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Finite-time integral sliding mode control for chaotic permanent magnet synchronous motor systems

Chibani A., Daaou B., Gouichiche A., Safa A., Messlem Y.

Archives of Electrical Engineering

2017

Vol. 66, nr 2

229--239

In this paper, an integral finite-time sliding mode control scheme is presented for controlling a chaotic permanent magnet synchronous motor (PMSM). The controller can stabilize the system output tracking error to zero in a finite time. Using Lyapunov’s stability theory, the stability of the proposed scheme is verified. Numerical simulation results are presented to present the effectiveness of the proposed approach.

A new 3-D jerk chaotic system with two cubic nonlinearities and its adaptive backstepping control

Vaidyanathan S.

Archives of Control Sciences

2017

Vol. 27, no. 3

409--439

This paper presents a new seven-term 3-D jerk chaotic system with two cubic nonlinearities. The phase portraits of the novel jerk chaotic system are displayed and the qualitative properties of the jerk system are described. The novel jerk chaotic system has a unique equilibrium at the origin, which is a saddle-focus and unstable. The Lyapunov exponents of the novel jerk chaotic system are obtained as L1 = 0:2974, L2 = 0 and L3 = −3:8974. Since the sum of the Lyapunov exponents of the jerk chaotic system is negative, we conclude that the chaotic system is dissipative. The Kaplan-Yorke dimension of the new jerk chaotic system is found as DKY = 2:0763. Next, an adaptive backstepping controller is designed to globally stabilize the new jerk chaotic system with unknown parameters. Moreover, an adaptive backstepping controller is also designed to achieve global chaos synchronization of the identical jerk chaotic systems with unknown parameters. The backstepping control method is a recursive procedure that links the choice of a Lyapunov function with the design of a controller and guarantees global asymptotic stability of strict feedback systems. MATLAB simulations are shown to illustrate all the main results derived in this work.

Different synchronization schemes for chaotic Rikitake systems

Ali Khan M.

International Journal of Applied Mechanics and Engineering

2013

Vol. 18, no. 2

383--393

This paper presents the chaos synchronization by designing a different type of controllers. Firstly, we propose the synchronization of bi-directional coupled chaotic Rikitake systems via hybrid feedback control. Secondly, we study the synchronization of unidirectionally coupled Rikitake systems using hybrid feedback control. Lastly, we investigate the synchronization of unidirectionally coupled Rikitake chaotic systems using tracking control. Comparing all the results, finally, we conclude that tracking control is more effective than feedback control. Simulation results are presented to show the efficiency of synchronization schemes.