Skip to main content
SpringerLink
Log in

Compensation strategies based on Bode step concept for actuator rate limit effect on first-order plus time-delay systems

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

Abstract

Rate limit of system actuators is one of the major restrictions in the physical world. However, in classical and modern control design, the actuator rate limit has always been neglected. The rate limit generates amplitude attenuation and phase delay of the control signal, which will deteriorate closed-loop system performance, and may even lead to system instability. In this study, the Bode step control method was applied to the first-order plus time-delay system to achieve a better tolerance of smaller rate limit value. A rate limit compensation strategy is proposed based on the describing function and the onset frequency of the rate limiter. Both illustrative example and hardware-in-the-loop experiments are given to show the effectiveness of Bode step controller and the proposed rate limit compensation method.

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

Similar content being viewed by others

References

  1. Sun, W., Gao, H., Kaynak, O.: Vibration isolation for active suspensions with performance constraints and actuator saturation. IEEE/ASME Trans. Mechatron. 20(2), 675–683 (2015). https://doi.org/10.1109/TMECH.2014.2319355

    Article  Google Scholar 

  2. Huang, S., Cai, M., Xiang, Z.: Robust sampled-data \(H_{\infty }\) control for offshore platforms subject to irregular wave forces and actuator saturation. Nonlinear Dyn. 88(4), 2705–2721 (2017)

    Article  Google Scholar 

  3. Shojaei, K.: Output-feedback formation control of wheeled mobile robots with actuators saturation compensation. Nonlinear Dyn. 89(4), 2867–2878 (2017)

    Article  MathSciNet  Google Scholar 

  4. McRuer, D.T.: National Research Council: Aviation Safety and Pilot Control: Understanding and Preventing Unfavorable Pilot-Vehicle Interactions. The National Academies Press, Washington, DC (1997)

  5. Duda, H.: Flight control system design considering rate saturation. Aerosp. Sci. Technol. 2(4), 265–275 (1998)

    Article  Google Scholar 

  6. Hanke, D.: Handling qualities analysis on rate limiting elements in flight control systems. In: Flight Vehicle Integration Panel Workshop on Pilot Induced Oscillations. AGARD-AR-335 (1994)

  7. Amato, F., Iervolino, R., Pandit, M., Scala, S., Verde, L.: Analysis of pilot-in-the-loop oscillations due to position and rate saturations. In: Proceedings of the 39th IEEE Conference on Decision and Control, vol. 4, pp. 3564–3569 (2000)

  8. Meng, J., Xu, H., Zhang, J.: A comparison of rate-limit phase compensator to prevent category II pilot induced oscillations. In: Proceedings of the 8th World Congress on Intelligent Control and Automation, pp. 3872–3877 (2010)

  9. Alstrom, R.B., Bollt, E., Marzocca, P., Ahmadi, G.: The application of nonlinear pre-filters to prevent aeroservoelastic interactions due to actuator rate limiting. In: Proceedings of the 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference (2012)

  10. Yuan, J., Chen, Y., Fei, S.: Analysis of actuator rate limit effects on first-order plus time-delay systems under fractional-order proportional–integral control. IFAC-PapersOnLine 51(4), 37–42 (2018)

    Article  Google Scholar 

  11. Brieger, O., Kerr, M., Leißling, D., Postlethwaite, I., Sofrony, J., Turner, M.: Flight testing of a rate saturation compensation scheme on the attas aircraft. Aerosp. Sci. Technol. 13(2–3), 92–104 (2009)

    Article  Google Scholar 

  12. Buchholz, J.J.: Time-delay induced by control surface rate saturation. Zeitschrift fur Flugwissenschaften und Weltraumforschung 17(5), 287–293 (1993)

    Google Scholar 

  13. Chalk, C.: Study of a software rate limit concept. Calspan Flight Research Memorandum (636) (1992)

  14. Tran, A.T., Sakamoto, N., Kikuchi, Y., Mori, K.: Pilot induced oscillation suppression controller design via nonlinear optimal output regulation method. Aerosp. Sci. Technol. 68, 278–286 (2017)

    Article  Google Scholar 

  15. Gatley, S.L., Turner, M.C., Postlethwaite, I., Kumar, A.: A comparison of rate-limit compensation schemes for pilot-induced-oscillation avoidance. Aerosp. Sci. Technol. 10(1), 37–47 (2006)

    Article  Google Scholar 

  16. Rundqwist, L., Stahl-Gunnarsson, K.: Phase compensation of rate limiters in unstable aircraft. In: Proceeding of the 1996 IEEE International Conference on Control Applications, pp. 19–24 (1996)

  17. Sofrony, J., Turner, M.C., Postlethwaite, I.: A simple anti-windup compensation scheme for systems with rate-limited actuators. In: IEEE 2009 ICCAS-SICE, pp. 3311–3316 (2009)

  18. Guilhem, P., Jean-Marc, B.: Application of robust antiwindup design to the longitudinal aircraft control to cover actuator loss. IFAC Proc. Vol. 46(19), 506–511 (2013)

    Article  Google Scholar 

  19. Zhou, S., Zheng, M., Tomizuka, M.: A generalized anti-windup scheme considering amplitude and rate saturations. In: ASME 2016 Dynamic Systems and Control Conference, pp. V002T22A007–V002T22A007. American Society of Mechanical Engineers (2016)

  20. EL W, B.: Network analysis and feedback amplifier design. D. vanNostrand p. 52 (1945)

  21. Banos, A., Cervera, J., Lanusse, P., Sabatier, J.: Bode optimal loop shaping with CRONE compensators. J. Vib. Control 17(13), 1964–1974 (2011)

    Article  MathSciNet  Google Scholar 

  22. Luo, Y., Zhang, T., Lee, B., Kang, C., Chen, Y.: Disturbance observer design with Bode’s ideal cut-off filter in hard-disc-drive servo system. Mechatronics 23(7), 856–862 (2013)

    Article  Google Scholar 

  23. Karimi, A., Garcia, D., Longchamp, R.: PID controller tuning using Bode’s integrals. IEEE Trans. Control Syst. Technol. 11(6), 812–821 (2003)

    Article  Google Scholar 

  24. Barbosa, R.S., Machado, J.T., Ferreira, I.M.: Tuning of PID controllers based on Bode’s ideal transfer function. Nonlinear Dyn. 38(1–4), 305–321 (2004)

    Article  Google Scholar 

  25. Mitchell, R.: Simplifying Bode’s maximum available feedback design. Int. J. Electr. Eng. Educ. 43(1), 34–47 (2006)

    Article  MathSciNet  Google Scholar 

  26. Gilbreath, G.P.: Prediction of pilot-induced oscillations (PIO) due to actuator rate limiting using the open-loop onset point (OLOP) criterion. Technical report, Air Force Inst of Tech Wright-Pattersonafb OH (2001)

  27. Duda, H.: Frequency domain analysis of rate limiting elements in flight control systems. Forschungsbericht- Deutsche Forschungsanstalt fuer Luft- und Raumfahrt, DLR-FB (94), 40 (1994)

  28. Lurie, B., Enright, P.: Classical Feedback Control: With MATLAB® and Simulink®, 2nd edn. Automation and Control Engineering. CRC Press, Boca raton (2016)

  29. Åström, K.J., Hägglund, T., Astrom, K.J.: Advanced PID control, vol. 461. ISA-The Instrumentation, Systems, and Automation Society Research Triangle (2006)

  30. Li, Z., Chen, Y.Q.: Identification of linear fractional order systems using the relay feedback approach. In: IEEE 2014 American Control Conference, pp. 3704–3709 (2014)

Download references

Author information

Authors and Affiliations

  1. Key Laboratory of Measurement and Control of CSE, Ministry of Education, School of Automation, Southeast University, Nanjing, 210096, China

    Jie Yuan & Shumin Fei

  2. Mechatronics, Embedded Systems and Automation Lab, University of California, Merced, CA, 95343, USA

    YangQuan Chen

Authors
  1. Jie Yuan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shumin Fei
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. YangQuan Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Jie Yuan or YangQuan Chen.

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

Yuan, J., Fei, S. & Chen, Y. Compensation strategies based on Bode step concept for actuator rate limit effect on first-order plus time-delay systems. Nonlinear Dyn 99, 2851–2866 (2020). https://doi.org/10.1007/s11071-019-05454-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-019-05454-z

Keywords

Search

Navigation