Title : Feasible Performance Evaluations of Digitally-Controlled Auxiliary Resonant Commutation Snubber-Assisted Three Phase Vo

International Journal of Industrial Electronics, Control and Optimization . © 2021 IECO. used to control and synchronization of chaotic dynamics in RCLSJ. The recursive approach has been employed to eliminate the chaotic behavior of the RCLSJ as well as to attain global asymptotic synchronization. In [19], an active backstepping method has been used to control chaos in RCLSJ model. In the proposed approach the number of control functions has been reduced from three to one that was reduced controller complexity. In [20], a nonlinear recursive method has been used to control the bifurcation as well as chaotic behavior of the Josephson junction. Here, a control signal based on the master and slave concept has been designed. In [21], a nonlinear sliding mode controller has been used to control and synchronize the chaos of the Josephson junctions considering the uncertainty of the model. Also, the Lyapunov stability theory has been used to analyze the stability of the system. In [22,23], an iterative learning control has been used for the linearized model of the error dynamics between two Josephson junctions. A real-time feed -forward procedure that uses iterative learning, to modify the trajectory error between systems for tracking two non-identical systems, has been used. In [24], a nonlinear controller based on sliding mode and neural fuzzy has been used for control and synchronization of the error dynamics. The neural fuzzy controller is used to provide a feedback linearization and sliding mode is used to deal with uncertainty in the model. In [25] a backstepping controller is used to achieve a hybrid combination synchronization of three Josephson junctions. One chaotic Josephson junction as the master and two Josephson junctions as the slaves. Model Predictive Control (MPC) is an interesting subject in control engineering. The benefit of MPC methods is their capability to handle dynamics with nonlinear elements and constraints [26]. MPC approaches have been employed in several practical examples, such as DC-DC Boost Converter [27], a six pulse rectifier [28], a Boost Converter [29], a quadrotor helicopter [30], and large-scale systems [31]. MPCs are classified into nonlinear and linear ones. Nonlinear Model Predictive Control (NMPC) typically involves non-convex optimization problems. An MPC problem can be expressed as an estimation problem. Likewise, an estimation problem can be expressed as a dynamic optimization problem. The combination of MPC and particle-based algorithms provides a tool for the calculation of the control signal in control [32]. In references [32–36], particle-based heuristic methods are used to compute the control signal. Also, the abovementioned references have not used particle-based heuristic methods to synchronize two Josephson junction models with slightly different parameters. The contribution of the current study is summarized as follows: a nonlinear model predictive control approach based on a generic particle filter is proposed to synchronize two Josephson junction models with different parameters. For this purpose, an appropriate objective function is defined to assess the particles within the state space. This objective function minimizes simultaneously the tracking error, control effort, and control smoothness. This nonlinear model predictive control problem, which is the dynamic optimization problem is solved using a generic particle filter. To the author’s knowledge, the use of a generic particle filter to synchronize two Josephson junction models with different parameters has not been proposed yet. The performance of the suggested approach is achieved in simulations using the Resistive Capacitive Inductive Shunted Josephson model. Numerical simulations are made to confirm the validity of the suggested controller. Moreover, to verify the implementation capability of the proposed algorithm, a processor in the loop experiment is performed. In this paper, the nonlinear Josephson junction equations are described in section 2. Section 3 explains the controller design. In Section 4, the results of nonlinear simulation and controller performance are presented. Finally, the conclusion is presented. II. STATEMENT OF THE PROBLEM The Josephson junction can be described with various electrical models such as Resistive Shunted Josephson (RCJ), Resistive Capacitive Shunted Josephson (RCSJ), and Resistive Capacitive Inductive Shunted Josephson (RCLSJ) [1,2]. Fig. 1 shows the RCSJ model; here,  is the phase difference between the two superconductors in the junction, R is the junction resistance, and C is the junction capacitor.