Synchronization of uncertain chaotic systems using fractional order nonlinear PID sliding surface

Subject Areas : Electrical engineering (electronics, telecommunications, power, control)

Mohammad Rasouli ¹ ( College of Skills and Entrepreneurship, Mashhad Branch, Islamic Azad University, Mashhad, Iran )
Assef Zare ² ( Department of Electrical Engineering, Gonabad Branch, Islamic Azad University, Gonabad, Iran )
Narges Shafaei ³ ( Islamic azad university )
Hassan Yaghoubi ⁴ ( Faculty of Electrical Engineering, Gonabad Branch, Islamic Azad University, Gonabad 6518115743, Iran )

Received: 2024-07-08 Accepted : 2024-08-20 Published : 2024-09-21

Keywords: Fractional order chaotic system, synchronization, sliding controller, robust adaptive,

Abstract :

In this research, a method for robust synchronization of chaotic fractional order systems is presented. The systems investigated in this article have an unknown time delay, disturbance and uncertainty with an unknown limit. The presence of time delay increases the complexity of the control problem and its unknownness increases the stabilization complexity. Uncertainty and disturbance limits are entered into the control system as unknowns and the adaptive controller uses the estimation of uncertainty and disturbance limits. For this purpose, first, a sliding surface based on the proportionality of the fractional-order non-linear derivative-integrator is presented, then a robust adaptive mechanism for synchronizing the base and follower systems is presented. By choosing the appropriate Lyapunov function while proving the stability of the proposed mechanism and guaranteeing the convergence of the synchronization error to zero, the update rules have been extracted to estimate the disturbance limit, uncertainty limit and time delays of the system. The proposed approach has been applied in order to synchronize the fractional order system with time-varying parameters, which shows the simulation results of the appropriate performance of the proposed approach. . . .. . . . .. . . . . . . . . . . .

References:

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