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On some control and observation issues related to high-precision positioning tables

Abstract : In this work, our concern is the study of high-precision positioning systems. They are one of the core elements entering the manufacturing processes of the semiconductor industry. We are more specifically interested in two major issues: conceiving an initialization algorithm for brushless synchronous motors and designing a control scheme to reject disturbances peculiar to these systems. The previously mentioned initialization procedure consists in estimating the initial phase of the magnetic field for brushless synchronous motors. Only displacement measurements are available (no current) while friction, load and motor parameters are supposed to be unknown. Because of friction, the system is modeled by a differential equation with a discontinuous right-hand side. Specific open-loop inputs are designed to get the initial phase as a function of the magnitude of the displacements along the corresponding trajectories. The estimation relies on a complete classification of the possible dynamical behaviors of the considered discontinuous right-hand side system with periodic input, whatever values the unknown parameters may take. For the sake of the online implementation, we propose an approximated formula of the initial phase. Some experimental results are given, together with a comparison of our method to an other technique that may be implemented in the same context. We then move to the problem of rejecting a class of disturbances affecting the considered high-precision positioning tables. These systems turn out to feature spatially periodic perturbations, preventing them from achieving the required accuracy in terms of trajectory tracking. Despite the nonlinear nature of this problem, we derive sufficient conditions for a linear time-varying controller to entirely get rid of these disturbances and allow global asymptotic convergence of the tracking error to zero. Such stability conditions result from a regular perturbation analysis, carried out with the use of the Bell polynomials of the second kind. We propose a linear time-varying observer-based controller that meets the previously mentioned stability conditions and only relies on position measurements. It is quite noteworthy that the observer equations are obtained by evaluating the spatially periodic perturbations along the desired trajectories, and not along the actual positions. We make use of the LMI formalism to cast the observer gains tuning issue into an optimization problem, subject to LMI constraints, carried out offline. Little computation is required online as the observer gains are constant. We then provide several experimental results to exhibit the performances of the proposed method. We namely address the experimental cancellation of cogging forces, as well as position measurements errors, known as interpolation errors.
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Submitted on : Wednesday, March 12, 2008 - 8:00:00 AM
Last modification on : Thursday, September 24, 2020 - 5:04:18 PM
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  • HAL Id : pastel-00003384, version 1


Jérémy Malaizé. On some control and observation issues related to high-precision positioning tables. Mathematics [math]. École Nationale Supérieure des Mines de Paris, 2007. English. ⟨NNT : 2007ENMP1499⟩. ⟨pastel-00003384⟩



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