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Implementation of a Real-time Hysteresis Compensation for Electromagnetic Actuators |
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Equipment, Machines & Instruments: Mechatronics |
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By combining electrodynamic drives with planar magnetic bearings, vacuum compatible integrated multi-coordinate drives with six degrees of freedom can reliably be realized, which are required for various modern applications, e.g. for the manufacture of integrated circuits. The magnetic bearings usually consist of several electromagnetic actuators. Besides the nonlinearities due to saturation effects and eddy currents the control performance is strongly influenced by the magnetic hysteresis, as no unambiguous coherence between input signal current and output signal force/position exists. To attain a linear force-current relation, a more precise modeling of nonlinearities is necessary as well as a real-time compensation of the dominating magnetic hysteresis.
To describe the B-H hysteresis of electromagnetic materials, D.C. Jiles and D.L. Atherton developed a method, which is based on the solution of a differential equation. This paper exemplarily shows with a given electromagnet, that the Jiles-Atherton model can also be applied for the reproduction of the F-I hysteresis. Thus an extension of the model is performed. In addition to the five Jiles-Atherton model parameters, two scaling parameters are introduced. With the (extended) inverse Jiles-Atherton model [1] the electromagnet’s force-current hysteresis can be compensated. This approach requires the knowledge of the model parameters, which all depend on the actual air gap length between fixed and moving part of the actuator.
To identify the parameters, at first the force-current hysteresis loops for different air gap lengths are measured. Yet the parameter values cannot be assigned to certain characteristics of the F-I hysteresis loop. Therefore search algorithms are applied, which try to minimize the deviation between measured and modeled hysteresis loop for a constant air gap length. Close compliances were gained with a combination of the evolutionary optimization method according to Schwefel and the Nelder-Mead Simplex algorithm [2]. An identification procedure is presented, which computes the parameter values in a way that finally only one scaling parameter depends on the air gap length and all other parameters remain constant.
The real-time hysteresis compensation quality of the extended inverse Jiles-Atherton model was investigated with an electromagnet, which was originally developed as part of a magnetic bearing system, operated in a hardware-in-the-loop test rig. An open-loop force control, which sets force according to supplied current, shows good succession behavior both for constant and variable air gap lengths. In the next step a closed loop position controller was tested both with and without the extended inverse Jiles-Atherton model. Several step responses with different heights were measured. The hysteresis compensation leads to an overshoot reduction of about 50%. Yet settling time and steady state error remain almost constant.
This paper particularly deals with the Jiles-Atherton model for hysteresis effects and its inversion as well as its extension for the reproduction of force-current hysteresis loops. The parameter identification procedure is presented for a given electromagnetic actuator. A position controller with real-time hysteresis compensation, implemented on a hardware-in-the-loop test rig, is presented. Experimental results gained at the test rig are shown and evaluated.
1. Sadowski, N., N.J. Batistela, J.P. Bastos and M. Lajoie-Mazenc, IEEE Transactions on Magnetics, vol. 38, no. 2, 797 (2002).
2. Ströhla, T. and S. Bode, IEEE Conf. Mechatronics & Robotics, Proc. vol. 2, 442 (2004).
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