{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:40:40Z","timestamp":1760060440292,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,9,1]],"date-time":"2025-09-01T00:00:00Z","timestamp":1756684800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Aiming at the characteristics of limited actuation capability of the semi-active control system and strong nonlinearity of the hydro-pneumatic suspension, a constrained nonlinear control strategy of a semi-active hydro-pneumatic suspension system is proposed. According to the mathematical model of nonlinear hydro-pneumatic suspension, the static stiffness and linear damping coefficient based on the equivalent energy are calculated, and then the control-oriented dynamic equation whose expression minimizes the nonlinear term is constructed. Combined with actuation capacity constraints, an optimization model with constraints is established to minimize the deviation between the actual overall control force and the expected optimal control force, and the optimal approximation from nonlinear control to linear quadratic optimal control is realized. The control simulation results of various methods show that the nonlinear control with constraints of the semi-active hydro-pneumatic suspension system, which effectively combines the actuation capacity constraints and nonlinear characteristics of the system, achieves a good comprehensive control effect for the nonlinear suspension control with constraints.<\/jats:p>","DOI":"10.3390\/computation13090206","type":"journal-article","created":{"date-parts":[[2025,9,1]],"date-time":"2025-09-01T13:27:44Z","timestamp":1756733264000},"page":"206","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Constrained Nonlinear Control of Semi-Active Hydro-Pneumatic Suspension System"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-0338-7197","authenticated-orcid":false,"given":"Biao","family":"Qiu","sequence":"first","affiliation":[{"name":"School of Engineering, King Mongkut\u2019s Institute of Technology Ladkrabang, Bangkok 10520, Thailand"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1451-4278","authenticated-orcid":false,"given":"Chaiyan","family":"Jettanasen","sequence":"additional","affiliation":[{"name":"School of Engineering, King Mongkut\u2019s Institute of Technology Ladkrabang, Bangkok 10520, Thailand"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,1]]},"reference":[{"key":"ref_1","first-page":"3188","article-title":"A Review on Controlling Methods for Semi-Active Suspension Systems","volume":"12","author":"Wagh","year":"2024","journal-title":"Int. J. Res. Appl. Sci. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Ni, F., Luo, Y., Xu, J., Liu, D., Sun, Y., and Ji, W. (2024). Review of Fault-Tolerant Control Methods for Suspension Systems: From Road Vehicles to Maglev Trains. Mathematics, 12.","DOI":"10.3390\/math12162576"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"10299","DOI":"10.1109\/TITS.2021.3090049","article-title":"Modeling and Second-Order Sliding Mode Control for Lateral Vibration of High-Speed Train With MR Dampers","volume":"23","author":"Wang","year":"2022","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Ab Talib, M.H., Muhammad Afandi, M.A.D., Mat Darus, I.Z., Mohd Yatim, H., Asus, Z., Mohd Yamin, A.H., and Hadi, M.S. (2021). Magnetorheological Damper Control for Semi-Active Suspension System Using Skyhook-Differential Evolution. Lecture Notes in Electrical Engineering, Springer.","DOI":"10.1007\/978-981-33-4597-3_16"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"103108","DOI":"10.1016\/j.mechatronics.2023.103108","article-title":"Geometric Optimization of Magnetorheological Damper for Prosthetic Ankles Using Artificial Neural Networks","volume":"98","author":"Kumar","year":"2024","journal-title":"Mechatronics"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1504\/IJVD.2016.078764","article-title":"Adaptive ride comfort and attitude control of vehicles equipped with active hydro-pneumatic suspension","volume":"71","author":"Saglam","year":"2016","journal-title":"Int. J. Veh. Des."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1001","DOI":"10.1007\/s12239-018-0097-x","article-title":"Development of Preview Active Suspension Control System and Performance Limit Analysis by Trajectory Optimization","volume":"19","author":"Soh","year":"2018","journal-title":"Int. J. Automot. Technol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1016\/j.automatica.2014.12.026","article-title":"A Clipped-Optimal Control Algorithm for Semi-Active Vehicle Suspensions: Theory and Experimental Evaluation","volume":"53","author":"Brezas","year":"2015","journal-title":"Automatica"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Sun, Q., Yin, C., and Wang, B. (2024). Experimental Validation of Truck Cab Suspension Model and Ride Comfort Improvement under Various Semi-Active Control Strategies. Processes, 12.","DOI":"10.3390\/pr12091880"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"61","DOI":"10.2478\/scjme-2018-0006","article-title":"Optimisation and Control of Vehicle Suspension Using Linear Quadratic Gaussian Control","volume":"68","author":"Likaj","year":"2018","journal-title":"Stroj. \u010dasopis-J. Mech. Eng."},{"key":"ref_11","first-page":"305","article-title":"Preview Model Predictive Control Controller for Magnetorheological Damper of Semi-Active Suspension to Improve Both Ride and Handling","volume":"4","year":"2020","journal-title":"SAE Int. J. Veh. Dyn. Stab. NVH"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"107569","DOI":"10.1016\/j.ymssp.2020.107569","article-title":"Investigation on the Dynamic Performance of a New Semi-Active Hydro-Pneumatic Inerter-Based Suspension System with MPC Control Strategy","volume":"154","author":"Yang","year":"2021","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2355","DOI":"10.1177\/0954407021990916","article-title":"Modelling and Control of a Semi-Active Dual-Chamber Hydro-Pneumatic Inerter-Based Suspension System","volume":"235","author":"Zhu","year":"2021","journal-title":"Proc. Inst. Mech. Eng. Part D J. Automob. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"071007","DOI":"10.1115\/1.4068636","article-title":"Constrained H\u221e Optimal Control for Nonlinear Active Suspensions Via Data-Driven Reinforcement Learning Algorithm","volume":"20","author":"Wang","year":"2025","journal-title":"J. Comput. Nonlinear Dyn."},{"key":"ref_15","first-page":"289","article-title":"Nonlinear Active Suspension System Based on Fuzzy Model Predictive Controller","volume":"16","author":"Jibril","year":"2021","journal-title":"J. Eng. Appl. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1243\/09544070JAUTO1111","article-title":"Feedback Linearization and Sliding Mode Control for Active Hydropneumatic Suspension of a Special-Purpose Vehicle","volume":"224","author":"Shi","year":"2009","journal-title":"Proc. Inst. Mech. Eng. Part D J. Automob. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1559","DOI":"10.1007\/s11071-021-06559-0","article-title":"Multi-Objective Command Filtered Adaptive Control for Nonlinear Hydraulic Active Suspension Systems","volume":"105","author":"Hao","year":"2021","journal-title":"Nonlinear Dyn."},{"key":"ref_18","first-page":"134","article-title":"Hybrid control of electromagnetic active suspension based on nonlinear actuators","volume":"33","author":"Hu","year":"2022","journal-title":"China Mech. Eng."},{"key":"ref_19","first-page":"955","article-title":"Adaptive Event-Triggered Control for Vehicle Active Suspension Systems With State Constraints","volume":"51","author":"Pan","year":"2018","journal-title":"IFAC-Pap."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1928","DOI":"10.1109\/TASE.2024.3372626","article-title":"A Joint Fault-Tolerant and Fault Diagnosis Strategy for Multiple Actuator Faults of Full-Vehicle Active Suspension Systems","volume":"22","author":"Yan","year":"2025","journal-title":"IEEE Trans. Automat. Sci. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1109\/TCYB.2022.3217404","article-title":"Neuroadaptive Control for Active Suspension Systems With Time-Varying Motion Constraints: A Feasibility-Condition-Free Method","volume":"54","author":"Feng","year":"2024","journal-title":"IEEE Trans. Cybern."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"020801","DOI":"10.1115\/1.4049946","article-title":"Bio-Inspired Vibration Isolation: Methodology and Design","volume":"73","author":"Yan","year":"2021","journal-title":"Appl. Mech. Rev."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3059","DOI":"10.1109\/TRO.2025.3562488","article-title":"Load-Transfer Suspended Backpack With Bioinspired Vibration Isolation for Shoulder Pressure Reduction Across Diverse Terrains","volume":"41","author":"Cao","year":"2025","journal-title":"IEEE Trans. Robot."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1109\/TCST.2017.2699158","article-title":"A Bioinspired Dynamics-Based Adaptive Tracking Control for Nonlinear Suspension Systems","volume":"26","author":"Pan","year":"2018","journal-title":"IEEE Trans. Contr. Syst. Technol."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Bosso, N., Zampieri, N., Som\u00e0, A., Mocera, F., and Conte, E. (2021). Simulation of a Hydropneumatic Suspension for Agricultural Working Vehicles. Advances in Mechatronics and Mechanical Engineering, IGI Global.","DOI":"10.4018\/978-1-7998-4939-1.ch012"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1016\/j.ymssp.2017.12.040","article-title":"Characterization of a Hydro-Pneumatic Suspension Strut with Gas-Oil Emulsion","volume":"106","author":"Yin","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_27","unstructured":"Dong, M.M., and Bian, N. (2016). Military Vehicle Suspension Design, Beijing Institute of Technology Press."},{"key":"ref_28","first-page":"6502412","article-title":"An Enhanced Adaptive Unscented Kalman Filter for Vehicle State Estimation","volume":"71","author":"Zhang","year":"2022","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Leonov, G.A., and Kuznetsov, N.V. (2013). Lyapunov Exponent Sign Reversal: Stability and Instability by the First Approximation. Nonlinear Systems and Complexity, Springer International Publishing.","DOI":"10.1007\/978-3-319-02353-3_2"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Aljarbouh, A., Fayaz, M., Qureshi, M.S., and Boujoudar, Y. (2021). Hybrid Sliding Mode Control of Full-Car Semi-Active Suspension Systems. Symmetry, 13.","DOI":"10.3390\/sym13122442"}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/13\/9\/206\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:37:22Z","timestamp":1760035042000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/13\/9\/206"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,1]]},"references-count":30,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2025,9]]}},"alternative-id":["computation13090206"],"URL":"https:\/\/doi.org\/10.3390\/computation13090206","relation":{},"ISSN":["2079-3197"],"issn-type":[{"type":"electronic","value":"2079-3197"}],"subject":[],"published":{"date-parts":[[2025,9,1]]}}}