Simulink Control Design 3.0

Trimming and Linearizing Simulink Models

Trimming the Model

Linear control design typically requires you to consider multiple operating points to account for the various setpoints of a nonlinear model. Simulink Control Design provides a GUI to determine model operating points. You can:

• Calculate operating points from user-defined setpoints using numerical optimization
• Take operating point snapshots at specific times or events during simulation

These operating points can be used to initialize a simulation at steady state or as a basis for linearization and control design.

Linearizing the Model

With Simulink Control Design you can linearize continuous, discrete, and multirate Simulink models. Using graphical signal annotations to specify loop opening and linearization inputs and outputs, you can linearize the whole model, a portion of the model, or a single block or subsystem. The signal annotations can be used for open- and closed-loop analysis. The annotations and analysis are nonintrusive and do not affect your model's simulation behavior.

Simulink Control Design automatically computes the linearized model and lets you visualize the results in a step response plot or Bode diagram. A Linearization Inspector is provided to visualize the impact of each block in your Simulink model on the linearization. You can fine-tune your results by specifying the linear behavior of any number of blocks in your model. The linear behavior can be specified as a matrix gain or LTI model, giving you flexibility to linearize Simulink models containing discontinuities or event-based components, such as Stateflow® charts or pulse-width modulation signal-based systems.

When working with Robust Control Toolbox™, you can compute an uncertain linear model by specifying uncertain values for transfer functions and gains directly in the model. The resulting uncertain linear model can be used to study the impact of uncertainty on the stability and performance of your control system.

All of these tools have a command-line API to write scripts for batch mode trimming and linearization. You can write these scripts yourself or automatically create MATLAB® code from the GUI.

Linearizing the model with Simulink Control Design. You can trim your model at a specific simulation time or operating condition (upper left), linearize it at any of the calculated operating points (upper right), inspect linearization results in the LTI Viewer (lower right), and automatically create MATLAB code from the GUI (lower left).

Computing the Frequency Response of the Model

Simulink Control Design provides tools for the simulation-based computation of a model’s frequency response. You can use these tools to:

• Verify the results of a linearization.
• Compute the model’s frequency response when linearization techniques are not appropriate, such as with models described by strong discontinuities or event-based dynamics.
• Study the effects of excitation signal amplitude on a nonlinear system’s gain and phase characteristics.

Simulink Control Design helps you construct the excitation signals, such as sine sweeps or chirp signals; run the simulations; collect the data; and calculate and plot the model’s frequency response. The algorithms used to compute the frequency response are designed to minimize the simulation time and support the Accelerator and Rapid Accelerator modes in Simulink to speed up the overall computation.

Computing the frequency response of the model. Simulink Control Design provides functions (top) for simulation-based computation of the frequency response (right) of a model (left).