Valérie Pommier-Budinger

Fractional robust control with iso-damping property

This article deals with the problem of the reduction of structural vibrations with isodamping property. The proposed methodology is based on: a contour defined in the Nichols plane and significant of the damping ratio of the closed-loop response and on a robust control method that uses fractional order integration. The methodology is applied to an aircraft wing model made with a beam and a tank whose different levels of fillings are considered as uncertainties.

Active Control of a clamped beam equipped with piezoelectric actuator and sensor using generalized predictive control

A predictive control method to perform the active damping of a flexible structure is here presented. The studied structure is a clamped-free beam equipped with collocated piezoelectric actuator/sensor. Piezoelectric transducers advantages lie in their compactness and reliability, making them commonly used in aeronautic applications, context in which our study fits. Theirs collocated placement allow the use of well-known control strategies with guaranteed stability. First an analytical model of this equipped beam is given, using the Hamiltons principle and the Rayleigh-Ritz method. After a review of the experimental setup (and notably of the piezoelectric transducers), two control laws are described. The chosen one, generalized predictive control (GPC), is compared to a typical control law in the domain of flexible structures, the positive position feedback, one of the control law mentioned above. Major befits of GPC lie in its robustness in front of model uncertainties and others disturbances. The results given come from experiments on the structure which performed by a DSP. GPC appears to suit for the considered studys context (i.e. damping of the first vibration mode). Some improvements may be reached. Among them, a more complex structure with more than a single mode to damp, and more uncertainties may be considered.

STABILITY OF CLOSED LOOP FRACTIONAL ORDER SYSTEMS AND DEFINITION OF DAMPING CONTOURS FOR THE DESIGN OF CONTROLLERS

Fractional complex order integrator has been used since 1991 for the design of robust control-systems. In the CRONE control methodology, it permits the parameterization of open loop transfer function which is optimized in a robustness context. Sets of fractional order integrators that lead to a given damping factor have also been used to build iso-damping contours on the Nichols plane. These iso-damping contours can also be used to optimize the third CRONE generation open loop transfer function. However, these contours have been built using nonband-limited integrators, even if such integrators reveal to lead to unstable closed loop systems. One objective of this paper is to show how the band-limitation modifies the left half-plane dominant poles of the closed loop system and removes the right half-plane ones. Also presented are how to obtain a fractional order open loop transfer function with a high phase slope and a useful frequency response, and how the damping contours can be used to design robust controllers, not only CRONE controllers but also PD and QFT controllers.

Damage localization map using electromechanical impedance spectrums and inverse distance weighting interpolation: Experimental validation on thin composite structures

Piezoelectric sensors are widely used for structure health monitoring technique. In particular, electromechanical impedance techniques give simple and low-cost solutions for detecting damage in composite structures. The purpose of the method proposed in this article is to generate a damage localization map based on both indicators computed from electromechanical impedance spectrums and inverse distance weighting interpolation. The weights for the interpolation have a physical sense and are computed according to an exponential law of the measured attenuation of acoustic waves. One of the main advantages of the method, so-called data-driven method, is that only experimental data are used as inputs for our algorithm. It does not rely on any model. The proposed method has been validated on both one-dimensional and two-dimensional composite structures.

Sizing optimization of piezoelectric smart structures with meta-modeling techniques for dynamic applications

This article shows an efficient method with a high industrial applicability to design piezoelectric smart structures for dynamic applications. This method allows sizing structures with requirements of dynamic displacements. The first step of this method consists in extracting dynamic reduced models from Finite Element simulations which will enable us to obtain a model for any structure, whatever its complexity, as opposed to analytical modeling methods. These models are computed for a set of design parameters. Then a meta-model, which is a simplified descriptive model of other models, is computed as a surface response model that expresses the design objectives and constraints as a function of the design variables. The combination of the results stemming from the meta-model allows working out the optimal values of the design parameters. The main advantage of the proposed method is to enable the quick design exploration of structures. As an example, the method is applied to a flexible structure whose dynamic displacements need to be controlled in bending and twisting. The theoretical results are validated in the end by experiments.

Modeling of a coupled fluid-structure system excited by piezoelectric actuators

Structural vibrations can have severe consequences on airplane design like fatigue, aeroelastic instability and reduced maneuverability. Fuel sloshing inside wing tanks can increase these problems. This work is intended to model a system that consists of a cantilever aluminum plate with a fluid tank near the free tip. Piezoelectric patches are used to excite the system. Three different methodologies were used to obtain a state-space model of the system: analytical (exact) solutions of simplified problems, numerical approximated methods and system identification techniques. Results show good agreement between theory and experiments.

A modified Preisach model for hysteresis in piezoelectric actuators

Piezoelectric actuators (PEAs) exhibit hysteresis nonlinearity in open-loop operation, which may lead to undesirable inaccuracy and limit system performance. Classical Preisach model is widely used for portraying hysteresis but it requires a large number of first-order reversal curves to ensure the model accuracy. All the curves may not be obtained due to limitations of experimental conditions, and the detachment between the major and minor loops is not taken into account. This paper aims to propose a modified Preisach model that demands relatively few measurements and that describes the detachment. The modified model is implemented by adding a derivative term in parallel with the classical Preisach model. The derivative gain is adjusted to an appropriate value so that the measured and predicted hysteresis loops are in good agreement. Experimental results prove that the proposed modified Preisach model can characterize hysteresis more accurately than the classical model.

Ultrasonic Ice Protection Systems: Analytical and Numerical Models for Architecture Tradeoff

Protection systems against ice conventionally use thermal, pneumatic or electro-thermal solutions. However, they are characterized by high energy consumption. This article focuses on low-consumption electromechanical deicing solutions based on piezoelectric transducers. After a review of the state of the art to identify the main features of electromechanical de-icing devices, piezoelectric transducer-based architectures are studied. Analytical models validated by numerical simulations allow trend studies to be performed which highlight the resonance modes and the ultrasonic frequency ranges that lead to low-consumption, compact ultrasonic deicing devices. Finally, de-icing systems widely studied with bonded ceramics and de-icing systems less usual with Langevin pre-stressed piezoelectric transducers are compared and a Langevin piezoelectric transducer-based device leading to an interesting compromise is tested.

Fractional robust control of lightly damped systems

The article proposes a method to design a robust controller ensuring the damping ratio of a closed-loop control. The method uses a contour parameterized by the damping ratio in the Nichols plane and the complex non-integer (or fractional) differentiation to compute a transfer function whose open-loop Nichols locus tangents this contour, thus ensuring dynamic performance. The proposed method is applied to a flexible structure (a clamped-free beam with piezoelectric ceramics). The aims of the control loop are to decrease the vibrations and to ensure the damping ratio of the controlled system.

Baffle silencer with tunable resonators for adaptive control of variable tonal noise

This article presents a baffle silencer with tunable resonators consisting of two superimposed and identically perforated plates associated with a partitioned cavity made of thermoplastic resin. One plate is fixed while the other is movable. Displacement of the mobile plate changes the internal shapes of the resonator necks and shifts the resonance frequency of the system to lower values. The contributions of this paper are firstly, the modeling of a panel with tunable resonators made of necks with a variable geometry and a partitioned cavity in resin and, secondly, the use of the model to elaborate a control strategy to attenuate variable tonal noise. All of the theoretical studies are validated by experimental measurements. Final results show the efficiency of the silencer in attenuating a tonal noise that varies between 2000 and 2800 Hz.