Simulink Control Design™ - MathWorks

δx(t) =x(t)−x 0

δu(t) =u(t)−u 0

δy(t) =y(t)−y 0

The linearized model in terms of δx, δu, and δy is valid when the values of these variables
are small:

δx ̇(t) =Aδx(t)+Bδu(t)

δy(t) =Cδx(t)+Dδu(t)

Applications of Linearization

Linearization is useful in model analysis and control design applications.

Exact linearization of the specified nonlinear Simulink model produces linear state-space,
transfer-function, or zero-pole-gain equations that you can use to:

• Plot the Bode response of the Simulink model.


• Evaluate loop stability margins by computing open-loop response.


• Analyze and compare plant response near different operating points.


• Design linear controller

Classical control system analysis and design methodologies require linear, time-

invariant models. Simulink Control Design automatically linearizes the plant when you

tune your compensator. See “Choose a Control Design Approach” on page 9-2.

• Analyze closed-loop stability.


• Measure the size of resonances in frequency response by computing closed-loop linear
  model for control system.


• Generate controllers with reduced sensitivity to parameter variations and modeling
  errors.

Linearization in Simulink Control Design

You can use Simulink Control Design software to linearize continuous-time, discrete-time,
or multirate Simulink models. The resulting linear time-invariant model is in state-space
form.

Linearize Nonlinear Models