H1 and h3 in a feedback configuration using:

H = feedback(H1,h3);

To apply positive feedback, use the syntax:

H = feedback(H1,h3,+1);

Figure 4: Feedback connection.

Summing Outputs

We can sum the outputs of models H1 and h3 using:

H = [ H1 , h3 ];

In matrix notation, this connection is equivalent to the horizontal concatenation of these models. Note that if H1 and h3 are SISO models, then the concatenated model H is a MIMO model with two inputs and one output.

Figure 5: Summing outputs.

Distributing Inputs

We can distribute inputs to models H1 and h3 using:

H = [ H1 ; h3 ];

In matrix notation, this connection is equivalent to the vertical concatenation of these models. Note that if H1 and h3 are SISO models, then the concatenated model H is a MIMO model with one input and two outputs.

Figure 6: Distributing inputs.

Appending Models

We can append the inputs and outputs of models H1 and h3 using

sys = append(H1,h3);

In matrix notation, this connection is equivalent to the block-diagonal concatenation of these models. Note that if H1 and h3 are SISO models, then the concatenated model H is a MIMO model withtwo inputs and two outputs.

Figure 7: Appending models.

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: