Below are the equations for a nonlinear system.
1. Below are the equations for a nonlinear system. This set of equations describes a Vanderpol model. Generate a simulink model to analyze this system. The equations are:
x+(x2-1)x+x=0
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x |
2 |
=x; x |
2 |
( |
0 |
=1 |
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) |
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x2 |
=x1 |
x |
1 |
( |
0 |
=1 |
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) |
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x= 1-x2 |
x-x |
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( |
) |
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1 |
2 |
1 |
2 |
Generate plots of x1 vs. time, x2 vs. time, and x1 vs. x2. Note that you need to use an integrator with an initial condition. Investigate the use of the xy plotter in the sink folder to generate the x1 vs. x2 plot.
If you save the model as vdpol.mdl, the following will permit you to solve the model from the command line. Put out the variables x1 and x2 to the workspace in an 2-D array.
Investigate the options of simulink using
>> options=simset; % generates the default options
>> options=simset('MaxStep',1,'MinStep',1e-5,'AbsTol',1e-3); % sets the options
>> [t,xv]=sim('vdpol',tf,options);% tf is the time for the simulation. Choose tf=10 and repeat for tf =50. The vector t is the time vector and xv is the 2-D array that contains the data.
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Solution: Below are the equations for a nonlinear system.