Design and Implementation of a Microcontroller Based Active Controller for the Synchronization of the Petrzela Chaotic System

Abstract

This paper presents an active control design for the synchronization of two identical Petrzela chaotic systems (Petrzela, J.; Gotthans, T. New chaotic dynamical system with a conic-shaped equilibrium located on the plane structure. Applied Sciences. 2017, 7, 976) on master-slave configuration. For the active control, the parameters of both systems are assumed to be a priori known, the control law by means of the dynamic of the error synchronization is designed to guarantee the convergence to zero of error states and the synchronization process is verified by numerical simulation. By taking advantage of the execution and implementation facilities of microcontroller based chaotic systems in digital devices, the active controller is implemented in a 32 bits ARM microcontroller. The experimental results were obtained by using the fourth order Runge-Kutta numerical method to integrate the differential equations of the controller, where the results were measured with a digital oscilloscope.

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“…The term chaos is used to describe the dynamic behavior of simple dynamical systems, which appears to be complex and very different from what was predicted (Akgul et al 2016b;Tuna and Fidan 2018). The behavior of these systems has a non-periodic property and can easily be confused with random behavior (Akkaya et al 2018;Rivera-Blas et al 2019). Chaotic systems are sensitive to initial conditions, complex and irregular in appearance, and occur in deterministic nonlinear time-dependent systems (Dursun and Kaşifoglu 2018;Tuna et al 2019a;Bonny and Elwakil 2018).…”