Chaos synchronization in josephson junction using nonlinear robust adaptive controller: HIL implementation

In this paper, a nonlinear robust adaptive controller is proposed to synchronize two Josephson junction models with slightly different parameters. The synchronization is obtained using the slave–master technique. Here, Josephson junction is described with the Resistive Capacitive Inductive Shunted Josephson model indicating that the equations governing the Josephson junction are nonlinear, uncertain, and have an unknown parameter. Also, the Lyapunov function is presented to analyze the stability of the close loop system. The simulation results show that the open-loop system, without the controller, has a chaotic behavior. Numerical simulations are performed to confirm the validity of the proposed controller. Also, the performance of the suggested controller is compared with the proportional integral derivative controller. For this purpose, certain criteria, containing the integral of time multiplied absolute error, the integral of absolute error, the integral of time multiplied square error, and the integral of square error are calculated besides analyzing the results of the closed-loop system. The simulation shows that the states of the controlled chaotic slave system exponentially synchronize with the state of the master system. Also, a hardware-in-the-loop experiment is done to verify the real-time implementation capability of the suggested controller.