Robust control of single input multi outputs systems
DOI:
https://doi.org/10.20998/2074-272X.2025.4.03Keywords:
nonlinear system, single input multi outputs system, stability, robustness, sliding mode controlAbstract
Introduction. Most of mechanical systems are nonlinear and complex, the complexity of these latter lies on highly nonlinear characteristics, or on dynamics that stimulate the development or change of the process through an applied force in a disturbed environment. Single input multi outputs (SIMO) systems, which are structured into subsystems, are considered as complex systems. The task to control their degrees of freedom is more complicated, and it is not easily reachable, due to the fact that nonlinear laws are not directly applicable to those systems, which requires to trait them in a particular way. Problem. First order sliding mode control (FOSMC) has already been applied in several previous works to this kind of systems, and due to its robustness property, this control gave good results in term of stabilization and tracking, but the chattering phenomenon remains a big problem, which affects the control structure and the actuators. Purpose. In order to address the problem of chattering encountered when applying the FOSMC to a category of second order subsystems, a second order sliding mode control (SOSMC) is designed. Methods. This work consists of developing an appropriate second order system structure, which can go with the sliding control expansion, and then studying the SOSMC for this chosen system. The hierarchical structure of the sliding surface which is made using a linear combination between subsurfaces, according to the system structure, allows the only control input to affect subsystems in graded manner from the last one to the first one. Results. We have applied the constructed control law to a SIMO system for two cases with and without disturbances. Simulation results of the application have shown the effectiveness and the robustness of the designed controller. References 30, figures 10.
References
Krzysztofik I., Koruba Z. Sliding Mode Control for a Gyroscope System. Problems of Mechatronics Armament Aviation Safety Engineering, 2017, vol. 8, no. 4, pp. 47-60. doi: https://doi.org/10.5604/01.3001.0010.7317.
Prabhakar Rao B., Sunil K. G. Sliding mode controller design for spacecraft attitude stabilization. International Journal of Advanced Engineering Sciences and Technologies, 2011, vol. 11, no. 1, pp. 183-189.
Wang X., Hou B. Sliding mode control of a 2-DOF manipulator with random base vibration based on modified exponential reaching law. Vibroengineering Procedia, 2016, vol. 10, pp. 247-252.
Glaoui H., Harrouz A. Sliding mode control of the dfig used in wind energy system. Electrical Engineering & Electromechanics, 2018, no. 3, pp. 61-67. doi: https://doi.org/10.20998/2074-272X.2018.3.08.
Gulshan Z.A., Ali M.Z.H., Shah M.S., Nouman D., Anwar M., Ullah M.F. A robust control design approach for altitude control and trajectory tracking of a quadrotor. Electrical Engineering & Electromechanics, 2021, no. 5, pp. 17-23. doi: https://doi.org/10.20998/2074-272X.2021.5.03.
Hamdi R., Hadri Hamida A., Bennis O. On modeling and real-time simulation of a robust adaptive controller applied to a multicellular power converter. Electrical Engineering & Electromechanics, 2022, no. 6, pp. 48-52. doi: https://doi.org/10.20998/2074-272X.2022.6.08.
Oualah O., Kerdoun D., Boumassata A. Comparative study between sliding mode control and the vector control of a brushless doubly fed reluctance generator based on wind energy conversion systems. Electrical Engineering & Electromechanics, 2022, no. 1, pp. 51-58. doi: https://doi.org/10.20998/2074-272X.2022.1.07.
Nebti K., Lebied R. Fuzzy maximum power point tracking compared to sliding mode technique for photovoltaic systems based on DC-DC boost converter. Electrical Engineering & Electromechanics, 2021, no. 1, pp. 67-73. doi: https://doi.org/10.20998/2074-272X.2021.1.10.
Yinxing Hao, Jianqiang Yi, Dongbin Zhao, Dianwei Qian. Design of a new incremental sliding mode controller. 2008 7th World Congress on Intelligent Control and Automation, 2008, pp. 3407-3412. doi: https://doi.org/10.1109/WCICA.2008.4593467.
Tuan L.A., Lee S.-G. Sliding mode controls of double-pendulum crane systems. Journal of Mechanical Science and Technology, 2013, vol. 27, no. 6, pp. 1863-1873. doi: https://doi.org/10.1007/s12206-013-0437-8.
Bessas A., Benalia A., Boudjema F. Integral Sliding Mode Control for Trajectory Tracking of Wheeled Mobile Robot in Presence of Uncertainties. Journal of Control Science and Engineering, 2016, vol. 2016, pp. 1-10. doi: https://doi.org/10.1155/2016/7915375.
Toujeni N., Mnasri C., Gasmi M. Repetitive Control based on Integral Sliding Mode Control of Matched Uncertain Systems. International Journal of Advanced Computer Science and Applications, 2018, vol. 9, no. 12, pp. 446-455 doi: https://doi.org/10.14569/IJACSA.2018.091263.
Zeghlache S., Saigaa D., Kara K., Harrag A., Bouguerra A. Fuzzy based sliding mode control strategy for an UAV type-quadrotor. The Mediterranean Journal of Measurement and Control, 2012, vol. 8, no. 3, pp. 436-445.
Hong G.B., Nguyen H.T., Nguyen M.T., Le T.T.H., Nguyen V.D.H. Trajectory tracking for futura pendulum by incremental sliding mode control. Robotica & Management, 2019, vol. 24, no. 1, pp. 4-7.
Chen P.C., Huang A.C. Adaptive multiple-surface sliding control of hydraulic active suspension systems based on the function approximation technique. Journal of Vibration and Control, 2005, vol. 11, no. 5, pp. 685-706. doi: https://doi.org/10.1177/1077546305052788.
Benkahla M., Taleb R., Boudjema Z. A new robust control using adaptive fuzzy sliding mode control for a DFIG supplied by a 19-level inverter with less number of switches. Electrical Engineering & Electromechanics, 2018, no. 4, pp. 11-19. doi: https://doi.org/10.20998/2074-272X.2018.4.02.
Guezi A., Bendaikha A., Dendouga A. Direct torque control based on second order sliding mode controller for three-level inverter-fed permanent magnet synchronous motor: comparative study. Electrical Engineering & Electromechanics, 2022, no. 5, pp. 10-13. doi: https://doi.org/10.20998/2074-272X.2022.5.02.
Hinda A., Khiat M., Boudjema Z. Fuzzy second order sliding mode control of a unified power flow controller. Electrical Engineering & Electromechanics, 2019, no. 6, pp. 55-61. doi: https://doi.org/10.20998/2074-272X.2019.6.08.
Mishra S.K., Chandra D. Stabilization and tracking control of inverted pendulum using fractional order PID controllers. Journal of Engineering, 2014, vol. 2014, pp. 1-9. doi: https://doi.org/10.1155/2014/752918.
Shah M.S., Mahmood T., Ullah M.F. Power quality improvement using ultra capacitor based dynamic voltage restorer with real twisting sliding mode control. Electrical Engineering & Electromechanics, 2022, no. 1, pp. 59-63. doi: https://doi.org/10.20998/2074-272X.2022.1.08.
Parvat B.J., Ratnaparkhi S.D. A Second Order Sliding Mode Controller Applications in Industrial Process. International Journal of Engineering Trends and Technology, 2015, vol. 19, no. 4, pp. 217-222. doi: https://doi.org/10.14445/22315381/IJETT-V19P238.
Chawengkrittayanont P., Pukdeboon C., Kuntanapreeda S., Moore E.J. Smooth second-order sliding mode controller for multivariable mechanical systems. SN Applied Sciences, 2021, vol. 3, no. 10, art. no. 816. doi: https://doi.org/10.1007/s42452-021-04800-4.
Bloch A.M., Leonard N.E., Marsden J.E. Stabilization of mechanical systems using controlled Lagrangians. Proceedings of the 36th IEEE Conference on Decision and Control, 1997, vol. 3, pp. 2356-2361. doi: https://doi.org/10.1109/CDC.1997.657135.
Bullo F., Lewis A.D. Geometric Control of Mechanical Systems. Modeling, Analysis, and Design for Simple Mechanical Control Systems. Springer, New York, 2005. 727 p. doi: https://doi.org/10.1007/978-1-4899-7276-7.
Bouraghda S., Sebaa K., Bechouat M., Sedraoui M. An improved sliding mode control for reduction of harmonic currents in grid system connected with a wind turbine equipped by a doubly-fed induction generator. Electrical Engineering & Electromechanics, 2022, no. 2, pp. 47-55. doi: https://doi.org/10.20998/2074-272X.2022.2.08.
Chih-Min Lin, Yi-Jen Mon. Decoupling control by hierarchical fuzzy sliding-mode controller. IEEE Transactions on Control Systems Technology, 2005, vol. 13, no. 4, pp. 593-598. doi: https://doi.org/10.1109/TCST.2004.843130.
Behnamgol V., Vali A.R., Mohammadzaman I. Second order sliding mode control with finite time convergence. AUT Journal of Modeling and Simulation, 2013, vol. 45, no. 2, pp. 41-52. doi: https://doi.org/10.22060/miscj.2015.528.
Benbouhenni H., Lemdani S. Combining synergetic control and super twisting algorithm to reduce the active power undulations of doubly fed induction generator for dual-rotor wind turbine system. Electrical Engineering & Electromechanics, 2021, no. 3, pp. 8-17. doi: https://doi.org/10.20998/2074-272X.2021.3.02.
Bartolini G., Pisano A., Punta E., Usai E. A survey of applications of second-order sliding mode control to mechanical systems. International Journal of Control, 2003, vol. 76, no. 9–10, pp. 875-892. doi: https://doi.org/10.1080/0020717031000099010.
Karam E.H., Jadoo E.H. Design modified second order sliding mode controller based on st algorithm for blood glucose regulation systems. Applied Computer Science, 2020, vol. 16, no. 2, pp. 18-31. doi: https://doi.org/10.23743/acs-2020-10.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 D. Zehar, K. Behih, A. Cherif
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Authors who publish with this journal agree to the following terms:
1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
