Design of sliding mode controller for chaotic Josephson-junction

Abstract

It is known that a shunted nonlinear resistive-capacitive-inductance Josephson-junction (RCLSJ) model has a chaotic attractor. This attractor is created as a result of Hopf bifurcation that occurs when a certain direct current (DC) applied to one of the junction terminals. This chaotic attractor prevents the system from reaching the phase-locked state and hence degrade the performance of the junction. This paper aims at controlling and taming this chaotic attractor induced in this model and pulling the system to the phase-locked state. To achieve this task, a sliding mode controller is proposed. The design procedures involve two steps. In the first one, we construct a suitable sliding surface so that the dynamic of the system follows the sliding manifolds in order to meet design specifications. Secondly, a control law is created to force the chaotic attractor to slide on the sliding surface and hence stabilizes system trajectory. The RCLSJ model under consideration is simulated with and without the designed controller. Results demonstrate the validity of the designed controller in taming the induced chaos and stabilizing the system under investigation.