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Using Identified Models for Control Design Applications

How Control System Toolbox Software Works with Identified Models

System Identification Toolbox™ software integrates with Control System Toolbox™ software by providing a plant for control design.

Control System Toolbox software also provides the LTI Viewer GUI to extend System Identification Toolbox functionality for linear model analysis.

Control System Toolbox software supports only linear models. If you identified a nonlinear plant model using System Identification Toolbox software, you must linearize it before you can work with this model in the Control System Toolbox software. For more information, see the linapp, linearize(idnlarx), or linearize(idnlhw) reference page.

    Note:   You can only use the System Identification Toolbox software to linearize nonlinear ARX (idnlarx) and Hammerstein-Wiener (idnlhw) models. Linearization of nonlinear grey-box (idnlgrey) models is not supported.

Using balred to Reduce Model Order

In some cases, the order of your identified model might be higher than necessary to capture the dynamics. If you have the Control System Toolbox software, you can use balred to compute a state-spate model approximation with a reduced model order.

For more information, see balred.

To learn how you can reduce model order using pole-zero plots, see Reducing Model Order Using Pole-Zero Plots.

Compensator Design Using Control System Toolbox Software

After you estimate a plant model using System Identification Toolbox software, you can use Control System Toolbox software to design a controller for this plant.

System Identification Toolbox models in the MATLAB® workspace are immediately available to Control System Toolbox commands. However, if you used the System Identification Tool to estimate models, you must first export the models to the MATLAB workspace. To export a model from the tool, drag the model icon to the To Workspace rectangle.

Control System Toolbox software provides both the SISO Design Tool and commands for working at the command line. You can import linear models directly into SISO Design Tool using the following command:


You can also identify a linear model from measured SISO data and tune a PID controller for the resulting model in the PID Tuner. You can interactively adjust the identified parameters to obtain an LTI model whose response fits your response data. The PID Tuner automatically tunes a PID controller for the identified model. You can then interactively adjust the performance of the tuned control system, and save the identified plant and tuned controller. To access the PID Tuner, enter pidtool at the MATLAB command line. For more information, see PID Controller Tuning.

Converting Models to LTI Objects

You can convert linear identified models into numeric LTI models (ss, tf, zpk) of Control System Toolbox software.

The following table summarizes the commands for transforming linear state-space and polynomial models to an LTI object.

Commands for Converting Models to LTI Objects


Convert to frequency-response representation.

ss_sys = frd(model)

Convert to state-space representation.

ss_sys = ss(model)

Convert to transfer-function form.

tf_sys = tf(model)

Convert to zero-pole form.

zpk_sys = zpk(model)

The following code converts the noise component of a linear identified model, sys, to a numeric state-space model:

noise_model_ss = idss(sys,'noise');

To convert both the measured and noise components of a linear identified model, sys, to a numeric state-space model:

model_ss = idss(sys,'augmented');

For more information about subreferencing the dynamic or the noise model, see Separation of Measured and Noise Components of Models.

Viewing Model Response Using the LTI Viewer

What Is the LTI Viewer?

If you have the Control System Toolbox software, you can plot models in the LTI Viewer from either the System Identification Tool GUI or the MATLAB Command Window.

The LTI Viewer is a graphical user interface for viewing and manipulating the response plots of linear models.

    Note:   The LTI Viewer does not display model uncertainty.

For more information about working with plots in the LTI Viewer, see the Control System Toolbox documentation.

Displaying Identified Models in the LTI Viewer

When the MATLAB software is installed, the System Identification Tool GUI contains the To LTI Viewer rectangle. To plot models in the LTI Viewer, drag and drop the corresponding icon to the To LTI Viewer rectangle in the System Identification Tool GUI.

Alternatively, use the following syntax when working at the command line to view a model in the LTI Viewer:


Combining Model Objects

If you have the Control System Toolbox software, you can combine linear model objects, such as idtf, idgrey, idpoly, idproc, and idss model objects, similar to the way you combine LTI objects. The result of these operations is a numeric LTI model that belongs to the Control System Toolbox software. The only exceptions are the model stacking and model concatenation operations, which deliver results as identified models.

For example, you can perform the following operations on identified models:

  • G1+G2

  • G1*G2

  • append(G1,G2)

  • feedback(G1,G2)

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