{"title":"Nonlinear Control of Chaotic Forced Duffing and Van der Pol Oscillators","authors":"Mohammed A. Alghassab, Amr Mahmoud, M. Zohdy","doi":"10.4236/IJMNTA.2017.61003","DOIUrl":null,"url":null,"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.","PeriodicalId":69680,"journal":{"name":"现代非线性理论与应用(英文)","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2017-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"现代非线性理论与应用(英文)","FirstCategoryId":"1093","ListUrlMain":"https://doi.org/10.4236/IJMNTA.2017.61003","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 9
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.
本文讨论了一种对两种不同强迫模型状态振荡器和执行器进行非线性控制的新技术和实现。本文首先讨论了具有二阶非线性微分方程描述复杂运动的Duffing振子模型和具有非线性阻尼的Van der Pol振子模型。在两个模型中都添加了一阶致动器以扩展振子的混沌行为。为了在不包含线性化的情况下对系统进行控制,采用了李雅普诺夫非线性控制。为系统量身定制了一个控制李雅普诺夫函数。这提高了控制器的可操作性和整个系统的性能。结果表明,该控制器具有系统跟踪效率高、响应速度快的特点。对控制和非控制两种情况进行了仿真。仿真结果最终证实了所提控制器的有效性。