Simulink Control Design™ - MathWorks

Exact Linearization Algorithm

Simulink Control Design software linearizes models using a block-by-block approach. The

software individually linearizes each block in your Simulink model and produces the

linearization of the overall system by combining the individual block linearizations.

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 finds the

linearization by perturbing the block inputs and states and measuring the response to

these perturbations. For more information, see “Perturbation of Individual Blocks” on

page 2-220.

Continuous-Time Models

Simulink Control Design software lets you linearize continuous-time nonlinear systems.

The resulting linearized model is in state-space form.

In continuous time, the state space equations of a nonlinear system are:

x ̇(t) =fx(t),u(t),t

y(t) =gx(t),u(t),t

where x(t) are the system states, u(t) are the input signals, and y(t) are the output signals.

To describe the linearized model, define a new set of variables of the states, inputs, and

outputs centered about the operating point:

2 Linearization