Integral Backstepping Sliding Mode Control of Chaotic Forced Van Der Pol Oscillator

Abstract

Forced Van der Pol oscillator exhibits chaotic behaviour and instability under certain parameters and this poses a great threat to the systems where it has been applied hence, the need to develop a control method to stabilize and control chaos in a Forced Van der Pol oscillator so as to avoid damage in the controlled system and also to prevent unmodeled dynamics from being introduced in the system. Sliding Mode control makes use of the regulatory variables derived from the controlled Lyapunov function to bring the new variables to stability. The essence of using Integral Backstepping was to prevent chattering which can occur in the control input and can cause instability to the system by igniting unmodeled dynamics. Simulation was done using MATLAB and the results were provided to show the effectiveness of the proposed control method. Integral Backstepping Sliding Mode control method was effective towards stability and chaos control. It was also robust towards matched and unmatched disturbance.