Françoise Lamnabhi-Lagarrigue

Adaptive PI Stabilization of Switched Power Converters

Linear proportional-integral (PI) controllers are widely used in power converter applications. In a recent paper, a methodology to design such controllers ensuring asymptotic stability was proposed. The technique relied on the basic fact that if an affine system can be rendered passive with a constant control, then it is stabilizable with a PI. A structural condition was imposed then on the power converter to satisfy the former property with a passive output generated as a linear combination of the states. This condition is technical and has no clear physical interpretation. In this brief this result is extended in three directions: first, the aforementioned condition is removed; second, a larger class of converters (with switching external sources) is considered; third, the load resistance is assumed unknown and an adaptive PI controller (with three different estimators) is proposed. Instrumental to establish the result is the proof that the nonlinear incremental model of power converters defines a passive map-a property first observed by Sanders and Verghese in the early 1990s. The methodology is applied to the problem of power factor compensation of a 3-phase voltage source rectifier, already considered in our previous paper, which is revisited from the incremental passivity perspective yielding simpler proofs. Also, a stable adaptive PI is designed for the output voltage regulation of a quadratic boost converter. Simulations complete the brief.

Sliding observer-controller design for uncertain triangular nonlinear systems

In order to achieve robust output tracking for a class of uncertain triangular systems, a combination of a robust sliding observer and a backstepping procedure is introduced.

Necessary conditions for asymptotic tracking in nonlinear systems

In the literature, it has been shown that if a single-input single-output analytic nonlinear plant 1) has a well-defined relative degree and 2) is minimum-phase, it is possible to achieve asymptotic tracking for an open set of output trajectories containing the origin in C/sup N/ [0, /spl infin/), the space of N-times continuously differentiable functions taking values in R. When either of these sufficient conditions is not met, various authors have investigated approximate analytic solutions, discontinuous solutions and solutions for restricted sets of trajectories. In this paper, it is shown that conditions 1) and 2) are necessary for the existence of an analytic compensator which yields asymptotic tracking for an open set of output trajectories. Analogous results are established for multi-input multi-output systems. >

Global exponential sampled-data observers for nonlinear systems with delayed measurements

Abstract This paper presents new results concerning the observer design for certain classes of nonlinear systems with both sampled and delayed measurements. By using a small gain approach we provide sufficient conditions, which involve both the delay and the sampling period, ensuring exponential convergence of the observer system error. The proposed observer is robust with respect to measurement errors and perturbations of the sampling schedule. Moreover, new results on the robust global exponential state predictor design problem are provided, for wide classes of nonlinear systems.

Cascade High Gain Predictors for a Class of Nonlinear Systems

This work presents a set of cascade high gain predictors to reconstruct the vector state of triangular nonlinear systems with delayed output. By using a Lyapunov-Krasvoskii approach, simple sufficient conditions ensuring the exponential convergence of the observation error towards zero are given. All predictors used in the cascade have the same structure. This feature will greatly improve the easiness of their implementation. This result is illustrated by some simulations.

An Online Simplified Rotor Resistance Estimator for Induction Motors

This brief presents an adaptive variable structure identifier that provides finite time convergent estimate of the induction motor rotor resistance under feasible persistent of excitation condition. The proposed rotor resistance scheme is based on the standard dynamic model of induction motor expressed in a fixed reference frame attached to the stator. The available variables are the rotor speed, the stator currents and voltages. Experiments show that the proposed method achieved very good estimation of the rotor resistance which is subjected to online large variation during operation of the induction motor. Also, the proposed online simplified rotor resistance estimator is robust with respect to the variation of the stator resistance, measurement noise, modeling errors, discretization effects and parameter uncertainties. Important advantages of the proposed algorithm include that it is an online method (the value of Rr can be continuously updated) and it is very simple to implement in real-time (this feature distinguishes the proposed identifier from the known ones).

Stability analysis of bilinear systems under aperiodic sampled-data control

This note considers the problem of local stability of bilinear systems with aperiodic sampled-data linear state feedback control. The sampling intervals are time-varying and upper bounded. It is shown that the feasibility of some linear matrix inequalities (LMIs), implies the local asymptotic stability of the sampled-data system in an ellipsoidal region containing the equilibrium. The method is based on the analysis of contractive invariant sets, and it is inspired by the dissipativity theory. The results are illustrated by means of numerical examples.

High gain observer design for nonlinear systems with time varying delayed measurements

This work presents a simple observer for triangular nonlinear systems with time varying delayed output measurement. A sufficient condition ensuring the asymptotic convergence of the observation error towards zero is given, as well as an explicit relation between the bound of the delay and the parameter of the observer. This result is illustrated by some simulations.

Application of a new functional expansion to the cubic anharmonic oscillator

A new representation of causal functionals is introduced which makes use of noncommutative generating power series and iterated integrals. This technique allows the solutions of nonlinear differential equations with forcing terms to be obtained in a simple and natural way. It generalizes some properties of Fourier and Laplace transforms to nonlinear systems and leads to effective computations of various perturbative expansions. Illustrations by means of the cubic anharmonic oscillator are given in both the deterministic and the stochastic cases.

Global stabilisation of nonlinear delay systems with a compact absorbing set

Predictor-based stabilisation results are provided for nonlinear systems with input delays and a compact absorbing set. The control scheme consists of an inter-sample predictor, a global observer, an approximate predictor, and a nominal controller for the delay-free case. The control scheme is applicable even to the case where the measurement is sampled and possibly delayed. The input and measurement delays can be arbitrarily large but both of them must be constant and accurately known. The closed-loop system is shown to have the properties of global asymptotic stability and exponential convergence in the disturbance-free case, robustness with respect to perturbations of the sampling schedule, and robustness with respect to measurement errors. In contrast to existing predictor feedback laws, the proposed control scheme utilises an approximate predictor of a dynamic type that is expressed by a system described by integral delay equations. Additional results are provided for systems that can be transformed to systems with a compact absorbing set by means of a preliminary predictor feedback.