Cécile PERNIN defended her PhD on april. 4th, 2025.
Place : Amphitheatre 2 in the W1 building of École Centrale de Lyon in Ecully
Jury :
Rapporteurs :
M. Thierry-Marie GUERRA, Professeur des universités, Université de Valenciennes
M. Driss MEHDI, Professeur des universités émérite, Université de Poitiers
Examinateurs :
Mme Isabelle DUFOUR, Professeur des universités, Université de Bordeaux
Encadrement :
M. Gérard SCORLETTI, Professeur des universités, Ecole Centrale de Lyon, directeur de thèse
M. Anton KORNIIENKO, Professeur des universités, Ecole Centrale de Lyon, co-directeur de thèse
M. Guillaume PAPIN, Docteur, Tronics Microsystems, co-encadrant de thèse
Abstract :
CVG (Coriolis Vibratory Gyroscope) MEMS (Micro Electro Mechanical Systems) gyroscopes are microelectronic sensors designed to measure rotational speed using the Coriolis effect. Compared to other types of gyroscopes, they are smaller and less expensive, but also less efficient. A major industrial challenge is to improve their performance. This requires the use of two feedback control laws. The first must allow a second-order linear time invariant (LTI) system to oscillate at its resonance frequency, which is not known a prior and may change over time. The second is to reject a non-linear, possibly unstable, disturbance generated by the previously oscillating system.
The aim of this thesis is to propose and experimentally validate such control laws and their design method. Due to the application context, the complexity must be limited and the control tools should be able to be integrated into industrial processes.
First, a review of the literature shows the value of using a nonlinear control law to ensure the oscillation of a system at its resonant frequency without knowing the latter. Among these control laws, the AGCNL (Automatic Gain Control Non Linear) law is the most promising for obtaining the desired oscillation while limiting complexity. It has already been used in the literature for gyroscopes, but without proper guarantee. We therefore demonstrate its relevance by presenting an idealized version of the AGCNL, corresponding to the direct expression of the control principle. To deal with implementable versions of this control law, we then adapt orbital stability tools based on the solution of sum-of-squares (SOS) problems. In this way, we provide standardised design tools.
We then propose an innovative control law to reject the disturbance generated by the previous oscillating system. We take into account the fact that its dynamics are controlled by the previous AGCNL structure. Consequently, the disturbance is non-linear, but since the signals at the origin of its dynamics are measurable, we propose a LPV (Linear Parameter-Varying) modelling of the disturbance, which expresses the physical coupling of the AGCNL corrector with the disturbance. This differs from the design methods for control laws in commercial sensors, where the disturbance to be rejected is modelled, for simplification, as a linear exogenous signal. However, this LPV modelling of the disturbance is potentially unstable. We therefore propose a method for determining a corrector that rejects an unstable perturbation. We first validate this method in the LTI case and then generalised it to the LPV case. We then obtain a LPV corrector using standard LPV synthesis methods. By exploiting the special structure of the problem and less standard LPV synthesis methods, for which still efficient algorithms of resolution exist, we also obtain a LPV corrector of reduced complexity. In comparison with a LTI corrector obtained with the simplifying assumptions made in the literature to model the disturbance, we show in simulation the superior efficiency of the standard LPV corrector and of the LPV controller of reduced complexity, for this latter only if there exists a priori a good estimation of the rotational speed.
Finally, the AGCNL control law is validated experimentally. To do this, a tuning method is proposed that takes into account certain practical implementation aspects that are ignored by simplification in the analysis and synthesis models.
Keywords:
Robust control, Feedback Sensor, System Design, Resonant MEMS Sensor, LPV Control