Modeling and Control of a 3 DOF Planar Motor for Precision Positioning

Kai Treichel, Remon Al Azrak, Johann Reger^* and Kai Wulff

This contribution is dedicated to the modeling and control of an electrodynamic planar motion stage for precision positioning. Subject of our investigation is a state-of-the-art non contact, high-precision Lorentz force planar motor of linear DC brushless type. We derive physical models of the relevant components and investigate the sources as well as the influence of various parasitic effects and disturbances. For the latter, phenomenological models are developed capturing the behavior observed throughout our experiments in a realistic manner. In order to overcome the position dependency of the Lorentz forces, as it is usual for motors of this type, a minimum power commutation law is proposed. Furthermore, model characteristics and parameters are identified using experimental data taken from the dedicated test rig. For the robust trajectory tracking control and disturbance rejection a simple composite control law is addressed. This includes a simple computed torque controller together with an extended Luenberger type of state and disturbance observer also known as extended state or generalized proportional integral observer (GESO/GPIO). We provide stability proofs and estimation error bounds of the GESO/GPIO related to the choice of the eigenvalues of the observer estimation error dynamics. Finally, we assess the performance of the proposed controller on the basis of the afore developed motion stage model reflecting the major challenges for control.

Mathematics Subject Classification: 93C95 93C85

Keywords: modeling, precision positioning, tracking control, disturbance rejection

Minisymposion: Modelling and Control of Mechatronic Systems