Skip to main content

Advertisement

SpringerLink
Log in

Multi-objective frequency domain-constrained static output feedback control for delayed active suspension systems with wheelbase preview information

  • Original paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

In this research, a multi-objective frequency domain-constrained static output feedback control is developed for the delayed active suspension system with wheelbase preview information. Firstly, the model of the half-vehicle active suspension system with wheelbase preview information and time delay is constructed by employing the augmented method. Secondly, in vertical vibration, the human body senses are more intense when the frequency of the external disturbance is in the range of 4–8 Hz. Therefore, a finite frequency control method is proposed for the controller design with robust \( H_{\infty } \) and generalized \( H_{2} \) performance. Thirdly, considering that a full online knowledge of states is not available in practical suspension systems, a static output feedback strategy is proposed to guarantee the feasibility of the controller by using a two-stage method. Finally, simulation study is given to explain the effectiveness and superiority of the presented controller.

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

Similar content being viewed by others

References

  1. Apkarian, P., Tuan, H., Bernussou, J.: Continuous-time analysis, eigenstructure assignment, and \( H_{2} \) synthesis with enhanced linear matrix inequalities (lmi) characterizations. IEEE Trans. Autom. Control 46(12), 1941–1946 (2001)

    Article  MATH  Google Scholar 

  2. Bender, E.: Optimum linear preview control with application to vehicle suspension. J. Basic Eng. 90(2), 213–221 (1968)

    Article  Google Scholar 

  3. Cao, F., Sun, H., Li, Y., Tong, S.: Fuzzy adaptive fault-tolerant control for a class of active suspension systems with time delay. Int. J. Fuzzy Syst. 21(7), 2054–2065 (2019)

    Article  MathSciNet  Google Scholar 

  4. Chen, H., Guo, K.H.: Constrained \(H_{\infty }\) control of active suspensions: an LMI approach. IEEE Trans. Control Syst. Technol. 13(3), 412–421 (2005)

    Google Scholar 

  5. Chen, S., Cai, Y., Wang, J., Yao, M.: A novel lqg controller of active suspension system for cehicle roll safety. Int. J. Control Autom. Syst. 16(5), 2203–2213 (2018)

    Article  Google Scholar 

  6. Crusius, C.A.R., Trofino, A.: Sufficient lmi conditions for output feedback control problems. IEEE Trans. Autom. Control 44(5), 1053–1057 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  7. Ding, S., Chen, W., Mei, K., Murray-Smith, D.J.: Disturbance observer design for nonlinear systems represented by input–output models. IEEE Trans. Ind. Electron. 67(2), 1222–1232 (2020)

    Article  Google Scholar 

  8. Dinh, H.T., Nguyen, T.G.: Saturated feedback control to improve ride comfort for uncertain nonlinear Macpherson active suspension system with input delay. IEEE Access 8, 129136–129145 (2020)

    Article  Google Scholar 

  9. Dong, J., Yang, G.: Robust static output feedback control synthesis for linear continuous systems with polytopic uncertainties. Automatica 49(6), 1821–1829 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  10. Guan, Y., Han, Q., Yao, H., Ge, X.: Robust event-triggered \(H_{\infty }\) controller design for vehicle active suspension systems. Nonlinear Dyn. 94(1), 627–638 (2018)

    Article  MATH  Google Scholar 

  11. Hao, Y., Duan, Z.: Static output-feedback controller synthesis with restricted frequency domain specifications for time-delay systems. IET Control Theory Appl. 9(10), 1608–1614 (2015)

    Article  MathSciNet  Google Scholar 

  12. Karim Afshar, K., Javadi, A., Jahed-Motlagh, M.R.: Robust \(H_{\infty }\) control of an active suspension system with actuator time delay by predictor feedback. IET Control Theory Appl. 12(7), 1012–1023 (2018)

    Article  MathSciNet  Google Scholar 

  13. Kazemy, A., Lam, J., Li, X.: Finite-frequency \(H_{\infty }\) control for offshore platforms subject to parametric model uncertainty and practical hard constraints. ISA Trans. 83, 53–65 (2018)

    Article  Google Scholar 

  14. Li, H., Jing, X., Karimi, H.R.: Output-feedback-based \(H_{\infty }\) control for vehicle suspension systems with control delay. IEEE Trans. Industr. Electron. 61(1), 436–446 (2014)

    Article  Google Scholar 

  15. Li, H., Liu, H., Hand, S., Hilton, C.: Design of robust \(H_{\infty }\) controller for a half-vehicle active suspension system with input delay. Int. J. Syst. Sci. 44(4–6), 625–640 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  16. Li, H., Zhang, Z., Yan, H., Xie, X.: Adaptive event-triggered fuzzy control for uncertain active suspension systems. IEEE Trans. Cybern. 49(12), 4388–4397 (2019)

    Article  Google Scholar 

  17. Li, P., Lam, J., Cheung, K.C.: Multi-objective control for active vehicle suspension with wheelbase preview. J. Sound Vib. 333(21), 5269–5282 (2014)

    Article  Google Scholar 

  18. Li, P., Lam, J., Cheung, K.C.: Velocity-dependent multi-objective control of vehicle suspension with preview measurements. Mechatronics 24(5), 464–475 (2014)

    Article  Google Scholar 

  19. Li, P., Li, P., Liu, Y., Bao, H., Lu, R.: \(H_{\infty }\) control of periodic piecewise polynomial time-varying systems with polynomial Lyapunov function. J. Franklin Inst. 356(13), 6968–6988 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  20. Li, W., Xie, Z., Wong, P.K., Cao, Y., Zhao, J.: Robust nonfragile \(H_{\infty }\) optimum control for active suspension systems with time-varying actuator delay. J. Vib. Control 25(18), 2435–2452 (2019)

    Article  MathSciNet  Google Scholar 

  21. Li, W., Xie, Z., Wong, P.K., Ma, X., Cao, Y., Zhao, J.: Nonfragile \(H_{\infty }\) control of delayed active suspension systems in finite frequency under nonstationary running. J. Dyn. Syst. Measur. Control-Trans. ASME 141(6), 61001 (2019)

    Article  Google Scholar 

  22. Li, W., Xie, Z., Zhao, J., Wong, P.K., Li, P.: Fuzzy finite-frequency output feedback control for nonlinear active suspension systems with time delay and output constraints. Mech. Syst. Signal Process. 132, 315–334 (2019)

    Article  Google Scholar 

  23. Li, X., Gao, H.: A heuristic approach to static output-feedback controller synthesis with restricted frequency-domain specifications. IEEE Trans. Autom. Control 59(4), 1008–1014 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  24. Liang, Z., Zhao, J., Dong, Z., Wang, Y., Ding, Z.: Torque vectoring and rear-wheel-steering control for vehicle’s uncertain slips on soft and slope terrain using sliding mode algorithm. IEEE Trans. Veh. Technol. 69(4), 3805–3815 (2020)

    Article  Google Scholar 

  25. Liberzon, A., Rubinstein, D., Gutman, P.O.: Active suspension for single wheel station of off-road track vehicle. Int. J. Robust Nonlinear Control 11(10), 977–999 (2001)

    Article  MATH  Google Scholar 

  26. Liu, L., Ding, S., Yu, X.: Second-order sliding mode control design subject to an asymmetric output constraint. IEEE Trans. Circuits Syst. II: Express Briefs 1 (2020)

  27. Liu, L., Zheng, W.X., Ding, S.: An adaptive sosm controller design by using a sliding-mode-based filter and its application to buck converter. IEEE Trans. Circuits Syst. I Regul. Pap. 67(7), 2409–2418 (2020)

    Article  MathSciNet  Google Scholar 

  28. Liu, Y.J., Zeng, Q., Tong, S., Chen, C.L.P., Liu, L.: Actuator failure compensation-based adaptive control of active suspension systems with prescribed performance. IEEE Trans. Ind. Electron. 67(8), 7044–7053 (2020)

    Article  Google Scholar 

  29. Ma, X., Wong, P.K., Zhao, J.: Practical multi-objective control for automotive semi-active suspension system with nonlinear hydraulic adjustable damper. Mech. Syst. Signal Process. 117, 667–688 (2019)

    Article  Google Scholar 

  30. Min, X., Li, Y., Tong, S.: Adaptive fuzzy optimal control for a class of active suspension systems with full-state constraints. IET Intel. Transp. Syst. 14(5), 371–381 (2020)

    Article  Google Scholar 

  31. Pan, H., Sun, W., Jing, X., Gao, H., Yao, J.: Adaptive tracking control for active suspension systems with non-ideal actuators. J. Sound Vib. 399, 2–20 (2017)

    Article  Google Scholar 

  32. Pang, H., Shang, Y., Yang, J.: An adaptive sliding mode-based fault-tolerant control design for half-vehicle active suspensions using t-s fuzzy approach. J. Vib. Control 26(17–18), 1411–1424 (2020)

    Article  MathSciNet  Google Scholar 

  33. Qin, Y., Rath, J.J., Hu, C., Sentouh, C., Wang, R.: Adaptive nonlinear active suspension control based on a robust road classifier with a modified super-twisting algorithm. Nonlinear Dyn. 97(4), 2425–2442 (2019)

    Article  Google Scholar 

  34. Qin, Y., Tang, X., Jia, T., Duan, Z., Zhang, J., Li, Y., Zheng, L., Kazmerski, L.: Noise and vibration suppression in hybrid electric vehicles: state of the art and challenges. Renew. Sustain. Energy Rev. 124, 109782 (2020)

    Article  Google Scholar 

  35. Qin, Y., Wang, Z., Xiang, C., Hashemi, E., Khajepour, A., Huang, Y.: Speed independent road classification strategy based on vehicle response: theory and experimental validation. Mech. Syst. Signal Process. 117, 653–666 (2019)

    Article  Google Scholar 

  36. Rao, L.V.V.G., Narayanan, S.: Optimal response of half car vehicle model with sky-hook damper using LQR with look ahead preview control. J. Brazil. Soc. Mech. Sci. Eng. 42(9), 1–9 (2020)

    Article  Google Scholar 

  37. Ryu, S., Park, Y., Suh, M.: Ride quality analysis of a tracked vehicle suspension with a preview control. J. Terrramech. 48(6), 409–417 (2011)

    Article  Google Scholar 

  38. Shao, X., Naghdy, F., Du, H., Li, H.: Output feedback \(H_{\infty }\) control for active suspension of in-wheel motor driven electric vehicle with control faults and input delay. ISA Trans. 92, 94–108 (2019)

    Article  Google Scholar 

  39. Sun, W., Gao, H., Kaynak, O.: Finite frequency \(H_{\infty }\) control for vehicle active suspension systems. IEEE Trans. Control Syst. Technol. 19(2), 416–422 (2011)

    Article  Google Scholar 

  40. Wang, G., Chen, C., Yu, S.: Optimization and static output-feedback control for half-car active suspensions with constrained information. J. Sound Vib. 378, 1–13 (2016)

    Article  Google Scholar 

  41. Wang, R., Jing, H., Yan, F., Karimi, H.R., Chen, N.: Optimization and finite-frequency \(H_{\infty }\) control of active suspensions in in-wheel motor driven electric ground vehicles. J. Frankl. Inst. 352(2), 468–484 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  42. Xu, S., Lam, J., Yang, C.: Robust \(H_{\infty }\) control for uncertain singular systems with state delay. Int. J. Robust Nonlinear Control 13, 1213–1223 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  43. Yin, X., Zhang, L., Zhu, Y., Wang, C., Li, Z.: Robust control of networked systems with variable communication capabilities and application to a semi-active suspension system. IEEE/ASME Trans. Mechatron. 21(4), 2097–2107 (2016)

    Article  Google Scholar 

  44. Zhang, H., Hong, Q., Yan, H., Yang, F., Guo, G.: Event-based distributed \(H_{\infty }\) filtering networks of 2dof quarter-car suspension systems. IEEE Trans. Ind. Inf. 13(1), 312–321 (2017)

    Article  Google Scholar 

  45. Zhang, H., Wang, R., Wang, J., Shi, Y.: Robust finite frequency \(H_{\infty }\) static-output-feedback control with application to vibration active control of structural systems. Mechatronics 24(4), 354–366 (2014)

    Article  Google Scholar 

  46. Zhang, J., Ding, F., Zhang, N., Chen, S., Zhang, B.: A new ssukf observer for sliding mode force tracking \(H_{\infty }\) control of electrohydraulic active suspension. Asian J. Control 22(2), 761–778 (2020)

    Article  MathSciNet  Google Scholar 

  47. Zhang, X., Yang, G.: Performance analysis for multi-delay systems in finite frequency domains. Int. J. Robust Nonlinear Control 22(8), 933–944 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  48. Zhao, J., Wong, P.K., Ma, X., Xie, Z.: Chassis integrated control for active suspension, active front steering and direct yaw moment systems using hierarchical strategy. Veh. Syst. Dyn. 55(1), 72–103 (2016)

    Article  Google Scholar 

  49. Zhu, Q., Ding, J., Yang, M.: LQG control based lateral active secondary and primary suspensions of high-speed train for ride quality and hunting stability. IET Control Theory Appl. 16(10), 1497–1504 (2018)

    Article  Google Scholar 

Download references

Acknowledgements

This work is supported by National Natural Science Foundation of China (Grant No. 51705084), the Fundamental Research Funds for the Central Universities (Grant No. N2003032), the Natural Science Foundation of Guangdong Province of China (Grant Nos. 2019A1515011602 and 2018MS46), the Opening Project of Guangdong Provincial Key Laboratory of Technique and Equipment for Macromolecular Advanced Manufacturing, South China University of Technology, China (Grant No. 2020kfkt05). This work is also supported by the research Grant of the University of Macau (Grant No. MYRG2019-00028-FST).

Author information

Authors and Affiliations

  1. School of Mechanical Engineering and Automation, and Key Laboratory of Vibration and Control of Aero-Propulsion Systems, Ministry of Education, Northeastern University, Shenyang, China

    Jing Zhao, Xiaowei Wang & Junru Jia

  2. Foshan Graduate School, Northeastern University, Foshan, China

    Jing Zhao, Xiaowei Wang & Junru Jia

  3. Department of Electromechanical Engineering, Faculty of Science and Technology, University of Macau, Taipa, Macao

    Pak Kin Wong

  4. School of Mechanical and Automotive Engineering, and Guangdong Provincial Key Laboratory of Technique and Equipment for Macromolecular Advanced Manufacturing, South China University of Technology, Guangzhou, China

    Zhengchao Xie & Wenfeng Li

Authors
  1. Jing Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaowei Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pak Kin Wong
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zhengchao Xie
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Junru Jia
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Wenfeng Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wenfeng Li.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhao, J., Wang, X., Wong, P.K. et al. Multi-objective frequency domain-constrained static output feedback control for delayed active suspension systems with wheelbase preview information. Nonlinear Dyn 103, 1757–1774 (2021). https://doi.org/10.1007/s11071-021-06204-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-021-06204-w

Keywords

Search

Navigation