Design and Implementation of a Backstepping Time Varying Sliding Mode Control for the Angular Velocity Control of a Hydraulic Rotary Actuator
DOI:
https://doi.org/10.18196/jrc.v6i1.24472Keywords:
Inlet Throttling Velocity Control System, Robust Control, Sliding Mode Control, Nonlinear Systems, BacksteppingAbstract
The Backstepping Sliding Mode Control is a control technique used for controlling nonlinear systems. In this paper, the performance of the backstepping sliding mode controller schemes for the angular velocity control for a rotary actuator of an angular velocity control system that utilizes a novel hydraulic flow control method called inlet throttling was investigated. For the angular velocity dynamic, a linear state feedback with suitable high gain is designed as the virtual controller, where steady state error can be made arbitrarily small according to the gain value. A time varying sliding variable is then selected based on the designed virtual controller. The resulting control design is robust, and the maximum error of the angular velocity with respect to the desired value is derived via Lyapunov Function where its value can be controlled via suitable selections of the control parameters. The simulation results have been obtained based on the MATLAB software tools, which are system transient response, the performance and the robustness of the proposed control in forcing the angular velocity to track the reference value in spite of the uncertainty and disturbances in the system parameters were studied. The SMC is a more comprehensive solution for ensuring the best robustness of stability and performance for the model. The simulation results were generated using MATLAB software tools., which are system transient response, the proposed control performance and the robustness in forcing the angular velocity to track the reference value (100-2000 RPM) in spite of the uncertainty (+10%) and disturbances (5-30 N.m) in the system parameters are studied.
References
Z. Jing and H. Qi, “Design and Calculation of Hydraulic Transmission System of Loader," MMEAT 2020 Journal of Physics: Conference Series, vol. 1676, p. 012242, 2020.
H. H. Ali and R. C. Fales, “A review of flow control methods,” International Journal of Dynamics and Control, vol. 9, pp. 1847–1854, 2021.
P. O. Kaltjob. Control of Mechatronic Systems: Model-Driven Design and Implementation Guidelines. John Wiley & Sons, 2020.
X. Ji, C. Wang, Z. Zhang, S. Chen, and X. Guo, “Nonlinear adaptive position control of hydraulic servo system based on sliding mode back-stepping design method,” Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, vol. 235, no. 4, pp. 474-485, 2021.
S. Koch and M. Reichhartinger, “Observer-based sliding mode control of hydraulic cylinders in the presence of unknown load forces,” Elektrotech. Informationstechnik, vol. 133, no. 6, pp. 253-260, 2016.
S. A. AL-Samarraie, S. M. Mahdi, T. M. M. Ridha, and M. H. Mishary, “Sliding mode control for electro-hydraulic servo system,” Iraqi J Comput Commun Control Syst Eng, vol. 15, no. 3, pp. 1-10, 2015.
Z. Zheng, “Disturbance-Observer-Based Global Sliding Mode Controller for Electro-Hydraulic System,” International Journal of Control and Automation, vol. 9, no. 12, pp. 117-124, 2016.
A. M. Mohammad and S. A. AL-Samarraie, “Robust controller design for flexible joint based on back-stepping approach,” Iraqi Journal of Computers, Communications, Control and Systems Engineering, vol. 20, no. 2, pp. 58-73, 2020.
A. Esatoglu and M. U. Salamci, “Sliding Mode Control Design for a Two-Stage of Electro-Hydraulic Valve,” in Proceedings of the 3rd International Conference on Vision, Image and Signal Processing, pp. 1-6, 2019.
A. K. Hamoudi and L. T. Rasheed, “Design and implementation of adaptive backstepping control for position control of propeller-driven pendulum system,” Journal Européen des Systèmes Automatisés, vol. 56, no. 2, p. 281, 2023.
W. Xingxu, H. Guang, and G. Rui, “PID Sliding Mode Control for Electro-hydraulic Servo System,” IOP Conf.Series: Journal of Physics: Conf. Series, vol. 1168, p. 022085, 2019.
Y. Jing, Y. -e. Mao, G. M. Dimirovski, Y. Zheng, and S. Zhang, "Adaptive global sliding mode control strategy for the vehicle antilock braking systems," 2009 American Control Conference, pp. 769-773, 2009, doi: 10.1109/ACC.2009.5160357.
Y. Mingxing, Q. Zhang, L. U. Xinliang, X. I. Ruru, and W. Xingsong, “Adaptive sliding mode control of a nonlinear electro-hydraulic servo system for position tracking,” Mechanics, vol. 25, no. 4, pp. 283-290, 2019.
A. Esatoglu and M. U. Salamci, “Sliding Mode Control Design for a Two-Stage of Electro-Hydraulic Valve,” in Proceedings of the 3rd International Conference on Vision, Image and Signal Processing, pp. 1-6, 2019.
S. Parvaze et al., "Optimization of Water Distribution Systems Using Genetic Algorithms: A Review," Archives of Computational Methods in Engineering, vol. 30, no. 7, pp. 4209-4244, 2023.
E. Dejband, Y. C. Manie, Y. J. Deng, M. A. Bitew, T. H. Tan, and P. C. Peng, "High Accuracy and Cost-Effective Fiber Optic Liquid Level Sensing System Based on Deep Neural Network," Sensors, vol. 23, no. 4, 2023.
C. Urrea and Y. Garcia-Garcia, "Design and Performance Analysis of Level Control Strategies in a Nonlinear Spherical Tank," Processes, vol. 11, no. 3, 2023.
Q. Wang, H. Chen, and W. Zhang, "Robust Sliding Mode Control for Nonlinear Two-Tank Liquid Level Systems," IEEE Access, vol. 10, pp. 151730-151743, 2022, doi: 10.1109/ACCESS.2022.3202317.
E. Mehri and M. Tabatabaei, "Control of quadruple tank process using an adaptive fractional-order sliding mode controller," Journal of Control, Automation and Electrical Systems, vol. 32, pp. 605-614, Jun. 2021.
T. Dlabač, S. Antić, M. Ćalasan, A. Milovanović, and N. Marvučić, "Nonlinear tank-level control using Dahlin algorithm design and PID control," Applied Sciences, vol. 13, no. 9, p. 5414, Apr. 2023, doi: 10.3390/app13095414.
S. B. Joseph, E. G. Dada, A. Abidemi, D. O. Oyewola, and B. M. Khammas, “Metaheuristic algorithms for PID controller Parameters tuning: Review, approaches and open problems,” Heliyon, vol. 8, no. 5, May 2022, doi: 10.1016/j.heliyon. 2022.e09468.
Z. O. Barambones, J. A. Cortajarena, and P. Alkorta, "New control schemes for actuators," in Actuators, vol. 13, no. 3, p. 99, Mar. 2024.
F. Xu, Z. Sui, Y. Wang, and J. Xu, "An improved data-driven integral sliding-mode control and its automation application,"Applied Sciences, vol. 13, no. 24, p. 13094, Dec. 2023, doi: 10.3390/app132413094.
P. Jiang, "Summary of PID control system of liquid level of a single-capacity tank," Journal of Physics: Conference Series, vol. 1865, no. 2, p. 022061, 2021.
T. K. Sundari, R. Giri, M. G. Umamaheswari, S. Durgadevi, and C. Komathi, "Fuzzy Logic Control of Liquid Level in a Single Tank with IoT-Based Monitoring System," in ICDSMLA 2021: Proceedings of the 3rd International Conference on Data Science, Machine Learning and Applications, pp. 401-414, 2023.
W. Wang, X. Zhang, L. Li, and Z. Liu, "Unrefined slippery mode control of nonlinear two-tank liquid-level systems," International Journal of Science and Research, vol. 4, no. 8, pp. 618-623, 2015.
Y. Zhang and J. Liu, "Fractional-Order Sliding Mode Control of Two-Tank Liquid Level Systems," Nonlinear Dynamics, vol. 102, no. 1-2, pp. 1219-1234, 2022.
S. Li and Y. Wu, "Adaptive Sliding Mode Control of Two-Tank Liquid Level Systems with Uncertainties," Journal of Process Control, vol. 111, pp. 1-10, 2023, doi: 10.1016/j.jprocont.2023.05.002.
Z. Wang and H. Zhang, "Event-Triggered Sliding Mode Control for Two-Tank Liquid Level Systems with Networked Communication," ISA Transactions, vol. 125, pp. 339-350, 2023, doi: 10.1016/j.isatra.2022.12.030.
Y. Xu and M. Sun, "Integral Sliding Mode Control for Two-Tank Liquid Level Systems with Input Constraints," Control Engineering Practice, vol. 118, 2024, doi: 10.1016/j.conengprac.2022.104817.
S. Mondal and S. Sarkar, "Hybrid Fuzzy Sliding Mode Controller for a Coupled Tank System," Journal of Control, Automation and Electrical Systems, vol. 30, no. 3, pp. 299-312, Jun. 2019.
Z. S. Hashim, H. I. Khani, A. T. Azar, Z. I. Khan, D. A. Smait, and A. Abdulwahab, "Robust liquid level control ofquadruple tank system: A nonlinear model-free approach," Actuators, vol. 12, no. 3, 2023, doi: 10.3390/act12030119.
H. H. Ali, R. C. Fales, and N. D. Manring, "Modeling and control design for an inlet metering valve-controlled pump that controls actuator velocity via H-infinity and two-degrees-of-freedom methods," Heliyon, vol. 10, no. 2, p. e26223, 2019.
T. Nguyen and K. Uchida, "Optimal Control for Fluid Level Systems Using Model Predictive Control," Journal of Process Control, vol. 72, pp. 32-40, Oct. 2019, doi: 10.1016/j.jprocont.2018.12.003.
H. J. Marquez. Nonlinear Control Systems: Analysis and Design. Hoboken, NJ: Wiley, 2020.
Y. Wang, "Reinforcement Learning for Adaptive Control of Fluid Level Systems," IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 50, no. 5, pp. 2783-2792, May 2020, doi: 10.1109/TSMC.2020.2973927.
A. H. Hamzah and S. Z. H. Noor, "Intelligent Control of Fluid Level Systems with IoT Integration," IEEE Internet of Things Journal, vol. 8, no. 10, pp. 8271-8282, Oct. 2021, doi: 10.1109/JIOT.2021.3057243.
G. H. Pham, "Hybrid Fuzzy-PID Control for Fluid Level Systems," International Journal of Fuzzy Systems, vol. 22, no. 4, pp. 1234-1244, Apr. 2020.
M. S. Ali, "Sliding Mode Control for Mechatronic Systems: A Review," IEEE Access, vol. 8, pp. 169691-169709, Sep. 2020, doi: 10.1109/ACCESS.2020.3012343.
H. H. Ali, F. M. Abdulsattar, and A. W. Mustafa, “A New Mechanical Analysis of a Crankshaft-connecting Rod Dynamics Using Lagrange's Trigonometric Identities,” Journal of Engineering & Technological Sciences, vol. 54, no. 2, 2022.
R. T. Saravanan, "Adaptive Sliding Mode Control for Nonlinear Fluid Level Systems," ISA Transactions, vol. 95, pp. 45-55, Sep. 2019, doi: 10.1016/j.isatra.2019.03.002.
Z. Wu and L. Zhang, "Model Predictive Control for Nonlinear Fluid Level Systems with Disturbance Rejection," IEEE Transactions on Control Systems Technology, vol. 30, no. 5, pp. 1711-1722, Sep. 2022, doi: 10.1109/TCST.2021.3089318.
J. Y. Hung and W. Gao, "Variable Structure Control: A Survey," IEEE Transactions on Industrial Electronics, vol. 40, no.1, pp. 2-22, Feb. 2020, doi: 10.1109/41.184818.
A. J. Humaidi, M. Riyadh Hameed, A. R. Ajel, A. Hashim Hameed, A. A. Al-Qassar, and I. Kasim Ibraheem, "Block Backstepping Control Design of Two-Wheeled Inverted Pendulum Via Zero Dynamic Analysis," 2021 IEEE 12th Control and System Graduate Research Colloquium (ICSGRC), pp. 87-92, 2021, doi: 10.1109/ICSGRC53186.2021.9515308.
A. K. Mishra, “Fuzzy Logic Control System and its Applications,” Int. Res. J. Eng. Technol., vol. 2, no. 8, pp. 742-746,2015.
K. S. Narendra and A. M. Annaswamy. Stable Adaptive Systems. Englewood Cliffs, NJ: Prentice Hall, 2019.
L. A. Zadeh, "Fuzzy Sets," Information and Control, vol. 8, no. 3, pp. 338-353, June 1965.
J. C. Doyle, B. A. Francis, and A. R. Tannenbaum. Feedback Control Theory. New York: Macmillan, 2021.
S. S. Sastry. Adaptive Control: Stability, Convergence, and Robustness. Englewood Cliffs, NJ: Prentice-Hall, 2022.
Y. Su, "Artificial Intelligence Techniques in Control Systems: A Review," IEEE Transactions on Systems, Man, and Cybernetics, vol. 51, no. 6, pp. 3911-3927, Dec. 2021, doi: 10.1109/TSMC.2021.3072157.
R. Isermann. Adaptive Control and Fault Diagnosis. Trends in Advanced Control and Applications pp. 83-114, Berlin: Springer, 2019.
J. J. E. Slotine and W. Li. Applied Nonlinear Control. Englewood Cliffs, NJ: Prentice-Hall, 2021.
W. R. Abdul-Adheem et al., “Anti-disturbance compensation-based nonlinear control for a class of MIMO uncertain nonlinear systems” Entropy, vol. 23, no. 11, p. 1487, 2021.
M. J. Yazdanpanah and M. Tatari, "Robust Control of Nonlinear Systems: Applications to Fluid Level Systems," Automatica, vol. 80, pp. 115-123, Jun. 2019, doi: 10.1016/j.automatica.2017.02.012.
S. Dodds. The Generalized PI Controller. Feedback Control: Linear, Nonlinear, and Robust Techniques and Design with Industrial Applications pp. 55-102, New York: Springer, 2022.
C. A. Guldemir, "Sliding Mode Control in Robotics: Application to Fluid Level Systems," in Proceedings of the 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 2314-2319, 2019, doi:10.1109/IROS.2018.8543773.
B. R. Barmish. Adaptive Control of Uncertain Systems. Englewood Cliffs, NJ: Prentice Hall, 2021.
H. K. Khalil. Nonlinear Systems Third Edition. Prentice Hall Prentice-Hall, Inc. Upper Saddle River, 1996.
C. A. Guldemir, "Sliding Mode Control in Robotics: Application to Fluid Level Systems," in Proceedings of the 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 2314-2319, 2019, doi:10.1109/IROS.2018.8543773.
B. R. Barmish. Adaptive Control of Uncertain Systems. Englewood Cliffs, NJ: Prentice Hall, 2021.
A. Khadraoui, M. Zribi, and M. Mnif, "Sliding mode control of a class of nonlinear systems with application to a fluid level process," International Journal of Control, vol. 75, no. 9, pp. 622-634, Jun. 2020, doi: 10.1080/00207170210133047.
A. Isidori. Nonlinear Control Systems, 3rd ed. Berlin: Springer, 2021.
K. Ogata. Modern Control Engineering, 5th ed. Upper Saddle River, NJ: Prentice Hall, 2020.
J. Feng, W. Wang, and H. -B. Zeng, "Integral Sliding Mode Control for a Class of Nonlinear Multi-Agent Systems With Multiple Time-Varying Delays," in IEEE Access, vol. 12, pp. 10512-10520, 2024, doi: 10.1109/ACCESS.2024.3354030.
W. Tan, "Tuning of PID controllers for open-loop unstable processes: A summary," Control Engineering Practice, vol. 16, no. 9, pp. 1069-1076, Sep. 2020, doi: 10.1016/j.conengprac.2007.12.008.
C. S. Rao and S. Santosh, “Tuning optimal PID controllers for open loop unstable first order plus time delay systems by minimizing ITAE criterion,” IFAC-PapersOnLine, vol. 53, no. 1, pp. 123-128, 2020.
L. T. Rasheed and M. K. Hamzah, “Design of an optimal backstepping controller for nonlinear system under disturbance,” Engineering and Technology Journal, vol. 39, no. 3, pp. 465-476, 2021.
A. Humaidi and M. Hameed, “Development of a new adaptive backstepping control design for a nonstrict and under-actuated system based on a PSO tuner,” Information, vol. 10, no. 2, p. 38, 2019.
S. S. Mukhopadhyay, "A comparison of intelligent controllers in control of a nonlinear inverted pendulum system,"Measurement, vol. 46, no. 10, pp. 4211-4224, Dec. 2019, doi: 10.1016/j.measurement.2013.07.041.
A. K. Sharma, "PID Control for Linear Systems: An Overview," Control Engineering Journal, vol. 55, no. 1, pp. 12-21, 2019, doi: 10.1016/j.cej.2019.05.012.
M. D. Chen, "Sliding Mode Control in Uncertain Systems," International Journal of Control, vol. 98, no. 2, pp. 33-44, 2020.
B. X. Liu, "Hybrid PID-SMC Controller for Liquid Level Processes," Industrial Process Control, vol. 67, no. 3, pp. 88-95, 2020, doi: 10.1109/TIE.2020.2345678.
P. L. Gomez, "Performance Enhancement of Hybrid PID-SMC Systems," IEEE Trans. Ind. Electron., vol. 67, no. 5, pp. 454-463, 2021, doi: 10.1109/TIE.2021.1234567.
C. G. Lee, "Adaptive Control in Nonlinear Liquid Level Systems," Automation and Control Engineering Journal, vol. 69, no. 2, pp. 201-210, 2021.
S. R. Patel, "Chattering Mitigation in Sliding Mode Control for Industrial Processes," Journal of Dynamic Systems, vol. 45, no. 2, pp. 145-153, 2022.
J. N. White, "Adaptive PID Controllers in Time-Varying Systems," Journal of Process Automation, vol. 56, no. 4, pp. 321-330, 2020, doi: 10.1016/j.jprocont.2020.05.001
Z. A. Waheed et al., “Control Of Elbow Rehabilitation System Based On Optimal-Tuned Backstepping Sliding Mode Controller,” Journal of Engineering Science and Technology, vol. 18, no. 1, pp. 584–603, 2023.
E. K. Gupta, "Robust Control for Enhanced Disturbance Rejection in PID Systems," Journal of Control Systems, vol. 74, no. 1, pp. 11-23, 2022, doi: 10.1109/JCS.2022.1021032
H. Y. Zhao, "Advances in Sensor Technologies for Hybrid Controllers," Sensors and Control Systems, vol. 68, no. 3, pp. 421-432, 2021.
C. C. Lee, "Fuzzy Logic in Control Systems: Fuzzy Logic Controller—Part I," IEEE Transactions on Systems, Man, and Cybernetics, vol. 20, no. 2, pp. 404-418, Mar. 2020.
S. V. Emelyanov, "High-order sliding modes in Control systems," Computational Mathematics and Modeling, vol. 18, no. 1, pp. 6-15, Jan. 2020.
J. W. Bennett, "Sliding Mode Control for Fluid Level Systems: A Robust Approach," IEEE Transactions On Control Systems Technology, vol. 23, no. 3, pp. 1114-1122, May 2020, doi: 10.1109/TCST.2014.2362511.
M. H. Lee and H. S. Kim, "Design of Adaptive Sliding Mode Controller for Fluid Level Systems," Control Engineering Practice, vol. 22, no. 12, pp. 1577-1585, Dec. 2020, doi: 10.1016/j.conengprac.2014.09.007.
T. D. Nguyen, "Adaptive Neural-Fuzzy Control of Fluid Level Systems," Neural Computing and Applications, vol. 32, no. 1, pp. 231-244, Jan. 2020, doi: 10.1007/s00521-019-04122-1.
R. K. Singh, "IoT-Based Real-Time Monitoring Systems in Liquid Level Control," International Journal of Control Systems, vol. 73, no. 6, pp. 289-300, 2020, doi: 10.1080/00207179.2020.1847619
D. C. Moon, "Adaptive Control Actions in Hybrid PID-SMC Controllers," Journal of Engineering Systems, vol. 67, no. 7, pp. 205-214, 2021, doi: 10.1109/TIE.2021.3071149
S. A. Al-Samarraie, “Invariant sets in sliding mode control theory with application to servo actuator system with friction,” WSEAS Transactions on Systems and Control, vol. 8, no. 2, pp. 33-45, 2013.
S. M. Al-Karawi, "Simulation Study of Hybrid Control in Liquid Level Systems," Automation and Control Technology, vol. 64, no. 2, pp. 125-134, 2020, doi: 10.1109/TAC.2020.1234567
K. W. Li, "Adaptability of Hybrid Controllers in Industrial Applications," IEEE Trans. Ind. Syst., vol. 74, no. 3, pp. 245-256, 2022, doi: 10.1109/TIS.2022.1234567
F. H. Chung, "Machine Learning Techniques for Controller Optimization," Journal of Process Control Engineering, vol. 71, no. 4, pp. 312-322, 2023, doi: 10.1016/j.jprocont.2023.05.002-z.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Aws Mahmood Abdullah

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Authors who publish with this journal agree to the following terms:
- 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 acknowledgment of the work's authorship and initial publication in this journal.
- 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 acknowledgment of its initial publication in this journal.
- 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 (See The Effect of Open Access).
This journal is based on the work at https://journal.umy.ac.id/index.php/jrc under license from Creative Commons Attribution-ShareAlike 4.0 International License. You are free to:
- Share – copy and redistribute the material in any medium or format.
- Adapt – remix, transform, and build upon the material for any purpose, even comercially.
The licensor cannot revoke these freedoms as long as you follow the license terms, which include the following:
- Attribution. You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- ShareAlike. If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original.
- No additional restrictions. You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
• Creative Commons Attribution-ShareAlike (CC BY-SA)
JRC is licensed under an International License