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

Panel of resonators with variable resonance frequency for noise control

The article focuses on acoustic resonators made of perforated sheets bonded onto honeycomb cavities. This kind of resonators can be used in adverse conditions such as high temperature, dirt and mechanical constraints. For all these reasons, they are, for example, widely used in aeronautic applications. The acoustic properties are directly linked to the size, shape and porosity of holes and to the thickness of air gaps. Unfortunately, the acoustic absorption of these resonators is selective in frequency and conventional acoustic resonators are only well adapted to tonal noises. In case of variable tonal noise, the efficiency is limited if the resonators are not tunable. One common solution is to control the depth of cavities based on the noise to be attenuated. This article proposes another technology of tunable resonators with only a very small mass and size increase. It consists of two superposed and identically perforated plates associated with cavities. One plate is fixed and bonded to the cavities and the other plate is mobile. The present concept enables to change the internal shapes of the holes of the perforated layers. The article describes this system and gives a theoretical model of the normal incidence acoustic impedance that allows to predict the acoustic behavior, in particular the resonance frequency. The model shows that the resonance frequency varies with hole profiles and that the absorption peak moves towards the lower frequencies. The proposed model is validated by measurements on various configurations of resonators tested in an impedance tube. The perspectives of this work are to adapt the hole profiles using an actuator in order to perform active control of impedance

Design of a fractional control using performance contours. Application to an electromechanical system

The article proposes a frequency-based method to design a controller ensuring dynamic behavior of a closed-loop control: the first overshoot of the step response in the tracking mode or in the regulation mode, the damping ratio and the natural frequency of its dominant oscillatory mode. This method uses two contours called “performance contours” and constructed on the Nichols diagram. The first contour is the common Nichols magnitude contour which can be considered as an iso-overshoot contour. The second contour, whose construction and analytic expression are given in this article, is a new contour defined on the Nichols diagram and parameterized by the damping ratio. The proposed method uses complex non-integer (or fractional) differentiation to compute a transfer function whose open-loop Nichols locus tangents both performance contours, thus ensuring stability margins (or stability degree). The method is applied to a DC motor whose speed is controlled

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 non band-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. It is also presented how to obtain a fractional order open loop transfer function with a high phase slope and a useful frequency response. It is presented how the damping contours can be used to design robust controllers, not only CRONE controllers but also PD and QFT controllers

Comparison of extensional and flexural modes for the design of piezoelectric ice protection systems

Many researches focus on piezoelectric ice protection systems with the objectives to develop light and low consumption electromechanical systems for de-icing. These systems use vibrations, generated by the excitation of flexural, extensional or coupled resonance modes, to produce tensile stresses in the ice or shear stresses at the interface ice/support in order to remove ice. The objectives of this work are to analyse flexural and extensional resonance modes according to important design drivers for this type of systems: resonance frequency range, generation of tensile and shear stresses, electromechanical coupling factor, damping and fracture propagation. A final comparison gives pro and cons of each mode type for each design drivers for helping the designer of piezoelectric ice protection systems

Ultrasonic ice protection systems

Protection systems against ice on leading edge conventionally use thermal and pneumatic solutions. In case of thermal solutions with piccolo tubes (the most usual technology), the hot air is extracted from engine, which decrease its efficiency. The trend is to move to all electric deicing systems. Electro-thermal solutions have been implemented but at the cost of a high energy consumption. This work focuses on low-consumption electromechanical deicing solutions based on piezoelectric transducers. After a review of deicing systems, the main features of electromechanical de-icing devices are identified and piezoelectric ceramic-based deicing systems are studied. Numerical simulations allow computing the configurations that lead to low-consumption, compact ultrasonic deicing devices. First tests of piezoelectric de-icing systems are performed on simple cases such as plates. These tests are promising and allow analyzing the key design drivers (the frequency range to use, the impact of the ice thickness on the system performance) for the design of such systems. First results on the voltage and the consumed current of such devices are also given

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

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 theirs 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 Hamilton's principle and the Rayleigh-Ritz method. After a review of the experimental setup (and notablv of the piezoelectric transducers), two control laws are described. The chosen one - Generalized Predictive Control (GPC) - will be compared to a typical control law in the domain of flexible structures, the Positive Position Feedback, one of the control lam mentioned above. Majors benefits of GPC lie in its robustness in front of model uncertainties and others disturbances. The results given come from experiments on the structure, performed thanks to a DSP. GPC appears to suit for the considered study's 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

Crone control of a nonlinear hydraulic actuator

The CRONE control (fractional robust control) of a hydraulic actuator whose dynamic model is nonlinear is presented. An input-output linearization under diffeomorphism and feedback is first achieved for the nominal plant. The relevance of this linearization when the parameters of the plant vary is then analyzed using the Volterra input-output representation in the frequency domain. CRONE control based on complex fractional differentiation is finally applied to control the velocity of the input-output linearized model when parametric variations occur

Damage location method for thin composites structures - application to an aircraft door

Piezoelectric sensors are widely used for Structure Health Monitoring (SHM) technique due to their high-frequency capability. In particular, electromechanical impedance (EMI) techniques give simple and low cost solutions for detecting damage in composite structures. For example, damage indicators computed from EMI deviations between the pristine structure and the damaged structure can be compared to a threshold in order to point damage. When it is question of damage localization, the simple analysis of the electromechanical impedance fails to furnish enough information. We propose a method based both on EMI damage indicators and on the acoustic attenuation level to locate damage. One of the main advantages of our method, so called data driven method, is that only experimental data are used as inputs for our algorithms. It does not rely on any model

Study of two robust controls for an hydraulic actuator

Two robust control design methodologies are analyzed and compared in this article: the H-infinity control system design and the CRONE control system design. The aim of this article is to give practical considerations that will help a designer to choose between these two methodologies. The example of an electrohydraulic actuator is given in order to evaluate the implementation of each methodology and to compare the final performance