Adaptive Backstepping Control and Synchronization of a Novel 3-D Jerk System with an Exponential Nonlinearity

Author(s):  
Sundarapandian Vaidyanathan ◽  
Ahmad Taher Azar
2018 ◽  
Vol 7 (3) ◽  
pp. 1936 ◽  
Author(s):  
Sundarapandian Vaidyanathan ◽  
Sifeu Takougang Kingni ◽  
Aceng Sambas ◽  
Mohamad Afendee Mohamed ◽  
Mustafa Mamat

Jerk systems are popular in mechanical engineering and chaotic jerk systems are used in many applications as they have simple structure and complex dynamic properties. In this work, we report a new chaotic jerk system with three nonlinear terms. Dynamical properties of the chaotic jerk system are analyzed through equilibrium analysis, dissipativity, phase portraits and Lyapunov chaos exponents. We show that the new chaotic jerk system has a unique saddle-focus equilibrium at the origin. Thus, the new chaotic jerk system has a self-excited strange attractor. Next, global chaos synchronization of a pair of new chaotic jerk systems is successfully achieved via adaptive backstepping control.


2021 ◽  
pp. 107754632199887
Author(s):  
Sinan Basaran ◽  
Fevzi Cakmak Bolat ◽  
Selim Sivrioglu

Many structural systems, such as wind turbines, are exposed to high levels of stress during operation. This is mainly because of the flow-induced vibrations caused by the wind load encountered in every tall structure. Preventing the flow-induced vibration has been an important research area. In this study, an active electromagnetic mass damper system was used to eliminate the vibrations. The position of the stabilizer mass in the active electromagnetic mass damper system was determined according to the displacement information read on the system without using any spring element, unlike any conventional system. The proposed system in this study has a structure that can be implemented as a vibration suppressor in many intelligent structural systems. Two opposing electromagnets were used to determine the instant displacement of the stabilizer mass. The control currents to be given to these electromagnets are determined by using an adaptive backstepping control design. The adaptive controller algorithm can predict the wind load used in the controller design without prior knowledge of the actual wind load. It was observed that the designed active electromagnetic mass damper structure is successful in suppressing system vibrations. As a result, the proposed active electromagnetic mass damper system has been shown to be suitable for structural systems in flow-induced vibration damping.


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