Adaptive Non-singular Fast Terminal Sliding Mode Control and Synchronization of a Chaotic System via Interval Type-2 Fuzzy Inference System with Proportionate Controller

Document Type : Research Paper

Authors

1 Faculty of Electrical Engineering, K.N. Toosi University of Technology, Tehran, Iran.

2 Electrical and Electronic Engineering Department, Shahed university, Persian Gulf Highway

3 Department of Material, Mechanical and Manufacturing, University of Nottingham, UK

Abstract

This paper introduces a novel adaptive nonsingular fast terminal sliding mode approach that benefits from an interval type-2 fuzzy logic estimator and a gain for control and synchronization of chaotic systems in the presence of uncertainty. The nonsingular fast terminal sliding mode controller is developed to increase the convergence rate and remove the singularity problem of the system. Using the proposed method, the finite-time convergence has been ensured. To eliminate the chattering phenomenon in the conventional sliding mode controller, the discontinuous sign function is estimated using an interval type-2 fuzzy inference system (FIS) based on the center of sets type reduction followed by defuzzification. By adding the proportionate gain to the interval type-2 FIS, the robustness and speed of the controller system is enhanced. An appropriate Lyapunov function is utilized to ensure the closed-loop stability of the control system. The performance of the controller is evaluated for a nonlinear time-varying second-order magnetic space-craft chaotic system with different initial conditions in the presence of uncertainty. The simulation results show the efficacy of the proposed approach for the tracking control problems. The time and frequency domain analysis of the control signal demonstrates that the chattering phenomenon is successfully diminished.

Keywords

Main Subjects

References

[1] P. Akbary, M. Ghiasi, M. R. R. Pourkheranjani, H. Alipour, N. Ghadimi, Extracting appropriate nodal marginal
prices for all types of committed reserve, Computational Economics, 53(1) (2019), 1-26.
[2] R. K. Amirabadi, O. S. Fard, A. Mansoori, A novel fuzzy sliding mode control approach for chaotic systems, Iranian
Journal of Fuzzy Systems, 18(6) (2021), 133-150.
[3] M. H. Barhaghtalab, S. Mobayen, F. Merrikh-Bavat, Design of a global sliding mode controller using hyperbolic func-
tions for nonlinear systems and application in chaotic systems, ICEE 2019 - 27th Iranian Conference on Electrical
Engineering, (2019), 1030-1034.
[4] M. Boukattaya, N. Mezghani, T. Damak, Adaptive nonsingular fast terminal sliding-mode control for the tracking
problem of uncertain dynamical systems, ISA Transactions, 77 (2018), 1-19.
[5] W. Cai, R. Mohammaditab, G. Fathi, K. Wakil, A. G. Ebadi, N. Ghadimi, Optimal bidding and o ering strategies
of compressed air energy storage: A hybrid robust-stochastic approach, Renewable Energy, 143 (2019), 1-8.
[6] F. Farivar, M. A. Shoorehdeli, M. A. Nekoui, M. Teshnehlab, Chaos synchronization of uncertain nonlinear gyros
via hybrid control, IEEE/ASME International Conference on Advanced Intelligent Mechatronics, AIM, 1 (2009),
1365-1370.
[7] Y. Feng, X. Yu, Z. Man, Non-singular terminal sliding mode control of rigid manipulators, Automatica, 38(12)
(2002), 2159-2167.
[8] K. Hooshmandi, F. Bayat, M. Jahedmotlagh, A. Jalali, Guaranteed cost nonlinear sampled-data control: Applications
to a class of chaotic systems, Nonlinear Dynamics, 100 (2020), 731-748.
[9] J. Huang, J. Yang, D. Xie, D. Wu, Optimal sliding mode chaos control of direct-drive wave power converter, IEEE
Access, 7 (2019), 90922-90930.
[10] Y. Jin, W. Cao, M.Wu, Y. Yuan, Data-based variable universe adaptive fuzzy controller with self-tuning parameters,
Applied Soft Computing, 123 (2022), 108944.
[11] S. Johari, M. Yaghoobi, H. R. Kobravi, Nonlinear model predictive control based on hyper chaotic diagonal recurrent
neural network, Journal of Central South University, 29(1) (2022), 197-208.
[12] R. Kavikumar, B. Kaviarasan, Y. G. Lee, O. M. Kwon, R. Sakthivel, S. G. Choi, Robust dynamic sliding mode
control design for interval type-2 fuzzy systems, Discrete and Continuous Dynamical Systems, 15(7) (2022), 1839.
[13] R. Khalili Amirabadi, O. S. Fard, A. Mansoori, A novel fuzzy sliding mode control approach for chaotic systems,
Iranian Journal of Fuzzy Systems, 18(6) (2021), 133-150.
[14] M. A. Khanesar, E. Kayacan, M. Reyhanoglu, O. Kaynak, Feedback error learning control of magnetic satellites
using type-2 fuzzy neural networks with elliptic membership functions, IEEE Transactions on Cybernetics, 45(4)
(2015), 858-868.
[15] M. A. Khanesar, J. M. Mendel, Maclaurin series expansion complexity-reduced center of sets type-reduction +
defuzzi cation for interval type-2 fuzzy systems, 2016 IEEE International Conference on Fuzzy Systems, no. D,
(2016), 1224-1231.
[16] M. A. L. Khaniki, M. B. Hadi, M. Manthouri, Tuning of novel fractional order fuzzy PID controller for automatic
voltage regulator using grasshopper optimization algorithm, Majlesi Journal of Electrical Engineering, 15(2) (2021),
39-45.
[17] S. Kumar, A. E. Matouk, H. Chaudhary, S. Kant, Control and synchronization of fractionalorder chaotic satel-
lite systems using feedback and adaptive control techniques, International Journal of Adaptive Control and Signal
Processing, 35(4) (2021), 484-497.
[18] M. A. Labbaf Khaniki, M. Salehi Kho, M. Aliyari Shoorehdeli, Control and synchronization of chaotic spur gear
system using adaptive non-singular fast terminal sliding mode controller, Transactions of the Institute of Measurement
and Control, 44(14) (2022). DOI:10.1177/01423312221087578.
[19] M. A. Labbaf Khaniki, M. TavakoliKakhki, Adaptive type-II fuzzy nonsingular fast terminal sliding mode controller
using fractionalorder manifold for secondorder chaotic systems, Asian Journal of Control, 26(3) (2021), 2653.
[20] J. Liu, C. Chen, Z. Liu, K. Jermsittiparsert, N. Ghadimi, An IGDT-based risk-involved optimal bidding strategy
for hydrogen storage-based intelligent parking lot of electric vehicles, Journal of Energy Storage, 27 (2020), 101057.
[21] H. F. L¨ochel, D. Eger, T. Sperlea, D. Heider, J. Wren, Deep learning on chaos game representation for proteins,
Bioinformatics, 36(1) (2020), 272-279.
[22] H. Medhaffar, M. Feki, N. Derbel, Stabilization of chaotic systems via fuzzy time-delayed controller approach,
Iranian Journal of Fuzzy Systems, 16(2) (2019), 17-29.
[23] M. Mehrpooya, N. Ghadimi, M. Marefati, S. A. Ghorbanian, Numerical investigation of a new combined energy
system includes parabolic dish solar collector, Stirling engine and thermoelectric device, International Journal of
Energy Research, 45(11) (2021), 16436-16455.
[24] N. Miladi, H. Dimassi, S. Hadj Said, F. M’Sahli, Explicit nonlinear model predictive control tracking control based
on a sliding mode observer for a quadrotor subject to disturbances, Transactions of the Institute of Measurement
and Control, 42(2) (2020), 214-227.
[25] M. Mir, M. Shafieezadeh, M. A. Heidari, N. Ghadimi, Application of hybrid forecast engine based intelligent
algorithm and feature selection for wind signal prediction, Evolving Systems, 11(4) (2020), 559-573.
[26] F. Mirzapour, M. Lakzaei, G. Varamini, M. Teimourian, N. Ghadimi, A new prediction model of battery and wind-
solar output in hybrid power system, Journal of Ambient Intelligence and Humanized Computing, 10(1) (2019),
77-87.
[27] S. Mondal, C. Mahanta, Adaptive second order terminal sliding mode controller for robotic manipulators, Journal
of the Franklin Institute, 351(4) (2014), 2356-2377.
[28] O. Solaymani Fard, R. Khalili, A. Mansoori, A novel fuzzy sliding mode control approach for chaotic systems,
Iranian Journal of Fuzzy Systems, 18(6) (2021), 133-150.
[29] K. Tahir, C. Belfedal, T. Allaoui, M. Dena¨ı, M. Doumi, A new sliding mode control strategy for variable-speed wind
turbine power maximization, International Transactions on Electrical Energy Systems, 28(4) (2018), 1-22.
[30] A. T. Vo, H. J. Kang, Adaptive neural integral full-order terminal sliding mode control for an uncertain nonlinear
system, IEEE Access, 7(c) (2019), 42238-42246.
[31] A. T. Vo, H. J. Kang, T. D. Le, An adaptive fuzzy terminal sliding mode control methodology for uncertain nonlinear
second-order systems, 10954 LNCS. Springer International Publishing, 2018.
[32] L. Xiong, P. Li, J. Wang, High-order sliding mode control of DFIG under unbalanced grid voltage conditions,
International Journal of Electrical Power and Energy Systems, 117 (2020), 105608.
[33] S. S. D. Xu, C. C. Chen, Z. L. Wu, Study of nonsingular fast terminal sliding-mode fault-tolerant control, IEEE
Transactions on Industrial Electronics, 62(6) (2015), 3906-3913.
[34] Z. Yang et al., Robust multi-objective optimal design of islanded hybrid system with renewable and diesel
sources/stationary and mobile energy storage systems, Renewable and Sustainable Energy Reviews, 148 (2021),
111295.
[35] Y. Yang, Y. Niu, Z. Zhang, Dynamic event-triggered sliding mode control for interval Type-2 fuzzy systems with
fading channels, ISA Transactions, 110(xxxx) (2021), 53-62.
[36] L. Yang, J. Yang, Nonsingular fast terminal sliding-mode control for nonlinear dynamical systems, International
Journal of Robust and Nonlinear Control, 21(16) (2011), 1865-1879.
[37] Y. Yu, Y. Yuan, H. Yang, H. Liu, Nonlinear sampled-data ESO-based active disturbance rejection control for
networked control systems with actuator saturation, Nonlinear Dynamics, 95(2) (2019), 1415-1434.
 
Iranian Journal of Fuzzy Systems
Volume 20, Issue 6
November and December 2023
Pages 171-185

Files

Share

How to cite

Statistics