Simulink Control Design 3.0

Linearization of Pneumatic System at Simulation Snapshots

Contents

This is a demonstration of the use of the time based operating point snapshot feature in Simulink® Control Design™. This demo uses a model of the dynamics of filling a cylinder with compressed air.

Pneumatic System Demo

scdpneumaticlin

Get the Initial Simulation

[t,x,y] = sim('scdpneumaticlin');

Embedded MATLAB parsing for model "scddemolib"...Done
Embedded MATLAB code generation for model "scddemolib"....Done
Embedded MATLAB compilation for model "scddemolib"...Done
Embedded MATLAB parsing for model "scdpneumaticlin"...Done
Embedded MATLAB code generation for model "scdpneumaticlin"...Done
Embedded MATLAB compilation for model "scdpneumaticlin"...        1 file(s) 
copied.
Done

Plot the Simulation Results

In this example, the supply pressure is closed and the system has an initial pressure of 0.2 MPa. The supply pressure is at 0.7 MPa and in the simulation the servo valve is opened to 0.5e-4 m. During the simulation, the pressure increases from the initial pressure of 0.2 MPa and eventually settles at the supply pressure.

plot(t,y);

Gathering Simulation Snapshots

To get operating point snapshots at various instants of the simulation use

op = findop('scdpneumaticlin',[0 10 20 30 40 50 60]);

The operating points are a vector that can be accessed using

op(2)

 Operating Point for the Model scdpneumaticlin.
 (Time-Varying Components Evaluated at time t=1.056031e+001)

States:
----------
(1.) scdpneumaticlin/Cylinder Pressure Model/dPc//dt
      x: 3.1e+005
(2.) scdpneumaticlin/Pipe Model/dPp//dt
      x: 3.11e+005

Inputs: None
----------

The operating point is now ready for linearization. First specify the input and output points using the commands:

io(1) = linio('scdpneumaticlin/x',1,'in');
io(2) = linio('scdpneumaticlin/Cylinder Pressure Model',1,'out');

Linearize the model and plot the Bode plot for each condition to see the variablity in the linearizations.

sys = linearize('scdpneumaticlin',op,io);
bode(sys)

bdclose('scdpneumaticlin')