Simulink Control Design™ - MathWorks

Linearize Model

After you specify a steady-state operating point and linear analysis points, you can
linearize your Simscape model using:

• The Linear Analysis Tool.


• The linearize function.


• An slLinearizer interface.

For general linearization examples, see “Linearize Simulink Model at Model Operating
Point” on page 2-74 and “Linearize at Trimmed Operating Point” on page 2-90.

Troubleshoot Simscape Network Linearizations

Simscape networks can commonly linearize to zero when a set of the system equation
Jacobians are zero at a given operating condition. Usually, poor initial conditions of the
network states cause these zero linearizations.

Zero Linearization Example

Consider a system where the mass flow rate from a variable orifice is controlling the
position of a piston. The mass flow rate equation of the variable orifice is:

q=CdA

2

μ

p

p^2 +pcr^2

0.25

Where:

• q is the mass flow rate.


• Cd is the discharge coefficient.


• A is the area of the variable orifice opening.


• μ is the fluid density.


• p is the pressure drop across the orifice, p = pa - pb.


• pcr is the critical pressure, which is a function of pa and pb.

The control variable for this system is the orifice area, A, which controls the mass flow
rate. The Jacobian of the mass flow rate with respect to the control variable is:

Linearize Simscape Networks......................... 2-