Specifications

Linearize Simulink Models
2-21
Linearize Simulink Models
Generally, real systems are nonlinear. To design an MPC controller for a nonlinear
system, you must model the plant in Simulink.
Although an MPC controller can regulate a nonlinear plant, the model used within the
controller must be linear. In other words, the controller employs a linear approximation
of the nonlinear plant. The accuracy of this approximation significantly affects controller
performance.
To obtain such a linear approximation, you linearize the nonlinear plant at a specified
operating point. The Simulink environment provides two ways to accomplish this:
• “Linearization Using MATLAB Code” on page 2-21
• “Linearization Using Linear Analysis Tool in Simulink Control Design” on page
2-24
Note: Simulink Control Design™ software must be installed to linearize nonlinear
Simulink models.
Linearization Using MATLAB Code
This example shows how to obtain a linear model of a plant using a MATLAB script.
For this example the CSTR model, CSTR_OpenLoop, is linearized. The model inputs
are the coolant temperature (manipulated variable of the MPC controller), limiting
reactant concentration in the feed stream, and feed temperature. The model states are
the temperature and concentration of the limiting reactant in the product stream. Both
states are measured and used for feedback control.
Obtain Steady-State Operating Point
The operating point defines the nominal conditions at which you linearize a model. It is
usually a steady-state condition.
Suppose that you plan to operate the CSTR with the output concentration, C_A, at
. The nominal feed concentration is , and the nominal feed
temperature is 300 K. Create an operating point specification object to define the steady-
state conditions.