Mohammed Alghassab^1,2*, Amr Mahmoud¹, Mohamed A. Zohdy¹

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¹ Electrical and Computer Engineering Department, Oakland University, Rochester, MI, USA.
² College of Engineering, Shaqra University, Riyadh, Saudi Arabia.
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Abstract: This paper discusses a novel technique and implementation to perform nonlinear control for two different forced model state oscillators and actuators. The paper starts by discussing the Duffing oscillator which features a second order non-linear differential equation describing complex motion whereas the second model is the Van der Pol oscillator with non-linear damping. A first order actuator is added to both models to expand on the chaotic behavior of the oscillators. In order to control the system without comprising linearization, Lyapunov non-linear control was used. A control Lyapunov function was tailored to the system. This led to improved maneuverability of the controller and the performance of the overall system. The controller was found to be highly efficient in system tracking and had swift response time. Simulations were performed on both the uncontrolled and controlled cases. Both simulation results ultimately confirmed the effectiveness of the proposed controller.

Keywords: Duffing Oscillator, Lyapunov Function, Nonlinear Control, Van der Pol Oscillator

Cite this paper: Alghassab, M. , Mahmoud, A. and Zohdy, M. (2017) Nonlinear Control of Chaotic Forced Duffing and Van der Pol Oscillators. International Journal of Modern Nonlinear Theory and Application, 6, 26-37. doi: 10.4236/ijmnta.2017.61003.

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