Skip to main content
SpringerLink
Log in

Finite-frequency H∞ control for active chatter suppression in turning

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

Regenerative chatter deteriorates machining precision and accelerates tool wear, thereby limiting productivity. This paper presents the design, analysis, and verification of a novel finite-frequency band (FFB) H∞ state feedback control strategy, which is dedicated to chatter control of turning processes. In comparison with the available entire-frequency domain (EFD) controllers, one uniqueness of the proposed controller is that it achieves the finite-frequency band optimal control of chatter, and the user can specify the frequency band for optimization according to actual requirements. Dynamics of regenerative delay, cutting model uncertainty, and actuator output constraint are incorporated into the controller design. Utilizing the Lyapunov–Krasovskii functional (LKF) method and the generalized Kalman-Yakubovich-Popov (GKYP) lemma, a set of linear matrix inequalities (LMI) are derived and adopted to synthesize the FFB H∞ controller. The superiority of the developed controller versus EFD controllers is verified by carrying out both simulation and experimental studies. Results demonstrate that the chatter-free region can be substantially enlarged with the proposed 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

Similar content being viewed by others

Data availability

All data generated or analyzed during this study are included in this published article.

References 

  1. Munoa J, Beudaert X, Dombovari Z, Altintas Y, Budak E, Brecher C, Stépán G (2016) Chatter suppression techniques in metal cutting. CIRP Ann - Manuf Technol 65(2):785–808

    Article  Google Scholar 

  2. Siddhpura M, Paurobally R (2012) A review of chatter vibration research in turning. Int J Mach Tools Manuf 61:27–47

    Article  Google Scholar 

  3. Ma H, Wu J, Xiong Z (2020) Active chatter control in turning processes with input constraint. Int J Adv Manuf Technol 108(11):3737–3751

    Article  Google Scholar 

  4. Dumanli A, Sencer B (2021) Active control of high frequency chatter with machine tool feed drives in turning. CIRP Ann - Manuf Technol 70(1):309–312

    Article  Google Scholar 

  5. van Dijk NJM, Doppenberg EJJ, Faassen RPH, van de Wouw N, Oosterling HAJ, Nijmeijer H (2010) Automatic in-process chatter avoidance in the high-speed milling process. J Dyn Syst Meas Control Trans ASME 132(3):031006

    Article  Google Scholar 

  6. Li Z, Song Q, Liu Z, Wang B, Cai Y (2022) Chatter suppression mechanism and parameters configuration of the spindle speed variation with piecewise characteristics. Int J Adv Manuf Technol 122:3041–3055

    Article  Google Scholar 

  7. Soliman E, Ismail F (1997) Chatter suppression by adaptive speed modulation. Int J Mach Tools Manuf 37(3):355–369

    Article  Google Scholar 

  8. Saciotto VR, Diniz AE (2022) An experimental evaluation of particle impact dampers applied on the tool for milling of hardened steel complex surface. Int J Adv Manuf Technol 119:7579–7597

    Article  Google Scholar 

  9. Yang Y, Muñoa J, Altintas Y (2010) Optimization of multiple tuned mass dampers to suppress machine tool chatter. Int J Mach Tools Manuf 50(9):834–842

    Article  Google Scholar 

  10. Yang Y, Dai W, Liu Q (2015) Design and implementation of two-degree-of-freedom tuned mass damper in milling vibration mitigation. J Sound Vib 335:78–88

    Article  Google Scholar 

  11. Miguelez M, Rubio L, Loya JA, Fernandez-Saez J (2010) Improvement of chatter stability in boring operations with passive vibration absorbers. Int J Mech Sci 52(10):1376–1384

    Article  Google Scholar 

  12. Ma H, Wu J, Yang L, Xiong Z (2017) Active chatter suppression with displacement-only measurement in turning process. J Sound Vib 401:255–267

    Article  Google Scholar 

  13. Chen M, Knospe CR (2007) Control approaches to the suppression of machining chatter using active magnetic bearings. IEEE Trans Control Syst Technol 15:220–232

    Article  Google Scholar 

  14. van Dijk NJM, van de Wouw N, Doppenberg EJJ, Oosterling HAJ, Nijmeijer H (2011) Robust active chatter control in the high-speed milling process. IEEE Trans Control Syst Technol 20(4):901–917

    Article  Google Scholar 

  15. Zhang X, Wang C, Liu J, Yan R, Cao H, Chen X (2019) Robust active control based milling chatter suppression with perturbation model via piezoelectric stack actuators. Mech Syst Signal Process 120:808–835

    Article  Google Scholar 

  16. Wan S, Li X, Su W, Yuan J, Hong J (2020) Active chatter suppression for milling process with sliding mode control and electromagnetic actuator. Mech Syst Signal Process 136:106528

    Article  Google Scholar 

  17. Mancisidor I, Pena-Sevillano A, Dombovari Z, Barcenac R, Munoa J (2019) Delayed feedback control for chatter suppression in turning machines. Mechatronics 63:102276

    Article  Google Scholar 

  18. Zhang HT, Wu Y, He D, Zhao H (2015) Model predictive control to mitigate chatters in milling processes with input constraints. Int J Mach Tools Manuf 91:54–61

    Article  Google Scholar 

  19. Monnin J, Kuster F, Wegener K (2014) Optimal control for chatter mitigation in milling-Part 1: Modeling and control design. Control Eng Pract 24:156–166

    Article  Google Scholar 

  20. Chen F, Hanifzadegan M, Altintas Y, Lu X (2015) Active damping of boring bar vibration with a magnetic actuator. IEEE/ASME Trans Mechatro 20(6):2783–2794

    Article  Google Scholar 

  21. Dumanli A, Sencer B (2022) Active chatter mitigation by optimal control of regenerative machining process dynamics. IEEE/ASME Trans Mechatro 27(5):3165–3173

    Article  Google Scholar 

  22. Ma H, Guo J, Wu J, Xiong Z, Lee K-M (2019) An active control method for chatter suppression in thin plate turning. IEEE Trans Ind Inf 16(3):1742–1753

    Article  Google Scholar 

  23. Ruttanatri P, Cole M, Pongvuthithum R, Huyanan S (2021) H-infinity controller design for chatter suppression in machining based on integrated cutting and flexible structure model. Automatica 130(1):109643

    Article  MathSciNet  MATH  Google Scholar 

  24. Ruttanatri P, Cole M, Pongvuthithum R (2021) Structural vibration control using delayed state feedback via LMI approach: with application to chatter stability problems. Int J Dyn Control 9:85–96

    Article  Google Scholar 

  25. Mizrachi E, Basovich S, Arogeti S (2020) Robust time-delayed H∞ synthesis for active control of chatter in internal turning. Int J Mach Tools Manuf 158(2):103612

    Article  Google Scholar 

  26. Astarloa A, Wahab F, Mancisidor I, Fernandes MH, Etxaniz I, Munoa J (2023) Reluctance-based modular active damper for chatter suppression in boring bars with different overhangs. IEEE/ASME Trans Mechatro. https://doi.org/10.1109/TMECH.2023.3295170

    Article  Google Scholar 

  27. Du J, Liu X, Long X (2022) Time delay feedback control for milling chatter suppression by reducing the regenerative effect. J Mater Process Technol 309:117740

    Article  Google Scholar 

  28. Emami M, Nasab VH, Akar S, Batako A (2023) Experimental investigation into the effect of magnetorheological fluid damper on vibration and chatter in straight turning process. J Manuf Process 99:25–847

    Article  Google Scholar 

  29. Hajdu D, Insperger T, Bachrathy D, Stépán G (2017) Prediction of robust stability boundaries for milling operations with extended multi-frequency solution and structured singular values. J Manuf Process 30:281–289

    Article  Google Scholar 

  30. Du J, Long X (2022) Chatter suppression for milling of thin-walled workpieces based on active modal control. J Manuf Process 84:1042–1053

    Article  Google Scholar 

  31. Zhang Z, Li H, Liu X, Zhang W, Meng G (2018) Chatter mitigation for the milling of thin-walled workpiece. Int J Mech Sci 138–139:262–271

    Article  Google Scholar 

  32. Wang C, Zhang X, Liu J, Cao H, Chen X (2019) Adaptive vibration reshaping based milling chatter suppression. Int J Mach Tools Manuf 141:30–35

    Article  Google Scholar 

  33. Iwasaki T, Hara S (2005) Generalized KYP lemma: unified frequency domain inequalities with design applications. IEEE Trans on Autom Control 50(1):41–59

    Article  MathSciNet  MATH  Google Scholar 

  34. Sun W, Zhao Y, Li J, Zhang L, Gao H (2012) Active suspension control with frequency band constraints and actuator input delay. IEEE Trans Ind Electron 59(1):530–537

    Article  Google Scholar 

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

    Article  Google Scholar 

  36. Park PG, Lee WI, Lee SY (2015) Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems. J Franklin Inst 352(4):1378–1396

    Article  MathSciNet  MATH  Google Scholar 

  37. Gahinet P, Apkarian P (1994) A linear matrix inequality approach to H∞ control. Int J of Robust Nonlinear Control 4(4):421–448

    Article  MathSciNet  MATH  Google Scholar 

  38. Löfberg J (2004) Yalmip: a toolbox for modeling and optimization in MATLAB. 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508), Taipei, Taiwan, pp 284–289. https://doi.org/10.1109/CACSD.2004.1393890

  39. Fallah M, Moetakef-Imani B (2019) Adaptive inverse control of chatter vibrations in internal turning operations. Mech Syst Signal Process 129:91–111

    Article  Google Scholar 

  40. Insperger T, Stépán G (2004) Updated semi-discretization method for periodic delay-differentilal equations with discrete delay. Int J Numer Methods Eng 61:117–141

    Article  MATH  Google Scholar 

  41. Li X, Wan S, Yuan J, Yin Y, Hong J (2021) Active suppression of milling chatter with LMI-based robust controller and electromagnetic actuator. J Mater Process Technol 297:117238

    Article  Google Scholar 

  42. Åström KJ (2008) Murray RM (2008) Feedback Systems: An Introduction for Scientists and Engineers. Princeton University Press, Princeton

    Google Scholar 

  43. Zhu Z-H, Huang P, To S, Zhu L-M, Zhu Z (2023) Fast-tool-servo-controlled shear-thickening micropolishing. Int J Mach Tools Manuf 184:103968

    Article  Google Scholar 

Download references

Funding

This work was supported by the Natural Science Foundation of China under Grant 52375450, Natural Science Foundation of Shandong Province under Grant ZR2022ZD06 and Shandong Provincial Key Research and Development Program (Major Scientific and Technological Innovation Project) under grant 2020CXGC010204.

Author information

Authors and Affiliations

  1. Key Laboratory of High Efficiency and Clean Mechanical Manufacture, Ministry of Education, School of Mechanical Engineering, Shandong University, Jinan, 250061, China

    Jie Chen, Haifeng Ma, Zhanqiang Liu & Qinghua Song

  2. National Demonstration Center for Experimental Mechanical Engineering Education, Shandong University, Jinan, 250061, China

    Jie Chen, Haifeng Ma, Zhanqiang Liu & Qinghua Song

  3. State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Zhenhua Xiong

Authors
  1. Jie Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Haifeng Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhanqiang Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Qinghua Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Zhenhua Xiong
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Jie Chen was responsible for the design of the algorithm and the analysis and validation of the experimental data. Haifeng Ma was responsible for conducting all the experiments and collecting the data. Haifeng Ma helped with data analysis and visualization. Haifeng Ma, Qinghua Song, Zhanqiang Liu, and Zhenhua Xiong were responsible for the discussion of ideas and methods, review of the manuscript, and financial support.

Corresponding author

Correspondence to Haifeng Ma.

Ethics declarations

Ethical approval

The authors declare that there are no ethical implications of this study.

Consent to participate

All authors agree to submit the manuscript to IJAMT.

Consent to publish

All authors agree to publish this study. There are no potential copyright/plagiarism issues involved in this study.

Competing interests

All authors declare no competing interests. 

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

Chen, J., Ma, H., Liu, Z. et al. Finite-frequency H∞ control for active chatter suppression in turning. Int J Adv Manuf Technol 129, 5075–5088 (2023). https://doi.org/10.1007/s00170-023-12593-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-023-12593-6

Keywords

Search

Navigation