Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32726
Modeling and System Identification of a Variable Excited Linear Direct Drive

Authors: Heiko Weiß, Andreas Meister, Christoph Ament, Nils Dreifke


Linear actuators are deployed in a wide range of applications. This paper presents the modeling and system identification of a variable excited linear direct drive (LDD). The LDD is designed based on linear hybrid stepper technology exhibiting the characteristic tooth structure of mover and stator. A three-phase topology provides the thrust force caused by alternating strengthening and weakening of the flux of the legs. To achieve best possible synchronous operation, the phases are commutated sinusoidal. Despite the fact that these LDDs provide high dynamics and drive forces, noise emission limits their operation in calm workspaces. To overcome this drawback an additional excitation of the magnetic circuit is introduced to LDD using additional enabling coils instead of permanent magnets. The new degree of freedom can be used to reduce force variations and related noise by varying the excitation flux that is usually generated by permanent magnets. Hence, an identified simulation model is necessary to analyze the effects of this modification. Especially the force variations must be modeled well in order to reduce them sufficiently. The model can be divided into three parts: the current dynamics, the mechanics and the force functions. These subsystems are described with differential equations or nonlinear analytic functions, respectively. Ordinary nonlinear differential equations are derived and transformed into state space representation. Experiments have been carried out on a test rig to identify the system parameters of the complete model. Static and dynamic simulation based optimizations are utilized for identification. The results are verified in time and frequency domain. Finally, the identified model provides a basis for later design of control strategies to reduce existing force variations.

Keywords: Force variations, linear direct drive, modeling and system identification, variable excitation flux.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 972


[1] H.-D. Stölting, E. Kallenbach, W. Amrhein, Handbuch Elektrische Kleinmaschinen, Hanser, 2011.
[2] A. E. Quaid, Y. Xu, R.L. Hollis, “Force characterization and commutation of planar linear motors, IEEE ICRA Proceedings, Albuquerque, 1997.
[3] P. Joerges, W. Schinköthe, “Geometrical optimized cogging forces at linear direct drives”, 8.ETG/GMM-Fachtagung Innovative Klein- und Mikroantriebstechnik, Würzburg, 2010.
[4] S. Lorand, I.A. Viorel, I. Chisu, Z. Kovacs, “A Novel Double Salient Permanent Magnet Linear Motor”, Proceedings of the International Conference on Power Electronics, Drives and Motion (PCIM), Nürnberg, 1999, vol. Intelligent Motion, pp. 285-290.
[5] J. Malaizé, J. Lévine, “An Observer-Based Design for Cogging Forces Cancellation in Permanent Magnet Linear Motors”, Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, Shanghai, 2009.
[6] H.-S. Ahn, Y.Q. Chen, H. Dou, “State-Periodic Adaptive Compensation of Cogging and Coulomb Friction in Permanent-Magnet Linear Motors”, IEEE Transactions on Magnetics, Vol. 41, No. 1, 2005.
[7] C. Röhrig, A. Jochheim, “Identification and Compensation of Force Ripple in Linear Permanent Magnet Motors”, Proceedings of the American Control Conference, Arlington, 2001.
[8] Y.W. Zhu, K.S. Jung, J.H. Cho, “The Reduction of Force Ripples of PMLSM Using Field Oriented Control Method”, CES/IEEE 5th International Power Electronics and Motion Control Conference, Shanghai, 2006.
[9] R. Wislati, H. Haase, “Using COMSOL Multiphysics for the Modelling of a Hybrid Linear Stepper Motor”, Proceedings of the COMSOL Users Conference, Grenoble, 2007.
[10] T. Treichl, S. Hofmann, D. Schröder, „Identification of Nonlinear Dynamic Systems with Multiple Inputs and Single Output using discrete-time Volterra Type Equations”, Proceedings of 15th International Symposium on Mathematical Theory of Networks and Systems, Notre Dame, Indiana, 2002.
[11] S. Beineke, H. Wertz, F. Schütte, H. Grotstollen, N. Fröhleke, “Identification of Nonlinear Two-Mass Systems for Self-Commissioning Speed Control of Electrical Drives”, Proceedings of the 24th Annual Conference of the IEEE, Industrial Electronics Society, Aachen, 1998.
[12] C. Audet, J. E. Dennis Jr., "Analysis of Generalized Pattern Searches.", SIAM Journal on Optimization, Volume 13, Number 3, 2003, pp. 889–903.
[13] F. Henrotte, K. Hameyer, “A Dynamical Vector Hysteresis Model Based on an Energy Approach”, IEEE Transactions on Magnetics, Vol. 42, pp. 899-902, 2006.
[14] C. Makkar, W.E. Dixon, W.G. Sawyer, G. Hu, “A New Continuously Differentiable Friction Model for Control Systems Design”, Proceedings of the 2005 IEEE/ASMEInternational Conference on Advanced Intelligent Mechatronics, Monterey, California, 2005.