Two loop control-based generalized cycle-to-cycle optimization for machining workpieces with non-circular curve in CNC grinding

  • Jing Wang
  • Yantao Tian
  • Zhen SuiEmail author
  • Zhongbo Sun


In many scenarios of machining system, a workpiece with non-circular curve is manufactured by repetitively performing a given command. The size of the workpiece, however, is quite unlikely to be precisely measured until one process (or a cycle) has been completely finished. Although in-process measurement and control are possible, it is often economically prohibitive or practically complex to be conducted. To overcome this drawback, a two loop control-based generalized cycle-to-cycle (GCTC) feedback control scheme, which is an offline optimization control method, is proposed for machining workpiece with non-circular curve in this study. Inner loop is a local controller which is used to guarantee the tracking accuracy. GCTC feedback control is adopted to serve as an optimization module for the closed-loop system under the local controller to update the reference in the outer loop. The GCTC control model is developed based on the reference and measure error of the prior cycle of the machining system. The equivalent dynamic model of the machining system can be obtained by the extended state observer and repetitive control in inner loop. The sufficient stability conditions and convergence of the GCTC control are derived in this study. The proposed GCTC controllers are developed comprehensibly. The simplicity of the method lies in that only a low-pass filter and a proportional gain are required to be chosen. The superiority is demonstrated by the simulations and experiments on CNC cam grinding based on GCTC control. The application results justify the effectiveness of the GCTC scheme.


A workpiece with non-circular curve Generalized cycle-to-cycle (GCTC) control Equivalent dynamic model CNC cam grinding 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


Funding information

This work is supported by the Ph.D. Programs Foundation of Henan Polytechnic University—The Intelligent Profile Error compensation in High Speed & High Precision CNC Cam Grinding (B2018-660807/027).


  1. 1.
    Huo F, Poo A-N (2012) Precision contouring control of machine tools. Int J Adv Manuf Technol 64(1–4):319–333Google Scholar
  2. 2.
    Xi X-C, Poo A-N, Hong G-S, Huo F (2010) Experimental implementation of Taylor series expansion error compensation on a biaxial CNC machine. Int J Adv Manuf Technol 53(1–4):285–299Google Scholar
  3. 3.
    Ernesto CA, Farouki RT (2009) Solution of inverse dynamics problems for contour error minimization in CNC machines. Int J Adv Manuf Technol 49(5–8):589–604Google Scholar
  4. 4.
    Deng C, Xie SQ, Wu J (2014) Position error compensation of semi-closed loop servo system using support vector regression and fuzzy PID control. Int J Adv Manuf Technol 71(5–8):887–898CrossRefGoogle Scholar
  5. 5.
    Pi S, Liu Q, Liu Q (2018) A novel dynamic contour error estimation and control in high-speed CNC. Int J Adv Manuf Technol 2:1–14. CrossRefGoogle Scholar
  6. 6.
    Koren Y (1980) Cross-coupled biaxial computer control for manufacturing systems. J Dyn Syst Meas Control 102(4):265.
  7. 7.
    Lee JH, Dixon WE, Ziegert JC (2005) Adaptive nonlinear contour coupling control for a machine tool system. Int J Adv Manuf Technol 61(9–12):1057–1065Google Scholar
  8. 8.
    Jiangzhao Yang ZL (2011) A novel contour error estimation for position loop-based cross-coupled control. IEEE/ASME Trans Mechatron 16(4):643–655. CrossRefGoogle Scholar
  9. 9.
    Su KH, Cheng MY (2008) Contouring accuracy improvement using cross-coupled control and position error compensator. Int J Mach Tool Manu 48(12):1444–1453CrossRefGoogle Scholar
  10. 10.
    Uchiyama M (2009) Formation of high-speed motion pattern of a mechanical arm by trial. Trans Soc Instrum Control Eng 14(6):706–712CrossRefGoogle Scholar
  11. 11.
    Zhou Y, Fei YU, Jianming XU (2011) The cascade type iterative learning cross-coupled contour error control method. Bull Sci Technol 27(5):737–739Google Scholar
  12. 12.
    Lee KS, Lee JH (2003) Iterative learning control-based batch process control technique for integrated control of end product properties and transient profiles of process variables. J Process Control 13(7):607–621CrossRefGoogle Scholar
  13. 13.
    Lin JW, Shen PF, Wen HP (2015) Repetitive control mechanism of disturbance cancellation using a hybrid regression and genetic algorithm. Mech Syst Signal Process 62–63(3):356–365CrossRefGoogle Scholar
  14. 14.
    Lee JH, Lee KS, Natarajan S (2001) A model-based predictive control approach to repetitive control of continuous processes with periodic operations. J Process Control 11(2):195–207CrossRefGoogle Scholar
  15. 15.
    Siu TS (2001) Cycle to cycle feedback control of manufacturing processes. Mass Inst Technol 114(2):158–174Google Scholar
  16. 16.
    Wang J, Sui Z, Sun ZB (2015) The cam contour control in grinding based on repetitive control and error compensation. IFAC Papersonline 48(28):841–846CrossRefGoogle Scholar
  17. 17.
    Li S, Yang J, Chen WH (2012) Generalized extended state observer based control for systems with mismatched uncertainties. IEEE Trans Ind Electron 59(12):4792–4802CrossRefGoogle Scholar
  18. 18.
    She JH, Fang M, Ohyama Y (2008) Improving disturbance-rejection performance based on an equivalent-input-disturbance approach. IEEE Trans Ind Electron 55(1):380–389CrossRefGoogle Scholar
  19. 19.
    Khalil HK (2001) Feedback systems: the small-gain theorem, in nonlinear systems, 3rd edn. Prentice-Hall, Upper Saddle River, pp 217–221Google Scholar
  20. 20.
    Costa-Castello R, Nebot J, Grino R (2005) Demonstration of the internal model principle by digital repetitive control of an educational laboratory plant. IEEE Trans Educ 48(1):73–80CrossRefGoogle Scholar
  21. 21.
    Na J, Ren X, Guo Y (2014) Repetitive control of servo systems with time delays. Robot Auton Syst 62(3):319–329CrossRefGoogle Scholar
  22. 22.
    Wang J, Sui Z, Tian YT (2015) A speed optimization algorithm based on the contour error model of lag synchronization for CNC cam grinding. Int J Adv Manuf Technol 80(5–8):1421–1432CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  • Jing Wang
    • 1
  • Yantao Tian
    • 2
    • 3
  • Zhen Sui
    • 2
    Email author
  • Zhongbo Sun
    • 4
  1. 1.School of Electrical Engineering and AutomationHenan Polytechnic UniversityJiaozuoChina
  2. 2.College of Communication EngineeringJilin UniversityChangchunChina
  3. 3.Key Laboratory of Bionics Engineering, Ministry of EducationJilin UniversityChangchunChina
  4. 4.School of Electrical and Electronic EngineeringChangchun University of TechnologyChangchunChina

Personalised recommendations