Synchronisation of Feed Axes with Differing Bandwidths Using Set Point Delay
Daniel Spescha*,†, Sascha Weikert*, Oliver Zirn**, and Konrad Wegener**
Technoparkstrasse 1, CH-8005 Zürich, Switzerland
**Institute of Machine Tools and Manufacturing, Swiss Federal Institute of Technology Zürich, Zürich, Switzerland
This paper presents an effective method for the synchronisation of multiple feed axes with differing controller bandwidths by delaying the set point trajectories of those axes with higher bandwidths. First, a simplified model of a cascade-controlled feed axis is defined, which allows the problem to be treated analytically. The problem of synchronisation of the feed axes is then analysed mathematically, leading to the hypothesis of synchronisation through a delay of the set points of the more dynamic axes. Subsequently, the dynamic error behaviour and boundaries of a feed axis are calculated. The optimal damping factor for a feed axis is shown to be 1/√2 and the dynamic error can be formulated in terms of the bandwidth and acceleration or jerk limit. The proposed method is proven through a simulation and verified based on experimental results. In addition, the stated error bounds are verified, and the limits of the applicability are determined.
-  A.-N. Poo, J. G. Bollinger, and G. W. Younkin, “Dynamic errors in type 1 contouring systems,” IEEE Trans. on Industry Applications, Vol.4, pp. 477-484, 1972.
-  M. Weck and C. Brecher, “Werkzeugmaschinen 3 – Mechatronische Systeme, Vorschubantriebe, Prozessdiagnose,” Springer, 2006.
-  H. Gross, G. Wiegartner, and J. Hamann, “Electrical Feed Drives in Automation: Basics, Computation, Dimensioning,” John Wiley & Sons, Inc., New York, 2001.
-  R. Sato and M. Tsutsumi, “Motion Control Techniques for Synchronous Motions of Translational and Rotary Axes,” CIRP 2012, Vol.1, pp. 265-270, 2012.
-  S. Weikert and O. Zirn, “Modellbildung und Simulation hochdynamischer Fertigungssysteme: Eine praxisnahe Einführung,” Springer, 2006.
-  M. Tomizuka, “Zero phase error tracking algorithm for digital control,” J. of Dynamic Systems, Measurement, and Control, Vol.109, No.1, pp. 65-68, 1987.
-  G. T.-C. Chiu and M. Tomizuka, “Coordinated Position Control of Multi-Axis Mechanical Systems,” J. of Dynamic Systems, Measurement, and Control, Vol.120, No.3, pp. 389-393, Sep. 1998.
-  Y. Xiao, K. Zhu, and H. C. Liaw, “Generalized synchronization control of multi-axis motion systems,” Control Engineering Practice, Vol.13, No.7, pp. 809-819, 2005.
-  P. Moore and C. Chen, “Fuzzy logic coupling and synchronised control of multiple independent servo-drives,” Control Engineering Practice, Vol.3, No.12, pp. 1697-1708, 1995.
-  R. Sato and M. Tsutsumi, “Modeling and controller tuning techniques for feed drive systems,” ASME 2005, pp. 669-679, American Society of Mechanical Engineers, 2005.
-  H. Lutz and W. Wendt, “Taschenbuch der Regelungstechnik: mit MATLAB und Simulink,” Verlag Harri Deutsch, Frankfurt am Main, 7th edition, 2007.
-  G. Stute, F. Breuer, and M. Weck, “Regelung an Werkzeugmaschinen,” Hanser, 1981.
-  O. Zirn, “Machine Tool Analysis – Modelling, Simulation and Control of Machine Tool Manipulators,” 2008.
-  O. Zirn, L. Katthän, and V. Welker, “Commissioning of Servo Drives Considering Structural Elasticities,” J. of Mathematics and System Science, Vol.4, No.8, pp. 546-556, 2014.
-  M. Weck and C. Brecher, “Werkzeugmaschinen 5 – Messtechnische Untersuchung und Beurteilung, dynamische Stabilität,” Springer, 2006.