Wael Zouaoui
email: wzouaoui@laas.fr

Carolina Albea Sanchez

Yann Labit
email: ylabit@laas.fr

Dynamic adaptive management of buffer for QoS guarantees and energy reduction

Keywords: Green Network, Adaptive system, Quality of Service, Energy, ADREAM, Control theory

Technological advances in communication networks have made to increase communication rate as well as energy consumption. Some equipments and protocol solutions have been developed to treat these problems e.g. Smart Sleeping and Rate Adaptation. We present an original and alternative adaptive solution from Automatic community to control the output flow of a node, in such a way that Quality of Service (QoS) improves and energy consumption is reduced. The controller is developed by using optimal control theory while guaranteeing asymptotic stability (Lyapunov stable) and avoiding losses. In order to validate this approach, we apply the adaptive controller in "Matlab-Simulink" and in the network simulator "NS-2". Within ADREAM framework 1 , this "control green" will allow to improve energy consumption regarding traffic load and available energy in communication networks.

INTRODUCTION

Since few years, the number of communication system users has significantly gone up, thereby energy consumption have also increased. According to [START_REF] Koomey | Worldwide electricity used in data centers[END_REF], the number of Internet users reached 2.4 billion of the population in 2012. Consequently, the energy consumption in communication networks represents 5.5% of annual world electricity production and a rate of 2% of carbon dioxide emissions (CO 2 ). The perspective for 2015, with probably 2.8 billion of Internet users, is to achieve a traffic 4 times larger and a double energy consumption (approximately 25% larger per year) [START_REF] Zhang | Effects of cloud horizontal inhomogeneity and drizzle on remote sensing of cloud droplet effective radius: Case studies based on large-eddy simulations[END_REF]. This issue requires to research new ways to reduce energy consumption. Some works have already been developed (mainly in the context of wireless networks) and several hardware and protocol solutions have been proposed to reduce energy consumption in communication networks included the following ones:

• ALR (Adaptive Link Rate): this idea adapts transmission rates depending and energy threshold in the nodes [START_REF] Gunaratne | Reducing the energy consumption of ethernet with adaptive link rate (alr)[END_REF].

• Smart sleeping: this proposition consists in switching off the inactive or idle routers [START_REF] Bianzino | A survey of green networking research[END_REF], [START_REF] Jimeno | A network connection proxy to enable hosts to sleep and save energy[END_REF].

1 http://www.laas.fr/ADREAM/

• Resizing network: this solution is complex and expensive, it modifies the architecture of communication networks [START_REF] Ceuppens | Power saving strategies and technologies in network equipment opportunities and challenges, risk and rewards[END_REF].

• Energy-aware routing: it calculates the best route in order to minimize the number of routers within the Quality of Service (QoS), particularly in terms of energy consumption [START_REF] Amaldi | Energy-aware IP traffic engineering with shortest path routing[END_REF].

In the industry domain, some important companies in the sector have already started a "green revolution" (development of "green" network equipments)). Among these companies, we cite the following ones: Cisco (EnergyWise), Alcatel-Lucent (GreenTouch), IBM (Big-Green), NetGear (routers, energyware switches) Intel, Microsoft, Toshiba, Hewlett-Packard (Advanced Configuration and Power Interface).

In this paper, a control mechanism is proposed from control theory. The control is locally implemented at each selected node of a network topology. The choice of the selected nodes is a problem in itself, and it is not an issue in this work. The adaptive law controls the traffic that crosses a node, by using the length-queue where packets are temporarily stored. This proposed law guarantees unsaturated output traffic to avoid packet loss, which ensures, simultaneously, a fast convergence to a reference level. This reference level in the buffer is given by the energy thresholds proposed by the ALR model, which ensures energy reduction [START_REF] Orgerie | Energy-efficient bandwidth reservation for bulk data transfers in dedicated wired networks[END_REF].

The proposed controller is validated in Matlab-Simulink [START_REF]MATLAB, version 8.2.0.701[END_REF] and NS-2 [START_REF] Fall | The ns manual," notes and documentation on the software ns2-simulator[END_REF]. Likewise, energy consumption measures are given by ECOFEN [START_REF] Orgerie | Energy-efficient bandwidth reservation for bulk data transfers in dedicated wired networks[END_REF] (implemented module in NS-2).

The rest of this paper is organized as follows: Section I presents the ALR model and the ECOFEN module. In Section II, a mathematical model and a controller are proposed. Finally, Section II presents the results of simulations in Matlab-Simulink and NS-2.

I. ALR MODEL AND ECOFEN MODULE

Firstly, let model the energy consumption of the network equipment. For this purpose, we consider a router model designed in NS-2. NS-2 is one of the most currently simulators used in network community [START_REF] Fall | The ns manual," notes and documentation on the software ns2-simulator[END_REF]. This simulator allows us to simulate large networks with realistic traffic and to obtain QoS measures.

The ECOFEN module (Energy Consumption Model for End-to-end Networks) was developed in NS-2. This module provides the instantaneous energy consumption of each equipment taking into account the traffic and the type of employed equipment (router, switch, network card, etc.) [START_REF] Orgerie | Energy-efficient bandwidth reservation for bulk data transfers in dedicated wired networks[END_REF]. This module is based on the ALR model (Adaptive Link Rate) which adapts transmission rates depending on link use-rate.

The power consumption mathematical equations are

P =                    P0 si wn = 0 a1wn + P1 si wn ∈]0; W1] . . . aiwn + (Pi -aiWi-1) si wn ∈]Wi-1; Wi] . . . aN wn + (PN -anWN-1) si wn ∈]WN-1; WN ] (1)
with:

• a i ∈ R + : the slope of the different linear section.

• w n ∈ R: the input traffic of each network element.

• W i ∈ R + : the use-rate thresholds.

• P i ∈ R + : the start power of each different stage. In this model, the input traffic depends on the consumed energy by the network element.

A. Router energy model

Let take previous model for studying energy consumption in a router. For this issue, we control input traffic, w n , of the controlled node. We artificially and temporarily delay a certain number of packets in a buffer to a pre-defined value q ref . The length-queue reference q ref is given according to the input traffic in the router. This selection may provide some problems in network QoS, in terms of "delay". In other words, there is a energy consumption reduction and transmission delay trade-off.

Therefore, model ( 1) is rewritten

P =                      P0 si wn = 0 a1wn + P1 + bq ref si wn ∈]0; W1] . . . aiwn + (Pi -aiWi-1) + bq ref si wn ∈]Wi-1; Wi] . . . a N wn + (Pn -a N W N -1 ) + bq ref si wn ∈]W N -1 ; W N ] (2)
with :

• q ref : the queue length reference.

• b: a coefficient of the queue length reference q ref .

A reliable adaptation of the queue length reference is mandatory in order to reduce energy consumption with QoS guarantees.

This selection of q ref depends on two key parameters:

• the update time-window for the queue length reference.

T q ref = T w β , (3)
where T w is the time-window related to the node input traffic. β is the number of changes of the value of q ref during the period T w . This allows to update more or less frequently q ref depending on the traffic variability.

• The queue length reference

q ref = ŵn γ , ( 4
)
where ŵn is the average input traffic on a fixed timewindow T w . γ is a step (weighting coefficient) for adapting the amplitude of the reference function w n .

Remark. The judicious choice of the input traffic average ŵn , on a fixed time window T w , take into account the high variability of this traffic.

II. TRAFFIC CONTROL

A. Network model

One of the most important challenge is to find a suitable network model for control purposes. In this section, an average simple network model is developed inspired by a flow system. This reasonable simple model can handle a vast of networks behaviors (see [START_REF] Mascolo | Congestion control in high-speed communication networks using the smith principle[END_REF], [START_REF] Srikant | The mathematics of Internet congestion control[END_REF]). Thus, the model is proposed to be

q k+1 = q k -T s (u k -ŵn ) (5)
with:

• q k ∈ R + : the average queue length node and it is a state variable.

• T s ∈ R + : the sampling time of the network model.

• u k ∈ R: the output traffic of each node. This is the control variable.

• ŵn : the mean input traffic of each node and it is considered constant.

Note that this is a discrete-time model.

B. Control law a)

Error equation for an selected node: :

Taking as error variable e k q ref -q k , the error equation is:

e k+1 = e k + T s (u k -ŵn ). (6)
The proposed control law is:

u k = sat C 0 {u k-1 + Kx k }, (7)
where Remark. The saturation function is added in order to satisfy the physical constraint of the network links, whose capacity has to be positive and less than C (or W N in Fig. 1).

K = [K 1 K 2 ]
b) Polytopic representation for the saturated control (7) and the error equation (6): :

The control law [START_REF] Amaldi | Energy-aware IP traffic engineering with shortest path routing[END_REF] presents an isolated nonlinearity which may be difficult to consider if we aim at designing effectively a controller. Therefore, the saturation is modeled as a polytopic model, which will be used to get efficient design methods as presented in the following lemmas. Define

χ k u k-1 x T k T .
The following lemma recalls how to encapsulate the saturation function into a polytope.

Lemma 1. [13]. Given K, G ∈ R 1×2 , for all, χ k ∈ R 3×1 , if χ k ∈ {χ k ∈ R 1×3 : [1 G]χ k ∈ [0 C]}, then sat C 0 {[1 G]χ k } ∈ Co {[1 K]χ k , [1 G]χ k } .
The next lemma proposes then a polytopic representation for the PI (Proportional Integral) control law :

Lemma 2. Assume there exist G ∈ R 1×2 , c > 0 and Ψ Θ 1 Θ 2 Θ T 2 P
> 0 ∈ R 3 where P ∈ R 2 is a positive definite matrix such that for any χ k ∈ X, where

X = χ k : χ T k Ψχ k ≤ c -1 , (8)
then, 0 < u k-1 + Gx k < C, and control law (7) admits the following representation

u k = α k (u k-1 + Kx k ) + (1 -α k )(u k-1 + Gx k ) = u k-1 + (α k Kx k + (1 -α k )Gx k ) = u k-1 + ūk ,
where ūk

(α k K + (1 -α k )G)x k with α k ∈ [0, 1], for all k > 0.
Then, Eq. ( 6) can be rewritten as:

e k+1 = e k + T s (u k-1 + ūk ) -T s ŵn (9)
From Lemma 1 and 2 and from [START_REF] Albea | Robust saturated control for low-power circuits[END_REF], we obtain:

x k+1 = Ax k + B ūk , (10)
where

A 2 -1 1 0 , B T s 0 .
Equation ( 10) can be rewritten in the following explicit closedloop form:

x k+1 = Ax k + B (α k K + (1 -α k )G) x k . (11)
c) Condition for unsaturated control: To ensure that the control signal do not saturate, we need to enforce that:

0 < u k-1 + Gx k < C, ∀χ k ∈ X ( 12
)
where X is given in [START_REF] Orgerie | Energy-efficient bandwidth reservation for bulk data transfers in dedicated wired networks[END_REF].

Subtracting C 2 in inequality [START_REF] Srikant | The mathematics of Internet congestion control[END_REF] and from [START_REF] Fridman | Regional stabilization and H∞ control of time-delay systems with saturating actuators[END_REF], it is seen that, ( 12) is satisfied if:

C > cx T k P x k + cu k-1 Θ 1 u k-1 + cx T k Θ T 2 u k-1 + cu k-1 Θ 2 x k -1 + C > 2u k-1 + 2Gx k -C. (13)
From Lemma 2, nequalities (13) can be rewritten as:

  1 ±u k-1 ±x k   T   2C -1 -1 -G -1 cΘ 1 cΘ 2 -G T cΘ T 2 cP     1 ±u k-1 ±x k   > 0 (14)
Employing the Schur's complement and some mathematical manipulations, defining Y i G i Q i with Q i ∈ R 2 an Hermitian matrix, applying Q i = P i -1 and pre-and postmultiplying by diag{I 2 , I 2 , Q i }, it can be shown that this last inequality is satisfied if

Λ   c -1 -Y -1 (2C -1)Θ 1 (2C -1)Θ 2 Q -Y T (2C -1)QΘ T 2 (2C -1)Q   > 0 (15)
C. Sub-Optimal robust saturated control design Firstly, we aim at minimizing the control signal u k as well as x k , (i.e. q k converges to q ref , as fast as possible). For this purpose, we propose to minimize a quadratic cost function:

J = ∞ k=0 (x T k Qx k + u k Ru k ). ( 16
)
where Q > 0 and R > 0, which implies that J is strictly positive.

Secondly, as the sampling period T s of the network is supposed to be constant, we aim also at designing this suboptimal gain K for the control law [START_REF] Amaldi | Energy-aware IP traffic engineering with shortest path routing[END_REF] in such a way that the system ( 5) is robust with respect to parameter uncertainty. Lemma 3. Assume there exist Q ∈ R 2 , R ∈ R and P > 0 associated with a Lyapunov function candidate V k , such that,

V k+1 -V k + x T k Qx k + u k Ru k < 0, (17)
then the performance index J is minimized at the same time that system stability is guaranteed.. Proof: By summing the inequality (17) from k = 0 to k = ∞, we obtain:

∞ k=0 (V k+1 -V k + x T k Qx k + u k Ru k ) = V ∞ -V 0 + J < -V 0 + J < 0,
thus J < V 0 ≤ x T 0 P x 0 , then the quadratic cost function J is minimized, and the system stability is ensured.

The uncertain parameter α k given above is now taken into account. We chose the extremes of this parameter (α (j) k = 0, 1 for j = {1, 2}) as the vertices of the polytope.

Next, a sufficient condition to satisfy lemma 3 is derived.

Theorem 1. Consider system [START_REF] Mascolo | Congestion control in high-speed communication networks using the smith principle[END_REF] and control law

u k = u k-1 + α (j) k Kx k + (1 -α (j) k )Gx k for α (j) k ∈ [0, 1], where K, G, S (j) ∈ R 1×2 . If there exist T, Y ∈ R 2×1 and Q = P -1 , Q ∈ R 2 with K = T Q -1 , G = Y Q -1 and R, c, µ > 0 for j = 1, 2 such that min K c, µ, P > 0 (18) Γ (j) k < 0 j = 1, 2, ( 19
) -µI 2 + Q -1 < 0 (20) Λ > 0 (21) being Γ (j) k
defined in (22) (given at the top of next page), are satisfied. Then, for all initial conditions in X, the states converge asymptotically to the equilibrium. The closed-loop system [START_REF] Mascolo | Congestion control in high-speed communication networks using the smith principle[END_REF] is unsaturated and sub-optimum with respect to J.

Proof: The goal is to satisfy Γ (j) k < 0 for both asymptotic stability and minimization of J in the entire polytope Υ j .

Then,

V (j) k+1 -V (j) k + x T k Qx k + u k Ru k = x T k+1 P x k+1 -x T k P x k + x T k Qx k + (u k-1 + Kx k )R(u k-1 + Kx k ) = x T k [ ĀT P Ā -P + Q + (S (j) + K)R(S (j) + K)]x k
where Ā(j)

A + α (j) k K T + (1 -α (j) k )G T for j = 1, 2 and S (j) [T -1 s -T -1 s ].
Straightforwardly, applying Schur's complement and pre-and post-multiplying by {Q 1 , I 2 , I 2 , I 2 }, it can be shown that if Γ (j) k < 0 then conditions for using Lemma 3 are satisfied and the closed loop stability is guaranteed. Furthermore, minimizing µ > 0, such that, P < µI 2 , allow to minimize J.

The sub-optimal gain K, obtained applying Theorem 1 guarantees both stability model of communication model, a transitional regime control and a controlled QoS.

III. ANALYTIC & SIMULATION RESULTS

The control gains for the node, control ( 7) is computed. To validate this approach, we take a simple topology composed of two nodes and one source, as shown in Figure 2. Two types of simulations, using T s = 0.05s, are performed. Firstly, we test the control law under Matlab-Simulink (A) to validate the assumption to take an average-model for computing a control law. Then, simulations are performed in NS-2 (B). These two simulators have been choosing for the following raison: NS-2 runs with events and Matlab-Simulink with discret time. Note that the modified ECOFEN model is implemented under NS-2.

In Figures 3 and5, the evolution of the input traffic generated by the source and the output traffic calculated from the control law are presented. Likewise, it is shown in Figures 4 and6, the queue length evolution. Note, that the Matlab-Simulink simulations are closed to NS-2 simulations. Thus, the simplification made about the average-model is validated. In addition, network traffic is unsaturated, so losses are avoided.

Figure 7 shows the power consumption with and without control law. Note, there is a significant improvement in power consumption from 0s to 6.2s which represents 62% of the total simulation time (10s). During this time period, packets are stored in the queue (with size q ref ), the output traffic is smaller than the input traffic. Moreover, power is smaller than a power threshold, hence the reduction of the energy consumption. Given the ALR model, if the output traffic is smaller than a threshold W i (see 1), the consumed energy will be smaller than without control. On the other hand, from 6.2s to 10s, queue length releases packets already stored. Hence, the output traffic is larger than the input traffic, what leads to a slight energy overconsumption, the difference is less than the reduction.

Note that the minimum power consumption of the ALR model is P 0 = 155W (Figure 7). This value is obtained when there is not traffic crossing the controlled node (w n = 0 M b/s). This is a minimum power consumption of the operational node without traffic.

In Figure 8, the two phases of energy consumption (reduced and increased energy consumption) are easily shown. In this simulation, it is shown that the global energy consumption for

Γ (j) k     -Q Q Ā(j) T + (α (j) k T T + (1 -α (j) k )Y T )B (j) -Q -Ā(j) T + α (j) k T T + (1 -α (j) k )Y T * -Q 0 0 * * -Q -1 0 * * * -(1 + R) -1     (22)
a time period of 10s is reduced 12.2% (energy gain) in the ALR model. The ratio between reduced and increased energy consumption is up to 60%.

A. Simulation Matlab-Simulink

IV. CONCLUSION

In this article, an alternative adaptive solution for reducing energy consumption in networks has been presented. This solution is developed from control theory. The controller was

Figure 1 Fig. 1 .

 11 Figure1shows the power model for a router.

  are the control gains and x k = [e k e k-1 ] T . The high-bound saturation C depends on the network capacity.

Fig. 2 .,

 2 Fig. 2. Network node for validation

Fig. 3 .Fig. 4 .Fig. 5 .Fig. 6 .

 3456 Fig. 3. Input (red) and output (blue) traffic.

Fig. 7 .Fig. 8 .

 78 Fig. 7. Power consumption with (blue) and without (red) flow control, on ALR model of a network node.

developed taking into account both the limitation of linkcapacities and minimization of a quadratic costs to ensure the fast convergence of the queue-length. In such a way, that a level of QoS is guaranteed (under a trade-off). Simulations under Matlab-Simulink and NS-2 validate this control law. In addition, an energy gain is shown, what let to call our control "control green". Future work will improve the optimization phases for (γ, β) parameters and the selection of adaptive nodes.


J L Petitniot

A Dolay

C Courtois

M Rguiti

S D'astorg

Breme

Potentialities for aeronautics of the development of an active core PZT fibre

traduit

Introduction

The desire to fly like birds, overcoming obstacles with grace and ease, subject which has always aroused admiration and curiosity, dates back to antiquity. At the beginning of the twentieth century the first aircraft concepts which tried to imitate birds used light and flexible flapping wings. Progress in propulsion and the abundance of cheap energy encouraged then the birth of aircraft with stiffer and heavier structures. The emergence of composite materials in the 70's with the economy related to the energy crisis and progress made in aerodynamics controls has led to a return to lighter and more flexible structures. The dream of having a progressive wing adapting in real time conditions to multiple variable use (gliding flight, rapid dive on a prey...) or reporting weaknesses and thereby exploit the possibilities of the aircraft in the near future could be realized through the development of active materials and adaptive structures. So an active camber of the wing with wingtip permeability varying with flight conditions may allow expect a reduction in drag with a deletion of slats and flaps, (figure 1). Active torsion of a helicopter blade is approached as a means to push the limits of dropping out, reduce vibration and noise pollution of aerodynamic origin, particularly intense in the descent phase.

Figure 1: bird and aircraft wingtip morphing.

In this domain, activity on smart materials at the centre of Lille of ONERA concerns applications of Shape Memory Alloys and piezoelectric actuators. Among these latter, APA ® from Cedrat Technologies, by their mode of action at 90°, was well perceived to be applied to the flap motion of active blades of helicopters. The use of carbon composite shell allows obtaining a noticeable energy density gap, and makes them now more competitive, [START_REF] Petitniot | Manufacture and properties of first industrial APAs Actuators using carbon epoxy Shells' 13th Actuator Conf[END_REF]. At another scale closer to that of the fibres of the composites, piezoelectric fibres and ribbons are promising in respect of their capacity characteristics and maximum strain energy density. They also have the added benefits of conformability, the controllability of the anisotropy. Existing AFC and MFC laminar actuators are however small and supplied by high driving voltages are rather brittle and don't have the ability to safely cover large areas use, (figure 2). They are more often bonded on surfaces and the efficiency of the force transfer is lower because they are not intimately interwoven with passive surrounding fibres. Short PZT hollow fibres exist but they are very brittle and not adapted to a continuous production process of long fibres. The idea of developing a low voltage Metal Core Piezoelectric Fibre (MCPF) was motivated to try to overcome these deficiencies. The fact that this fibre is likely more robust, continuous and sufficiently long should also allows it to be worked with conventional textile processes. Moreover the fact that the metal core can serve as an internal electrode may allow integrating directly these fibres in conductive matrices (CFRP or GFRP). The aspect ratio of a MCPF fibre is defined by: α = t / r 0 = 1 / (1+ r c /t) First analytical calculations have been made with a mono dimensional model. The capacity of deformation is reduced by metal core presence and all the more so that the stiffness is high.

Curves exhibit various optimum aspect ratios depending on the core elastic modulus (figure 3). Potential candidates for the core are listed in table 1. The optimal aspect ratio ranges from 0.70 and 0.85 procuring a d 31 from 0.82 to 0.70 of bulk ceramic.

However, the analytical model does not take into account the transverse effect of the Poisson coefficient.

Table 1: Properties of potential metals and alloys for the metal core. Piezoelectric material A soft PZT powder was used as starting material. It can be fully densified at 1200° C for six hours in air atmosphere. The different phases of the work concerned the synthesis of powder (composition, grinding, calcination) to have a good densification and get optimum properties compared to bulk ceramics, the selection of the core material, the fibre forming and the sintering technique in order to produce a cheap fibre.

Manufacture techniques

Four processes have envisaged: the hydrothermal synthesis, the deposit by electrophoresis, the coextrusion, and the dip-coating. Hydrothermal synthesis and electrophoresis appear to not be suitable to produce long fibres with high ceramics thickness. So only co-extrusion and dip-coating have been investigated. Co-extrusion involves extruding the wire and simultaneously paste temporarily plastic containing ceramic particles. Ceramic paste is a Thermoplastic mixture of solvents, organic agents (binders, plasticizers ...) and PZT ceramic particles. The medium may be aqueous or non aqueous. The co-extrusion technique should allow have a perfectly centred wire and a homogeneous deposition. The adjustment parameters (temperature, pressure, extrusion speed...), the wire tension and the load rate of PZT powder should be properly selected. A copper wire of diameter 150 µm was chosen for these preliminary tests, figure 4. It seems however that the method does not allow obtaining fibres with an outside diameter less than 200µm because extrusion pressures become too great [START_REF] Sato | Development of the piezoelectric fibre and application for the smart board[END_REF].

Figure 4: co extrusion device.

Dip-coating has been largely used in this research. It consists in plunging the material, here the wire, in a bath and in removing it at a constant speed for depositing a film thereon (figure 5). The deposited thickness depends primarily on the speed of withdrawal and of the rheological properties of the bath (which depends on the composition and on the temperature) but also the dimensions of the substrate and its surface finish. The withdrawal speed was limited to 1.4 mm/s. Dip-coating test have been done on a platinum wires of diameters 0.4 and 1 mm. With the slurry composition used, dip coating allows to deposit layers of about 15 microns. A multiple dipping process has been used to obtain higher ceramic thickness compatible with actuation mode. Intermediary thermal treatments are done between each ceramics deposit to insure a good microstructure homogeneity inside the thickness. Various coated alloys core have been also experimented but because of the high sintering temperature presented some diffusion problems occur.

Sintering operation

The technique should allow densification of the ceramic without damaging the metal core. The standard sintering operation consists in a heating at 1200°C during 6 hours in an industrial air oven. A work atmosphere with an oxygen partial pressure is however preferable Some tests have been done by classical laser sintering but the result was inconclusive because of the too high power of the available laser. Flash Spark Plasma Sintering (SPS) has not been tested but seems difficult to implement on a so small cylindrical shape with such a dual PZT/metal core combination. Microwave sintering has been tested at the University of Caen. First results are encouraging. The advantages are a lower heating with few mechanical stresses and a very short sintering duration. Twenty minutes at 950°C seem to be a feasible goal, which is very promising to choose a core material less onerous than platinum, to reduce the manufacturing duration online, and therefore the global cost of the fibre. Adjuvants such a mixture of Cu 2 O and PbO have been added to reduce the sintering temperature to 900-950°C instead of 1200°C allowing the use of other pure metals, refractory alloys or metals and alloys coated with gold or silver without risk of oxidation and also reduce the sintering duration. However the use of a glass phase will necessary lead to a reduction in piezoelectric property of the metal core fibre.

Analytical and F.E modellings

Simultaneously analytical and F.E modellings of the MCPF, of actuator with several fibres embedded in a resin or in a reinforced carbon composite have been performed to compare and consolidate the experimental results. More accurate and detailed calculations are done with ATILA F.E Code and the GiD pre-post processor. The mesh of the MCPF fibre is built in cylindrical coordinates with 6 to 15 nodes triangular volume elements. To reduce the number of nodes, linear interpolation functions have been used. Patran MSC Software has been also used to define more precisely the fibre mesh and properly the good connectivity with the other middles.

Figure 7: Comparison of analytical and numerical

modelling for single fibre. The finite element calculation performed to model the behaviour of the fibre and determine the longitudinal strain has shown that the analytical model, which neglects any transverse effect, overestimates by almost 15% deformation (figure 7). Considering fibre 250 microns with a platinum core and an aspect ratio of 0.7 the free deformation is about 160 µdef and clamping force is about 0.60 N. The integration of these fibres in structures (with high volume fractions (60% of active fibres) reduces the maximum strain: about 5% for a flexible epoxy structure and about 55% for structure CFRP UD, (figure 8). The use of samples with higher aspect ratios and therefore more sensitive will eventually allow better correlate the modelling results with the experimental results of the tests made.

Electromechanical tests

Vibration tests have been done to verify the good running of fibres as actuator and sensor. For an aspect ratio of 0.4, an effective piezoelectric coefficient d 31 of -16 pm/V has been measured.

Other tests realized on tensile micro machines at the USTL of Lille and at the Ecole Nationale Supérieure des Mines de Douai (ENSMD) has given -21 pm/V, (figure 10). The objective of these tests where the fibre is pulled and more linear is also to determine the blocking force and the free stroke of the fibre. Active concepts can also be evaluated safely on fixed wing UAVs.

Conclusions and further investigations

Multi dip-coating is a good technique for the elaboration MCPF fibre. Investigation has still to be made to replace onerous platinum by another metal. The goal of realizing thinner fibres is not yet reached and the dip-coating technique needs to be adapted. An investigation on another process such Viscous Plastic Process (VPP), has also to be examined. Electromechanical tests will be made on a greater number of samples and better quality to develop suitable characterization techniques to measure effective properties of such fibres.

Figure 2 :

 2 Figure 2: AFC and MFC laminar actuators.

Figure 3 :

 3 Figure 3: d 31 versus α and core elastic modulus Y c .

Figure 5 :

 5 Figure 5 : Principle of dip-coating.Main tests have been done with 3 to 5 layers, corresponding respectively to 0.38 and 0.6 for the aspect ratios.

Figure 6 :

 6 Figure 6: Pt core coated with 1 and 5 PZT layers.

Figure 8 :

 8 Figure 8: Elongation versus force for various aspect ratio and soft and rigid matrices

Figure 9 :

 9 Figure 9: Operation in sensor mode.

Figure 10 :

 10 Figure 10: Tests on micro tensile machines.Numerous tests on a great number of perfectly linear samples and for various and higher aspect ratios have to be done to assert these results. Applications Various uses and products are perceived for this fibre: confection of low voltage unidirectional patches, woven, knitted fabrics, smart furs and robotized fibre placement.

Figure 11 :

 11 Figure 11: ONERA microdrone Remanta and wing prototype obtained by stereo photolithographyONERA Remanta project is inspired by insect bio mechanism which is to recreate the vibration deformation of the thorax of the dragonfly, inducing the wings flapping, (figure11). This technique allows insects flap their wings at very high frequency using a minimum of energy. At present time, the torsion of the passive wing is a flapping result. It can be imagined that bundles of fibres may replace the carbon ribs as the veins of a leaf and electrically powered by selective electrodes contributes to the deformation of the light and flexible wing to reach the 3D wished shape.Active concepts can also be evaluated safely on fixed wing UAVs.