Preliminary Design Rules for Electromechanical Actuation Systems Effects of Saturation and Compliances

Transcription

1 Preliinary Deign Rule for Electroechanical Actuation Syte Effect of Saturation and Coliance ABSTRACT Jian FU, Ion HAZYU, Jean-Charle MARÉ Intitut Cléent Ader, INSA-Touloue, Univerité de Touloue 35 Avenue du Rangueil, 3077, Touloue Cedex 4, France Electroechanical actuator (EMA) i a tye of ower-by-wire (PBW) actuator that i becoing widely ileented in aeroace indutry. Given the alication area, deigning an EMA i highly contrained in weight, integration ace, aintenance cot, dynaic erforance, reliability, etc. In order to reduce the EMA deign tie, cot and effort, all thee contraint hould be conidered in the reliinary deign tage. The roble i that at uch early deign tage, yte engineer need ile and exlicit odel. Thu, thi counication i atteting to forulate ile relation that account for torque and velocity aturation of the EMA a well a coliance effect on it dynaic erforance. The ile and araetric odel redict the ain iact of the izing variable on erforance. eyword: Aeroace, EMA, Flight Control, Preliinary Deign, Modeling and Siulation ABBREVIATIONS F e, F ex EMA out and aerodynaic action force [N] I, I DC ulied and otor current [A] J Inertia of the rotor [kg ] Poition controller gain [N/] Poition controller gain for eed liit control architecture [(rad/)/] v, v Claical and eed liited architecture velocity controller gain [N/(rad/)] k a, k, k t, k z Anchorage, nut-crew, traniion and tructural coliance [N/] k e EMA equivalent coliance [N/] M t, M, M EMA rod, equivalent flight urface and equivalent otor a [g] Lead of roller crew [] T r, T, T e, T li EMA reference, outut, electroagnetic and liit torque [N] t, t u, t Ideal iniu, unaturated and aturated reone tie [] U, U Sulied DC and otor voltage [V] V e, V ex EMA outut and aerodynaic linear velocity [/] x c, x e, x EMA coand, rod and flight urface oition [], T EMA rotation eed and torque aturation ratio [-], d Static oition and tatic diturbance tracking error [], u, Ideal unaturated and aturated overhoot [-] r,, li Motor reference, actual and liit velocity [rad/] n Natural frequency [rad/] Daing factor [-] BLDC, PMSM SHA, EHA, EMA LVDT PDE Bruhle Direct Current and Peranent Magnet Synchronou Motor Servo-Hydraulic, Electro-Hydrotatic and Electroechanical Actuator Linear Variable Dilaceent Tranducer Power Drive Electronic CEAS 05 aer no. 57 Page Thi work i licened under the Creative Coon Attribution International Licene (CC BY). Coyright 05 by author().

2 INTRODUCTION A the raid growth of air traffic arket in recent year, an-ade CO eiion into the atohere increaed largely by civil aviation. The aircraft indutry ha to face both econoic and environental iue []. Currently, an interi and attractive olution i toward More Electric Aircraft (MEA) uing ore electric ower technological advanceent for non-roulive yte of aircraft. Thi i a key te for the ultiate goal to achieve the All Electric Aircraft (AEA) [, 3], a far a to reduce aircraft weight and fuel conution. Therefore, for next-generation airlane, electrical ower network in lace of the conventional hydraulic, neuatic and echanical one are an inexorable trend. On thi bai, today aircraft actuation yte refer ower-by-wire (PBW) and have centered on novel aroache to deign and develo electrical ower actuator, uch a electro-hydrotatic actuator (EHA) and electroechanical actuator (EMA). Lat decade, nuber of invetigation exlored EHA technologie and achieved dee undertanding tudie in aeroace indutry. The EHA are already ileented in latet Airbu A380 and A350 airlane a backu for riary flight control. However, EHA reove only the central hydraulic ower ditribution, but interval ue of hydraulic in the actuator. EMA coared to EHA, eliinate all the hydraulic circuit, a how the ucceful alication in Boeing 787 for econdary flight control [4]. The ue of EMA i urued not only becaue of it clean energy but alo for fuel conution reduction (becaue of lower weight) and aintenance cot reduction for aircraft actuation yte [5]. Hence, EMA technologie are crucial for the concet of All Electric Aircraft. Neverthele, nowaday in aircraft flight control field, the aturity level of EMA technology i far behind that of conventional hydraulic actuator. One big challenge in EMA i jaing a reult of nuerou linkage echani. Thu at reent tage for the aircraft afety, introducing redundant ath or clutch device i indienable, but in thi way, it will increae extra weight and occuy ore intallation ace [6]. Thi i an undeired reult and incoatible olution for aircraft actuation yte deign and develoent. Therefore, weight aving and ize liit for EMA deign on bai of not to influence dynaic erforance and reliability. Electric Power Network Poition Coand Flight Control Couter (Electronic) Seed Power Drive Electronic Current M EMA Surface Aerodynaic Force Direct Drive or Gearbox Screw Poition Senor Figure : Overview of an EMA flight control actuation yte Currently, two tye of linear EMA are regarded for flight control alication: geared and direct drive. A hown in Figure, in the cae of the nut crew directly connect to the rotor of otor for a whole integration, thi architecture i direct drive. When the otor and echanical traniion are earated, the echanical ower i through a gearbox then to a nut crew echani, thi architecture i geared EMA. Whichever tye of EMA, the electric energy i converted into echanical one by a rotary electric otor which tranfer the echanic ower to the control urface through a gearbox and/or nut-crew echani. Direct drive EMA cancel the gear reduction and offer a high otential for geoetrical CEAS 05 aer no. 57 Page Thi work i licened under the Creative Coon Attribution International Licene (CC BY). Coyright 05 by author().

3 integration of the nut-crew reducer and the electric otor. Thi concet ay be lighter and ore coact, and thu ore uitable and coetitive for aeroace alication. The illutrative exale ued in thi counication i a linear direct drive aileron actuator. Firt, are exlained the dynaic erforance (tability, ettling tie and firt overhoot) under the aution of a linear odel of EMA. Since ultiloo control architecture i otly ued for the control of uch yte, linear control theory how that any deired dynaic can be achieved by the controlled yte (refer to ection 3 for the deontration). However, owing to the above-entioned contraint, the EMA oerate in condition that are not catured by the linear odel ued for controller deign. For intance, ince the airfrae i deigned to be a light a oible, the actuator anchorage coliance i not negligible. Since the driven load inertia and the force diturbance are iortant, the coliance of the EMA nut crew ay becoe a critical araeter. In thee condition, the couling between the tructural and the actuator dynaic alter the erforance of the whole actuation function that can even becoe untable. A the actuator i alo ubjected to a and volue contraint, the otor rated torque ha to be iniized. Conequently, thi liit introduce a aturation effect between the deanded and the roduced electroagnetic torque. Thu, thee technological liitation/ierfection ake the real erforance far different fro the erforance exected when a liner odel i ued for control deign. Moreover, ince the control becoe a contrained roble, oe erforance requireent ay be even unreachable. In thee condition the controller will have to live with thee liitation and till enure the required erforance. Thi counication i organized in 6 ection. Section introduce the tudy objective and contribution of thi aer. Section decrit the conidered EMA conit, then etablihe it linear atheatical odel and reent claic control tructure. In ection 3, the yte erforance requireent are introduced. Section 4 analyze the aturation effect and how oe iulation reult. Section 5 dicue the coliance effect and reent the reult of iulation. Finally, concluion are drawn in ection 6. EMA SYSTEM DESCRIPTION An equivalent linear EMA yte with the conventional cacade control architecture i illutrated in Figure : Here can be identified the current loo (inner loo), eed loo (iddle loo) and oition loo (outer loo). The control yte get oition reference fro the ilot/autoilot and calculate the duty cycle for the ower electronic in order to eet the EMA dynaic erforance requireent. Poition coand Control Syte Torque reference Electric Power PDE Dilaceen t Roller crew Motor Nut Senor Surface AerodynaIc Force Senor Current(torque) loo Seed loo Poition loo. Baic Structure Figure : Multiloo control tructure for a direct drive linear EMA yte In thi counication it i conidered that a direct drive linear EMA ha the following coonent: CEAS 05 aer no. 57 Page 3 Thi work i licened under the Creative Coon Attribution International Licene (CC BY). Coyright 05 by author().

4 . A control yte for oition control An electric otor (DC tye or 3-hae BLDC, PMSM) A ower drive electronic A current enor, a eed reolver and a LVDT A roller-crew traniion echani A flight urface. Silification and Aution In thi aer, the conidered dynaic erforance of the EMA yte are the tability the ettling tie and the firt overhot. Uually, the controller deign i baed on a liner odel of the yte, which i ot often of low order. However, technological liitation uch a torque/velocity aturation render the odel nonlinear while the reence of the coliance increae it order. We will tudy earately the iact of thee two effect. Therefore, three odel will be ued along the aer: a low order odel without aturation and coliance in order to exre the exected dynaic when the controller i deigned; a iulation odel that add aturation to the forer odel; and finally the third one odeling the effect of the coliance (but without the effect of the aturation). Along the three reented odeling tage, oe ilification and aution are conidered:.3 The bandwidth of the PDE and the current loo of the otor are uch higher (tyically 500Hz- Hz) a coared to the other two, o it can be neglected in our tudy. For the firt two odel, the anchorage, the joint between the otor and the roller-crew and the EMA rod are conidered erfectly rigid. The otor and roller-crew inertia are erged in a ingle lued inertia, while the rod a i neglected. The friction effect are neglected (correonding to the wort cae, affect yte tability) [7]. The backlah and reload in the EMA kineatic are neglected. The ower liitation and aturation are neglected in the third odeling. The digital ignal effect (delay, aling, quantizing, etc.) are neglected. Linear Virtual Prototye The cheatic of EMA functional architecture with it control yte i hown in Figure 3. We can identify all the three control loo. However, when the current loo i ignored, the inut of the otor (actually it echanical art) becoe the electroagnetic torque T e. If torque aturation of the otor i not conidered, the electroagnetic torque T e i equal to the coand of the velocity loo T r. Poition Coand c Control Syte G () U I T r PDE U T F e G v () Motor Nut-crew Surface + G i () I V e F ex V ex I x e x e Figure 3: Block diagra of EMA linear rototye architecture For the atheatical odeling of the controlled yte we can develo the following hyical equation. The torque balance at the otor haft i: CEAS 05 aer no. 57 Page 4 Thi work i licened under the Creative Coon Attribution International Licene (CC BY). Coyright 05 by author().

5 T T J () e ω The echanical ower tranferred fro rotational otion into tranlational one through the nut-crew i: Ve Fe T ω () The urface dynaic equation can be exreed a: F F M x (3) e ex For all angular dilaceent of the urface (aileron), it can be aued that: (4) e Alying Lalace tranfor to the uer equation () to (3), the dilaceent can be exreed a: Tr Fex 4 M J (5) It i worth entioning that equation (5) how that even a all otor inertia will reflect a huge equivalent a (becaue i very all) at the EMA rod level, which trongly affect the yte dynaic erforance: M 4 J J ( ) M (7) (6) Alo equation (6) how that the oen loo of the EMA linear odel i a econd order yte, with one air of ure iaginary ole. The abence of the daing i exlained by the deliberate oiion of the vicou friction, which correond to the wort cae cenario..4 Controller Deign On the bai of the EMA oen loo linear odel analyi, for a no daing and oor natural dynaic, a ile roortional oition controller cannot eet the cloed-loo requireent. One of the coon way get around thi roble i to deign a roortional derivative (PD) oition controller and/or to introduce a eed loo. Coaring thee two aroache for controller deign, the latter ha the clear advantage of: Uing the actual rotor eed CEAS 05 aer no. 57 Page 5 Thi work i licened under the Creative Coon Attribution International Licene (CC BY). Coyright 05 by author().

6 No need to derivate the inut oition coand ignal, thu reducing aling error No derivation of the eaureent noie Eay to earate anticiation and tabilization regulator. A oition and eed feedback will be ued for EMA control. The oition gain i [N/] and the eed gain i v [N/(rd/)]. The block diagra of the cloed-loo EMA yte i dilayed in Figure 4. Controller EMA F ex c T r T e T Fe M t Ve Ve J V ω ω Figure 4: Block diagra of the EMA control (linear odel) Note that on the uer EMA linear odel block diagra, the eed gain v ha the ae effect a the yte vicou friction coefficient. Since the latter i not alway known during the reliinary deign tage, the eed gain adjutent can be conidered a alternative rocedure for yte level friction odeling. The oition controlled cloed-loo tranfer function of EMA linear odel can be exreed a following: c Fex M J v (8) 3 PERFORMANCE REQUIREMENTS OF THE SYSTEM Generally, the regarded erforance requireent for cloed-loo control yte are ainly: Stability Raidity Accuracy for oition uruit and load rejection tracking error. For econd order yte, the dynaic erforance are coletely characterized by two araeter: the daing ratio and the natural frequency 0, which in our cae can be exreed a: ξ ωn v 3 ( M ) 3 M ( M M ) (9) CEAS 05 aer no. 57 Page 6 Thi work i licened under the Creative Coon Attribution International Licene (CC BY). Coyright 05 by author().

7 For a et of required dynaic erforance, ioed by the araeter ˆξ and ˆω n, the control araeter and v, can be obtained fro equation (9)-() a: ˆω n ( M M ) ˆ ˆ M M v ξω n ( ) ( ) (0) When for econd order yte the daing ratio equal 0.707, the yte i table with an overhoot of 5%. So an ideal inial reone tie t calculated a: if.9 ˆξ t () ˆω n Moreover, becaue of the ure integrator in the direct loo, the yte tatic tracking error for a te et-oint i zero. By ubtituting equation () into (9), the tatic diturbance error for load rejection can be exreed a: ε d Fex () Therefore, for the diturbance inut, with the low-frequency cloed-loo of EMA linear odel ha an equivalent tiffne of: k e (3) Thu, analyzing the uer reult, it can be concluded that the yte can achieve any required dynaic erforance. However, we can iagine that in the reence of ower liitation and technologic ierfection it i not oible to attain any required erforance. 4 SATURATION EFFECTS Maxial ower i alway a deign araeter for EMA. Maxiu voltage liit iact the axial otor eed while axiu current iact the axial otor torque. Thee aturation can be odeled a hown in Figure 5. Controller li T li c r T r T e v ( J J ) Seed aturation Electroagnetic torque aturation F ex Figure 5: Cacade controller conidering torque and velocity aturation for EMA CEAS 05 aer no. 57 Page 7 Thi work i licened under the Creative Coon Attribution International Licene (CC BY). Coyright 05 by author().

8 Note that thee two aturation will not alter the tability of the yte (if the unaturated yte i deigned to be table), which ai to identify and quantify the iact of the eed and torque aturation of the control EMA in order to take into account during the reliinary deign. Coared to the equation (), the nuerical exreion of controller gain can be written a: ' ˆω n v ˆξ ' ˆ ξω ˆ v v n ( ) ( M M ) (4) In the oition-controlled, when the et-oint alitude i c and the control yte i unaturated, the eed and torque reference are given a: ' ω r ( xc x ) T x x ' ' r [ ( c ) ω ] v (5) Thu we can etiate that the axial value of thee reference are: T ' ω rax x c x ' ' rax v c (6) In order to evaluate the influence of thee nonlinearitie on the dynaic erforance we can define the eed aturation ratio and torque aturation ratio a: ωli α ω [0, 00%] (7) ω rax Tli α T [0, 00%] (8) T rax Multile iulation of the aturated odel fro Figure 5 are carried out in MATLAB/Siulink, fro above equation, a known that the yte reone tie i a function of oition controller gain and EMA lead of nut-crew, the equivalent otor a doe not affect the reone tie, but require the eed controller gain to be adjuted. Firtly, a iulation work i aied to a ecific urface a (600 kg) and crew lead (.54 ) in EMA yte but varying the deired reone tie t in 5 tyical level: 0.0, 0.05, 0., 0.5, and, eanwhile change the equivalent otor a fro to 00 tie bigger than urface a. The iulation reult reented in Table, it how that the change otor equivalent a (variable otor inertia) for EMA deign ha nearly no influence on the erforance degradation for any reone tie deire but need to the eed controller to be adjuted at the ae tie. Therefore uing a ecific otor a for following tudy aturation effect i available. CEAS 05 aer no. 57 Page 8 Thi work i licened under the Creative Coon Attribution International Licene (CC BY). Coyright 05 by author().

9 T () Table : Ratio of reone tie obtained and reone tie deire T u /T Ratio of the equivalent otor a and urface a: M /M Then in next, the torque or eed aturation ratio were varied. For each value of the aturation ratio, different value of inertia, lead of the nut-crew and required cloed-loo natural frequency where teted a well. The obtained reult were ued to trace the degradation of the reone tie (in Figure 6) and firt overhoot (in Figure 7) a a function of the eed aturation and torque aturation. It turn out that inertia, nut-crew lead and the cloed-loo natural frequency do not have any iact on the curve reented in Figure 6 and 7 ( and v are autoatically recalculated for the new et of araeter). On the abcie, 0% ean that the aturation T li rereent a tenth of the axial unaturated coand while 00% ean that there i no aturation. The ae hold for the eed aturation. The iulation reult of Figure 6 and 7 how that lower ercentage eed aturation ha tronger effect for yte reone tie. A 0% eed aturation ratio will increae by 3 tie the reone tie coaring to the deired one obtained without aturation. However, it irove yte tability by reducing yte overhot. Regarding the torque aturation, it iact coniderably the reone tie when it get below 5%. It effect i very trong, on both the reone tie and the overhot li / rax 0% eed aturation 40% eed aturation 60% eed aturation 80% eed aturation no eed aturation Ideal reone tie log(t /t u ) Torque aturation,t li /T rax,% Figure 6: Dienionle reone tie deending on torque and eed aturation CEAS 05 aer no. 57 Page 9 Thi work i licened under the Creative Coon Attribution International Licene (CC BY). Coyright 05 by author().

10 Thu thee curve can be ued to extract oe bet ractice rule to be ued during reliinary deign of EMA, uch a: for a given et of dynaic erforance and yte araeter, The torque aturation of about 5-30% and eed aturation of 60% can be acceted. The cited value are given only a an illutrative exale if for intance a reone tie degradation of 50% i tolerated % eed aturation 40% eed aturation 60% eed aturation 80% eed aturation no eed aturation Ideal overhoot log( / u ) li / rax Figure 7: Dienionle firt overhoot deending on torque and eed aturation 5 COMPLIANCE EFFECTS Torque aturation,t li /T rax,% Mot of the analyi and reearch work on EMA yte ue a rigid odel where the actuator i rigidly attached between the ain tructure and the load. However, due to the harh environent and trend of integrated deign, the coliance ay becoe iortant and alter the yte tability [8]. A tructural diagra of EMA i decribed in Figure 8. Generally, it can be identified the anchorage (k a ) and traniion (k t ) tiffne coing fro the aircraft tructure, and the tiffne of the EMA nut-crew echani (k ). In order to conider the wort cae of control yte tability, the tructural daing coefficient are aued to be negligible. In thee condition oe ocillation of the control urface and the EMA aear fro the cobination of a (M, M t and M ) and coliance (k a, k and k t ). In ractice, the actuator body and rod ae are very all coared to the equivalent otor inertia (ee relation (6)), o they can be neglected. To ilify the analyi, the anchorage and traniion tiffne can be conidered in erie connection which give a ingle tructural tiffne (k z ), exreed a: k z kk a t k k a t (8) CEAS 05 aer no. 57 Page 0 Thi work i licened under the Creative Coon Attribution International Licene (CC BY). Coyright 05 by author().

11 Electric Power Torque deand T r PDE t Anchorage k a Motor Nut Roller crew M t Traniion k t Surface M External force F ex J k Figure 8: EMA configuration with tructural coliance The conidered control tructure in thi cae i till cacade control but the effect of the torque and eed aturation are not conidered here. The equivalent cheatic diagra with the controller i hown in Figure 8. Conidering a realitic integration of the oition enor, the oition feedback i obtained at the EMA rod level ( t ) and not at the control urface level ( ). Ignoring the rod a, the order of yte tranfer function i 4. The cloed-loo tranfer function for et-oint tracking (F ex = 0) i: kkz M ( ) t () k kz kt c () k k k k k k k M M 4 M [ ( M M ) M ] z z z v c v k kz k kz k kz k kz (9) The control urface oition when conidering the traniion coliance effect, can be exreed a: kz ( ) ( ) c M k z (0) The characteritic equation of the cloed loo yte becoe: k k k k k k k D M M M M M M 4 3 z z z ( ) 4 v [ ( c) ] 4 v k kz k kz k kz k kz () and cloed-loo tranfer function of load rejection ( c = 0) at the road level i: kz kz kk z M 4 v t () k kz k kz k kz () F ( ) D( ) ex The cloed-loo coliance tranfer function of the urface control level i: kkz k M 4 v () k kz k kt (3) F ( ) D( ) ex CEAS 05 aer no. 57 Page Thi work i licened under the Creative Coon Attribution International Licene (CC BY). Coyright 05 by author().

12 T e EMA k k z M M t M F ex ω t c T r G i () Controller v Figure 9: Equivalent cheatic of oition controlled EMA with coliance The firt tudied effect of the coliance i the verification of yte tability. For a fourth-order odel, eq. (3), the aroriated ethod to tudy tability i to ue the Routh Stability Criterion [9]. The obtained criterion for tability i: k k ˆω n ( M M ) (4) Equation (4) indicate that the yte tability deend only on the oition gain of the controller. Since the latter deend on the yte equivalent a and deired dynaic, we get another good ractice rule for reliinary deign. In order to reach a deire control erforance (reone tie), the coliance hould atify the contraint fro eq. (4). When conidering coliance effect, fro equation (4) for diturbance rejection. The tatic oition error under external load i: ε d ( ) Fex (5) k t Coaring equation (5) and (3), it how that the tructural coliance will reduce the cloed loo yte tiffne and increae the tatic diturbance. A iulation of oition erforance, coaring without and with coliance i given in Figure. A linear oition te coand c = 0 for flight urface i alied at t = 0., which i followed by a 0 N external aerodynaic force te occurring at t =.5 (diturbance). The controller wa deigned to get a deired reone tie T = 0.05 and a firt overhoot of < 5%. Note that et-oint tracking and diturbance rejection dynaic are very different: In the reence of coliance the urface dilaceent ha a big ocillation alitude with a frequency about 35 Hz, the realitic reone tie i 0.3, which i 6 tie longer than that of the ideal econdorder without coliance effect. Becaue of the traniion coliance the tatic diturbance iact i alo bigger. CEAS 05 aer no. 57 Page Thi work i licened under the Creative Coon Attribution International Licene (CC BY). Coyright 05 by author().

13 ε d Dilaceent (c) Phae (deg) Magnitude (db) Poition deand c Without coliance = t Surface dilaceent Rod dilaceent t Alied load Force load (N) Tie () Figure 0: Poition uruit and rejection conidering coliance 40 0 Increaing k k t = N/ t = Linear econd-order odel (without coliance) 8Hz, 4Hz, 8Hz, 30Hz, 3Hz, 34Hz, 35Hz -- Linear econd-order odel (without coliance) Increaing k Frequency (Hz) 0 Figure : Bode diagra of urface oition tracking with coliance effect CEAS 05 aer no. 57 Page 3 Thi work i licened under the Creative Coon Attribution International Licene (CC BY). Coyright 05 by author().

14 The frequency reone of the urface dilaceent with reect to the oition et-oint can be iulated, and the reult are hown in Figure. The ideal linear econd-order EMA odel without coliance i coared with the odel of variou coliance. The ractical traniion coliance k t i et to N/, we change the EMA echani coliance k in a ratio of 7 (fro 0 7 to N/) to vary the global yte coliance but with the ae controller deign. By alication of a trajectory for reone tie 0.05 that i urface frequency in 9Hz according to eq. (). In Figure, which how that firtly there i no reonant eak for linear econd-order odel (red dahed), and it i table in thi cae of controller deign. However, during k increaing (fro all to huge deign), the tability of odel conidering coliance i varying fro untable (firt 3 curve) to table (latet 4). Thi verifie the yte tability rule in eq. (4). Even though deigned an infinite EMA coliance, which only can eliinate the EMA rod reonance but not the urface reonance eak, becaue it exit realitic traniion coliance. Therefore, the coliance effect in EMA yte are cro-linked, which affect the coonent deign and whole yte dynaic erforance. 6 CONCLUSION In the reence of aturation and coliance it i iortant to ake available generic reliinary deign rule for electro-echanical oition actuation yte. Mechanical engineer can ue thee relation a bet ractice rule [0] for the ecification and reliinary deign of the echanical art, enabling the dynaic erforance requireent to be et in ractice. Control engineer ay ue thee deign rule to reduce the nuber of deign iteration through raid verification of conitency between cloed-loo erforance requireent and early choice and definition of the echanical coonent. It ha been hown that the erforance reduction becoe ignificant when the torque and eed aturation decreae to about 5% of the unaturated odel. Alo, becaue of tructural tiffne, the urface and rod dilaceent i not the ae and ay enter in reonance. To revent thi, eaier the control erforance hould be revied, eaier the echanical art hould be choen conecutively. REFERENCES []. Roboa, B. Sareni, and A. D. Andrade, "More electricity in the air: Toward otiized electrical network ebedded in ore-electrical aircraft," Indutrial Electronic Magazine, IEEE, vol. 6,. 6-7, 0. [] S. L. Botten, C. R. Whitley, and A. D. ing, "Flight control actuation technology for next-generation all-electric aircraft," Technology Review Journal, vol. 8, , 000. [3] W. Cao, B. C. Mecrow, G. J. Atkinon, J. W. Bennett, and D. J. Atkinon, "Overview of electric otor technologie ued for ore electric aircraft (MEA)," Indutrial Electronic, IEEE Tranaction on, vol. 59, , 0. [4] J. Roero, J. Ortega, E. Aldaba, and L. Roeral, "Moving toward a ore electric aircraft," Aeroace and Electronic Syte Magazine, IEEE, vol.,. 3-9, 007. [5] M. Villani, M. Turini, G. Fabri, and L. Catellini, "High reliability eranent agnet bruhle otor drive for aircraft alication," Indutrial Electronic, IEEE Tranaction on, vol. 59, , 0. [6] M. Todechi, "Airbu-EMA for flight control actuation yte-erective," in Recent Advance in Aeroace Actuation Syte and Coonent, Touloue, 00,. -8. [7] J.-C. Maré, "Friction odelling and iulation at yte level: a ractical view for the deigner," Proceeding of the Intitution of Mechanical Engineer, Part I: Journal of Syte and Control Engineering, , 0. [8] J.-C. Maré, "Electro hydraulic force generator for the certification of a thrut vector actuator," in Recent Advance in Aeroace Actuation Syte and Coonent, Touloue, 00, [9] F. Golnaraghi and B. uo, Autoatic control yte vol., 00. [0] J.-C. Maré, "Bet ractice in yte level virtual rototying - alication to echanical traniion in electroechanical actuator " in 5th International Workho on Aircraft Syte Technologie, Haburg, 05. CEAS 05 aer no. 57 Page 4 Thi work i licened under the Creative Coon Attribution International Licene (CC BY). Coyright 05 by author().