Sliding mode control for impulsive electrohydraulic position servo systems with external disturbances

i

This article has been updated. A Correction to this article was published on .

i

The Original Article was published on

i

The Original Article was published on

i

This article has been updated

i

This article was retracted on

i

This article has been updated

Abstract

This paper studied the trajectory tracking performance of electrohydraulic position servo systems subject to impulsive disturbance via sliding mode control. Different from traditional sliding mode control, which in applied in continuous state space, our proposed sliding mode control could restrain the negative effect of impulsive disturbance. The proposed method is based on the linear matrix inequality method; some sufficient conditions were presented to ensure the reachability of the sliding surface and the stability of the resulting sliding mode dynamics, where a relationship between continuous dynamics, impulsive strength, and impulsive frequency was established. It showed that this relationship can fully estimate the effect of impulsive disturbance. Moreover, we provided the estimation of the reaching time, which was related to the impulse actions and initial state. Finally, the simulations demonstrated the validity of the obtained results.

Keywords

electrohydraulic position servo system / impulsive disturbance / linear matrix inequality / reaching time / sliding mode control

CHANGE HISTORY

A Correction to this paper has been published:
https://doi.org

The Retraction Note was updated to reflect reception of statements of disagreement from all authors.

This article has been retracted.Please see the Retraction Notice for more detail:
https://doi.org

References

[1] Y. Chu, X. Han, R. Rakkiyappan, Finite-time lag synchronization for two-layer complex networks with impulsive effects, Math. Model. Control, 4 (2024), 71-85. https://doi.org/10.3934/mmc.2024007

[2] T. Yang, Impulsive Control Theory , Springer, 2002. https://doi.org/10.1007/3-540-47710-1

[3] X. He, X. Li, S. Song, Finite-time input-to-state stability of nonlinear impulsive systems, Automatica, 135 (2022), 109994. https://doi.org/10.1016/j.automatica.2021.109994

[4] Y. He, Y. Bai, Finite-time stability and applications of positive switched linear delayed impulsive systems, Math. Model. Control, 4 (2024), 178-194. https://doi.org/10.3934/mmc.2024016

[5] W. M. Haddad, V. Chellaboina, S. G. Nersesov, Impulsive and Hybrid Dynamical Systems: Stability, Dissipativity, and Control , Princeton University Press, 2006. https://doi.org/10.1515/9781400865246

[6] P. Naghshtabrizi, J. P. Hespanha, A. R. Teel, Exponential stability of impulsive systems with application to uncertain sampled-data systems, Syst. Control Lett., 57 (2008), 378-385. https://doi.org/10.1016/j.sysconle.2007.10.009

[7] R. Wang, C. Zhang, L. Feng, Z. Wu, Prescribed-time stabilization of uncertain nonlinear impulsive systems with multiple delays, Electron. Res. Arch., 33 (2025), 5207-5230. https://doi.org/10.3934/era.2025233

[8] Y. Li, J. Feng, J. Wang, Mean square synchronization for stochastic delayed neural networks via pinning impulsive control, Electron. Res. Arch., 30 (2022), 3172-3192. https://doi.org/10.3934/era.2022161

[9] W. Zhou, K. Wang, W. Zhu, Synchronization for discrete coupled fuzzy neural networks with uncertain information via observer-based impulsive control, Math. Model. Control, 4 (2024), 17-31. https://doi.org/10.3934/mmc.2024003

[10] W. Zhao, K. Li, Y. Shi, Exponential synchronization of neural networks with mixed delays under impulsive control, Electron. Res. Arch., 32 (2024), 5287-5305. https://doi.org/10.3934/era.2024244

[11] G. Zheng, Y. Orlov, W. Perruquetti, J. P. Richard, Finite-time-observer design for nonlinear impulsive systems with impact perturbation, Int. J. Control, 87 (2014), 2097-2105. https://doi.org/10.1080/00207179.2014.902998

[12] J. Liu, X. Liu, W. C. Xie, Input-to-state stability of impulsive and switching hybrid systems with time-delay, Automatica, 47 (2011), 899-908. https://doi.org/10.1016/j.automatica.2011.01.061

[13] V. Djordjevic, L. Dubonjic, M. M. Morato, D. Pršić, V. Stojanović, Sensor fault estimation for hydraulic servo actuator based on sliding mode observer, Math. Model. Control, 2 (2022), 34-43. https://doi.org/10.3934/mmc.2022005

[14] Z. Liu, J. Sun, D. Yue, X. Zuo, H. Gao, K. Feng, A review on integral evolution of electro-hydraulic actuation in three momentous domains: Aerospace, engineering machinery, and robotics, in Fourth International Conference on Mechanical Engineering, Intelligent Manufacturing, and Automation Technology (MEMAT 2023), 13082 (2024), 141-159. https://doi.org/10.1117/12.3026210

[15] W. Sun, H. Pan, H. Gao, Filter-based adaptive vibration control for active vehicle suspensions with electrohydraulic actuators, IEEE Trans. Veh. Technol., 65 (2015), 4619-4626. https://doi.org/10.1109/TVT.2015.2437455

[16] J. Li, L. Kong, H. Liang, W. Li, Review of development and characteristics research on electro-hydraulic servo system, Recent Pat. Eng., 18 (2024), 140-154. https://doi.org/10.2174/1872212118666230711165517

[17] X. Yang, H. Chen, J. Mao, Y. Wei, Dynamical behavior of coal shearer traction-swing coupling under corrected loads, Sci. Rep., 10 (2020), 8630. https://doi.org/10.1038/s41598-020-65184-w

[18] H. Feng, W. Ma, C. Yin, D. Cao, Trajectory control of electro-hydraulic position servo system using improved pso-pid controller, Autom. Constr., 127 (2021), 103722. https://doi.org/10.1016/j.autcon.2021.103722

[19] H. Liu, Y. Li, Y. Zhang, Y. Chen, Z. Song, Z. Wang, et al., Intelligent tuning method of pid parameters based on iterative learning control for atomic force microscopy, Micron, 104 (2018), 26-36. https://doi.org/10.1016/j.micron.2017.09.009

[20] G. Qiu, Y. Hao, G. Chen, G. Yan, Y. Chen, Prescribed performance trajectory tracking control for electro-hydraulic servo pump-controlled systems with input and state delays, Machines, 13 (2025), 1147. https://doi.org/10.3390/machines13121147

[21] X. Ren, Q. Guo, T. Li, Initial condition-free prescribed performance fault-tolerant control of electro-hydraulic servo systems with state constraints, Nonlinear Dyn., 113 (2025), 11723-11743. https://doi.org/10.1007/s11071-024-10804-7

[22] Y. Zhang, W. Ju, Q. Liu, L. Wei, C. Yin, X. Feng, et al., Control design of the hydraulic support pushing system based on saturation, Electron. Res. Arch., 34 (2026), 336-350. https://doi.org/10.3934/era.2026016

[23] G. Mihalev, S. Yordanov, K. Ormandzhiev, H. Stoycheva, T. Todorov, Synthesis of model predictive control for an electrohydraulic servo system using orthonormal functions, in 2024 5th International Conference on Communications, Information, Electronic and Energy Systems (CIEES), (2024), 1-6. https://doi.org/10.1109/CIEES62939.2024.10811237

[24] G. Shen, Z. Zhu, J. Zhao, W. Zhu, Y. Tang, X. Li, Real-time tracking control of electro-hydraulic force servo systems using offline feedback control and adaptive control, ISA Trans., 67 (2017), 356-370. https://doi.org/10.1016/j.isatra.2016.11.012

[25] V. Stojanović, Fault-tolerant control of a hydraulic servo actuator via adaptive dynamic programming, Math. Model. Control, 3 (2023), 181-191. https://doi.org/10.3934/mmc.2023016

[26] H. Ding, Y. Wang, H. Zhang, Robust output feedback position control of hydraulic support with neural network compensator, in Actuators, MDPI, 12 (2023), 263. https://doi.org/10.3390/act12070263

[27] Q. Guo, G. Shi, D. Wang, C. He, Neural network-based adaptive composite dynamic surface control for electro-hydraulic system with very low velocity, in Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 231 (2017), 867-880. https://doi.org/10.1177/0959651817731976

[28] C. Wang, J. Wang, Q. Guo, Z. Liu, C. P. Chen, Disturbance observer-based fixed-time event-triggered control for networked electro-hydraulic systems with input saturation, IEEE Trans. Ind. Electron., 72 (2024), 1784-1794. https://doi.org/10.1109/TIE.2024.3429638

[29] L. Cheng, Z. C. Zhu, G. Shen, S. Wang, X. Li, Y. Tang, Real-time force tracking control of an electro-hydraulic system using a novel robust adaptive sliding mode controller, IEEE Access, 8 (2019), 13315-13328. https://doi.org/10.1109/ACCESS.2019.2895595

[30] N. Kumar, K. S. Chaudhary, Position tracking control of nonholonomic mobile robots via H_∞-based adaptive fractional-order sliding mode controller , Math. Model. Control, 5 (2025), 121-130. https://doi.org/10.3934/mmc.2025009

[31] Z. Mokhtare, M. T. Vu, S. Mobayen, A. Fekih, Design of an lmi-based fuzzy fast terminal sliding mode control approach for uncertain MIMO systems, Mathematics, 10 (2022), 1236. https://doi.org/10.3390/math10081236

[32] K. Naseri, M. T. Vu, S. Mobayen, A. Najafi, A. Fekih, Design of linear matrix inequality-based adaptive barrier global sliding mode fault tolerant control for uncertain systems with faulty actuators, Mathematics, 10 (2022), 2159. https://doi.org/10.3390/math10132159

[33] Q. Li, Z. Jin, L. Qiao, A. Du, G. Liu, Distributed optimization of nonlinear singularly perturbed multi-agent systems via a small-gain approach and sliding mode control, AIMS Math., 9 (2024), 20865-20886. https://doi.org/10.3934/math.20241015

[34] K. A. Alattas, M. T. Vu, O. Mofid, F. F. El-Sousy, A. K. Alanazi, J. Awrejcewicz, et al., Adaptive nonsingular terminal sliding mode control for performance improvement of perturbed nonlinear systems, Mathematics, 10 (2022), 1064. https://doi.org/10.3390/math10071064

[35] H. M. Chen, J. C. Renn, J. P. Su, Sliding mode control with varying boundary layers for an electro-hydraulic position servo system, Int. J. Adv. Manuf. Technol., 26 (2005), 117-123. https://doi.org/10.1007/s00170-004-2145-0

[36] M. Yang, Q. Zhang, X. Liu, R. Xi, X. Wang, Adaptive sliding mode control of a nonlinear electro-hydraulic servo system for position tracking, Mechanics, 25 (2019), 283-290. https://doi.org/10.5755/j01.mech.25.4.22822

[37] C. Sun, X. Dong, M. Wang, J. Li, Sliding mode control of electro-hydraulic position servo system based on adaptive reaching law, Appl. Sci., 12 (2022), 6897. https://doi.org/10.3390/app12146897

[38] H. Dong, X. Yang, M. V. Basin, Practical tracking of permanent magnet linear motor via logarithmic sliding mode control, IEEE/ASME Trans. Mechatronics, 27 (2022), 4112-4121. https://doi.org/10.1109/TMECH.2022.3142175

[39] W. H. Chen, X. Deng, W. X. Zheng, Sliding-mode control for linear uncertain systems with impulse effects via switching gains, IEEE Trans. Autom. Control, 67 (2021), 2044-2051. https://doi.org/10.1109/TAC.2021.3073099

[40] K. Guo, J. Wei, Q. Tian, Nonlinear adaptive position tracking of an electro-hydraulic actuator, Proc. Inst. Mech. Eng. C, 229 (2015), 3252-3265. https://doi.org/10.1177/0954406214568821

[41] A. K. Behera, B. Bandyopadhyay, X. Yu, Periodic event-triggered sliding mode control, Automatica, 96 (2018), 61-72. https://doi.org/10.1016/j.automatica.2018.06.035