Malaizé, Jérémy (2007) On Some Control and Observation Issues Related to High-Precision Positioning Tables. PhD thesis Mathématiques et Automatique, Centre automatique et systèmes, ENSMP p.120.
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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.
| Item Type: | PhD Thesis (PhD) |
|---|---|
| Thesis Supervisor: | Lévine, Jean |
| Date: | 20 December 2007 |
| Board of examiners: | Bastin, Georges and El Ghaoui, Laurent and Steinbuch, Maarten and Desailly, Roger and Durieu, Cécile and Lévine, Jean |
| Ecole Doctorale: | ED 431 INFORMATION, COMMUNICATION, MODELISATION ET SIMULATION |
| Discipline: | Mathématiques et Automatique |
| Collection (Fonds): | ENSMP |
| Institution: | ENSMP |
| Department: | Centre automatique et systèmes |
| Subjects: | 1. Mathematics and Applications |
| Uncontrolled Keywords: | Synchronous motor, Periodic orbit, Periodic perturbation, Asymptotic convergence, Non linear observer, Constrained optimization, Control theory, Moteur électrique, Observateur non linéaire identification, Classification d'orbites périodiques, Perturbations périodiques en l'état, Suivi de trajectoire haute précision |
| ID Code: | 3384 |
| Deposited By: | Jérémy Malaizé |
| Deposited On: | 12 March 2008 |
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