Non-linear Control Assignment: R J Patton
The Van der Pol oscillator
..
.
x +  ( x 2 − 1) x + x = 0
 0
has limit cycle behaviour.
(a) Simulate this system using Matlab/Simulink for various initial conditions x(0),
demonstrating the limit cycle time behaviour around the amplitude A = 2 and frequency
 = 1 . The oscillation can be considered to be approximated by x = A sin ( t ) .
It will be helpful to represent the oscillator by two state equations, x1 = x2 , etc.
(b) By devising a method of estimating the frequency  use your simulation to investigate
what happens when the parameter  is varied over the range 0.5, 1.0, 5, 10, 20, 100
(c) Use a simple stability analysis (based on the lecture note) to determine the limit cycle
stability for   0
Your solutions should be well explained, with suitable code and diagrams and with careful
justification of the results.