Modelling an Electro-hydraulic Proportional Valve in a Closed-Loop Control System using Matlab/Simulink

António Ferreira da Silva; Adriano A. Santos; Filipe Pereira; Carlos Felgueiras; António M. Lopes; Fernando G. de Almeida; Paulo J. Silva; António Ramos Silva

Authors

António Ferreira da Silva Polytechnic Institute of Porto https://orcid.org/0000-0003-2067-7601
Adriano A. Santos Polytechnic Institute of Porto https://orcid.org/0000-0001-8991-6768
Filipe Pereira Polytechnic Institute of Porto https://orcid.org/0000-0001-7809-5554
Carlos Felgueiras Polytechnic Institute of Porto https://orcid.org/0000-0002-4202-5551
António M. Lopes Universidade do Porto https://orcid.org/0000-0001-7359-4370
Fernando G. de Almeida Universidade do Porto https://orcid.org/0000-0001-8573-967X
Paulo J. Silva Polytechnic Institute of Porto https://orcid.org/0000-0002-9879-8414
António Ramos Silva Universidade do Porto https://orcid.org/0000-0002-4146-6224

Keywords:

Control, Electro-hydraulic actuators, Mathematical model, Non-linear, Position control, Proportional valves, Simulation

Abstract

In this paper the main components of a hydraulic positioning unit are modelled and simulated using the software Matlab/Simulink. That includes the actuator, the pressure relief valve, connecting pipes and of course the proportional directional control valve. With this model the positioning unit was tested under different conditions to make predictions on how the system is going to react. The simulation of the proportional directional control valve was divided into a static and dynamic part. Based on flow, pressure and leakage curves given by the manufacturer, pseudo-section functions have been created. These functions characterize the relationship between normalized spool position and flow rate. For simulating dynamic behaviour, a non-linear Simulink model was created. The model was fitted to non-linear frequency response analysis (NFR) data points by using a Nelder-Mead simplex optimization algorithm. Several experiments were carried out to test the methodologies as well as the models with the manufacturer's data and experimentally verifying the adjustability of the results and the validation of the approach. The valve model shows high positioning accuracy and robust behaviour in both simulation and experimentation. The amplitude response curves for 10% and 25% showed some oscillation, but with a stable behaviour around the measurement. On the other hand, the amplitude curve for 100% of the coil path showed a very acceptable approximation and even coincided with the manufacturer's curve.

Author Biographies

António Ferreira da Silva, Polytechnic Institute of Porto

Received his PhD degree in Mechanical Engineering, from University of Porto, Portugal. He is Director of Automation Lab. and Associate Professor at Mechanical Engineering Department of School of Engineering, Polytechnic of Porto. Is a member of the Institute of Science and Innovation in Mechanical Engineering and Industrial Engineering (INEGI) and CIDEM. He is the author of numerous national and international publications, including journal articles, Books and book chapters, and reviews of international papers. His main interests are related to mechatronic (pneumatic and oil-hydraulics) systems, Robotics, AI and Mechanical engineering. ORCID 0000-0003-2067-7601.

Adriano A. Santos, Polytechnic Institute of Porto

Is Graduated in Mechanical Engineering-Production Management at de School of Engineering (ISEP), from Polytechnic of Porto (P.Porto); Master Degree in Mechanical Engineering-Industrial Maintenance at the Faculty of Engineering of the University of Porto (FEUP), Portugal, and at the same university he got the Ph.D. degree in Mechanical Engineering in the field of Automation. He is an Assistant Professor at Mechanical Engineering Department of School of Engineering, Polytechnic of Porto, Portugal, and Head of the Postgraduate Program in Industrial Automation and Robotics. He is co-author of 3 books in the field of Industrial Automation, and author or co-author of more than 40 articles, book chapters in journals and conference proceedings paper. He is a reviewer for some of the most prestigious international journals and member of the research group of Intelligent Systems & Control at LAETA-INEGI and CIDEM at ISEP, in Porto, Portugal. His main interests are related to Industry 4.0, more specifically in the design of the mechatronic (pneumatic and oil-hydraulics) system, Maintenance, Robotics, AI and Mechanical engineering. ORCID 0000-0001-8991-6768.

Filipe Pereira, Polytechnic Institute of Porto

Is a specialist in Electronics, Automation, Robotics, and Industrial Control with 24 years of experience. He holds a PhD in Electronic and Computer Engineering and a Master's in Electronic Engineering and Computer Science, both with a focus on Automation and Industrial Control. Filipe is a member of the MEtRICs and Algoritmi Research Centers at the University of Minho and INEGI. He has authored numerous national and international publications, including journal articles and book chapters, and reviews international papers. As a certified trainer in Automation, Robotics, and Industry 4.0, he collaborates with leading companies. Filipe is also vice-president of the Electronics and Telecommunications college at OET. His interests include Industry 4.0, Robotics, AI, and Electronics. ORCID 0000-0001-7809-5554.

Carlos Felgueiras, Polytechnic Institute of Porto

Is achieved a PhD in Electrical and Computer Engineering from the Faculty of Engineering-University of Porto, Portugal in 2008. His PhD addressed the development of mechanisms to support testing and debugging operations in mixed-signals circuits. Professional career activities included: testing of products, developing and maintenance of electronic equipment, training teacher at Texas Instruments plant. His teaching activity started in 1993 and is Adjunct Professor at the Department of Electrical Engineering at ISEP- P.Porto, and is Integrated Researcher at CIETI since 2001. He was Deputy Director of the Electrical Department between and Director of the master’s degree in Sustainable Energies between. His areas of research include Design for Debugging and Testing Mixed Signal Circuits, Remote Experimentation, e-learning, Renewable Energy Sources and Smart Buildings. ORCID-0000-0002-4202-5551.

António M. Lopes, Universidade do Porto

Has the Ph.D. and Habilitation in mechanical engineering from the Faculty of Engineering of the University of Porto (FEUP). He is with the Associated Laboratory for Energy, Transport, and Aeronautics (LAETA), Institute of Science and Innovation in Mechanical Engineering and Industrial Engineering (INEGI). He is the coordinator of the research group Intelligent Systems & Control at LAETA-INEGI. His research areas are Automation, Robotics, Complex systems, and Fractional-order systems. He coauthored more than 230 SCI journal papers. He is coeditor-in-chief of the Journal of Environmental Accounting and Management, and Journal of Machine Design and Automation Intelligence, and Section editor-in-chief of Fractal and Fractional. He is currently an Associate Professor of Mechanical Engineering at FEUP. ORCID 0000-0001-7359-4370.

Fernando G. de Almeida, Universidade do Porto

Professor Associado

Departamento de Engenharia Mecânica

Secção de Automação, Instrumentação e Controlo

Paulo J. Silva, Polytechnic Institute of Porto

Civil Engineering

Master in Sustainable Energies

António Ramos Silva, Universidade do Porto

Is a mechanical engineer and researcher affiliated with the Faculty of Engineering at the University of Porto. His career began in industrial maintenance, where he specialized in automation, hydraulic and pneumatic systems, and machine components. Over the years, his work has evolved to focus on dynamic modeling, control systems, and the development of hardware and software for advanced automation solutions.

Since 2010, António has actively contributed to over a dozen funded research projects, with applications ranging from non-destructive testing and image processing to smart medical devices and experimental setups. His scientific interests include thermal imaging analysis, haptic feedback systems, and the application of neural networks and intelligent systems to engineering challenges. He is also engaged in research collaborations at an international level, including a long-term project with Harvard University on evolving neural network architectures inspired by human learning.

In academia, António has been teaching since 2014, delivering theoretical, practical, and lab-based courses in automation, instrumentation, control systems, and industrial processes. He has supervised numerous master’s and doctoral students and contributed to the advancement of experimental learning through hands-on prototyping and project development. His work bridges the gap between research and industry, particularly in intelligent automation and next-generation control systems.

References

[1] Sârbu FA, Arnăuţ F, Deaconescu A, Deaconescu T. Theoretical and Experimental Research Concerning the Friction Forces Developed in Hydraulic Cylinder Coaxial Sealing Systems Made from Polymers. Polymers 2024; 16(1):157. https://doi.org/10.3390/polym16010157.

[2] Xuan Bo Tran, Nur Hafizah, Hideki Yanada. Modeling of dynamic friction behaviors of hydraulic cylinders. Mechatronics 2012; 2I2(1):65-75. https://doi.org/10.1016/j.mechatronics.2011.11.009.

[3] Jaiswal, S., Sopanen, J. & Mikkola, A. Efficiency comparison of various friction models of a hydraulic cylinder in the framework of multibody system dynamics. Nonlinear Dyn 2021; 104:3497–3515. https://doi.org/10.1007/s11071-021-06526-9.

[4] Xuyao Mao, Wei Duan, Chao Xiang, Chao Wu1 and Ze Wang. Design and Simulation of a Position and Average Velocity Closed-loop Control Method of a Hydraulic Servo System. Journal of Physics: Conference Series 2022; 2364:012061. https://doi.org/10.1088/1742-6596/2364/1/012061.

[5] Wonohadidjojo, D.M., Kothapalli, G. & Hassan, M.Y. Position Control of Electro-hydraulic Actuator System Using Fuzzy Logic Controller Optimized by Particle Swarm Optimization. Int. J. Autom. Comput. 2013; 10:181–193. https://doi.org/10.1007/s11633-013-0711-3.

[6] Santhosh K. R, M. Kumar, Sireesha Koneru. Simulation of Hydraulic Circuits by using Matlab-Simulink Software. Int. Jour. of Mech. and Prod. Eng. Res. and Dev. (IJMPERD) 2019; 9(3):1643-1654. doi:10.24247/ijmperdjun2019173.

[7] Tony Thomas, A., Thangarasu, S.K., Sowmithra, T. Modeling and Simulation of an Electro-Hydraulic System Using Fuzzy Logic Approach. In: Prabu, T., Viswanathan, P., Agrawal, A., Banerjee, J. (eds) Fluid Mechanics and Fluid Power. Lecture Notes in Mechanical Engineering. Springer, Singapore 2021; pp. 807-822. https://doi.org/10.1007/978-981-16-0698-4_89.

[8] Sahu GN, Singh S, Singh A, Law M. Static and Dynamic Characterization and Control of a High-Performance Electro-Hydraulic Actuator. Actuators 2020; 9(2):46. https://doi.org/10.3390/act9020046.

[9] Zhang Z, Du H, Chen S, Huang H. Frequency domain modeling, analysis and verification of electro-hydraulic servo steering system for heavy vehicles. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 2020; 234(12):2836-2850. doi:10.1177/0954407020918696.

[10] Erzan Topçu E. PC-based control and simulation of an electro-hydraulic system. Comput Appl Eng Educ. 2017; 25:706–718. https://doi.org/10.1002/cae.21831.

[11] Xianju Yuan, Sixiu Shi, Chuyan Wang, Lifeng Wei, Chen Luo, Junjie Chen. Dynamic modeling method for an electro-hydraulic proportional valve coupled mechanical–electrical-electromagnetic-fluid subsystems. Journal of Magnetism and Magnetic Materials 2023; 587:171312. https://doi.org/10.1016/j.jmmm.2023.171312.

[12] Li X, Zhang L, Yang S, Liu N. Analysis and experiment of HMT stationary shift control considering the effect of oil bulk modulus. Advances in Mechanical Engineering 2020; 12(11). doi:10.1177/1687814020968324.

[13] Noah D. Manring, Roger C. Fales. Hydraulic Control Systems, 2nd Edition. John Wiley & Sons: Hoboken, NJ, USA, 2019.

[14] Boulet, B., Daneshmend, L., Hayward, V., Nemri, C. System Identification and Modelling of a High Performance Hydraulic Actuator. Springer: Berlin/Heidelberg Germany. 1993.

[15] Bing Xu, Qi Su, Junhui Zhang, Zhenyu Lu. Analysis and compensation for the cascade dead-zones in the proportional control valve. ISA Transactions 2017; 66:393-403. https://doi.org/10.1016/j.isatra.2016.10.012.

[16] Habibi, S.; Goldenberg, A. A mechatronics approach for the design of a new high performance electrohydraulic actuator. SAE Trans. 1999; 108:353–360. http://www.jstor.org/stable/44723058.

[17] Jianyong, Y.A.; Zongxia, J.I.; Bin, Y.A. Robust control for static loading of electro-hydraulic load simulator with friction compensation. Chin. J. Aeronaut 2012; 25:954–962. https://doi.org/10.1016/S1000-9361(11)60467-6.

[18] Huang J, Song Z, Wu J, Guo H, Qiu C, Tan Q. Parameter Adaptive Sliding Mode Force Control for Aerospace Electro-Hydraulic Load Simulator. Aerospace 2023; 10(2):160. https://doi.org/10.3390/aerospace10020160.

[19] Yuan, H.; Na, H.; Kim, Y. System identification and robust position control for electro-hydraulic servo system using hybrid model predictive control. J. Vib. Control 2018; 24:4145-4159. https://doi.org/10.1177/1077546317721417.

[20] Wang, H., Wang, X., Huang, J. et al. Flow Control for a Two-Stage Proportional Valve with Hydraulic Position Feedback. Chin. J. Mech. Eng. 2020; 33:93. https://doi.org/10.1186/s10033-020-00517-4.

[21] Siddique MAA, Kim W-S, Kim Y-S, Kim T-J, Choi C-H, Lee H-J, Chung S-O, Kim Y-J. Effects of Temperatures and Viscosity of the Hydraulic Oils on the Proportional Valve for a Rice Transplanter Based on PID Control Algorithm. Agriculture 2020; 10(3):73. https://doi.org/10.3390/agriculture10030073.

[22] Li N, Ji H, Wei L, Dong W, Zhan P, Liu X. Generation mechanism of high-frequency oscillation in proportional valve with a high-speed on/off valves bridge as the pilot stage. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 2024; 238(9):4033-4043. https://doi.org/10.1177/09544062231200694.

[23] William de Paula Ferreira, Fabiano Armellini, Luis Antonio De Santa-Eulalia. Simulation in industry 4.0: A state-of-the-art review. Computers & Industrial Engineering 2020; 149:106868.https://doi.org/10.1016/j.cie.2020.106868.

[24] Wagg, D. J., Worden, K., Barthorpe, R. J., and Gardner, P. Digital Twins: State-of-the-Art and Future Directions for Modeling and Simulation in Engineering Dynamics Applications. ASME J. Risk Uncertainty Part B 2020; 6(3):030901. https://doi.org/10.1115/1.4046739.

[25] Santos, Adriano A., Pereira, F. and Felgueiras, C. Optimization and improving of the production capacity of a flexible tyre painting cell. Int J Adv Manuf Technol 2024; 13(9):3957-3969. https://doi.org/10.1007/s00170-024-13208-4.

[26] Lunze, J. Zielstellung und theoretische Grundlagen der Regelungstechnik. In: Regelungstechnik 1. Springer Vieweg, Berlin, Heidelberg, 2020, pp. 1-19. https://doi.org/10.1007/978-3-662-60746-6_1.

[27] Norbert Gebhardt, Jürgen Weber. Hydraulik – Fluid-Mechatronik; Grundlagen, Komponenten, Systeme, Messtechnik und virtuelles Engineering. Springer Vieweg Berlin, Heidelberg 2020. https://doi.org/10.1007/978-3-662-60664-3.

[28] H. Watter. Hydraulik und Pneumatik, Grundlagen und Übungen - Anwendungen und Simulation, 6 ed. Wiesbaden: Springer Vieweg, 2022. https://doi.org/10.1007/978-3-658-35866-2.

[29] Bora Eryilmaz, Bruce H. Wilson. Unified modeling and analysis of a proportional valve. Journal of the Franklin Institute 2006; 343(1):48-68. https://doi.org/10.1016/j.jfranklin.2005.07.001.

[30] D. Will, H. Ströhl und N. Gebhardt, Hydraulik - Grundlagen, Komponenten, Schaltungen, 7 ed. Berlin: Springer, 2020. https://doi.org/10.1007/978-3-662-60664-3.

[31] Hao Xu, Bin Meng, Chenhang Zhu, Yaozhen Heng, and Jian Ruan. Multi-objective optimization design of two-dimensional proportional valve with magnetic coupling. Advances in Mechanical Engineering 2022; 14(11):1-18. https://doi.org/10.1177/16878132221134986.

[32] Bosch Rexroth. 4/3 directional high-response control valves, RE 29067/11.05. https://www.boschrexroth.com/media/ccb8ea97-7f84-40b6-a76d-d2a5c4ae3389 last accessed 03 March 2025.

[33] National Instruments. Position & Displacement Measurement with LVDTs. https://www.ni.com/en/shop/data-acquisition/measuring-position-and-displacement-with-lvdts.html last accessed 04 March 2025.

[34] N. Hanson. Hydraulic Proportional and Closed Loop System Design, Bosch Rexroth. https://www.cmafh.com/enewsletter/pdfs/dch_hydraulicproportional.pdf last accessed 4 March 2025.

[35] P. Beater. Entwurf hydraulischer Maschinen - Modellbildung, Stabilitätsanalyse und Simulation hydrostatischer Antriebe und Steuerungen. Springer Berlin, Heidelberg, 1999. https://doi.org/10.1007/978-3-642-58395-7.

[36] Aboelela, M. A. S., Essa, M. E. S. M., & Hassan, M. A. M. Modeling and identification of hydraulic servo systems. International Journal of Modelling and Simulation 2018; 38(3):139–149. https://doi.org/10.1080/02286203.2017.1405713.

[37] Ferreira, J. A., De Almeida, F. G., & Quintas, M. R. Semi-empirical model for a hydraulic servo-solenoid valve. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 2002; 216(3): 237-248. https://doi.org/10.1177/095965180221600303.

[38] MathWorks – Help Center Homepage, https://www.mathworks.com/help/matlab/ref/fminsearch.html, last accessed 4 March 2025.

[39] J. A. F. Ferreira: Modelação de sistemas hidráulicos para simulação com hardware-in-the-loop. Ph.D. Thesis. Universidade de Aveiro, Portugal 2002. http://hdl.handle.net/10773/10859.

[40] Graça Sobral: Desenvolvimento de uma interface gráfica para controlo de uma válvula direcional proporcional. Master Thesis. Instituto Politécnico do Porto, Portugal 2018. https://recipp.ipp.pt/entities/publication/3229d785-91a5-4559-8a08-cc0817a569af.

[41] Formelsammlung und Berechnungsprogramme Maschinen- und Anlagenbau, Reibwerte von verschiedenen Materialien Homepage, https://www.schweizer-fn.de/stoff/reibwerte/reibwerte.php last accessed 4 March 2025.

Modelling an Electro-hydraulic Proportional Valve in a Closed-Loop Control System using Matlab/Simulink

Authors

Keywords:

Abstract

Author Biographies

António Ferreira da Silva, Polytechnic Institute of Porto

Adriano A. Santos, Polytechnic Institute of Porto

Filipe Pereira, Polytechnic Institute of Porto

Carlos Felgueiras, Polytechnic Institute of Porto

António M. Lopes, Universidade do Porto

Fernando G. de Almeida, Universidade do Porto

Paulo J. Silva, Polytechnic Institute of Porto

António Ramos Silva, Universidade do Porto

References

Downloads

Published

How to Cite

Issue

Section

License

Funding data

Make a Submission

Current Issue

Keywords