Skip to main content
SpringerLink
Log in

Attitude Tracking Control of All-Terrain Vehicle with Tandem Active–Passive Suspension

  • Connected Automated Vehicles and ITS, Vehicle Dynamics and Control
  • Published:
International Journal of Automotive Technology Aims and scope Submit manuscript

Abstract

When vehicles with traditional passive suspension systems are driving on complex pavement, the large vibration of the body will result in relatively negative effects on ride comfort, vehicle handling, and stability of passengers and goods. Body attitude tracking control based on tandem active–passive suspension can improve vehicle attitude stability and passability by enabling the body attitude to track an ideal position. In addition, the performance limitations of the actuator are considered in the design of the attitude tracking control algorithms. The attitude tracking performances are investigated in both simulations and real car tests. Two control algorithms which adopt linear quadratic regulator (LQR) and model predictive control (MPC) algorithms, are compared and analyzed in terms of theory and control performance. The simulations and real car tests results show that both attitude tracking control algorithms can effectively track the ideal body attitude with acceptable errors under different pavements, and the control effect of MPC is slightly better than that of LQR. In this way, attitude tracking of car body shows a lot of potential when a vehicle is in harsh environments.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29

Similar content being viewed by others

Data availability

The data that support the findings of this study are available from the article author upon reasonable request.

References

  • Arana, C., Evangelou, S. A., & Dini, D. (2017). Series Active Variable Geometry Suspension application to comfort enhancement. Control Engineering Practice, 59, 111–126.

    Article  Google Scholar 

  • Bartlett, R. A., Biegler, L. T., Backstrom, J., & Gopal, V. (2002). Quadratic programming algorithms for large-scale model predictive control. Journal of Process Control, 12(7), 775–795.

    Article  Google Scholar 

  • Chan, J. H. (2002). Stabilization of discrete system zeros: An improved design. International Journal of Control, 75(10), 759–765.

    Article  MathSciNet  Google Scholar 

  • Chen, G., Peng, W., Wang, Z. Y., Tu, J. J., Hu, H. S., Wang, D. H., Cheng, H., & Zhang, L. Y. (2023b). Modeling of swimming posture dynamics for a beaver-like robot. Ocean Engineering, 279, 114550.

    Article  Google Scholar 

  • Chen, G., Xu, Y. D., Yang, C. G., Yang, X., Hu, H. S., Chai, X. X., & Wang, D. H. (2023a). Design and control of a novel bionic mantis shrimp robot. IEEE/ASME Transactions on Mechatronics, 28(6), 3376–3385.

    Article  Google Scholar 

  • Du, M. M., Zhao, D. X., Yang, B., & Wang, L. (2018). Terminal sliding mode control for full vehicle active suspension systems. Journal of Mechanical Science and Technology, 32(6), 2851–2866.

    Article  Google Scholar 

  • ElMadany, M. M., Al Bassam, B. A., & Fayed, A. A. (2011). Preview control of slow-active suspension systems. Journal of Vibration and Control, 17(2), 245–258.

    Article  MathSciNet  Google Scholar 

  • Enders, E., Burkhard, G., & Munzinger, N. (2020). Analysis of the influence of suspension actuator limitations on ride comfort in passenger cars using model predictive control. Actuators, 9(3), 77.

    Article  Google Scholar 

  • Gao, J., & Han, P. F. (2022). Analysis and optimization of suspension spring stiffness for improving frequency response characteristics of the vehicle. Mathematical Problems in Engineering, 2022, 1–19. https://doi.org/10.1155/2022/9557483

    Article  Google Scholar 

  • Gao, Y., Wang, D. L., Wei, W., Yu, Q. D., Liu, X. D., & Wei, Y. H. (2022a). Constrained predictive tracking control for unmanned hexapod robot with tripod gait. Drones, 6(9), 246.

    Article  Google Scholar 

  • Gao, Y., Wei, W., Wang, X. M., Wang, D. L., Li, Y. J., & Yu, Q. D. (2022b). Trajectory tracking of multi-legged robot based on model predictive and sliding mode control. Inform Sciences, 606, 489–511.

    Article  Google Scholar 

  • Gu, C., Yin, J., & Chen, X. (2018). Robust control and optimization of a rocker-pushrod electromagnetic active suspension (Article). Qiche Gongcheng/automotive Engineering, 40(1), 34–40.

    Google Scholar 

  • Haslwanter, T. (2018). 3D Kinematics. Springer International Publishing AG.

    Book  Google Scholar 

  • Jia, W. W., Zhang, W. Z., Ma, F. W., & Wu, L. (2023). Attitude control of vehicle based on series active suspensions. Actuators, 12(2), 67.

    Article  Google Scholar 

  • Kappen, H. J. (2011). Optimal control theory and the linear Bellman equation. In: Bayesian time series models, pp. 363–387. https://www.cambridge.org/core/books/abs/bayesian-time-series-models/optimalcontrol-theory-and-the-linear-bellman-equation/A764A2F4E54FBC1716E52192AE9B6B96

  • Konieczny, J., Kowal, J., Raczka, W., & Sibielak, M. (2013). Bench tests of slow and full active suspensions in terms of energy consumption. Journal of Low Frequency Noise Vibration and Active Control, 32(1–2), 81–98.

    Article  Google Scholar 

  • Li, W. F., Xie, Z. C., Wong, P. K., Cao, Y. C., Hua, X. Q., & Zhao, J. (2019). Robust nonfragile H infinity optimum control for active suspension systems with time-varying actuator delay. Journal of Vibration and Control, 25(18), 2435–2452.

    Article  MathSciNet  Google Scholar 

  • Ma, F. W., Ni, L. W., Wei, L. L., Nie, J. H., Wu, L., & Jia, W. W. (2020a). Posture control of all terrain mobile robot with vibration isolation system. Advances in Dynamics of Vehicles on Roads and Tracks, Iavsd, 2019(205), 1794–1807.

    Article  Google Scholar 

  • Ma, F. W., Nie, J. H., Wu, L., Ni, L. W., Xu, G. J., & Jia, W. W. (2020b). Trajectory Tracking of a Four-Wheel-Steering Vehicle on Harsh Road. Advances in Dynamics of Vehicles on Roads and Tracks, Iavsd, 2019(138), 1189–1198.

    Article  Google Scholar 

  • Moradi, S. M., Akbari, A., & Mirzaei, M. (2019). An offline LMI-based robust model predictive control of vehicle active suspension system with parameter uncertainty. Transactions of the Institute of Measurement and Control, 41(6), 1699–1711.

    Article  Google Scholar 

  • Nguyen, T. A. (2020). Control an active suspension system by using PID and LQR controller. International Journal of Mechanical and Production Engineering Research and Development, 10(3), 7003–7012.

    Article  Google Scholar 

  • Ni, L. W., Ma, F. W., Ge, L. H., & Wu, L. (2021). Design and posture control of a wheel-legged robot with actively passively transformable suspension system. Journal of Mechanisms and Robotics-Transactions of the Asme, 13(1), 011014.

    Article  Google Scholar 

  • Ni, L. W., Ma, F. W., & Wu, L. (2020). Posture control of a four-wheel-legged robot with a suspension system. Ieee Access, 8, 152790–152804.

    Article  Google Scholar 

  • Ni, L. W., Wu, L., & Zhang, H. S. (2022). Parameters uncertainty analysis of posture control of a four-wheel-legged robot with series slow active suspension system. Mechanism and Machine Theory, 175, 104966.

    Article  Google Scholar 

  • Ni, T., Li, W. H., Zhang, H. Y., Yang, H., & Kong, Z. (2019). Pose prediction of autonomous full tracked vehicle based on 3D sensor. Sensors, 19(23), 5120.

    Article  Google Scholar 

  • Pan, H. H., Sun, W. C., Gao, H. J., Hasawar, T., & Alsaadi, F. (2015). Constrained robust adaptive control for vehicle active suspension systems. International Journal of Vehicle Design, 68(1–3), 5–21.

    Article  Google Scholar 

  • Patra, A. K., Mishra, A. K., & Agrawal, R. (2021). Fuzzy logic controller design for stabilizing and trajectory tracking of vehicle suspension system. Smart Innovation, Systems and Technologies, 194, 575–587.

    Article  Google Scholar 

  • Pinon, A., Favela-Contreras, A., Felix-Herran, L. C., Beltran-Carbajal, F., & Lozoya, C. (2021). An ARX model-based predictive control of a semi-active vehicle suspension to improve passenger comfort and road-holding. Actuators, 10(3), 47.

    Article  Google Scholar 

  • Renczes, B. (2017). Accurate floating-point argument calculation for sine-fitting algorithms. Ieee Transactions on Instrumentation and Measurement, 66(11), 2988–2996.

    Article  Google Scholar 

  • Shadmand, M. B., Jain, S., & Balog, R. S. (2019). Autotuning technique for the cost function weight factors in model predictive control for power electronic interfaces. Ieee Journal of Emerging and Selected Topics in Power Electronics, 7(2), 1408–1420.

    Article  Google Scholar 

  • Shi, X. H., Jiang, X., & Zhao, J. (2018). Seven degrees of freedom vehicle response characteristic under four wheel random pavement excitation. Gongcheng Kexue Yu Jishu/advanced Engineering Science, 18(27), 71–78.

    Google Scholar 

  • Taghavifar, H. (2019). Reduced vibration of off-road vehicle nonlinear suspension system using an adaptive integral sliding mode-neural network controller. International Journal of Dynamics and Control, 8(1), 291–301.

    Article  MathSciNet  Google Scholar 

  • Tchamna, R., Lee, M., Youn, I., Maxim, V., Zidek, K., & Kelemenova, T. (2016). Management of linear quadratic regulator optimal control with full-vehicle control case study. International Journal of Advanced Robotic Systems, 13, 172988141666761.

    Article  Google Scholar 

  • Theunissen, J., Sorniotti, A., Gruber, P., Fallah, S., Ricco, M., Kvasnica, M., & Dhaens, M. (2020). Regionless Explicit Model Predictive Control of Active Suspension Systems With Preview. IEEE Transactions on Industrial Electronics, 67(6), 4877–4888.

    Article  Google Scholar 

  • Tian, W. P., Dou, J. M., & Xu, X. X. (2021). Modelling and characteristics of hybrid coupling hydro-pneumatic suspension for a seven-axle vehicle. Proceedings of the Institution of Mechanical Engineers Part D-Journal of Automobile Engineering, 235(7), 1892–1901.

    Article  Google Scholar 

  • van der Westhuizen, S. F., & Els, P. S. (2013). Slow active suspension control for rollover prevention. Journal of Terramechanics, 50(1), 29–36.

    Article  Google Scholar 

  • Wu, L., Ahmad, E., Khan, M. A., & Youn, I. (2021). Integration of active tilting control and full-wheel steering control system on vehicle lateral performance. International Journal of Automotive Technology, 22(4), 979–992.

    Article  Google Scholar 

  • Wu, L., Khan, M. A., Youn, E., & Tomizuka, M. (2018). Attitude motion control of vehicle including the active passenger seat system. International Journal of Vehicle Design, 78(1–4), 131–160.

    Google Scholar 

  • Wu, L., Zhang, W. Z., Yuan, D. F., Youn, I., & Jia, W. W. (2024). Model predictive control of a semi-active vehicle-mounted vibration isolation platform. Sensors, 24(1), 243.

    Article  Google Scholar 

  • Ye, X. L., Yao, J. S., Xiong, X., Gong, C., & Jin, T. (2020). A quality control algorithm for cosine similarity and moving curved surface fitting. (English). China Sciencepaper, 15(5), 577–592.

    Google Scholar 

  • Yerrawar, R. N., & Arakerimath, R. R. (2016). Performance assessment and control policies for semiactive suspension using SIMSCAPE, 2016 International Conference on Automatic Control and Dynamic Optimization Techniques (ICACDOT), Pune, India, 2016, pp. 1163–1168.

  • Youn, I., Im, J., & Tomizuka, M. (2006). Level and attitude control of the active suspension system with integral and derivative action. Vehicle System Dynamics, 44(9), 659–674.

    Article  Google Scholar 

  • Youn, I., Wu, L., Youn, E., & Tomizuka, M. (2015). Attitude motion control of the active suspension system with tracking controller. International Journal of Automotive Technology, 16(4), 593–601.

    Article  Google Scholar 

  • Zhu, J. H. (2005). On stochastic Riccati equations for the stochastic LQR problem. Systems & Control Letters, 54(2), 119–124.

    Article  MathSciNet  Google Scholar 

  • Zhu, Z. H., Wang, R. C., Yang, L., Sun, Z., & Meng, X. (2021). Modelling and control of a semi-active dual-chamber hydro-pneumatic inerter-based suspension system. Proceedings of the Institution of Mechanical Engineers Part D-Journal of Automobile Engineering, 235(9), 2355–2370.

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the Science and Technology Development Plan Project of Jilin Province (YDZJ202101ZYTS190, 20210601155FG), the National Natural Science Foundation of China (51705185), the National Key Research and Development Program of China (2017YFC0601604), the Science and Technology Department Outstanding Young Talent Fund of Jilin Province (20190103056JH)

Author information

Authors and Affiliations

  1. State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun, 130012, China

    Liang Wu, Weizhou Zhang & Liwei Ni

  2. Changsha Automotive Innovation Research Institute, Changsha, 410036, China

    Liang Wu

  3. School of Mechanical Engineering, Henan College of Engineering, Zhengzhou, 451191, China

    Liwei Ni

  4. School of Management Science and Information Engineering, Jilin University of Finance and Economics, Changchun, 130117, China

    Weiwei Jia

  5. School of Mechanical and Aerospace Engineering, Gyeongsang National University, Jinju, 660-701, South Korea

    Iljoong Youn

Authors
  1. Liang Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Weizhou Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Liwei Ni
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Weiwei Jia
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Iljoong Youn
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Weiwei Jia.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wu, L., Zhang, W., Ni, L. et al. Attitude Tracking Control of All-Terrain Vehicle with Tandem Active–Passive Suspension. Int.J Automot. Technol. (2024). https://doi.org/10.1007/s12239-024-00085-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12239-024-00085-9

Keywords

Search

Navigation