This paper presents a novel parametrization strategy for optimal contouring control of flexible feed drives. The aim of the new strategy is to maximize the structural damping of the drive and counteract the deformations of the structure. Using a simplified flexible multibody model, the analytical relationships for the design of velocity and position control gains were derived. This results in a controller bandwidth increase of up to 20% compared to the previous state-of-the-art in parametrization of standard cascaded controllers. Through analytical and numerical calculations, it was demonstrated that such an increase is feasible without a decrease in structural damping if the position and velocity controller gains are both considered. Furthermore, it is shown that the ratio between the position and velocity loop gains influences the quasistatic deformation between the encoder and tool center point (TCP). A formula for the optimal choice of the ratio was derived to compensate for the error. This leads to a new straightforward step-by-step approach for axis controller setting, which is then applied to a test bench and its simulation model. It can be shown that the new parametrization strategy leads to a significant reduction in path error at the TCP. Importantly, the analytical approach should simplify the task of setting up a standard cascaded controller significantly by avoiding time-consuming iterations.

1. [1] T.-C. Tsao and M. Tomizuka, “Adaptive zero phase error tracking algorithm for digital control,” J. of Dynamic Systems, Measurement and Control, Vol.109, Issue 4, pp. 349-354, 1987.
2. [2] Y. Altintas, K. Erkorkmaz, and W.-H. Zhu, “Sliding mode controller design for high speed feed drives,” CIRP Annals, Vol.49, Issue 1, pp. 265-270, 2000.
3. [3] B. Sencer and A. Dumanli, “Optimal control of flexible drives with load side feedback,” CIRP Annals, Vol.66, Issue 1, pp. 357-360, 2017.
4. [4] H. K. Shirvani, ”Multivariable System Identification, Enhanced Disturbance Rejection, and Precision Motion Control for CNC Machine Tool Feed Drives,” Ph.D. thesis, University of Waterloo, 2021.
5. [5] Y. Altintas, A. Verl, C. Brecher, L. Uriarte, and G. Pritschow, “Machine tool feed drives,” CIRP Annals, Vol.60, Issue 2, pp. 779-796, 2011.
6. [6] O. Zirn, “Machine tool analysis: modelling, simulation and control of machine tool manipulators,” Habilitation thesis, ETH Zürich, 2008.
7. [7] E. Batzies, T. Schbller, V. Welker, and O. Zirn, “Optimal Control of Direct Driven Feed Axes with Flexible Structural Components,” Proc. of the 7th Int. Conf. on Power Electronics and Drive Systems, pp. 1127-1131, 2007.
8. [8] O. Franco, X. Beudaert, and K. Erkorkmaz, “Effect of rack and pinion feed drive control parameters on machine tool dynamics,” J. of Manufacturing and Materials Processing, Vol.4, Issue 2, Article No.33, 2020.
9. [9] D. Spescha, S. Weikert, O. Zirn, and K. Wegener, “Synchronisation of feed axes with differing bandwidths using set point delay,” Int. J. Automation Technol., Vol.11, No.2, pp. 155-164, 2017.
10. [10] N. Lanz, “Framework for Overcoming Structural Dynamic Limitations of Machine Tools Using Additional Tool Center Point Measurements,” Ph.D. thesis, ETH Zürich, 2021.
11. [11] M. Steinlin, S. Weikert, and K. Wegener, “Open loop inertial cross-talk compensation based on measurement data,” Proc. of the 25th Annual Meeting of the American Society for Precision Engineering (ASPE’10), 2010.
12. [12] S. Weikert, “Beitrag zur Analyse des dynamischen Verhaltens von Werkzeugmaschinen,” Ph.D. thesis, ETH Zürich, 2000.
13. [13] D. Spescha, S. Weikert, and K. Wegener, “Design to specifications – A strategy for specification-based machine design,” Procedia CIRP, Vol.77, pp. 561-565, 2018.
14. [14] S. Thoma, T. Haas, M. H. Nguyen, S. Weikert, and K. Wegener, “In- and Cross-Talk Evaluation of Different Machine Concepts,” Proc. of the 11th Int. Conf. and Exhibition on Laser Metrology, Coordinate Measuring Machine and Machine Tool Performance (LAMDAMAP), pp. 160-169, 2015.
15. [15] Heidenhain Co., “Messgeräte zur Abnahme und Kontrolle von Werkzeugmaschinen,” 2017.
16. [16] S. Weikert, “R-test, a new device for accuracy measurements on five axis machine tools,” CIRP Annals, Vol.53, Issue 1, pp. 429-432, 2004.
17. [17] N. Lanz, D. Spescha, S. Weikert, and K. Wegener, “Efficient Static and Dynamic Modelling of Machine Structures with Large Linear Motions,” Int. J. Automation Technol., Vol.12, No.5, pp. 622-630, 2018.
18. [18] inspire AG, “MORe Simulations.” https://www.more-simulations.ch [Accessed June 10, 2022]