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Discrete-time Takagi-Sugeno singular systems with unmeasurable decision variables: state and fault fuzzy observer design

Khaoula Aitdaraou Mohamed Essabre Abdellatif El Assoudi El Hassane El Yaagoubi
Archives of Control Sciences | 2023 | vol. 33 | No 2 | 321-328 | DOI: 10.24425/acs.2023.146278
Keywords observer design unmeasurable decision variable SVD approach Lyapunov function LMIs
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Abstract

The studied problem in this paper, treat the issue of state and fault estimation using a fuzzy observer in the case of unmeasurable decision variable for Discrete-Time Takagi-Sugeno Singular Sytems (DTSSS). First, an augmented system is introduced to gather state and fault into a single vector, then on the basis of Singular Value Decomposition (SVD) approach, this observer is designed in explicit form to estimate both of state and fault of a nonlinear singular system. The exponential stability of this observer is studied using Lyapunov theory and the convergence conditions are solved with Linear Matrix Inequalities (LMIs). Finally a numerical example is simulated, and results are given to validate the offered approach.
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Authors and Affiliations

Khaoula Aitdaraou
1 2
Mohamed Essabre
3
Abdellatif El Assoudi
1 2
El Hassane El Yaagoubi
1 2
  1. Laboratory of High Energy Physics and Condensed Matter, Faculty of Science, Hassan II University of Casablanca, B.P 5366, Maarif Casablanca, Morocco
  2. ECPI, Department of Electrical Engineering, ENSEM Hassan II University of Casablanca, B.P 8118, Oasis Casablanca, Morocco
  3. Laboratory of Materials, Energy and Control Systems, Faculty of Sciences and Technologies Mohammedia, Hassan II University of Casablanca, Morocco

On the region of attraction of dynamical systems: Application to Lorenz equations

M.A. Hammami N.H. Rettab
Archives of Control Sciences | 2020 | vol. 30 | No 3 | 389-409 | DOI: 10.24425/acs.2020.134671
Keywords nonlinear dynamical systems Lyapunov function Basin of attraction Lorenz equations
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Abstract

Many nonlinear dynamical systems can present a challenge for the stability analysis in particular the estimation of the region of attraction of an equilibrium point. The usual method is based on Lyapunov techniques. For the validity of the analysis it should be supposed that the initial conditions lie in the domain of attraction. In this paper, we investigate such problem for a class of dynamical systems where the origin is not necessarily an equilibrium point. In this case, a small compact neighborhood of the origin can be estimated as an attractor for the system. We give a method to estimate the basin of attraction based on the construction of a suitable Lyapunov function. Furthermore, an application to Lorenz system is given to verify the effectiveness of the proposed method.

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Authors and Affiliations

M.A. Hammami
N.H. Rettab

Stability analysis of engineering/physical dynamic systems using residual energy function

Cim Civelek
Archives of Control Sciences | 2018 | vol. 28 | No 2 | DOI: 10.24425/123456
Keywords stability analysis residual energy function as Lyapunov function physicaldynamic systems coupled engineering systems
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Abstract

In this article, an engineering/physical dynamic system including losses is analyzed inrelation to the stability from an engineer’s/physicist’s point of view. Firstly, conditions for a Hamiltonian to be an energy function, time independent or not, is explained herein. To analyze stability of engineering system, Lyapunov-like energy function, called residual energy function is used. The residual function may contain, apart from external energies, negative losses as well. This function includes the sum of potential and kinetic energies, which are special forms and ready-made (weak) Lyapunov functions, and loss of energies (positive and/or negative) of a system described in different forms using tensorial variables. As the Lypunov function, residual energy function is defined as Hamiltonian energy function plus loss of energies and then associated weak and strong stability are proved through the first time-derivative of residual energy function. It is demonstrated how the stability analysis can be performed using the residual energy functions in different formulations and in generalized motion space when available. This novel approach is applied to RLC circuit, AC equivalent circuit of Gunn diode oscillator for autonomous, and a coupled (electromechanical) example for nonautonomous case. In the nonautonomous case, the stability criteria can not be proven for one type of formulation, however, it can be proven in the other type formulation.
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Authors and Affiliations

Cim Civelek

Exponential stability of impulsive delayed nonlinear hybrid differential systems

Qianqian Jia Chaoying Xia
Archives of Electrical Engineering | 2019 | vol. 68 | No 3 | 553-564 | DOI: 10.24425/aee.2019.129341
Keywords impulsive delayed nonlinear hybrid systems global exponential Lyapunov function Razumikhin technique
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Abstract

In recent years, with the rapid development of digital components, digital electronic computers, especially microprocessors, digital controllers have replaced analog controllers on many occasions. The application of digital controller makes the performance analysis of impulsive system more and more important. This paper considers global exponential stability (GES) of impulsive delayed nonlinear hybrid differential systems (IDNHDS).Through the application of the Lyapunov method and the Razumikhin technique, a series of uncomplicated and useful guiding principles have been obtained. The results of a numerical simulation are presented to demonstrate that the method is correct and effective.

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Authors and Affiliations

Qianqian Jia
Chaoying Xia

The Stability Interval of the Set of Linear System

Talgat Mazakov Waldemar Wójcik Sholpan Jomartova Nurgul Karymsakova Gulzat Ziyatbekova Aisulu Tursynbai
International Journal of Electronics and Telecommunications | 2021 | vol. 67 | No 2 | 155-161 | DOI: 10.24425/ijet.2021.135958
Keywords automatic control system stability matrix minor characteristic polynomial Hurwitz criterion Lienard-Shipard criterion of interval mathematics Lyapunov function
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Abstract

The article considers the problem of stability of interval-defined linear systems based on the Hurwitz and Lienard- Shipar interval criteria. Krylov, Leverier, and Leverier- Danilevsky algorithms are implemented for automated construction and analysis of the interval characteristic polynomial. The interval mathematics library was used while developing the software. The stability of the dynamic system described by linear ordinary differential equations is determined and based on the properties of the eigenvalues of the interval characteristic polynomial. On the basis of numerical calculations, the authors compare several methods of constructing the characteristic polynomial. The developed software that implements the introduced interval arithmetic operations can be used in the study of dynamic properties of automatic control systems, energy, economic and other non-linear systems.
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Bibliography

[1] Y. Y. Aleksankin, A. E. Brzhozovsky, V. A. Zhdanov and others, "Automateddesign of automatic control systems," ed. V. V. Solodovnikov, Moscow: Mashinostroenie, 1990, pp. 1-332.
[2] A. A. Voronov and I. A. Orourke, "Analysis and optimal synthesis of computer control systems," Moscow: Nauka, 1984, pp. 1–344.
[3] V. E. Balnokin and P. I. Chinaev, "Analysis and synthesis of automatic control systems on a computer. Algorithms and programs: Reference," Moscow: Radio and communications, 1991, pp 1–256.
[4] P. D. Krutko, A. I. Maximov and L. M. Skvortsov, "Algorithms and programs for designing automatic systems," Moscow: Radio and communications, 1988, 1–306.
[5] G. Davenport, I. Sira and E. Tournier, "Computer algebra," Moscow: Mir, 1991, pp. 1-352. [6] D. M. Klimov, V. M. Rudenko, "Methods of computer algebra in problems of mechanics," Moscow: Nauka, 1989, pp. 1–215.
[7] N. G. Chetayev, "Stability of motion," Moscow: GITL, 1955, pp. 1–207.
[8] V. I. Zubov, "Dynamics of managed systems," High School, 1982, pp. 1– 286.
[9] V. M. Matrosov, "On the theory of motion stability," Applied Mathematics and Mechanics, no 6, pp. 992-1002, 1962.
[10] R. Bellman, "Vector Lyapunov function," J. Soc. Indastr. Appl. Math., vol. 1., no 1, pp. 32-34, 1962.
[11] V. M. Matrosov and S. N. Vasilyev, "Comparison principle for derivation of theorems in mathematical system theory," International Conference on Artificial Intelligence. Moscow: USSR, 1975, pp. 25-34.
[12] V. M. Popov, "On the absolute stability of non-linear automatic control systems," Automatics and Telemechanics, vol. XXII, no. 8., pp. 50-59, 1961.
[13] V. M. Popov, "Hyper-Stability of automatic systems," Moscow: Nauka, 1970, pp. 1–456.
[14] V. Rezvan, "Absolute stability of automatic systems with delay," Moscow: Nauka, 1983, pp. 1–360.
[15] V. V. Rumyantsev and A. S. Oziraner "Stability and stabilization of motion in relation to a part of variables," Moscow: Nauka, 1987, pp. 1– 256.
[16] V. I. Vorotnikov, "Stability of dynamic systems in relation to some variables," Moscow: Nauka, 1991, pp. 1–288.
[17] K. G. Valeev and O. A. Zhautykov, "Infinite systems of differential equations," Alma-ATA: Nauka, 1974, pp. 1–415.
[18] A. K. Bedelbaev, "Stability of nonlinear automatic control systems," Almaty: ed. an KazSSR, 1960, pp. 1–163.
[19] B. J. Magarin, "The Stability and quality of non-linear automatic control systems," Almaty: Science of The Kazakh SSR, 1980. pp. 1–316.
[20] S. A. Aisagaliev, "Analysis and synthesis of autonomous nonlinear automatic control systems," Almaty: Science of The Kazakh SSR, 1980, pp. 1–244.
[21] R. E. Moor, "Interval analysis," New Jersey: Prentice-Hall, 1966, pp. 1- 245. [22] Y. I. Shokin, "Interval analyze," Novosibirsk: Science, 1986, pp. 1–224.
[23] T. I. Nazarenko and L. V. Marchenko, "Introduction to interval methods of computational mathematics, " Irkutsk: Publishing house of Irkutsk University, 1982, pp. 1–108.
[24] S. A. Kalmykov, Y. I. Shokin and Z. H. Yuldashev, "Methods of interval analyze. – Novosibirsk: Science, 1986. – 224 p.
[25] Yu. M. Gusev, V. N. Efanov, V. G. Krymsky and V. Yu. Rutkovsky, "Analysis and synthesis of linear interval dynamic systems (state of the problem)," RAN. Technical cybernetics, no. 1, 1991, pp. 3-30.
[26] E. M. Smagina, A. N. Moiseev and S. P. Moiseeva, "Methods for calculating the IHP coefficients of interval matrices," Computational Technologies, vol. 2, no.1. 1997, pp. 52-61.
[27] V. A. Pochukaev and I. M. Svetlov, "Analytical method of constructing Hurwitz interval polynomials," Automatics and Telemechanics, no. 2, 1996, pp. 89-100.
[28] N. A. Bobylev, S. V. Emelyanov and S. K. Korovin, "On positive definiteness of interval families of symmetric matrices," Automatics and Telemechanics, no. 8, 2000, pp. 5-10.
[29] S. B. Partushev, "Improving the accuracy of interval estimates of voltage deviations in General-purpose electrical networks," Computational Technology, no. 1, 1997, pp. 45-51.
[30] I. V. Svyd, A. I. Obod, G. E. Zavolodko, I. M. Melnychuk, W. Wójcik, S. Orazalieva and G. Ziyatbekova, "Assessment of information support quality by “friend or foe” identification systems," Przegląd Elektrotechniczny, vol. 95, no. 4, 2019, pp. 127-131.
[31] T. Zh. Mazakov, Sh. A. Jomartova, T. S. Shormanov, G. Z. Ziyatbekova, B. S. Amirkhanov and P. Kisala, "The image processing algorithms for biometric identification by fingerprints," News of the National Academy of Sciences of the Republic of Kazakhstan. Series of Geology and Technical Sciences, vol. 1, no 439. 2020, pp. 14-22.
[32] V. M. Belov, V. A. Sukhanov, E. V. Lagutina, "Interval approach for solving problems of kinetics of simple chemical reactions," Technol, no. 1, 1997, pp. 10-18.
[33] A. Kydyrbekova, M. Othman, O. Mamyrbayev, A. Akhmediyarova and Z. Bagashar, "Identification and authentication of user voice using DNN features and i-vector," Cogent Engineering, vol. 7, 2020, pp. 1-22.
[34] I. Nurdaulet, M. Talgat, M. Orken, G. Ziyatbekova, "Application of fuzzy and interval analysis to the study of the prediction and control model of the epidemiologic situation," Journal of Theoretical and Applied Information Technology, Pakistan, vol. 96, no. 14, 2018, pp. 4358-4368.
[35] V. N., Podlesny and V. G. Rubanov, "A simple frequency criterion for robust stability of a class of linear interval dynamic systems with delay," Automatics and Telemechanics, no. 9, 1996, pp. 131-139.
[36] A. P. Molchanov and M. V. Morozov, "Sufficient conditions for robust stability 5f linear non-stationary control systems with periodic interval restrictions," Automatics and Telemechanics, no. 1, 1997, pp. 100-107.
[37] A. M. Letov, "Stability of nonlinear control systems, " Moscow: Fizmatgiz, 1962, pp. 1–312.
[38] N. S. Bakhvalov, "Numerical methods," Moscow: Nauka, 1973. pp. 1–632.
[39] A. I. Lurie , "Some nonlinear problems of the automatic control theory," Moscow: GITL, 1951, pp. 1–216.
[40] K. I. Babenko, "Fundamentals of numerical analysis," Moscow: Nauka, 1986. pp. 1–744.
[41] B. P. Demidovich, I. A. Maron and E. Z. Shuvalova, "Numerical methods of analysis. Approximation of functions, differential and integral equations," Moscow: Nauka, 1967, pp. 1–368 p.
[42] V. N. Afanasiev, V. B. Kolmanovsky and V. R. Nosov, "Mathematical theory of designing control systems," Moscow: Higher. SHK., 1989, pp. 1–447.
[43] G.A. Amirkhanova, A. I. Golikov and Yu.G. Evtushenko, "On an inverse linear programming problem," Proceedings of the Steklov Institute of Mathematics, vol. 295. no. 1, 2016, pp. S21-S27.




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Authors and Affiliations

Talgat Mazakov
1
Waldemar Wójcik
2
Sholpan Jomartova
1
Nurgul Karymsakova
3
Gulzat Ziyatbekova
1
Aisulu Tursynbai
3
  1. Institute of Information and Computational Technologies CS MES RK, Al-Farabi Kazakh National University, Almaty, Kazakhstan
  2. Lublin Technical University, Poland
  3. Al-Farabi Kazakh National University, Almaty, Kazakhstan

Hybrid synchronization and parameter estimation of a complex chaotic network of permanent magnet synchronous motors using adaptive integral sliding mode control

Nazam Siddique Fazal U. Rehman
Bulletin of the Polish Academy of Sciences Technical Sciences | 2021 | 69 | 3 | e137056 | DOI: 10.24425/bpasts.2021.137056
Keywords chaotic systems hybrid synchronization (HS) complex chaotic permanent magnet synchronous motor adaptive integral sliding mode control (ISMC) Lyapunov function
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Abstract

The synchronisation of a complex chaotic network of permanent magnet synchronous motor systems has increasing practical importance in the field of electrical engineering. This article presents the control design method for the hybrid synchronization and parameter estimation of ring-connected complex chaotic network of permanent magnet synchronous motor systems. The design of the desired control law is a challenging task for control engineers due to parametric uncertainties and chaotic responses to some specific parameter values. Controllers are designed based on the adaptive integral sliding mode control to ensure hybrid synchronization and estimation of uncertain terms. To apply the adaptive ISMC, firstly the error system is converted to a unique system consisting of a nominal part along with the unknown terms which are computed adaptively. The stabilizing controller incorporating nominal control and compensator control is designed for the error system. The compensator controller, as well as the adopted laws, are designed to get the first derivative of the Lyapunov equation strictly negative. To give an illustration, the proposed technique is applied to 4-coupled motor systems yielding the convergence of error dynamics to zero, estimation of uncertain parameters, and hybrid synchronization of system states. The usefulness of the proposed method has also been tested through computer simulations and found to be valid.
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Bibliography

  1.  A.C. Fowler, J.D. Gibbon, and M.J. McGuinness, “The complex Lorenz equations”, Physica D 4, 139–163 (1982).
  2.  P. Liu, H. Song, and X. Li, “Observe-based projective synchronization of chaotic complex modified Van Der Pol-Duffing oscillator with application to secure communication”, J. Comput. Nonlinear Dyn. 10, 051015 (2015).
  3.  G.M. Mahmoud and A.A. Shaban, “On periodic solutions of parametrically excited complex non-linear dynamical systems”, Physica A 278(3‒4), 390–404 (2000).
  4.  G.M. Mahmoud and A.A. Shaban, “Periodic attractors of complex damped non-linear systems”, Int. J. Non-Linear Mech. 35(2), 309–323 (2000).
  5.  G.M. Mahmoud, “Periodic solutions of strongly non-linear Mathieu oscillators”, Int. J. Non-Linear Mech. 32(6), 1177–1185 (1997).
  6.  G.M. Mahmoud and E.E. Mahmoud, “Lag synchronization of hyperchaotic complex nonlinear systems”, Nonlinear Dynamics 67, 1613– 1622 (2012).
  7.  P. Liu and S. Liu, “Anti-synchronization between different chaotic complex systems”, Phys. Scr. 83, 065006 (2011).
  8.  S. Liu and P. Liu, “Adaptive anti-synchronization of chaotic complex nonlinear systems with unknown parameters”, Nonlinear Anal.-Real World Appl. 12, 3046–3055 (2011).
  9.  N. Siddique and F.U. Rehman, “Parameter Identification and Hybrid Synchronization in an Array of Coupled Chaotic Systems with Ring Connection: An Adaptive Integral Sliding Mode Approach”, Math. Probl. Eng. 2018, 6581493 (2018).
  10.  G.M. Mahmoud, E.E. Mahmoud, and A.A. Arafa, “Projective synchronization for coupled partially linear complex-variable systems with known parameters”, Math. Meth. Appl. Sci. 40(4), 1214–1222 (2017).
  11.  D.W. Qian, Y.F Xi, and S.W. Tong, “Chaos synchronization of uncertain coronary artery systems through sliding mode”, Bull. Pol. Acad. Sci. Tech. Sci. 67(3), 455–462 (2019).
  12.  G.M. Mahmoud, E.E. Mahmoud, and A.A. Arafa, “On modified time delay hyperchaotic complex Lü system”, Nonlinear Dynamics 80(1‒2), 855–869 (2015).
  13.  G.M. Mahmoud, T. Bountis, M.A. Al-Kashif, and A.A. Shaban, “Dynamical properties and synchronization of complex nonlinear equations for detuned lasers”, Dynam. Syst. 24(1), 63–79 (2009).
  14.  J.-B. Hu, H. Wei, Y.-F. Feng, and X.-B. Yang, “Synchronization of fractional chaotic complex networks with delay”, Kybernetika 55, 203–215 (2019).
  15.  N.A. Almohammadi, E.O. Alzahrani, and M.M. El-Dessoky, “Combined modified function projective synchronization of different systems through adaptive control”, Arch. Control Sci. 29, 133–146 (2019).
  16.  H. Su, Z. Rong, M.Z.Q. Chen, X. Wang, G. Chen and H. Wang, “Decentralized adaptive pinning control for cluster synchronization of complex dynamical networks”, IEEE Trans. Cybern. 43, 2182–2195 (2013).
  17.  A. Khan and U. Nigar, “Sliding mode disturbance observer control based on adaptive hybrid projective compound combination synchronization in fractional-order chaotic systems”, Int. J. Control Autom. Syst. 31, 885–899 (2020).
  18.  G.M. Mahmoud, E.A. Mansour, and T.M. Abed-Elhameed, “On fractional-order hyperchaotic complex systems and their generalized function projective combination synchronization”, Optik 130, 398–406 (2017).
  19.  S. Wang, X. Wang, X. Wang, and Y. Zhou, “Adaptive generalized combination complex synchronization of uncertain real and complex nonlinear systems”, AIP Adv. 6, 045011 (2016).
  20.  J. Zhou, A. Oteafy, and N. Smaoui, “Adaptive synchronization of an uncertain complex dynamical network”, IEEE Trans. Autom. Control 51, 652–656 (2006).
  21.  X. Chen, J. Qiu, J. Cao, and H. He, “Hybrid synchronization behavior in an array of coupled chaotic systems with ring connection”, Neurocomputing 173, 1299–1309 (2016).
  22.  F. Zhang, C. Mu, X. Wang, I. Ahmed, and Y. Shu, “Solution bounds of a new complex PMSM system”, Nonlinear Dynamics 74, 1041–1051 (2013).
  23.  Y.Wang, Y. Fan, Q.Wang, and Y. Zhang, “Stabilization and synchronization of complex dynamical networks with different dynamics of nodes via decentralized controllers”, IEEE Trans. Circuits Syst. I-Regul. Pap. 59, 1786–1795 (2012).
  24.  L. Zarour, K. Abed, M. Hacil, and A Borni, “Control and optimisation of photovoltaic water pumping system using sliding mode”, Bull. Pol. Acad. Sci. Tech. Sci. 67(3), 605–611 (2019).
  25.  N. Siddique, F.U. Rehman, M. Wasif, W. Abbasi, and Q. Khan, “Parameter Estimation and Synchronization of Vaidyanathan Hyperjerk Hyper-Chaotic System via Integral Sliding Mode Control”, 2018 AEIT Conference IEEE, 1–5 (2018).
  26.  K. Urbanski, “A new sensorless speed control structure for PMSM using reference model”, Bull. Pol. Acad. Sci. Tech. Sci. 65(4), 489–496 (2017).
  27.  X. Sun, Z. Shi, Y. Zhou, W. Zebin, S. Wang,B. Su, L. Chen, and K. Li, “Digital control system design for bearingless permanent magnet synchronous motors”, Bull. Pol. Acad. Sci. Tech. Sci. 66(5), 687–698 (2018).
  28.  T. Tarczewski, M. Skiwski, L.J. Niewiara, and L.M. Grzesiak, “High-performance PMSM servo-drive with constrained state feedback position controller”, Bull. Pol. Acad. Sci. Tech. Sci. 66(1), 49–58 (2018).
  29.  W. Xing-Yuan and Z. Hao, “Backstepping-based lag synchronization of a complex permanent magnet synchronous motor system”, Chin. Phys. B 22, 048902 (2013).
  30.  Z. Zhang, Z. Li, M.P. Kazmierkowski, J. Rodríguez, and R. Kennel, “Robust Predictive Control of Three-Level NPC Back-to-Back Power Converter PMSG Wind Turbine Systems With Revised Predictions”, IEEE Trans. Power Electron. 33(11), 9588– 9598 (2018).
  31.  N. Hoffmann, F.W. Fuchs, M.P. Kazmierkowski, and D. Schröder, “Digital current control in a rotating reference frame – Part I: System modeling and the discrete time-domain current controller with improved decoupling capabilities”, IEEE Trans. Power Electron. 31(7), 5290–5305 (2016).
  32.  H. Won, Y.-K. Hong, M. Choi, H.-s. Yoon, S. Li and T. Haskew, “Novel Efficiency-shifting Radial-Axial Hybrid Interior Permanent Magnet Sychronous Motor for Electric Vehicle”, 2020 IEEE Energy Conversion Congress and Exposition (ECCE), Detroit, USA, 2020, pp. 47–52.
  33.  C. Jiang and S. Liu, “Synchronization and Antisynchronization of-Coupled Complex Permanent Magnet Synchronous Motor Systems with Ring Connection”, Complexity 4, 1–15 (2017).
  34.  M. Karabacak and H.I. Eskikurt, “Speed and current regulation of a permanent magnet synchronous motor via nonlinear and adaptive backstepping control”, Math. Comput. Model. 53, 2015–2030 (2011).
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Authors and Affiliations

Nazam Siddique
1
ORCID: ORCID
Fazal U. Rehman
1
  1. Capital University of Science and Technology, Islamabad Expressway, Kahuta Road, Zone-V Islamabad, Pakistan

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