Pauline Bernard

Observers for a non-Lipschitz triangular form

Abstract We address the problem of designing an observer for triangular non locally Lipschitz dynamical systems. We show the convergence with an arbitrary small error of the classical high gain observer in presence of nonlinearities verifying some Holder-like condition. Also, for the case when this Holder condition is not verified, we propose a novel cascaded high gain observer. Under slightly more restrictive assumptions, we prove the convergence of a homogeneous observer and of its cascaded version with the help of an explicit Lyapunov function.

On the triangular canonical form for uniformly observable controlled systems

Abstract We study controlled systems which are uniformly observable and differentially observable with an order larger than the system state dimension. We establish that they may be transformed into a (partial) triangular canonical form but with possibly non locally Lipschitz functions. We characterize the points where this Lipschitzness may be lost and investigate the link with uniform infinitesimal observability.

Robustness of rotor position observer for permanent magnet synchronous motors with unknown magnet flux

Abstract We introduce a new sensorless rotor position observer for permanent magnet synchronous motors which does not require the knowledge of the magnet’s flux : only electrical measurements and (approximate) knowledge of the resistance and inductance are needed. This observer extends the gradient observer from Lee et al. [2010] with the estimation of the magnet’s flux and makes it globally convergent provided the rotation speed remains away from zero. We study its sensitivity to uncertainties on the resistance and inductance and to the presence of saliency. Its performances in open-loop are illustrated via an implementation using real data and compared to other existing magnet flux independent observers in terms of computational cost and robustness.