Élaboration d’un contrôleur pour actionneurs piézoélectriques

Élaboration d’un contrôleur pour

actionneurs piézoélectriques

N. ZosoAEREX

F.C. WongRDDC Valcartier

Defence R&D Canada – ValcartierNote Technique

DRDC Valcartier TN 2007-238Septembre 2007

Elaboration d’un controleur pouractionneurs piezoelectriques

N. ZosoAEREX

F.C. WongRDDC Valcartier

R et D pour la défense Canada – ValcartierNote technique

DRDC Valcartier TN 2007–238

20 septembre 2007

Auteurs

Nathaniel Zoso, Frank Wong

Approuve par

Alexandre Jouan

Chef de section, Armes de precision

Publication approuve par

Christian Carrier

Scientifique en chef, RDDC Valcartier

Ce projet a ete realise sous WBE 12pn02 en juillet 2007.

Conditions de diffusion: Cette note technique est une publication non officielle de RDDC Valcartier destinee al’usage interne seulement.

c© Her Majesty the Queen as represented by the Minister of National Defence, 2007

c© Sa majeste la reine, representee par le ministre de la Defense nationale, 2007

Resume

Une solution alternative a l’utilisation de servomoteurs dans le cas de tres petitsvehicules aeriens inhabites (UAV) est l’utilisation d’actionneurs piezo-electriques. Lesactionneurs utilises dans ce projet sont fabriques par la compagnie APC, American PiezoCeramic International. Pour les controleurs, la solution choisie consiste a generer unetension de 150 V sur les electrodes externes du piezo. Une tension entre 0 et 150 V estmise sur l’electrode centrale de facon a controler la flexion de l’actionneur. La solutionpour generer la tension continue est un convertisseur DC/DC de type hacheur Boost, quia ete teste et est fonctionnel. Pour generer une tension variable, cependant, la solutionideale est un amplificateur operationnel en mode amplificateur noninverseur. Cette piecedoit etre concue pour fonctionner a une tension elevee. En l’absence d’un tel composant,un second hacheur Boost a ete concu, et permet de generer une tension entre 24 et 150 Vpour une tension d’entree entre 0,8 et 5 V. Si la tension d’entree descend sous 0,8 V,cependant, le hacheur sature. Les circuits ont ete concus pour fonctionner avec unetension d’alimentation de 24 V.

DRDC Valcartier TN 2007–238 i

Intentionnellement en blanc

ii DRDC Valcartier TN 2007–238

Table des matieres

Resume.....................................................................................................................i

Table des matieres ................................................................................................... iii

Liste des figures.......................................................................................................iv

Liste des tableaux .................................................................................................... vi

1. Introduction..................................................................................................1

2. Travaux precedents et base de la technique ..................................................... 2

3. Developpement des circuits Boost et Buck-Boost............................................6

4. Mesures et observations...............................................................................11

5. Limites du systeme et solutions alternatives ..................................................22

6. Conclusion .................................................................................................23

7. Bibliographie..............................................................................................24

Annexe A...............................................................................................................25

Annexe B............................................................................................................... 28

Liste de distribution.................................................................................................39

DRDC Valcartier TN 2007–238 iii

Table des figures

Figure 1. Tensions sur le piezo. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Figure 2. Diagramme du circuit Boost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Figure 3. Fonctionnement du circuit Boost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Figure 4. Diagramme du circuit Buck-Boost. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Figure 5. Fonctionnement du circuit Buck-Boost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Figure 6. Schema d’utilisation du TL494 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Figure 7. Detail du controleur PI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Figure 8. Circuit Boost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Figure 9. Circuit Buck-Boost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Figure 10. Signal DC 150 V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Figure 11. Sortie de l’optocoupleur sans charge a 100 kHz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Figure 12. Sortie de l’optocoupleur avec charge a 10 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Figure 13. Sortie de l’optocoupleur avec charge a 1 kHz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Figure 14. Sortie de l’optocoupleur avec charge a 100 kHz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Figure 15. Circuit Boost pour le signal de controle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Figure 16. Onde carree de 50 Hz en entree. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Figure 17. Onde sinusoıdale de 50 Hz en entree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Figure 18. Onde triangulaire de 50 Hz en entree. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17







Figure 25. Saturation du signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Figure 26. Amplificateur non-inverseur a gain de 30 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Figure A1. Entrees et sorties du controleur . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

iv DRDC Valcartier TN 2007–238

Figure A2. Detail du controleur. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Figure A3. Branchement de l’actionneur piezoelectrique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

DRDC Valcartier TN 2007–238 v

Liste des tableaux

Table 1. Composants de la compagnie Digikey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Table 2. Caracteristiques des signaux de sortie . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

vi DRDC Valcartier TN 2007–238

1. Introduction

L’objectif de ce projet est de concevoir un controleur pour des actionneurspiezoelectriques. Ce controleur recoit un signal de commande de [0-5]V dont lafrequence maximale est de 50 Hz. Il controle un actionneur piezo de type "stripeactuator" de la compagnie APC, American Piezo Ceramic International [1]. Ceci signifiequ’il faut une tension de sortie continue a 150 V et une seconde entre 0 et 150 V,proportionnelle au signal de commande. Ce controleur est alimente par des batteries dontla tension nominale est de 24 V.

DRDC Valcartier TN 2007–238 1

2. Travaux precedents et base de la technique

Divers travaux ont ete realises avec des piezos. Un exemple est resume dans l’articlepresente a l’annexe B et tire du "IEEE Robotics and Automation Magazine", edition dejuin 2007 [2]. D’autres exemples sont les travaux de Song [3], Jordan [4], Yan [5], Steltz[6], Montane [7], et la compagnie DSM [8]. Le principe general est de convertir unefaible tension DC en tension elevee. Dans le cas present, il faut une tension continue de150 V entre la borne positive et celle negative du piezo, puis une seconde, variable, entrela borne centrale et celle negative. Les tensions necessaires sont representees a la figure 1respectivement comme Vcc et Vcmd.

Figure 1. Tensions sur le piezo

Pour ce faire, diverses solutions sont disponibles. Celle detaillee ci-dessous utilise unconvertisseur DC/DC de type hacheur Boost et un second de type Buck-Boost. D’autressolutions plus sophistiquees mais plus onereuses ou plus complexes sont disponibles etdetaillees plus tard.

Afin d’obtenir une tension continue de 150 V a partir d’une alimentation de 24 V, il faututiliser un hacheur Boost, comme illustre a la figure 2. Son fonctionnement se resume adeux phases (voir la figure 3). Quand l’interrupteur (un MOSFET canal Nhabituellement) est ferme, c’est le "on-state", ou la phase de conduction. A ce moment, ladiode se bloque et l’inductance se charge. De l’autre cote du circuit, le condensateur sevide dans la resistance. La seconde phase, le "off-state" ou phase de recuperation, estl’etape ou l’interrupteur s’ouvre et la diode conduit. A cet instant, l’inductance se videdans le condensateur et dans la resistance. Plus la duree de la conduction est elevee parrapport a celle de la recuperation, plus la tension moyenne dans le condensateur estelevee.

La principale limite du hacheur Boost est que la tension de sortie ne peut pas etreinferieure a l’alimentation. Pour obtenir une sortie variable entre 0 et 150 V, il faututiliser un hacheur Buck-Boost, dont le schema est represente a la figure 4. Sonfonctionnement, illustre a la figure 5, consiste de deux phases, conduction etrecuperation, presque identiques a celles du Boost. La difference principale est que la

2 DRDC Valcartier TN 2007–238

Figure 2. Diagramme du circuit Boost

Figure 3. Fonctionnement du circuit Boost


sortie du circuit peut etre inferieure ou superieure a l’alimentation.

Figure 4. Diagramme du circuit Buck-Boost

Figure 5. Fonctionnement du circuit Buck-Boost

Les interrupteurs, habituellement des MOSFET, sont controles par un generateur de’pulse-width-modulation’ (PWM) en boucle fermee : au travers d’un controleurproportionel-integral (PI), le generateur compare la tension generee en sortie du hacheuravec une tension de reference, et ajuste le "Duty cycle" du PWM de facon a ce que lesdeux signaux soient egaux. Si la tension d’entree est 5 V mais que l’on veut 150 V ensortie du convertisseur DC/DC, il suffit de prendre un potentiometre en diviseur detension. En mettant le potentiometre a un rapport 1 :29, le PWM se stabilise quand latension en sortie du potentiometre rejoint 5 V, mais la tension en sortie du hacheur est de150 V. Le schema d’utilisation du TL494 est a la figure 6 ; les resistances R1 et R2, ainsique le condensateur C1 sont instrumentaux car ils creent le controleur PI. La figure 7illustre mieux l’effet du controleur, dont les parametres sont definis dans l’equation 1.L’ampli-op represente a la figure 7 se trouve en fait a l’interieur du TL494.

La resistance R freq ainsi que le condensateur C freq permettent de determiner la


frequence de fonctionnement du hacheur, frequence a laquelle le MOSFET va commuter.Les autres resistances ont un effet negligeable, la resistance R3 servant a diminuer le bruitcapte par le condensateur et la resistance R4 servant a limiter le courant traversant lespattes 8 et 9. En effet, entre ces pattes se trouve un transistor, qui determine si la tensionV PWM est de 24V ou de 0V. Toutes les resistances sont ordinaires et de puissance 1

4W.

P =(R2R1

); C =

(1

C1 ·R1

)(1)

Figure 6. Schema d’utilisation du TL494


Figure 7. Detail du controleur PI

3. Developpement des circuits Boost et Buck-Boost

Les formules utilisees dans cette section sont des modeles theoriques ideaux, ou lecondensateur n’a aucune fuite, l’inductance n’a aucune resistance parasite, le MOSFETet la diode ne dissipent aucune puissance et le controleur PI est parfaitement ajuste poursuivre la dynamique du systeme. Ceci signifie que ces calculs sont imprecis, et que lesvaleurs mesurees ainsi que les pieces ultimement utilisees dans les circuits serontdifferentes de celles calculees. Cependant, alors qu’il devient tres complexe de simulerefficacement les circuits de puissance Boost et Buck-Boost, les calculs theoriques sontd’excellents points de depart, et quelques iterations en laboratoire permettent d’ajusterles valeurs pour que le fonctionnement soit optimal.

Le circuit le plus simple est le Boost. En effet, il lui suffit de maintenir une tension de150V constante. La premiere etape est de determiner le rapport cyclique theorique duPWM permettant de convertir 24 V (Vcc) en 150 V (Vc). Ce rapport, α, est defini commesuit :

α = 1− V cc

V c(2)

ce qui donne α = 0.84. En utilisant la frequence de hachage maximale (ce qui permet unmeilleur controle du systeme) a laquelle le circuit entier est capable de suivre, soit 100kHz, ceci signifie que le transistor sera ferme 8.4µs et ouvert 1.6µs pour une periodetotale de 10µs.

Puisque quand le transistor est ferme, le condensateur se vide dans la charge, la tension ases bornes oscille a une frequence de 100 kHz. L’amplitude de cette oscillation estdefinie par l’equation


∆V =α

1− α· Vcc ·

Ts

RC(3)

ou Ts est la periode du hachage, ou 10µs et R = 100000 en considerant une resistance decharge de 100 kΩ. Cette charge est en fait un potentiometre permettant de lire la tensionV retroaction. Si le condensateur utilise possede une valeur moyenne de 10µF, on obtientque ∆V est de 1.3 mV. Cette valeur est assez petite, en tenant compte qu’elle peut etreplus elevee en realite.

Le second parametre important est le courant moyen traversant l’inductance. Il estcalcule ainsi :

iL =1

(1− α)2Vcc

R(4)

ce qui donne 9.4mA pour α = 0.84 et Vcc = 24 V, en considerant toujours la charge de100 kΩ. Comme le courant est relativement faible, l’inductance, la diode et le MOSFETpeuvent etre de faible puissance. Pour que le circuit fonctionne en mode continu (lecourant dans l’inductance est toujours non-nul), il faut que l’oscillation du courant soitinferieur a 9.4mA. Cette oscillation est calculee par la formule

∆I = αVcc

L· Ts (5)

donnant 2 mA pour une valeur d’inductance de 100 mH. De leur cote, la diode et leMOSFET doivent etre concus pour resister a une tension de 150 V.

Le circuit concu et implante est represente a la figure 8.

Le second circuit, le Buck-Boost, est bien plus complexe. En effet, il doit generer unetension de 0 a 150 V a une frequence de 50 Hz. Le probleme dans ce cas est que le circuitpeut forcer la tension du condensateur a monter, mais il ne peut pas la forcer aredescendre. Pour ce faire, l’inductance doit se vider dans le condensateur et laresistance, puis le condensateur se vide dans la resistance. La premiere partie est pluscomplexe a simuler, mais peut etre ignoree si l’inductance est de valeur suffisammentfaible. Suite a ca, la tension diminue comme un circuit RC simple. On compte donc quepour parcourir 99% du spectre des tensions possibles, il faut 5 constantes de temps dansun circuit du premier ordre. Comme la periode de la fonction est de 20 ms, il faut que laconstante de temps soit de l’ordre de 2 ms pour que le condensateur arrive a se vider dansla resistance suffisamment rapidement. En utilisant un condensateur de 1µF, on en deduitqu’une resistance de 2 kΩ serait ideale. Cependant, avec une tension de 150 V, lapuissance dissipee dans la resistance depasse 10W. Pour cela, la resistance testee estaugmentee a 2.4 kΩ et le condensateur est diminue a 0.5 µF.

Le rapport cyclique, α, est defini par


Figure 8. Circuit Boost


α =1(

VccVc

)+ 1

(6)

ou l’alimentation, Vcc, reste a 24 V, et Vc varie entre 0 et 150, ce qui donne un α entre 0et 0.8621. L’ondulation de la tension sur le condensateur est donnee par

∆V =α2

1− α· Vcc ·

Ts

RC(7)

et, pour les valeurs de R et C respectivement de 2.4 kΩ et 1 µF et ou Ts, la periode duhachage, est de 10µs, l’oscillation maximale est de 1.080 V.

Le courant que l’inductance doit porter est

iL =(

α

1− α

)2 Vcc

R(8)

qui donne, pour les valeurs definies ci-dessus, un maximum de 390 mA pour un α de0.8621. Lorsque la tension Vc diminue, α diminue jusqu’a 0, comme iL. Ce courant doitdonc etre supporte par l’inductance, la diode et le transistor, comme dans le cas du Boost.Ceci implique donc un transistor, diode et inductance de haute puissance, car ils doiventetres concus pour une tension d’au moins 150 V et un courant d’au moins 400 mA.

Pour eviter les pics de courant dans le systeme qui endommageraient les composants, ilfaut limiter l’ondulation du courant, definie par la formule

∆I = αVcc

L· Ts (9)

qui donne 6 mA, une valeur acceptable, pour une inductance de 35 mH, une valeurfacilement trouvable.

Puisque le circuit de controle lit une fraction de la tension de sortie pour completer laboucle de retroaction, et que cette tension ne partage aucune masse commune par rapportau transistor, il faut controler cet element au travers d’un optocoupleur. Cette piecepermet d’activer un MOSFET sur une masse a partir d’un signal par rapport a une autremasse. Le signal en entree controle une diode electroluminescente interne, qui commuteune serie de transistors internes. Ces transistors, qui commandent le MOSFET, ne sontaucunement relies a la masse du signal d’entree, un peu comme un transformateur.

Le circuit concu et implante est represente a la figure 9.

Le tableau 1 contient la liste des composants utilises, avec le numero du fournisseurDigikey.


Figure 9. Circuit Buck-Boost


Tableau 1. Composants de la compagnie Digikey

Piece Numero chez Digikey QuantiteTL494 296-10194-5-ND 2Diode 1 A 200 V MUR120RLGOSCT-ND 2Inductance 100 mH M8337-ND 1MOSFET canal N 200V 600 mA IRFD210PBF-ND 2Inductance 70.2 mH (double) 1.38 A 237-1216-ND 1Condensateur 0.1 µF 250 V 445-2637-ND 2Condensateur 1 µF 160 V 493-1157-ND 1Condensateur 10 µF 160 V PCE3421CT-ND 1Resistance 2.4 kΩ 10 W 2.4KW-10-ND 1Potentiometre 100 kΩ SP064W-100K-ND 2Optocoupleur 425-2598-5-ND 1

Note : Les condensateurs de 0.01µF et les resistances de 14W ne sont pas inclues dans cette liste.

4. Mesures et observations

Le circuit Boost generant une tension DC de 150 V est implante, teste et fonctionnel. Ilutilise une entree de 24 V et sort un signal constant de 150 V. En utilisant un multimetre,l’oscillation mesuree sur la tension est de 5 mV sur une tension de 151 V.

Le circuit Buck-Boost n’a pu etre realise. En implantant le circuit de la figure 9, il a eteobserve que l’optocoupleur n’arrive pas a controler le MOSFET. A pleine charge,diverses pieces brulaient.

Les figures 11, 12, 13 et 14 illustrent en jaune le signal que l’optocoupleur emet sanscharge, transmet au MOSFET a 10 Hz, 1kHz et 100 kHz. Le signal bleu representel’entree. Tous ces tests ont ete faits a une tension d’alimentation et sortie diminuee, defacon a ne pas bruler le circuit. Pour une frequence superieure a 10 Hz, on observe uneaugmentation drastique de la tension en sortie de l’optocoupleur quand il est branche auMOSFET, ainsi que des harmoniques qui s’ajoutent au signal. Ceci indique un retour del’oscillation de la tension et du courant dans l’optocoupleur, qui n’arrive pas a maintenirla tension en sortie. Comme le reste du circuit est teste et fonctionnel, il faut obtenir unnouvel optocoupleur.

Puisque un circuit complet et fonctionnel de Buck-Boost n’a pas pu etre produit, lasolution alternative est d’utiliser un circuit Boost avec les memes pieces que celles quidoivent aller dans le Buck-Boost. Le controleur PI du circuit de controle a ete ajuste poureviter l’instabilite du systeme. La figure 9 tient compte de ces modifications. Dansl’eventualite ou le circuit Buck-Boost etait implante et fonctionnel, il faudra utiliser lecontroleur adapte aux pieces du Buck-Boost et, par la meme occasion, du nouveau Boost.Le schema du nouveau circuit Boost est represente a la figure 15.


Figure 10. Signal DC 150 V

Figure 11. Sortie de l’optocoupleur sans charge a 100 kHz


Figure 12. Sortie de l’optocoupleur avec charge a 10 Hz

Figure 13. Sortie de l’optocoupleur avec charge a 1 kHz


Figure 14. Sortie de l’optocoupleur avec charge a 100 kHz

Avec le circuit de la figure 15, divers tests ont ete effectues. Les figures 16, 17 et 18comparent le signal de commande a 50 Hz avec un trentieme du signal de sortie. Lesfigures 19, 20 et 21 presentent les signaux a 30 Hz et les figures 22, 23 et 24 presententles memes signaux a 10 Hz. On observe une bonne fidelite de la sortie par rapport al’entre a 10 et 30 Hz. A 50 Hz, la sortie commence a etre amortie, rejoignant 140 V aulieu de 150 V. La figure 25 illustre le probleme du circuit Boost. Le signal d’entreeoscille entre 0 et 5 V, ce qui requiert que le circuit produise un signal entre 0 et 150 V. Onobserve la saturation a 24 V, tension d’alimentation.

Le tableau 2 presente quelques caracteristiques des signaux de sortie par rapport a ceuxd’entree. Les signaux carres sont toujours assez precis, mais la qualite des autres signauxse degrade avec l’augmentation de la frequence. La perte de signal ne depasse pas 16 V,qui est approximativement 13 % de l’amplitude theorique du signal de sortie (120 V), ou-2.86 dB. D’autres parts, le retard reste dans l’ordre de 1 ms, peu importe la nature dusignal ou la frequence.

Des tests ont ete faits en utilisant un piezo 600/200/0.60-SA de la compagnie APC [9].Le bon fonctionnement des circuits a ete observe visuellement a faible frequence. A plusde 30 Hz, le piezo ne suit plus le signal de commande, qui se situe sans doute a unefrequence bien plus elevee que la frequence de coupure du piezo. La perte de signal a 50Hz ne peut donc pas etre observee, car le mouvement physique est deja tres attenue.


Figure 15. Circuit Boost pour le signal de controle


Figure 16. Onde carree de 50 Hz en entree

Figure 17. Onde sinusoıdale de 50 Hz en entree


Figure 18. Onde triangulaire de 50 Hz en entree










Figure 25. Saturation du signal


Tableau 2. Caracteristiques des signaux de sortie

Caracteristique Signal d’entree Signal de sortieValeur maximale, onde carree 50 Hz 5 V 150 VValeur minimale, onde carree 50 Hz 1 V 30 VValeur maximale, onde carree 30 Hz 5 V 150 VValeur minimale, onde carree 30 Hz 1 V 30 VValeur maximale, onde carree 10 Hz 5 V 150 VValeur minimale, onde carree 10 Hz 1 V 30 VRetard par rapport a l’entree – 1.5 msTemps pour rejoindre la valeur finale – 4 msValeur maximale, onde sinusoıdale 50 Hz 5 V 140 VValeur minimale, onde sinusoıdale 50 Hz 1 V 35 VValeur maximale, onde sinusoıdale 30 Hz 5 V 144 VValeur minimale, onde sinusoıdale 30 Hz 1 V 32 VValeur maximale, onde sinusoıdale 10 Hz 5 V 148 VValeur minimale, onde sinusoıdale 10 Hz 1 V 30 VRetard par rapport a l’entree – 1 msValeur maximale, onde triangulaire 50 Hz 5 V 139 VValeur minimale, onde triangulaire 50 Hz 1 V 35 VValeur maximale, onde triangulaire 30 Hz 5 V 144 VValeur minimale, onde triangulaire 30 Hz 1 V 34 VValeur maximale, onde triangulaire 10 Hz 5 V 147 VValeur minimale, onde triangulaire 10 Hz 1 V 32 VRetard par rapport a l’entree – 1 ms


5. Limites du systeme et solutions alternatives

La solution implementee, utiliser deux hacheurs Boost, possede ses limites.Premierement, le circuit amplifiant le signal de controle est limite entre 24 et 150 V, cequi fait perdre un sixieme de l’amplitude maximale possible, soit 150 V. La solutioninitialement envisagee, utiliser un hacheur Buck-Boost, regle ce probleme. Cependant, lecourant consomme en moyenne est pres de 400 mA, ce qui signifie que le circuit dissipepres de 10 W a 24 V, malgre le fait que l’actionneur piezoelectrique ne consommepratiquement pas de courant. De plus, le circuit n’arrive pas parfaitement a suivre lesignal d’entree. Il attenue et retarde le signal d’entree.

Une solution alternative serait d’utiliser un ampli-op qui puisse etre alimente avec 150 V.Il suffirait de concevoir un amplificateur non-inverseur avec un gain de 30 avec cetampli-op. La sortie serait donc 30 fois l’entree, et un signal 0-5 V serait transforme en0-150 V. Puisque la frequence maximale d’un ampli-op est tres elevee, le signal de sortieresterait tres fidele a celui d’entree. La compagnie Apex [10] fabrique de tels ampli-ops.Le circuit Boost concu lors de ce projet peut alimenter.

Une seconde solution consiste a relier les deux electrodes externes de l’actionneurpiezoelectrique entre elles. Le signal de commende est mis entre cette nouvelle electrodeet l’electrode centrale du piezo. Le signal de commande doit se trouver entre -50 et 50 Vpour ne pas endommager l’actionneur piezo. La difficulte a implementer cette solutionreside a amplifier un signal alternatif par un facteur 20, si 5 V d’entree generent un ecartde 100 V en sortie. Un convertisseur DC/DC ne peut pas effectuer cette amplification. Ilfaut donc utiliser un ampli-op de puissance. Puisque ce dernier doit etre alimente par unetension de 50 et -50 V, il faut deux hacheurs Boost pour mettre en pratique cette solution.

La solution recommandee, plus simple mais plus dispendieuse, reste de controlerl’actionneur piezoelectrique avec une tension 150 V DC, provenant d’un hacheur, et unsignal 0-150 V, provenant d’un ampli-op de puissance. Le circuit amplifiant le signal 0-5V est represente a la figure 26, et doit posseder comme alimentation les tensions de 0 et150 V. Pour avoir un gain de 30, il suffit que la resistance R2 ait une valeur 29 foissuperieure a celle de R1.

Figure 26. Amplificateur non-inverseur a gain de 30


6. Conclusion

Les objectifs principaux de ce projet, generer une tension continue de 150 V et convertirune tension 0-5 V a une tension 0-150 V ont ete majoritairement realises. La tensioncontinue est obtenue a partir d’une source de 24 V, comme par exemple, une batterie.Pour ce faire, un convertisseur DC/DC hacheur Boost a ete concu et est controle par uncircuit TL494, qui genere un PWM en fonction du signal provenant d’un controleur PI.Le systeme a ete implante et genere la tension desiree de 150 V avec une oscillation de 5mV. Le second objectif est partiellement rempli par un second convertisseur DC/DChacheur Boost, controle par un TL494 et un controleur PI. La difference principale, estque la commande en entree du controleur PI est un signal 0-5 V. Cependant, le circuitBoost ne peut pas generer de tension inferieure a l’alimentation ou 24 V. Comme le gaindu systeme est de 30, la sortie du Boost suit, avec un retard moyen de 1 ms. Le signald’entree tant que ce dernier est entre 0,8 et 5 V. Quand ces conditions sont respectees, lasortie du Boost est assez fidele au signal d’entree pour une frequence inferieure a 50 Hz.

Pour remplir completement le second objectif, il faut utiliser un ampli-op de lacompagnie Apex. Un tel ampli-op est concu pour avoir une alimentation de l’ordre de200V. Un amplificateur noninverseur pourrait alors multiplier le signal 0-5 V par un gainde 30, donnant en sortie un signal 0-150 V.

Le systeme actuel a ete teste avec un actionneur piezo de la compagnie American PiezoCeramics jusqu’a une frequence de 50 Hz. La flexion est proportionnelle au signal24-150 V, mais est attenuee pour des frequences superieures a 30 Hz. A 50 Hz, lemouvement de l’actionneur devient imperceptible a l’oeil, ce qui cache l’attenuation dusignal d’entree. En effet, a cette frequence, le convertisseur Boost actuel attenue le signalde sortie de -2,86 dB.


7. Bibliographie

1. American Piezo Ceramics, Stripe actuatorshttp ://www.americanpiezo.com/products services/stripe actuators.html (5 juillet2006).

2. Wood, Robert J. et al.,"An Autonomous Palm-sized Gliding Micro Air Vehicle",IEEE Robotics & Automation Magazine, June 2007.

3. Song, Chunping et al., "Combined Optimization of Active Structural Systems andDrive Circuits", Proceedings of SPIE’s 2002 North American Symposium on SmartStructures and Materials : Modeling, Signal Processing and Control, March 2002.

4. Jordan, T. et al., "Electrical Properties and Power Condiderations of a PiezoelectricActuator", NASA-Langley Research Center, personal communication, 1999.

5. Yan, B. et al., "A Linear High-Voltage High-Power Amplifier for Use WithPiezoelectric Actuators", Proceedings of 6th CanSmart Workshop on Smart Materialsand Structures, October 2003.

6. Steltz, E. et al., "Power Electronics Design Choice for Piezoelectric Microrobots",Proceedings of the 2006 IEEE/RSJ International Conference on Intelligent Robotsand Systems, October 2006.

7. Montane, E., et al., "High-voltage smart power integrated circuits to drivepiezoceramic actuators for microrobotic applications", IEEE Proc.-Circuits DevicesSyst., Vol. 148, No. 6, December 2001.

8. Compagnie DSM, "Highly Efficient Electronic Power Drives for PiezoelectricActuators", feuille technique, www.dynamic-structures.com (25 juillet 2007)

9. American Piezo Ceramics, Stripe actuators, information techniquehttp ://www.americanpiezo.com/products services/stripe actuators/stripe background.html(5 juillet 2006).

10. Compagnie Apex, http ://eportal.apexmicrotech.com/mainsite/, (26 juillet 2006).


Annexe A

La figure A1 illustre la position des diverses entrees et sorties du circuit controleurimplante. La figure A2 detaille une partie de ce meme circuit, et la figure A3 montrecomment correctement brancher un actionneur piezo-electrique au circuit de controleur.

Figure A1. Entrees et sorties du controleur


Figure A2. Detail du controleur


Figure A3. Branchement de l’actionneur piezoelectrique


Annexe B


JUNE 2007 IEEE Robotics & Automation Magazine 83

velocity such that the precise wind speed may be regulated bya traditional feedback control system. This velocity and theservo angle are controlled via xPC (from MathWorks, Natick,MA) as is shown in Figure 2.

The lift and drag coefficients are then measured as a func-tion of both fluid velocity and angle of attack. Sample resultsare shown in Figure 3. From this optimization, airfoils with alift-to-drag coefficient greater than 8 are achievable in this lowReynolds number environment (Re ≈ 7000).

Control SurfacesFor construction simplicity and minimal mass, a V-tail config-uration is developed. The MicroGlider uses only two controlsurfaces, both mounted on the tail, which produce normalforces on the tail surfaces that map the two actuator inputs toroll, pitch, and yaw body torques. Similar to a microelectro-mechanical systems (MEMS) approach to create Micro-Flaps[19] using actuated hinged structures, the MicroGlider controlsurfaces are manipulated by piezoelectric bending actuators[20] which require a motion-amplifying transmission systemthat will be discussed in this section.

Control Surface KinematicsThe tail, actuator, and control surface form a closed parallelchain via an additional laser-micromachined link. The distalend of the actuator is connected to the control surface hingethrough a slider-crank to form a four bar mechanism (similarto the mechanisms in [18] and [21]) as is shown in Figure 4.Thus, the small displacement (δ) of the actuator is amplifiedinto a larger rotation (φ) at the base of the control surface.

The forward kinematics for such a chain are determined bythe relative lengths of the constituent members [16]. Thus theamplification of the actuator motion can be selected basedupon the relative geometries to ensure adequate body torques.To determine what deflection is sufficient to achieve thedesired level of maneuverability, control surface forces aremeasured and transformed into torques using a simplifiedrigid body model of the MicroGlider.

Glider Torque EstimationDue to power, mass, and size limitations, theprocessing power of the MicroGlider con-troller will be significantly less than that oftraditional robotic systems. This places limitson the fidelity of control. One solution tothis problem is to characterize the bodytorques produced by various control inputsand choose appropriate spaces in this map togenerate independent body torques in a dis-crete manner. The first step in this process isto model the overall system by way of thefollowing mapping:

[s l

s r

]T→

[τ r

τp

τy

](1)

Figure 1. Complete 2 g MicroGlider.

Battery

10 cm

Fuselage

Control/Power PCBControl Surfaces

Actuators

Airfoil

10 mm

Subsystem Mass (mg) Power (mW)Airfoil 265 —Fuselage 130 —Control surfaces & tail 150 —Actuators 50 3.5Control/power PCB 440 —

H.V. electronics — 6.5 control electronics — 6

Optic flow 325 29Sensors1 200 5Battery 700 —

Total 2220 501goal specifications

Table 1. Preliminary mass and power budgets.

Figure 2. Wind tunnel airfoil measurement setup.

Wind Tunnel

Air FlowAirfoil

Servo

Force Transducer

Anemometer Motor

PC

where the subscripts r, p, and y representroll, pitch, and yaw with respect to thebody moments about the center of gravity(CG) and s l and s r are the left and rightcontrol signals. Ideally, this map would bemeasured directly as a two input, three out-put system using a three axis torque sensorwhile spanning the appropriate space of thetwo input voltages. This is impractical sinceexisting multi axis torque sensors are eithertoo insensitive (>> 10mN-mm resolution),have insufficient bandwidth (< 100Hz), orare simply too bulky to be placed in thewind tunnel with the glider. As an alternateapproach, the individual control surface liftand drag forces are measured using the air-foil setup shown in Figure 2. A single con-trol surface is r igidly attached to thetwo-axis force sensor and the lift and dragare measured as a function of the actuatorinput voltage. Now the following mappingcan be described:

[s]Ts→

[Flift

Fdrag

](2)

This map can be used to develop the desired mapping (1)through the glider geometry. An example of this map isshown in Figure 5.

Now let θ, le , and l f represent the ‘V-tail’ dihedral angle,the distance from the fuselage to the individual control surfacecenter of pressure, and the length from the CG to the controlsurface center of pressure respectively (see Figure 6). Thus, asimplified map from control surface lift forces to body torquescan be derived and is shown in the following:

[τ r

τp

τy

]=

[ le − lel f sin(θ/2) l f sin(θ/2)

l f cos(θ/2) − l f cos(θ/2)

][F l

F r

](3)

where F l and Fr are the control surface normal forces from(2) for the left and right control surface respectively (again, seeFigure 6). Note again that since the control surface drag forcesare constant, they are a static disturbance and will not be con-sidered in the formulation of the body torques. Finally, thesetwo maps are combined (along with linearized control surfacelift data from Figure 5) to give the desired map T. Subsectionsof this map are used by the flight control system to performappropriate maneuvers during flight. The expected magni-tudes range from ±20mN-mm roll, ±50mN-mm pitch, and±50mN-mm yaw.

Fuselage and FabricationThe airfoil, control surfaces, tail, and fuselage each consist ofultra high modulus composite materials. This gives great ver-satility to the manufacturing process since unidirectional orwoven lamina of these materials are easily molded. In

IEEE Robotics & Automation Magazine JUNE 200784

Figure 5. Control surface lift (normal) and drag (tangential)measurements as a function of actuator voltage. Note that thedrag is relatively independent of the applied voltage.

0 50 100 150 200−0.5

0

0.5

1

1.5

2

Drive Voltage (V)

For

ce (

mN

)

LiftDrag

Figure 3. Lift and drag coefficients for a sample airfoil.

−20−10

010

20

4,0005,000

6,0007,000

8,0009,000

10

5

0

5

10

α (°)Re

CL/

CD

Figure 4. Detail of control surface transmission system.

Slider Crank

Actuator

Control Surface

φ

δ

addition, the composites are initially in a form called prepregwhich consists of sheets of bundled fibers impregnated with acatalyzed but uncured epoxy. The epoxy in these laminanegates the need for additional bonding layers when formingmore complex structures. The airfoil is cut as a prepreg andcompression molded while curing to give the desired crosssection (as determined previously). The control surfaces arealso cut as prepreg and are fixed in a mold with the cylindricalcarbon fiber fuselage and cured. The control surfaces are fixedto the tail via laser-micromachined links and hinges to formthe transmission [18]. Finally, the actuators are fixed to the tailand wired by hand.

Control and Power ElectronicsAs seen in Figure 1, the electronics and control reside on adiscrete PCB mounted to the center portion of the fuselage.This board performs all control tasks, collaborates sensing andcommunication, conditions the battery power, protects thebattery with low voltage detection, and contains the highvoltage electronics required to control the actuators. Figure 7displays an overview of the electronics on board theMicroGlider. The power for the MicroGlider is supplied by asingle 20 mAh lithium polymer (LiPo) battery. This chemistryallows very high discharge rates (>5C)and can thus yield approximately 400mW for 10 min flight durations.

Several commercially available controlboards were considered, including prod-ucts by Softbaugh (part number T1121,1.7 g) and Didel (for example,WdPicDev84). However, the MicroGlid-er requires a board under 500 mg (includ-ing high voltage electronics). Since theMicroGlider will employ piezoelectricactuators, some type of power amplifier toboost the battery voltage to 200 volts isrequired. To the authors’ knowledge, noexisting board meets these specifications.

Other researchers have constructedcustom piezoelectric microrobot controlboards, such as Brufau, et al. [22] andMontane, et al. [23]. However, most ofthese boards are meant to power piezo-electric stack actuators, which requirevoltages much lower than the MicroGlid-er’s cantilever actuators (≈ 20–50 V forstack actuators versus 200 V for thebimorphs used here).

Power ElectronicsThe bimorph piezoelectr ic actuatorsrequire both a high-voltage bias supply(Vb ) and a dr ive signal (Vd ) rangingbetween ground and Vb to create dis-placement (see [20] for details on thisdrive method). To minimize weight, a

pulse-width modulated n-channel MOSFET in series with apair of resistors is used to modulate the bias supply. A 10-M

resistor is used to charge the actuator and a 2-M resistor isused to discharge the actuator. The time constant associatedwith the actuator’s capacitance and these series resistors filtersthe PWM square wave to create the desired low-frequencywaveform. The amplifier and bimorph schematics are shownin Figure 8.

Piezo Bias dc-dc ConverterThere are a number of existing approaches to boost thebattery voltage to the desired bias level, however low mass and


Figure 7. Block diagram of glider electronics and control. Filled boxes representwork in progress.

Centeye MG1Imager, OpticFlow, Ocelli

PIC18LF2520

(Slave)

BatteryMonitor

dc-dcConverter

3.3V 200V

PIC18LF2520(Master)

l2C

DriveElectronics Actuators

Target Sensors(Audio, RF, Light)

TX/RX(RFID, LowPower RF)

Target Location

PWM

BatteryKokam,20 mAh

Figure 6. Simplified glider drawing showing rigid body geometric parameters.

Side View Rear View

F1 Fr

le

le

lf

θ

τr

τp

Center of Control Surface Lift

Center of Gravity

There are many applicationsappropriate for MAVs including

reconnaissance, hazardousenvironment exploration, and

search and rescue.

high efficiency are crucial in this application. A custom IC isdesirable but is cost prohibitive and has an extensive lead time.Instead, a low-power boost converter (Linear TechnologyLTC1615-1) is used as a first boost stage. This topology(Figure 9) uses a simple inductor rather than a heavier trans-former. A pulsed waveform (ranging between zero and 32 V) isformed across the boost converter diode. The charge-pumpmultiplies this voltage by a factor of n (ideally), where n is thenumber of charge pump stages, to produce the bias voltage.

Although the charge pump involves a number of capacitorsand diodes, its weight is minimized through the use of 0402capacitors and multidiode surface-mount components. Whenbuilt, the converter outputs 205 V when driven from the bat-tery (using seven charge pump stages). Over the expectedoperating range, the converter is between 51 and 63 percent efficient. The losses are attributed to the quiescentpower draw and switching loss of the boost converter IC. Thedc output impedance is 48.2 k and the bandwidth is 3 Hz.The converter’s components weigh approximately 120 mg,neglecting the PCB weight, and occupy 70 mm2 of boardspace (with components on both sides).

Control ElectronicsThe MicroGlider master processor is the Microchip PIC18LF2520. This processor was chosen for its internal oscilla-tor, low power consumption, and small outline (28 pin QFNpackage, approximately 90 mg). The microcontroller also hastwo PWM outputs (to switch the two drive MOSFETs) andseveral A/D converters to measure sensors on the board.Additionally, the microcontroller interface to the optical flowsensor is straightforward using the I2C protocol (as discussedin the following). The completed board (shown in Figure 10)weighs 440 mg, and consumes approximately 12.5 mW(driving actuators and running a program at 1 MIPS).

Figure 11 shows a simulation for both the drive voltage,Vd , and output power for a 250 Hz PWM signal controllingone actuator. Note that since the load is mostly capacitive, thepower required to hold an actuator at a given field is very low.Also, note that in Figure 11 the drive voltage is a nonlinear

function of the duty cycle. Since this is aknown nonlinearity it can be compensat-ed for. This nonlinearity arises from thesimplicity of the drive method and couldeasily be corrected with the consequenceof lower efficiency and higher mass.

Sensors and NavigationThe MicroGlider is fitted with an opticalflow sensor for obstacle avoidance andwith a target localizing sensor. This archi-tecture is biomimetic in nature and assuch, biomimetic sensor morphologiesand control strategies will be presentedand discussed in this section.

Target LocalizationA typical mission for the MicroGliderinvolves locating a target and descendingtoward it while avoiding obstacles. Twotarget localization sensors are proposedhere, however, the general controlarchitecture is identical for any of these.Minimal power and mass are empha-sized in the selection and design of sen-sor technologies.


Figure 9. Schematic of boost converter and chargepump stages used to create thehigh voltage supply.

3.3V

Enable LT1615-1

1 2 3 n - 1 nVb

...

...

Figure 10. MicroGlider power/control board (top side).

30 mm

10 m

m

Figure 8. (a) Schematics of amplifier. (b) Dual-source bimorphdrive method.

PWM

Vd

Vb

Vb

VdPZT

PZT

(a) (b)

First, inspired by the optical horizon detection sensorfound in many insects [24], a light source sensor called anocelli is developed for global orientation estimation [25]. Thissensor uses discrete photoreceptors (photodiodes or photo-transistors) to view distinct areas of the sky sphere. Pair-wisesubtraction of bilateral ocellus signals gives an estimate of thebody orientation with respect to a prominent light source.Figure 12 shows the output of a prototype ocelli when its ori-entation relative to a fixed light source is varied.

Second, tracking an audio source is possible via two micro-phones positioned at distant geometric locations on the glider.The sound signals detected by the two microphones are fedinto two hardware phase locked loops (PLLs) [16]. The volt-age controlled oscillator output of each PLL is a pulse trainphase locked to the input sound signal. This works well sincethe signal to be detected is expected to be narrow-band. Thetwo pulse trains are then fed into a hardware XOR gate. Bymeasuring the duration for which the XOR gate is high, theduration for which the two pulse trains have differing valuescan be calculated. Since the pulse trains are phase locked tothe incoming sound signals, the duty cycle of the XOR out-put is directly proportional to the phase difference of the twoincoming sound signals. This phase difference is proportional

to the direction of the target. The audio sensor was proto-typed and proved the concept by accurately detecting thesource location up to a distance of approximately 20 m.

Saccade-Based NavigationThe higher level navigation scheme is split into two dis-tinct phases: far field navigation and near field navigation,based on whether the MicroGlider is far from or near thetarget respectively.

In far field navigation, the controller attempts to fly theMicroGlider directly toward the target using one of the sen-sors described in the previous section. When the MicroGlider


Figure 11. Drive voltage Vd (solid) and power (dashed) as afunction of PWM duty cycle.

250

200

150

Driv

e V

olta

ge (

V)

Output P

ower (m

W)

100

50

00 20 40 60

Duty Cycle (%)

80 1000

1

2

3

4

5

Figure 12. Ocelli response to rotation in the presence of afixed light source.

1

0.5

0

Oce

lli O

utpu

t

−0.5

−1−40 −20 0

Horizon Angle (°)20 40

2 mm

Figure 13. Audio target localization overview.

Mic 1

Mic 2

HardwarePLL

HardwarePLL

XOR

Hardware

Software

PICProcessor Phase

Diff

Figure 14. Near field navigation scheme.

Saccade Triggered byOptic Flow Sensor

Saccade Triggeredby Target

Localizing Sensor

To determine the optimalMicroGlider airfoil design,

an empirical approach is used.

detects that it is sufficiently close to the target, the controllerswitches to a saccade-based homing algorithm inspired by thenavigation of real insects [26]. In this scheme (shown in Figure 14), the MicroGlider tries to keep the target directly tothe right (or left). In this manner, the aircraft flies without anynavigation input (i.e., in straight line segments) until either the

optical flow sensor detects an obstacle or the target is nolonger on its right (or left).

Optical Flow Architecture and ImplementationObstacles will be detected and avoided with the use of opticalflow sensing. Optical flow [27] is the apparent visual motionthat results from relative motion between an imager (oreyeball) and other objects in the environment (Figure 15).Consider an aircraft traveling in the forward direction. Theground will appear to move from front to back, with a ratethat increases as the aircraft approaches the ground or as theglider flies over tall objects. Objects in front of the aircraft willgrow in size, creating an expanding optical flow pattern. If theaircraft approaches a wall or tree line at an angle, the opticalflow in the direction of that object will increase, indicating animminent collision.

In order to integrate the imaging and image processingin a package suitable for integration onto the MicroGlider,a custom vision chip for optical flow processing has beendesigned. A die photograph of the vision chip is shown inFigure 16. This vision chip includes both image acquisitionand low-level image processing on the same die. Thearchitecture and circuitry is similar to that used in opticalflow sensors developed by Barrows in earlier work [28].The vision chip forms the focal plane of a camera-likeimaging system. The image itself is formed by a lens or apinhole. A 15-by-17 array of photoreceptors grabs a low-resolution image of the environment. An array of featuredetectors, implemented with simple analog circuits, com-putes the presence of edges, saddle points, or other featuresin the visual field. The last layer of processing on the visionchip analyzes the feature detector outputs, and generates asingle bit for each pixel. The bit is high or low indicatingthe presence or absence of a particular feature of interest.The optical flow processing is completed with a PIC18LF2520, identical to the master MicroGlider microcon-troller. Optical flow is computed by tracking the motion ofthe high bit values generated by the vision chip. The opti-cal flow sensor communicates with the power/controlboard using the I2C serial interface built into these micro-controllers.


Figure 16. Photograph of optical flow vision chip.

Figure 15. Optical flow, as seen from an aircraft.

Figure 17. 325 mg optical flow sensor prototype. The opticsover the vision chip have been removed for display purposes.

Tracking an audio source is possible via two microphonespositioned at distant geometriclocations on the glider.

Earlier versions of these optical flow sensors have beenfabricated in packages weighing 4.5 g, which is clearly tooheavy for the MicroGlider. However by using QFN-pack-aged PICs, extremely thin PC board material, and barevision chip dies, we have been able to reduce the mass of asingle optical flow sensor to 325 mg (with a pinhole lens).Figure 17 shows one prototype sensor, fabricated on thesame flex-circuit material as the power/control boardshown in Figure 10.

Obstacle avoidance will be performed using various flight-control strategies observed in flying insects. The reader isreferred to another paper [29] for a compilation of flightcontrol strategies. Sample strategies include turning away fromregions of high optical flow to avoid obstacles, equalizingoptical flow on the left and right sides to fly down a corridor,and making zig-zag flight patterns to detect narrow objects.

SimulationTo assist in design and testing, a software tool has beendeveloped to accurately simulate the MicroGlider in flight.This simulator is being used to quickly evaluate body designchanges to the MicroGlider and their effects in a virtualenvironment. In addition, the use of the simulator to testthe performance of different flight control algorithms hasbegun.

The simulator is a three-axis, six-degree-of-freedom simu-lator implemented in Matlab. The simulator combines classicrigid body dynamics with empirically measured MicroGliderparameters to calculate the state of the system during a virtualflight. The model parameters used in the simulator include

the mass and inertial matrix of the MicroGlider, the size andposition of various glider components, as well as the lift anddrag coefficients of the wings, body, and tail. These parame-


Figure 19. Left and right turns toward a light source. This image is the combination of a sequence of five video frames (the ini-tial flight direction is into the page and the sequence is labeled in ascending time order) where the gliders are indicated by thearrows and the light sources are the bright areas (marked with a “T”) on the left and right, respectively.

T T

1 1

2

2

5

5

4 43

3

Target on Left Target on Right

Figure 18. Simulated MicroGlider executing a steady turn tothe right after initial horizontal launch (arrows represent thelocal coordinate frame for each time step).

0

5

−6

−4

−2

0

4

6

8

10

x

y

z

ters can be modified to analyze their effects and maximizeflight performance.

In addition to simulating the trajectory of the MicroGlider,the simulator is used to estimate the response for the varioussensor configurations discussed in previous sections, as well asdifferent simulated environments. This allows the user to eval-uate what the MicroGlider perceives, and to utilize this infor-mation to design superior control strategies. As an example ofthe simulator functionality, Figure 18 shows the predictedresponse for a typical flight mode.

DiscussionThis article has concentrated on the development of a set ofcore technologies key to the realization of an autonomous 2-g glider. One aspect which was not discussed in detail wasthe ease of construction and low cost of an individualMicroGlider. Integration is simplified through a number ofrapid prototyping techniques and the low costs of most com-ponents allow rigorous testing to be done without worry ofsubstantial damage.

IntegrationThe five subsystems, control surfaces and fuselage, airfoil,control PCB, imager PCB, and battery are integrated togeth-er using molded short-fiber composite clips. This allows eachpiece to remain modular and its position with respect to theCG to be adjustable. Once each subsystem is completed, theglider is attached to a low friction model aircraft balance andthe position of each piece is selected to place the CG in thedesired position (with respect to the roll and pitch axes). Theeffect of altering the CG can be observed with the flight sim-ulator, however it is generally understood that it should beslightly forward and slightly below the center of lift for maxi-mum stability and maneuverability.

Initial Flight TestsTwo initial tests are described here which demonstrate thefunctionality of the MicroGlider: A turning test without astimulus and a test with bilaterally positioned light sourcesto trigger a turn. Both tests were performed in a controlledlaboratory environment using a custom launch apparatus toensure consistency in the initial flight conditions. The pur-pose of the first turning test (the open-loop test) is to cali-brate the MicroGlider response to control surface actuation.Once the turns were effectively tuned by adjusting the mag-nitude and timing of the control surface actuation, theMicroGlider was fitted with an ocelli and a light source was

positioned on either side. The controller was programmedto trigger a saccade toward the light source when it wasdetected on either side. Sample flight sequences are shownin Figure 19.

Note that Figure 19 shows the MicroGlider initiating aturn shortly after release in the direction of the target lightsource. This test demonstrated that the MicroGlider was ableto recognize a target stimulus in flight and react appropriately.

AcknowledgmentsThis material is based upon work supported by the NationalScience Foundation (NSF) under Grant IIS-0412541. Anyopinions, findings, conclusions, or recommendationsexpressed in this material are those of the author(s) and do notnecessarily reflect the views of the NSF. The authors wouldlike to gratefully acknowledge the Defense AdvancedResearch Projects Agency for support under Fund\#FA8650-05-C-7138.

KeywordsMicro air vehicles, aerial robotics, optical flow, target tracking.

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[7] S. Avadhanula, R. Wood, D. Campolo, and R. Fearing, “Dynamicallytuned design of the MFI thorax,” in Proc. IEEE Int. Conf. on Robotics andAutomation, Washington, DC, May 2002, pp. 52–59.

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[10] A. Cox, D. Monopoli, M. Goldfarb, and E. Garcia, “The developmentof pizeoelectrically actuated micro-air vehicles,” in Proc. SPIE Conf. onMicrorobotics Microassembly, Boston, MA, Sept. 1999, vol. 3834, pp. 101–108.

[11] A. Cox, D. Monopoli, D. Cveticanin, M. Goldfarb, and E. Garcia,“The development of elastodynamic components for piezo-electricallyactuated flapping micro-air vehicles,” J. Intell. Mater. Syst. Struct., vol. 13,pp. 611–615, Sept. 2002.

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The low costs of most componentsallow rigorous testing to be donewithout worry of substantialdamage.

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[14] J. Yan, R. Wood, S. Avadhanula, and M.S. amd R.S. Fearing, “Towardsflapping wing control for a micromechanical flying insect,” in Proc.IEEE Int. Conf. Robotics and Automation, Seoul, Korea, May 2001, pp.3901–3908.

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[27] J. Gibson, The Ecological Approach to Visual Perception. Boston, MA:Houghton Mifflin, 1950.

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sensing and flight control,” Aero. J. Royal Aero. Soc., vol. 107, no. 1069,pp. 159–168, Mar. 2003.

Robert J. Wood received a M.S. degree in 2001 and a Ph.D.in 2004, both in EECS from University of California atBerkeley. He is an assistant professor in the School of Engi-neering and Applied Sciences at Harvard University where hehas been since January 2006. His research interests include themechatronics of microrobotic devices, particularly mobilemicrorobots for aerial, terrestrial, and aquatic environments.He is also interested in the control of under-actuated proces-sor-limited systems.

S. Avadhanula is with the Dept. of Electrical Engineeringand Computer Sciences at University of California, Berkeley.

E. Steltz is with the Dept. of Electrical Engineering andComputer Sciences at University of California, Berkeley.

M. Seeman is with the Dept. of Electrical Engineering andComputer Sciences at University of California, Berkeley.

J. Entwistle is with the Dept. of Electrical Engineering andComputer Sciences at University of California, Berkeley.

A. Bachrach is with the Dept. of Electrical Engineering andComputer Sciences at University of California, Berkeley.

G. Barrows is with Centeye, Inc., Washington, DC.

S. Sanders is a professor in the Dept. of Electrical Engineer-ing and Computer Sciences at University of California,Berkeley.

Ronald S. Fearing received S.B. and S.M. degrees inelectrical engineering and computer sciences from MIT in1983 and a Ph.D. in electrical engineering from Stanford in1988. He is a professor in the Dept. of Electrical Engineer-ing and Computer Sciences at University of California,Berkeley, which he joined in January 1988. He was Vice-Chair for Undergraduate Matters from 2000-2006. His cur-rent research interests are in microrobotics, including flyingand crawling microrobots, microassembly, parallelnanograsping, and rapid prototyping. He has worked in tac-tile sensing, teletaction, and dextrous manipulation. Hereceived the Presidential Young Investigator Award in 1991,and is the coinventor on five U.S. patents.

Address for Correspondence: Robert J. Wood, School of Engi-neering and Applied Sciences, Harvard University, Cam-bridge, MA 02138 USA. E-mail: [email protected].


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3. TITLE (Its classification should be indicated by the appropriate abbreviation (S, C, R or U) Élaboration d'un contrôleur pour actionneurs piézoéléctriques

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Une solution alternative à l'utilisation de servomoteurs dans le cas de très petits véhicules aériens inhabités (UAV) est l'utilisation d'actionneurs piézo-électriques. Les actionneurs utilisés dans ce projet sont fabriqués par la compagnie APC, "American Piezo Ceramic" International. Pour les contrôler, la solution choisie consiste à générer une tension de 150 V sur les électrodes externes du piézo. Une tension entre 0 et 150 V est mise sur l'électrode centrale, de façon à contrôler la flexion de l'actionneur. La solution pour générer la tension continue est un convertisseur DC/DC de type hacheur Boost, qui a été testé et est fonctionnel. Pour générer une tension variable, cependant, la solution idéale est un amplificateur opérationnel en mode amplificateur non-inverseur. Cette pièce doit être conçue pour fonctionner à une tension élevée. En l'absence d'un tel composant, un second hacheur Boost a été conçu, et permet de générer une tension entre 24 et 150 V pour une tension d'entrée entre 0.8 et 5 V. Si la tension d'entrée descend sous 0.8 V, cependant, le hacheur sature. Les circuits ont été conçus pour fonctionner avec une tension d'alimentation de 24 V.

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piézo-éléctrique, actionneur, convertisseur, amplificateur, hacheur, DC, piezo-electric, actuator, power, driver, amplifier, buck-boost, boost, circuit

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