Simulink Control Design™ - MathWorks

The software determines the input and state levels for each block from the operating

point, and requests the Jacobian for these levels from each block.

For some blocks, the software cannot compute an analytical linearization. For example:

• Some nonlinearities do not have a defined Jacobian.


• Some discrete blocks, such as state charts and triggered subsystems, tend to linearize
  to zero.


• Some blocks do not implement a Jacobian.


• Custom blocks, such as S-Function blocks and MATLAB Function blocks, do not have
  analytical Jacobians.

You can specify a custom linearization for any such blocks for which you know the

expected linearization. If you do not specify a custom linearization, the software linearizes

the model by perturbing the block inputs and states and measuring the response to these

perturbations. For each input and state, the default perturbation level is 10 −^5 1+x ,

where x is the value of the corresponding input or state at the operating point. For

information on how to change perturbation levels for individual blocks, see “Change

Perturbation Level of Blocks Perturbed During Linearization” on page 2-191.

For more information, see “Linearize Nonlinear Models” on page 2-3 and “Exact

Linearization Algorithm” on page 2-218

Full-Model Numerical Perturbation

You can linearize your system using full-model numerical perturbation, where the

software computes the linearization of the full model by perturbing the values of root-

level inputs and states. To do so, create a linearizeOptions object and set the

LinearizationAlgorithm property to one of the following:

• 'numericalpert' — Perturb the inputs and states using forward differences; that is,
  by adding perturbations to the input and state values. This perturbation method is
  typically faster than the 'numericalpert2' method.


• 'numericalpert2' — Perturb the inputs and states using central differences; that is,
  by perturbing the input and state values in both positive and negative directions. This
  perturbation method is typically more accurate than the 'numericalpert' method.

For each input and state, the software perturbs the model and computes a linear model

based on the model response to these perturbations. You can configure the state and

input perturbation levels using the NumericalPertRel linearization options.

15 Alphabetical List