PHYSCON 2009, Catania, Italy, September, 1–September, 4 2009 CONTROL SYSTEM FOR SYNCHRONIZATION OF GENERALIZED CHUA’S CIRCUITS IN FPGA Can Eroglu Electrical and Electronics Engineering Izmir Institute of Technology Turkey caneroglu@iyte.edu.tr F. Acar Savaci Electrical and Electronics Engineering Izmir Institute of Technology Turkey acarsavaci@iyte.edu.tr Abstract In this study, feedback control system for synchro- nization of Generalized Chua’s circuits (GCC) has been implemented on Field Programmable Gate Ar- ray (FPGA). The feedback control rule has been de- rived by feedback linearization method. In order to implement the designed synchronized system, Matlab Simulink design for the GCCs has been translated to Xilinx System Generator design to generate a Very- High-Speed Integrated Circuits Hardware Description Language (VHDL) code which is used to produce a bitstream file. By Xilinx Integrated Software Environ- ment (ISE) program, a VHDL code is converted to a bitstream file which has been embedded into FPGA by Field Upgradeable Systems Environment (FUSE). Fi- nally, the synchronized GCCs states and attractor have been observed on the HP 54540C oscilloscope. Key words Generalized Chua’s circuit, Synchronization, FPGA. 1 Introduction Synchronization of chaos is an important topic in the nonlinear science. There are various notions of chaos synchronizations such as generalized synchronization [Afraimovich, Verichev and Rabinovich 1987], com- plete synchronization [Pecora and Carrol 1991; Fe- mat and Solis-Perales 2008], partial synchronization [Maistrenko and Popovych 2000] and phase synchro- nization [Rosenblum, Pikovsky and Kurths 1997]. The pioneering work [Pecora and Carrol 1991], has in- creased the interest in synchronization after having re- cently found many applications particularly in telecom- munications [Abel and Schwarz 2002], in mechani- cal systems [Blekhman, Landa and Rosenblum] and in control theory [Nijmeijer 2001]. Some different forms of synchronization of chaotic systems such as practical synchronization and almost synchronization have been studied by [Femat and Solis-Perales 1999]. The paper is organized as follows: In Section 2 the complete synchronization problem and the feedback linearization method are explained based on the liter- ature [Vidyasagar 1993; Fradkov 2007]. In Section 3, the control command for complete synchronization of GCCs have been derived. In Section 4, this control sys- tem is simulated by Matlab Simulink then the simulated design is converted to Xilinx System Generator design and the designed synchronized GCCs is implemented by FPGA by using ISE and FUSE programs. To the best of our knowledge, although FPGA implementa- tion of chaotic circuits exist in the literature [Sobhy, Elkouny, Aseeri and Zakria 2003; Wang 2008], the im- plementation of synchronized chaotic system by FPGA is given as a first time by this manuscript. The imple- mentation results of the GCCs have been observed on the HP54540 scope. Finally, in Section 5, conclusions are presented. 2 Complete Synchronization In this study, the complete synchronization problem will be considered as the tracking of the master system trajectories by the slave system trajectories. The differ- ence between master and slave system is called as the error system which can be constructed using the defini- tion given below. Definition 2.1: Let ˙ x = F M (x) and ˙ y = F S (y)+ g(y)u(y) be two chaotic systems in a manifold M ⊂ R n . F M , F S smooth vector fields with scalar output functions s M = h(x), s S = h(y) and x, y ∈ R n and g(y) ∈ R n is a smooth input vector [Femat and Solis-Perales 2008] where subscripts M and S stands for master and slave, respectively. ˙ x = F M (x), (1) ˙ e = F M (x) - F S (x, e) - g(x, e)u, (2) s e = h(x, e), (3)