Document Type : Research Articles

Authors

1 2Faculty of Electrical and Computer, Malek-Ashtar University of Technology, Iran.

2 Faculty of Electrical and Computer, Malek-Ashtar University of Technology, Iran.

3 Research Assistant, Department of Electrical and Computer, Malek-Ashtar University of Technology, Iran.

Abstract

In this paper, a 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. The dynamic optimization problem is solved using a generic particle filter. Here, Josephson junction is described with Resistive Capacitive Inductive Shunted Josephson model, and the synchronization is obtained using the slave–master technique. Moreover, to verify the implementation capability of the proposed algorithm, a processor in loop experiment is performed. The results show that the open-loop system, without the controller, has a chaotic behavior. Numerical simulations are conducted to assess the performance of the proposed algorithm. The results show that the proposed approach can be implemented in a real-time application. Also, the performance of the suggested controller is compared with the proportional integral derivative controller and sliding mode controller.

Keywords

Main Subjects

[1] KK. Likharev, Dynamics of Josephson Junctions and Circuits,
1th ed, Gordon and Breach science publishers, 1986.

[2] SK. Dana, DC. Sengupta, KD.Edoh, “Chaotic Dynamics in
Josephson Junction”. IEEE Trans Circuits Syst I Fundam
Theory, Vol. 48, No. 8, pp. 990-996, Apr 2001.

[3] F. Salam, S.Sastry, “Dynamics of the Forced Josephson
Junction Circuit: the Regions of Chaos”. IEEE Trans Circuits
Syst, Vol. 32, No. 8, pp. 784-796, Aug 1985.

[4] H. Mehrara, F. Raissi, A. Erfanian, “Vortex-Antivortex Pair
Interaction With Microwave Standing Waves: A Chaos
Analysis of Josephson Fluxonic Diode for Microwave
Applications”, IEEE Trans Appl Supercond, Vol. 29, No. 7,
pp. 150-158, Oct 2019.

[5] B. Rezaie, M.R.J. Motlagh, M. Analoui, S. Khorsandi,
“Stabilizing fixed points of time-delay systems close to the
Hopf bifurcation using a dynamic delayed feedback control
method”, J. Phys. A Math. Theor, Vol. 42, No. 39, pp. 1-24,
Sep 2009.

[6]
S.H. Shahalami, F. Rajab Nejad, “Design of Adaptive Back-
Stepping Controller for Chaos Control in Boost Converter and

Controller Coefficients Optimization Using CHPSO

Algorithm”,
Int. J. Ind. Electron. Control Optim, Vol. 3, No.
3,
pp. 249257, Sum 2020.

[7]
K. Akbari, B. Rezaie, S. Khari, “Designing full-order sliding
mode controller based on ANFIS approximator for uncertain

nonlinear chaotic systems”,
Int. J. Ind. Electron. Control
Optim
, Vol. 2, No. 1, pp. 3946, Win 2019.

[8]
C. Eichler, A. Wallraff, “Controlling the Dynamic Range of a
Josephson Parametric Amplifier”,
EPJ Quantum Technol, Vol.
1, No. 2,
pp. 119, Dec 2014.

[9]
S.P. Benz, C.A. Hamilton, “Application of the Josephson
effect to voltage metrology”.
Proc. IEEE, pp. 16171629,
2004.

[10] DS. Goldobin, LS. Klimenko, “Resonances and
Multistability in a Josephson Junction Connected to a
Resonator”, Phys Rev E, Vol. 97, No. 2, pp. 022203, Feb 2018.

[11] J. Diggins, JF. Ralph, TP. Spiller, TD. Clark, H. Prance, RJ.
Prance, et al, “Chaos Generated Noise in Radio Frequency
SQUID Magnetometers”. AIP Conf. Proc., Vol. 371, Apr
1996

[12] F. Raissi, A. Khooshemehri, A.Erfanian, “Three-Terminal
Superconducting Digital Transistor”. IEEE Trans Appl
Supercond, Vol. 29, No. 4, pp. 1-6, Dec 2018.

[13] CA. Donnelly, JA. Brevik, NE. Flowers-Jacobs, AE. Fox, PD.
Dresselhaus, PF. Hopkins, et al, “Quantized Pulse Propagation
in Josephson Junction Arrays”, IEEE Trans Appl Supercond,
Vol. 30, No. 3, pp. 1-8, Jul 2019.

[14] Y. Zhang, P. Zhou, J. Tang, J. Ma, “Mode selection in a
neuron driven by Josephson junction current in presence of
magnetic field”, Chinese J. Phys, Vol. 71, No. 1, pp. 7284,
Jun 2021.

[15]
Y. Zhang, Y. Xu, Z. Yao, J. Ma, “A feasible neuron for
estimating the magnetic field effect”,
Nonlinear Dyn. Vol. 102,
No. 3,
pp. 18491867, Nov 2020.

[16] A. Uçar, KE. Lonngren, E-W, Bai, “Chaos Synchronization
in RCL-Shunted Josephson Junction Via Active Control”.
Chaos, Solitons & Fractals, Vol. 31, No. 1, pp. 105111, Jan
2007.

[17] AM. Harb, BA. Harb, “Controlling Chaos in Josephson-
Junction Using Nonlinear Backstepping Controller”. IEEE
Trans Appl Supercond, Vol. 16, No. 4, pp. 1988-1998, Dec
2006.

[18] UE. Vincent, A. Ucar, JA. Laoye, SO. Kareem, “Control and
Synchronization of Chaos in RCL-Shunted Josephson
Junction Using Backstepping Design”. Phys C Supercond,
Vol. 485, No. 5, pp. 374-382, Mar 2008.

[19] A.N. Njah, K.S. Ojo, G.A. Adebayo, A.O. Obawole,
“Generalized control and synchronization of chaos in RCL-
shunted Josephson junction using backstepping design”, Phys.
C Supercond, Vol. 470, No. 13, pp. 558564, Jul 2010.

[20] AM. Harb, BA. Harb, “Chaos Synchronization in Josephson
Junctions”. J Supercond Nov Magn, Vol. 25, No. 6, pp. 1647-
1653, Aug 2012.

[21] D-Y. Chen, W-L. Zhao, X-Y. Ma, R-F. Zhang, “Control and
Synchronization of Chaos in RCL-Shunted Josephson
Junction with Noise Disturbance Using Only One Controller
Term”. Abstr. Appl. Anal., Vol 2012, No. 1, pp. 1-15, Jul 2012.

[22] C.-K. Cheng, P.C.-P. Chao, “Trajectory tracking between
Josephson junction and classical chaotic system via iterative
learning control”, Appl. Sci. Vol. 8, No. 8, pp. 1285, Aug 2018.

[23] C-K .Cheng, PC-P. Chao, “Chaos Synchronization Between
Josephson Junction and Classical Chaotic System via Iterative
Learning Control”. IEEE Int. Conf. Appl. Syst. Invent, pp.
12325, Jun 2018.

[24] TBT. Nguyen, “Adaptive MIMO Controller Design for
Chaos Synchronization in Coupled Josephson Junctions via
Fuzzy Neural Networks”. J Adv Eng Comput, Vol. 1, No. 1,
pp. 80-86, Dec 2017.

[25] K.S. Ojo, A.N. Njah, O.I. Olusola, M.O. Omeike,
“Generalized reduced-order hybrid combination
synchronization of three Josephson junctions via backstepping
technique”, Nonlinear Dyn, Vol. 77, No. 3, pp. 583595, Aug
2014.

[26] E. Camacho, Alba C. Model Predictive Control, Springer
science & business media, 2013.

[27] M. Ehsani, M. Saeidi, H. Radmanesh, A. Abrishamifar,
“Comparisons between Generalized Predictive Control and
Linear Controllers in Multi-Input DC-DC Boost Converter”,
Int. J. Ind. Electron. Control Optim. Vol. 3, No. 1, pp. 2734 ,
Win 2020.

[28] H. Radmanesh, M. Saeidi, Linear Modelling of Six Pulse
Rectifier and Designee of Model Predictive Controller with
Stability Analysis. Int. J. Ind. Electron. Control Optim, Vol.
3, No. 4, pp. 491501, Sum 2020.

[29] M. Heidari, “Maximum Wind Energy Extraction by Using
Neural Network Estimation and Predictive Control of Boost
Converter”, Int. J. Ind. Electron. Control Optim. Vol. 1, No. 2
pp. 115120, Sum 2018.

[30] S. Jalili, B. Rezaie, Z. Rahmani, A novel hybrid model
predictive control design with application to a quadrotor
helicopter. Optim. Control Appl. Methods, Vol. 39, No. 4, pp.
13011322, Jul 2018.

[31] A. Mirzaei, A. Ramezani, “Cooperative distributed
constrained model predictive control for uncertain nonlinear
large scale systems”. Int. J. Ind. Electron. Control Optim. Vol.
4, No. 1, pp. 87-98, Jan 2020.

[32] H. Nobahari, S. Nasrollahi, “A Non-Linear Estimation and
Model Predictive Control Algorithm Based on Ant Colony
Optimization”. Trans Inst Meas Control, Vol. 41, No. 4, pp.
1123-1138, Feb 2019.

[33] S. Botchu, S. Ungarala, “Nonlinear Model Predictive Control
Based on Sequential Monte Carlo State Estimation”. IFAC
Proc, Vol. 40, Jan 2007.

[34] D. Stahl, J. Hauth , “PF-MPC: Particle Filter-Model
Predictive Control”. Syst & Control Lett, Vol. 60, No. 8, pp.
632-643, Aug 2011.

[35] M. Sarailoo, Z. Rahmani, B. Rezaie, “A Novel Model
Predictive Control Scheme Based on Bees Algorithm in a
Class of Nonlinear Systems: Application to a Three Tank
System”. Neurocomputing, Vol. 152, No. 1, pp. 294-304, Mar
2015.

[36] F. Rajabi, B. Rezaie, Z. Rahmani, “A Novel Nonlinear Model
Predictive Control Design Based on a Hybrid Particle Swarm
Optimization-Sequential Quadratic Programming Algorithm:
Application to an Evaporator System”. Trans Inst Meas
Control, Vol. 38, No. 1, pp. 23-32, Dec 2016.

[37] T. Van Duzer, CW. Turner, Principles of Superconductive
Devices and Circuits, Edward Arnold, USA, 1981.

[38] D. Simon, Optimal state estimation: Kalman, H infinity, and
nonlinear approaches; John Wiley & Sons, 2006.

[39] M.S. Arulampalam, S. Maskell, N. Gordon, T. A Clapp,
“Tutorial on particle filters for online nonlinear/non-Gaussian
Bayesian tracking " Signal Process IEEE Trans, Vol. 50, No.
2, pp. 174188, Aug 2002.

[40] B. Ristic, S. Arulampalam, N. Gordon, Beyond the Kalman
filter: Particle filters for tracking applications, Artech house
Boston Press, 2004.

[41] J.A. Rossiter, Model-based predictive control: a practical
approach, CRC press, 2003.

[42] R.Y. Rubinstein, D.P. Kroese, Simulation and the Monte
Carlo method, John Wiley & Sons press, 2016.

[43]
H. Nobahari, Hadi, S. Nasrollahi, “A nonlinear robust model
predictive differential game guidance algorithm based on the

particle swarm optimization”,
J Franklin Inst, Vol. 357, No.
15,
pp. 11042-11071, Aug 2020.

[44] A. Kurniawan, Getting Started with Matlab Simulink and
Arduino, PE Press, 2013