Control design of the hydraulic support pushing system based on saturation

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Abstract

This paper focused on the control design problem regarding the hydraulic support pushing system, with full consideration of the saturation structure of the control input. With the help of the backstepping technique, some sufficient conditions were established to ensure local exponential stability of the error system between the hydraulic support pushing system and the reference system, simultaneously providing an estimation of the attractive domain. In addition, a potential relationship between the saturation structure and attractive domain was established, which was crucial for achieving local exponential stability in the framework of saturation limitations. It showed that the size of the attractive domain was not only determined by the structure of control input but was also affected by the saturation structure. Finally, some simulations were presented to illustrate the effectiveness of the proposed results.

Keywords

hydraulic support pushing system / saturation / backstepping technique / attractive domain / local exponential stability

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References

[1] G. Wang, H. Ren, G. Zhao, S. Gong, Y. Du, Z. Xue, et al., Digital model and giant system coupling technology system of smart coal mine, J. China Coal Soc., 47 (2022), 61-74.

[2] Z. Zhang, Y. Liu, L. Bo, Y. Wang, Enhanced path tracking control of hydraulic support pushing mechanism via adaptive sliding mode technique in coal mine backfill operations, Heliyon, 10 (2024).

[3] V. Milić, Ž. Šitum, M. Essert, Robust hosition position control synthesis of an electro-hydraulic servo system, ISA Trans., 49 (2010), 535-542. https://doi.org/10.1016/j.isatra.2010.06.004

[4] T. Hou, C. Shi, Z. Kou, J. Wu, B. Zhang, Y. Peng, Research on positioning control strategy of hydraulic support pushing system based on multistage speed control valve, Sci. Rep., 14 (2024), 19046. https://doi.org/10.1038/s41598-024-70087-1

[5] S. Shanmugam, R. Vadivel, S. Sabarathinam, P. Hammachukiattikul, N. Gunasekaran, Enhancing synchronization criteria for fractional-order chaotic neural networks via intermittent control: An extended dissipativity approach, Math. Modell. Control, 5 (2025), 31-47. https://doi.org/10.3934/mmc.2025003

[6] Y. Wang, K. Li, Exponential synchronization of fractional order fuzzy memristor neural networks with time-varying delays and impulses, Math. Modell. Control, 5 (2025), 164-179. https://doi.org/10.3934/mmc.2025012

[7] R. Zhou, L. Meng, X. Yuan, Z. Qiao, Research and experimental analysis of hydraulic cylinder position control mechanism based on pressure detection, Machines, 10 (2021), 1. https://doi.org/10.3390/machines10010001

[8] S. Jiang, H. Wang, G. Zhao, Research on neural network model reference adaptive disturbance rejection control of digital hydraulic cylinder, Adv. Mech. Eng., 14 (2022), 16878132221140706. https://doi.org/10.1177/16878132221140706

[9] Y. Zhang, H. Zhang, K. Gao, Q. Zeng, F. Meng, J. Cheng, Research on intelligent control system of hydraulic support based on position and posture detection, Machines, 11 (2022), 33. https://doi.org/10.3390/machines11010033

[10] C. Wang, X. Ji, Z. Zhang, B. Zhao, L. Quan, A. Plummer, Tracking differentiator based back- stepping control for valve-controlled hydraulic actuator system, ISA Trans., 119 (2022), 208-220. https://doi.org/10.1016/j.isatra.2021.02.028

[11] R. Yang, M. Queiroz, M. Li, Neural network-based control of neuromuscular electrical stimulation with input saturation, IFAC-PapersOnLine, 51 (2019), 170-175. https://doi.org/10.1016/j.ifacol.2019.01.061

[12] E. Farantatos, R. Huang, G. Cokkinides, A. Meliopoulos, A predictive generator out- of-step protection and transient stability monitoring scheme enabled by a distributed dynamic state estimator, IEEE Trans. Power Delivery, 31 (2015), 1826-1835. https://doi.org/10.1109/TPWRD.2015.2512268

[13] O. Brieger, M. Kerr, D. Leißling, I. Postlethwaite, J. Sofrony, M. Turner, Flight testing of a rate saturation compensation scheme on the ATTAS aircraft, Aerosp. Sci. Technol., 13 (2009), 92-104. https://doi.org/10.1016/j.ast.2008.05.003

[14] G. Stein, Respect the unstable, IEEE Control Syst. Mag., 23 (2003), 12-25. https://doi.org/10.1109/MCS.2003.1213600

[15] S. Wu, X. Li, Finite-time stabilization of nonlinear systems with actuator saturation, IEEE Trans. Autom. Sci. Eng., 22 (2024), 7582-7589. https://doi.org/10.1109/TASE.2024.3466049

[16] X. Li, C. Zhu, Saturated impulsive control of nonlinear systems with applications, Automatica, 142 (2022), 110375. https://doi.org/10.1016/j.automatica.2022.110375

[17] K. Dehingia, A. Das, E. Hincal, K. Hosseini, S. Din, Within-host delay differential model for SARS-CoV-2 kinetics with saturated antiviral responses, Electron. Res. Arch., 20 (2023), 20025-20049. https://doi.org/10.3934/mbe.2023887

[18] K. Gao, Global boundedness of classical solutions to a Keller-Segel-Navier-Stokes system involving saturated sensitivity and indirect signal production in two dimensions, Electron. Res. Arch., 20 (2023), 1710-1736. https://doi.org/10.3934/era.2023089

[19] T. Hu, Z. Lin, B. Chen, An analysis and design method for linear systems subject to actuator saturation and disturbance, Automatica, 38 (2002), 351-359. https://doi.org/10.1016/S0005-1098(01)00209-6

[20] X. Lin, S. Li, Y. Zou, Finite-time stabilization of switched linear time-delay systems with saturating actuators, Appl. Math. Comput., 299 (2017), 66-79. https://doi.org/10.1016/j.amc.2016.11.039

[21] A. Akram, M. Hussain, N. Saqib, M. Rehan, Dynamic anti-windup compensation of nonlinear time-delay systems using LPV approach, Nonlinear Dyn., 90 (2017), 513-533. https://doi.org/10.1007/s11071-017-3678-8

[22] M. Hussain, M. Rehan, C. Ahn, K. Hong, N. Saqib, Simultaneous design of AWC and nonlinear controller for uncertain nonlinear systems under input saturation, Int. J. Robust Nonlinear Control, 29 (2019), 2877-2897. https://doi.org/10.1002/rnc.4529

[23] A. Rehman, M. Rehan, M. Riaz, M. Abid, N. Iqbal, Consensus tracking of nonlinear multi- agent systems under input saturation with applications: A sector-based approach, ISA Trans., 107 (2020), 194-205. https://doi.org/10.1016/j.isatra.2020.07.030

[24] M. Razaq, M. Rehan, M. Tufail, C. Ahn, Multiple Lyapunov functions approach for consensus of one-sided Lipschitz multi-agents over switching topologies and input saturation, IEEE Trans. Circuits Syst. II Express Briefs, 67 (2020), 3267-3271. https://doi.org/10.1109/TCSII.2020.2986009

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

[26] L. Zhou, J. Hu, B. Li, Partial-nodes-based state estimation for complex networks under hybrid attacks: A dynamic event-triggered approach, Math. Modell. Control, 5 (2025), 202-215. https://doi.org/10.3934/mmc.2025015

[27] M. Krstic, P. Kokotovic, I. Kanellakopoulos, Nonlinear and Adaptive Control Design , John Wiley & Sons, Inc., 1995.

[28] I. Kanellakopoulos, P. Kokotovic, A. Morse, Systematic design of adaptive controllers for feedback linearizable systems, in 1991 American Control Conference, (1991), 649-654. https://doi.org/10.23919/ACC.1991.4791451

[29] P. Kokotovic, The joy of feedback: Nonlinear and adaptive, IEEE Control Syst. Mag., 12 (1992), 7-17. https://doi.org/10.1109/37.165507

[30] Y. Sun, M. Zhu, Y. Zhang, T. Chen, Adaptive incremental backstepping control of stratospheric airships using time-delay estimation, Electron. Res. Arch., 33 (2025), 2925-2946. https://doi.org/10.3934/era.2025128

[31] M. Krstić, I. Kanellakopoulos, P. Kokotović, Adaptive nonlinear control without overparametrization, Syst. Control Lett., 19 (1992), 177-185. https://doi.org/10.1016/0167-6911(92)90111-5

[32] M. Krstic, P. Kokotovic, Adaptive nonlinear design with controller-identifier separation and swapping, IEEE Trans. Autom. Control, 40 (1995), 426-440. https://doi.org/10.1109/9.376055

[33] C. Kwan, F. Lewis, Robust backstepping control of nonlinear systems using neural networks, IEEE Trans. Syst. Man Cybern Part A Syst. Hum., 30 (2002), 753-766. https://doi.org/10.1109/3468.895898

[34] Y. Zhang, P. Peng, Z. Jiang, Stable neural controller design for unknown nonlinear systems using backstepping, IEEE Trans. Neural Networks, 11 (2000), 1347-1360. https://doi.org/10.1109/72.883443

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

[36] X. Zheng, J. Wang, K. Shi, Y. Tang, J. Cao, Novel stability criterion for DNNs via improved asymmetric LKF, Math. Modell. Control, 4 (2024), 307-315. https://doi.org/10.3934/mmc.2024025