Chua’s Circuit with Nonlinear Energy Storages and Its Synchronization

The paper deals with the development of a theoretical framework to study and control electrical devices with saturated magnetic circuit. We use the interval methods to replace the nonlinear function with its piecewise linear boundaries. These boundaries allow us to define the domain in the state space where all system motions are defined. One can use the above-mentioned domain to reduce the area of study system possible motions and design a closed-loop control system to form desired motions of system state variables. We show the main points of our approach by considering Chua’s circuit, which is modified by using a coil with a ferromagnetic core as well as using controllable voltage sources. We use voltage sources to control any of Chua’s circuit state variables easily. Our studies show that the use of an unideal coil changes the circuit attractor. Moreover, changing the operation point of the coil gives us the possibility to form unsymmetrical attractors and chaotic oscillations. We think it is a way to improve the security features of the considered circuit. Another way is the use piecewise linear functions instead of the nonlinear ones. The small differences between nonlinear and piecewise linear functions form after a time the entirely different motion trajectory. Since there are several methods to define piecewise linear boundaries for nonlinear functions, one can define different functions and build different circuits based on Chua’s circuit with a ferromagnetic core coil. On another hand these different boundaries allow us to define a control signal to compensate for the circuit’s inner dynamic and perform its synchronization with an error of less than 0.1%.