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, x1 = 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.