Models with Time Delays

Choose Approximate Versus Exact Time Delays

Simulink^® Control Design™ lets you choose whether to linearize models using exact representation or Pade approximation of continuous time delays. How you treat time delays during linearization depends on your nonlinear model.

Simulink blocks that model time delays are:

• Transport Delay block

• Variable Time Delay block

• Variable Transport Delay block

• Delay block

• Unit Delay block

By default, linearization uses Pade approximation for representing time delays in your linear model.

Use Pade approximation to represent time delays when:

• Applying more advanced control design techniques to your linear plant, such as LQR or H-infinity control design.

• Minimizing the time to compute a linear model.

Specify to linearize with exact time delays for:

• Minimizing errors that result from approximating time delays

• PID tuning or loop-shaping control design methods in Simulink Control Design

• Discrete-time models (to avoid introducing additional states to the model)

  The software treats discrete-time delays as internal delays in the linearized model. Such delays do not appear as additional states in the linearized model.

Specify Exact Representation of Time Delays

Before linearizing your model:

• In the Model Linearizer:

  1. On the Linear Analysis tab, click More Options.

  2. In the Options for exact linearization dialog box, in the Linearization tab, check Return linear model with exact delay(s).

• At the command line, create a linearizeOptions option set, setting the UseExactDelayModel to 'on'.