Linearization Options

Accessing Linearization Options

If you have Simulink® Control Design™, you can set several options for linearization. These options include the linearization methods and the sample time of the linear systems.

To set linearization options, click Options in the Response Optimization tool. A window opens. Select the Linearization Options tab.

Configuring Linearization Options

Models with 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 How Delays are Treated.  To specify whether the linearization should approximate delays or use them exactly, set the Use exact delays check box appropriately.

Linearization Sampling Time

To specify the sampling time of the linearized model, use the Linear system sample time box. By default, the software chooses the slowest applicable sampling time. Use 0 to specify a continuous-time linear model.

Linearization Rate Conversion Method

When you linearize models with multiple sample times, such as a discrete controller with a continuous plant, a rate conversion algorithm generates a single-rate linear model. The rate conversion algorithm affects linearization results.

Rate Conversion MethodWhen to Use
Zero-Order HoldUse when you need exact discretization of continuous dynamics in the time-domain for staircase inputs.
TustinUse when you need good frequency-domain matching between a continuous-time system and the corresponding discretized system, or between an original system and the resampled system.
Tustin with PrewarpingUse when you need good frequency domain matching at a particular frequency between the continuous-time system and the corresponding discretized system, or between an original system and the resampled system.
Upsampling when possible (Zero-Order Hold, Tustin, and Tustin with Prewarping)Upsample discrete states when possible to ensure gain and phase matching of upsampled dynamics. You can only upsample when the new sample time is an integer multiple of the sample time of the original system. Otherwise, the software uses an alternate rate conversion method.

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