Comprehensive Dynamic Model of Vertical Pneumatic Bellows Actuator System Considering Bidirectional Asymmetric Hysteresis

Huai Xiao; Xuzhi Lai; Qingxin Meng; Jinhua She; Edwardo F. Fukushima; Min Wu

doi:10.1109/JAS.2025.125162

Volume 12 Issue 10

Oct. 2025

IEEE/CAA Journal of Automatica Sinica

JCR Impact Factor: 19.2, Top 1 (SCI Q1)

CiteScore: 28.2, Top 1% (Q1)
Google Scholar h5-index: 95， TOP 5

Turn off MathJax

Article Contents

Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2025 > 12(10): 2115-2126

H. Xiao, X. Lai, Q. Meng, J. She, E. F. Fukushima, and M. Wu, “Comprehensive dynamic model of vertical pneumatic bellows actuator system considering bidirectional asymmetric hysteresis,” IEEE/CAA J. Autom. Sinica, vol. 12, no. 10, pp. 2115–2126, Oct. 2025. doi: 10.1109/JAS.2025.125162

Citation:

H. Xiao, X. Lai, Q. Meng, J. She, E. F. Fukushima, and M. Wu, “Comprehensive dynamic model of vertical pneumatic bellows actuator system considering bidirectional asymmetric hysteresis,” IEEE/CAA J. Autom. Sinica, vol. 12, no. 10, pp. 2115–2126, Oct. 2025. doi: 10.1109/JAS.2025.125162

Citation:

H. Xiao, X. Lai, Q. Meng, J. She, E. F. Fukushima, and M. Wu, “Comprehensive dynamic model of vertical pneumatic bellows actuator system considering bidirectional asymmetric hysteresis,” IEEE/CAA J. Autom. Sinica, vol. 12, no. 10, pp. 2115–2126, Oct. 2025. doi: 10.1109/JAS.2025.125162

PDF( 4352 KB)

Comprehensive Dynamic Model of Vertical Pneumatic Bellows Actuator System Considering Bidirectional Asymmetric Hysteresis

doi: 10.1109/JAS.2025.125162

Funds: This work was supported in part by the Young Scientists Fund of National Natural Science Foundation of China (62203408), the Hubei Provincial Natural Science Foundation of China (2015CFA010), the 111 Project (B17040), and China Scholarship Council (202206410070)

More Information

Author Bio:
Huai Xiao (Student Member, IEEE) received the B.S. degree in engineering from China University of Geosciences in 2019. He is currently pursuisng the Ph.D. degree at the School of Automation, China University of Geosciences. From December 2022 to December 2024, he was a visiting Ph.D. student at the School of Engineering, Tokyo University of Technology, Japan. His current research interests include design and control of soft robots, and nonlinear system control

Xuzhi Lai received the B.S., M.S., and Ph.D. degrees in engineering from Central South University, in 1988, 1991, and 2001, respectively. In 1991, she joined the School of Information Science and Engineering, Central South University, and was promoted to Professor in 2004. From 2004 to 2006, she was a Visiting Scholar with the Department of Mechanical Engineering, University of Toronto, Canada, and the School of Engineering, University of Guelph, Canada.In 2014, she joined the China University of Geosciences, where she is currently a Professor with the School of Automation. Her current research interests include intelligent control, robot control, and nonlinear system control

Qingxin Meng (Member, IEEE) received the B.S. degree in engineering from Hebei University of Technology, in 2016, and the Ph.D. degree in engineering from China University of Geosciences, in 2021. From August 2019 to August 2021, he was a Research Intern with the Department of Mechanical, Industrial and Aerospace Engineering, Concordia University, Canada. In 2022, he joined the School of Automation, China University of Geosciences, where he is currently a Professor. His main research interest is robot control

Jinhua She (Fellow, IEEE) received the B.S. degree in engineering from Central South University, in 1983, and the M.S. and Ph.D. degrees in engineering from the Tokyo Institute of Technology, Japan, in 1990 and 1993, respectively.In 1993, he joined the School of Engineering, Tokyo University of Technology, Japan, where he is currently a Professor. His research interests include the application of control theory, repetitive control, process control, mobile education, and assistive robotics.Dr. She is a Member of the Society of Instrument and Control Engineers, the Institute of Electrical Engineers of Japan, the Japan Society of Mechanical Engineers, and the Asian Control Association. He received the Control Engineering Practice Prize Paper Award from the International Federation of Automatic Control in 1999 (jointly with M. Wu and M. Nakano)

Edwardo F. Fukushima (Member, IEEE) received the B.Eng. degree in electric engineering from the Federal University of Technology – Parana’(UTFPR), Brazil, in 1989, and the M.Eng. and D.Eng. degrees in mechanical science engineering from Tokyo Institute of Technology, Japan, in 1993 and 2002, respectively.During September–December 2001, he was a Visiting Researcher at Stanford University, and during August–September 2004 he was a Visiting Scientist at University of Zurich, Switzerland. In 1994, he joined the Department of Mechanical and Aerospace Engineering, Tokyo Institute of Technology, Japan. In 2014, he joined Tokyo University of Technology, Japan, where he is currently a Professor. His research interests include development of demining robots, new brushless motors and drives, and design of controllers for intelligent robots.Dr. Fukushima is a Member of the Society of Instrument and Control Engineers, the Robotics of Society of Japan, the Japan Society of Mechanical Engineers, and the Institute of Electrical and Electronics Engineers. In 2014, he also received the Best Paper Award from SICE, Japan

Min Wu (Fellow, IEEE) received the B.S. and M.S. degrees in engineering from Central South University, in 1983 and 1986, respectively, and the Ph.D. degree in engineering from the Tokyo Institute of Technology, Japan, in 1999.He was a Faculty Member of the School of Information Science and Engineering at Central South University from 1986 to 2014, and was promoted to Professor in 1994. He was a Visiting Scholar with the Department of Electrical Engineering, Tohoku University, Japan, from 1989 to 1990, and a Visiting Research Scholar with the Department of Control and Systems Engineering, Tokyo Institute of Technology, from 1996 to 1999. He was a Visiting Professor with the School of Mechanical, Materials, Manufacturing Engineering and Management, University of Nottingham, U.K., from 2001 to 2002. In 2014, he joined the China University of Geosciences, where he is currently a Professor with the School of Automation. His current research interests include process control, robust control, and intelligent systems.Dr. Wu is a Fellow of the Chinese Association of Automation (CAA Fellow). He received the IFAC Control Engineering Practice Prize Paper Award in 1999 (together with M. Nakano and J. She)
Corresponding author: Xuzhi Lai, e-mail: laixz@cug.edu.cn
Received Date: 2024-07-07
Revised Date: 2024-10-03
Accepted Date: 2025-01-05

Available Online: 2025-01-22

Abstract

Abstract

The complex nonlinear characteristics of pneumatic soft actuators, such as asymmetric hysteresis, rate-dependence, and mechanical load-dependence, pose a challenge in accurately modeling their dynamics. To address this challenge, this paper proposes a comprehensive dynamic model aimed at describing bidirectional asymmetric hysteresis, rate-dependent, and mechanical load-dependent characteristics of a vertical pneumatic bellows actuator (PBA) system. The dynamic model contains a hysteresis submodel and a load-dependent dynamic submodel. The hysteresis submodel consists of several sets of weighted double-side play (DSP) and weighted dead-zone (DZ) operators connected in series, and it is used to model the bidirectional asymmetric hysteresis of the system. The load-dependent dynamic submodel is built based on the gated recurrent unit (GRU) neural network, and it is used to fit the nonlinear relationship between the displacement of the system and the frequency of the input air pressure as well as the mechanical load. The model parameters of the hysteresis submodel and the load-dependent dynamic submodel are determined by intelligent optimization method and neural network training method, reseparately. The fitness value (FV) between the output of the dynamic model and the experimental data is calculated to be 96.1736%, demonstrating that the parameters of the dynamic model are valid. We conduct six set of experiments to compare the model output with the experimental data, and calculate the root-mean-square errors and the maximum error, respectively. The experimental results show that, the root-mean-square error remains consistently below 2.7700%, while the maximum error remains below 8.4000% across all experiments, thereby substantiating the validity and generality of the proposed model.
- Bidirectional asymmetric hysteresis,
- dynamic model,
- rate-dependent and mechanical load-dependent,
- soft actuator

FullText(HTML)

References(36)

References

[1]	F. Xu and H. Wang, “Soft robotics: Morphology and morphology-inspired motion strategy,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 9, pp. 1500–1522, Sep. 2021. doi: 10.1109/JAS.2021.1004105
[2]	Z. Li, Z. Li, H. Xu, X. Zhang, and C.-Y. Su, “Development of a butterfly fractional-order backlash-like hysteresis model for dielectric elastomer actuators,” IEEE Trans. Ind. Electron., vol. 70, no. 2, pp. 1794–1801, Feb. 2023. doi: 10.1109/TIE.2022.3163553
[3]	J. Wu, W. Ye, Y. Wang, and C.-Y. Su, “Modeling of photo-responsive liquid crystal elastomer actuators,” Inf. Sci., vol. 560, pp. 441–455, Jun. 2021. doi: 10.1016/j.ins.2021.01.009
[4]	Q. Xie, T. Wang, and S. Zhu, “Simplified dynamical model and experimental verification of an underwater hydraulic soft robotic arm,” Smart Mater. Struct., vol. 31, no. 7, p. 075011, Jul. 2022. doi: 10.1088/1361-665X/ac736f
[5]	A. H. Khan, Z. Shao, S. Li, Q. Wang, and N. Guan, “Which is the best PID variant for pneumatic soft robots? An experimental study,” IEEE/CAA J. Autom. Sinica, vol. 7, no. 2, pp. 451–460, Mar. 2020. doi: 10.1109/JAS.2020.1003045
[6]	Y. Zhang, H. Liu, T. Ma, L. Hao, and Z. Li, “A comprehensive dynamic model for pneumatic artificial muscles considering different input frequencies and mechanical loads,” Mech. Syst. Signal Process., vol. 148, p. 107133, Feb. 2021. doi: 10.1016/j.ymssp.2020.107133
[7]	J. Wu, W. Ye, Y. Wang, and C.-Y. Su, “Modeling based on a two-step parameter identification strategy for liquid crystal elastomer actuator considering dynamic phase transition process,” IEEE Trans. Cybern., vol. 53, no. 7, pp. 4423–4434, Jul. 2023. doi: 10.1109/TCYB.2022.3179433
[8]	J. Sun, W. Liao, and Z. Yang, “Additive manufacturing of liquid crystal elastomer actuators based on knitting technology,” Adv. Mater., vol. 35, no. 36, p. 2302706, Sep. 2023. doi: 10.1002/adma.202302706
[9]	Y. Zhang, Y. Wang, J. Wu, Q. Meng, and C.-Y. Su, “Adaptive control method for conically shaped dielectric elastomer actuator with different loads,” IEEE Trans. Autom. Sci. Eng., vol. 21, no. 3, pp. 2613–2621, Jul. 2024. doi: 10.1109/TASE.2023.3265707
[10]	G.-Y. Gu, U. Gupta, J. Zhu, L.-M. Zhu, and X. Zhu, “Modeling of viscoelastic electromechanical behavior in a soft dielectric elastomer actuator,” IEEE Trans. Robot., vol. 33, no. 5, pp. 1263–1271, Oct. 2017. doi: 10.1109/TRO.2017.2706285
[11]	J. Ciambella and G. Tomassetti, “A form-finding strategy for magneto-elastic actuators,” Int. J. Nonlinear Mech., vol. 119, p. 103297, Mar. 2020. doi: 10.1016/j.ijnonlinmec.2019.103297
[12]	D. Kumar, V. Yadav, and S. Sarangi, “Modeling and analysis of an electro-magneto-elastic rotating cylindrical tube actuator,” J. Intell. Mater. Syst. Struct., vol. 33, no. 14, pp. 1862–1876, Aug. 2022. doi: 10.1177/1045389X211072188
[13]	J. Shintake, V. Cacucciolo, D. Floreano, and H. Shea, “Soft robotic grippers,” Adv. Mater., vol. 30, no. 29, p. 1707035, Jul. 2018. doi: 10.1002/adma.201707035
[14]	S. Shakiba, M. Ourak, E. V. Poorten, M. Ayati, and A. Yousefi-Koma, “Modeling and compensation of asymmetric rate-dependent hysteresis of a miniature pneumatic artificial muscle-based catheter,” Mech. Syst. Signal Process., vol. 154, p. 107532, Jun. 2021. doi: 10.1016/j.ymssp.2020.107532
[15]	X. Wang, Q. Zhang, D. Shen, and J. Chen, “A novel rescue robot: Hybrid soft and rigid structures for narrow space searching,” in Proc. IEEE Int. Conf. Robotics and Biomimetics, Dali, China, 2019, pp. 2207–2213.
[16]	Y. Cao and J. Huang, “Neural-network-based nonlinear model predictive tracking control of a pneumatic muscle actuator-driven exoskeleton,” IEEE/CAA J. Autom. Sinica, vol. 7, no. 6, pp. 1478–1488, Nov. 2020. doi: 10.1109/JAS.2020.1003351
[17]	X. Zhang, N. Sun, G. Liu, T. Yang, and Y. Fang, “Hysteresis compensation-based intelligent control for pneumatic artificial muscle-driven humanoid robot manipulators with experiments verification,” IEEE Trans. Autom. Sci. Eng., vol. 21, no. 3, pp. 2538–2551, Jul. 2024. doi: 10.1109/TASE.2023.3263535
[18]	H. Ru, J. Huang, W. Chen, and C. Xiong, “Modeling and identification of rate-dependent and asymmetric hysteresis of soft bending pneumatic actuator based on evolutionary firefly algorithm,” Mech. Mach. Theory, vol. 181, p. 105169, Mar. 2023. doi: 10.1016/j.mechmachtheory.2022.105169
[19]	S. Zhao, Z. Yan, Q. Meng, H. Xiao, X. Lai, and M. Wu, “Modified three-element modeling and robust tracking control for a planar pneumatic soft actuator,” IEEE Trans. Ind. Electron., vol. 70, no. 9, pp. 9237–9247, Sep. 2023. doi: 10.1109/TIE.2022.3206693
[20]	H. Xiao, J. Wu, W. Ye, and Y. Wang, “Dynamic modeling for dielectric elastomer actuators based on LSTM deep neural network,” in Proc. 5th Int. Conf. Advanced Robotics and Mechatronics, Shenzhen, China, 2020, pp. 119–124.
[21]	H. Ru, J. Huang, and B. Wang, “ESN-based control of bending pneumatic muscle with asymmetric and rate-dependent hysteresis,” in Proc. 4th Int. Conf. Neural Computing for Advanced Applications, Hefei, China, 2023, pp. 3–17.
[22]	M. A. Vasquez-Beltran, B. Jayawardhana, and R. F. Peletier, “Modeling and analysis of duhem hysteresis operators with butterfly loops,” IEEE Trans. Autom. Control, vol. 68, no. 10, pp. 5977–5990, Oct. 2023. doi: 10.1109/TAC.2023.3238177
[23]	M. Ismail, F. Ikhouane, and J. Rodellar, “The hysteresis bouc-wen model, a survey,” Arch. Comput. Methods Eng., vol. 16, no. 2, pp. 161–188, Jun. 2009. doi: 10.1007/s11831-009-9031-8
[24]	T. Kosaki and M. Sano, “Control of a parallel manipulator driven by pneumatic muscle actuators based on a hysteresis model,” J. Environ. Eng., vol. 6, no. 2, pp. 316–327, Mar. 2011. doi: 10.1299/jee.6.316
[25]	H. Xiao, Q. Meng, X. Lai, Y. Wang, J. She, E. F. Fukushima, and M. Wu, “Design, performance analysis and applications of pneumatic bellows actuator for building block soft robots,” Inf. Sci., vol. 676, p. 120814, Aug. 2024. doi: 10.1016/j.ins.2024.120814
[26]	Y. Yang, J. Han, Z. Liu, Z. Zhao, and K.-S. Hong, “Modeling and adaptive neural network control for a soft robotic arm with prescribed motion constraints,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 2, pp. 501–511, Feb. 2023. doi: 10.1109/JAS.2023.123213
[27]	H. Ru, Y. Yang, B. Wang, and J. Huang, “Model predictive control for a bending pneumatic muscle based on an online modified generalized prandtl-ishlinskii model,” Neural Comput. Appl., vol. 36, no. 20, pp. 12371–12383, Jul. 2024. doi: 10.1007/s00521-024-09666-2
[28]	M. Al Saaideh and M. Al Janaideh, “On prandtl-ishlinskii hysteresis modeling of a loaded pneumatic artificial muscle,” ASME Lett. Dyn. Syst. Control, vol. 2, no. 3, p. 031008, Jul. 2022. doi: 10.1115/1.4054779
[29]	K. Xu, Z. Zhang, and J. Mao, “Modeling of stress dependent hysteresis nonlinearity based on fuzzy tree for GMA,” in Proc. IEEE Int. Conf. Automation and Logistics, Qingdao, China, 2008, pp. 331–335.
[30]	X. Zhang, Y. Tan, M. Su, and Y. Xie, “Neural networks based identification and compensation of rate-dependent hysteresis in piezoelectric actuators,” Phys. B: Condens. Matter, vol. 405, no. 12, pp. 2687–2693, Jun. 2010. doi: 10.1016/j.physb.2010.03.050
[31]	P.-K. Wong, Q. Xu, C.-M. Vong, and H.-C. Wong, “Rate-dependent hysteresis modeling and control of a piezostage using online support vector machine and relevance vector machine,” IEEE Trans. Ind. Electron., vol. 59, no. 4, pp. 1988–2001, Apr. 2012. doi: 10.1109/TIE.2011.2166235
[32]	H. Xiao, Q.-X. Meng, X.-Z. Lai, Z. Yan, S.-Y. Zhao, and M. Wu, “Design and trajectory tracking control of a novel pneumatic bellows actuator,” Nonlinear Dyn., vol. 111, no. 4, pp. 3173–3190, Feb. 2023. doi: 10.1007/s11071-022-07979-2
[33]	Y. Zhang, J. Wu, P. Huang, C.-Y. Su, and Y. Wang, “Inverse dynamics modelling and tracking control of conical dielectric elastomer actuator based on GRU neural network,” Eng. Appl. Artif. Intell., vol. 118, p. 105668, Feb. 2023. doi: 10.1016/j.engappai.2022.105668
[34]	H. Xiao, J. Wu, W. Ye, and Y. Wang, “Dynamic modeling of dielectric elastomer actuators based on thermodynamic theory,” Mech. Adv. Mater. Struct., vol. 29, no. 11, pp. 1543–1552, Nov. 2022. doi: 10.1080/15376494.2020.1829757
[35]	S. Xie, J. Mei, H. Liu, and Y. Wang, “Hysteresis modeling and trajectory tracking control of the pneumatic muscle actuator using modified Prandtl-Ishlinskii model,” Mech. Mach. Theory, vol. 120, pp. 213–224, Feb. 2018. doi: 10.1016/j.mechmachtheory.2017.07.016
[36]	D. Chicco, M. J. Warrens, and G. Jurman, “The coefficient of determination R-squared is more informative than SMAPE, MAE, MAPE, MSE and RMSE in regression analysis evaluation,” PeerJ Comput. Sci., vol. 7, no. 3, p. e623, Jul. 2021.

Supplements(0)

Cited By

Proportional views

Proportional views

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Figures(13) / Tables(3)

Get Citation

PDF

XML

Article Metrics

Article views (247) PDF downloads(16)

Comprehensive Dynamic Model of Vertical Pneumatic Bellows Actuator System Considering Bidirectional Asymmetric Hysteresis

doi: 10.1109/JAS.2025.125162

Abstract

References

Proportional views

Catalog

通讯作者: 陈斌, bchen63@163.com

Article Metrics

Export File

Citation

Format

Content