Received: Januay 3, 27 2 Speed Contol of a Doubly-Fed nduction Moto (DFM) Baed on Fuzzy Sliding Mode Contolle Loukal Keltoum * Benalia Leila Bouguea Abdeahmen Electical Engineeing Reeach Laboatoy, Depatment of Electical Engineeing, Mohamed Boudiaf Univeity of M Sila, Algeia * Coeponding autho Email: muohtlek@yahoo.f Abtact: The mean of thi pape i fuzzy liding mode contol of a Doubly Fed nduction Moto (DFM); it the coupling of the fuzzy logic contol and liding mode contol (SMC). The ue of the liding mode method povide vey acceptable pefomance fo DFM contol, and the chatteing phenomenon effect i alo eliminated by the fuzzy logic mode. n the fit pat, we caied out biefly a tudy of modeling on the full ytem. Thi model i intended to facilitate the pocedue fo etting and contolling the peed. We intoduced the paamete vaiation to tet the obutne of the contol law. The eult of ou imulation ae conducted to validate the theoy and indicate that the contol pefomance of the DFM i atifactoy and the popoed fuzzy liding mode contol (FSMC) can achieve favoable tacking pefomance. Keywod: Doubly Fed nduction Moto (DFM), Vecto Contol, Fuzzy Logic, Sliding mode, Fuzzy Sliding mode contol.. ntoduction Since the ealy yea of indutialization, the eeache wee faced with "how to contol the electic machine at vaiable peed." Electic dive equie high pefomance, inceaed eliability, and educed cot. Among thee machine i doubly fed induction machine (DFM) [-3] i an aynchonou machine with wound oto which can be upplied at the ame time by the tato and the oto with extenal ouce voltage [4]. t wa fit tudied to be ued a a high-peed moto. The many benefit of thi machine ae: educed manufactuing cot, elatively imple contuction, highe peed and do not equie ongoing maintenance. n ecent decade, the advance in technology of powe electonic and micocompute, diffeent application of DFM became poible. Thei inteet lie mainly in the peed contol option with and without mechanical eno a well a the egime in eithe moto o geneato opeation with flux contol powe fo hypo and hype-ynchonou featue [5]. Fo ntenational Jounal of ntelligent Engineeing and Sytem, Vol., No.3, 27 opeation at diffeent peed a convete PWM (Pule Width Modulation) mut be ineted between the machine and the netwok. Whateve the peed of the machine, the voltage i ectified and an invete connected to the netwok ide i eponible to enue conitency between the netwok fequency and that deliveed by the device. The DFM i eentially nonlinea, due to the coupling between the flux and the electomagnetic toque. The vecto contol o field oientation contol allow a decoupling between the toque and the flux [6] [7]. With the field oientation contol (FOC) method, induction machine dive ae becoming a majo candidate in high-pefomance motion contol application, whee evo quality opeation i equied. Fat tanient epone i made poible by decoupled toque and flux contol Sliding mode contol (SMC) technique, due to it ode diminution, ditubance elimination, obutne and imple ealization, i one of the popective contol methodologie fo electical machine [8] [9]. DO:.22266/ijie27.63.3
Received: Januay 3, 27 2 The main featue of SMC i the obutne againt paamete vaiation and extenal ditubance. Vaiou application of SMC have been conducted, uch a obotic manipulato, aicaft, moto, chaotic ytem, and o on [-2]. SMC ha been employed to the contol of the many type of machine. But becaue of the dicete law contol witch featue of SMC, the chatteing can occu in the contol ytem [3], [4 6]. Fuzzy logic i a potent tool fo contolling illdefined o paamete-vaiant plant. By genealizing Fuzzy ule, a Fuzzy logic contolle can cope well with evee uncetaintie. Fuzzy cheme with explicit expeion fo tuning can avoid the heavy computational buden [7-2]. n ode to educe o eliminate the phenomena chatteing, eeache have popoed the fuzzy liding mode [9] [2] [22], and the adaptive fuzzy liding mode contol fo Buhle Doubly Fed Machine [23] and in the powe ytem [24]. n thi wok, fo thei implicity and efficiency to captue the evee nonlineaitie of the DFM, the fuzzy liding mode contol will be ued. Till now, fuzzy liding mode contol ha been ued in vey few contol application uch a, nonlinea contol and the peed contol of machine. Nevethele it i till poible to achieve obutne and highly efficient dynamic uing a contol technique. Thi i the cae with the contolle peented heein whee a fuzzy liding mode contolle i deigned to achieve the peed tabilization of DFM. The peent wok deal with a fuzzy liding mode contolle method fo contolling the peed of DFM in a vectocontol mode. The pape i oganized a follow: n Section 2 mathematical model of the DFM i peented. n ection 3, we begin with the DFM oiented model in view of the vecto contol; next the tato flux ϕ S ae etimated. Fuzzy liding mode i peented in ection 4 and give the deign pocedue of the popoed contolle with the imulation eult given in ection 5. Finally, ome concluion ae dawn in ection 6. 2. Deciption and modeling of DFM n the taining of high powe a the olling mill, thee i a new and oiginal olution uing a double feed induction moto (DFM). The tato i feed by a fixed netwok while the oto by a vaiable upply which can be eithe a voltage o cuent ouce. The thee phae induction moto with wound oto i doubly fed when, a well a the tato winding being upplied with thee phae powe at an angula fequency ω the oto winding ae alo fed with thee phae powe at a fequency ω. The electical model of the DFM peented in figue, i expeed in a (d-q) ynchonou otating fame. 2. Refeence fixed elative to the otating field (d, q) Fo a efeence elated to the otating field, the following electical equation ae deduced: Vd R d d d d V q R q dt q q () Vd R d d d d V q R q dt q q (2) With,, V and V denote tato cuent, oto cuent, tato teminal voltage and oto teminal voltage, epectively. The ubcipt and tand fo tato and oto while ubcipt d and q tand fo vecto component with epect to a fixed tato efeence fame [25]. The fluxe ae given by: d ld Md q lq Mq d l d Md q l q Mq (3) Whee ϕ, ϕ,, and M epeent the tato flux, the oto flux, the tato inductance, the oto inductance and the mutual inductance, epectively. q Figue. Defining the eal axe of DFM fom the efeence (d, q) θ θ θob d Sa Ra ntenational Jounal of ntelligent Engineeing and Sytem, Vol., No.3, 27 DO:.22266/ijie27.63.3
Received: Januay 3, 27 22 Replace (3) in () and (2) we obtained: dd dd Vd Rd l M lq Mq dt dt dq dq Vq Rq l M ld Md dt dt dd d V d d R d l M l q M q dt dt dq dq Vq R q l M l d Md dt dt (4) Whee ω, ω, R and R denote tato pulation, oto pulation, tato eitance and oto eitance, epectively. 2.2 DFM model in the fom of tate equation Fo the DFM the contol vaiable ae the tato and oto voltage, [26] by conideing: An input-output cuent decoupling i et fo all cuent; The (d-q) fame i oiented with the tato flux; Due to the lage gap between the mechanical and electical time contant, the peed can be conideed a invaiant with epect to the tate vecto. Unde thee condition, the electical equation of the machine ae decibed by a time vaiant tate pace ytem a hown in (5) X A. X BU. Y C. X (5) With X, A, B, U, Y and C epeent the tate vecto, ytem tate evolution matix, matix of contol, vecto of the contol ytem, output vecto and output matix (obevation matix) epectively, Whee X i i i i (6) d q d q T Fom a matix epeentation: d L M q L M d dt d M L q M L a a2 a3 a4d a2 a22 a23 a24 q a3 a32 a33 a34 d a4 a42 a43 a44 q L M Vd L M Vq M L V d M L Vq Let: L Z L M L M, M L M L And a a2 a3 a4 a2 a22 a23 a24 a3 a32 a33 a34 a4 a42 a43 a44 a a22 a33 a44 R a2 L ; a3 ; a4 M a2 L ; a23 M; a24 a3 ; a32 ( ) M; a34 a4 ( ) M; a42 ; a43 ( ) L (8) U V V V V (7) d q d q Uing the fequently adopted aumption, like inuoid ally ditibuted ai-gap flux denity ditibution and linea magnetic condition and conideing the tato voltage (V d, V q) and oto voltage (V d, V q) a contol input, the tato cuent ( d, q), and the oto cuent ( d, q) a tate vaiable. ntenational Jounal of ntelligent Engineeing and Sytem, Vol., No.3, 27 T Then the equation (5) become: dx L. Z. X L. U (9) dt n analogy to equation (9) with equation (5) we find A=[L] -. [Z] and B=[L] -. [25] DO:.22266/ijie27.63.3
Received: Januay 3, 27 23 a a a3 a5 a a a5 a 3 A a4 a6 a2 a6 a4 a2 b b3 b b 3 B b3 b2 b3 b2 C () () (2) 3. Vecto contol by diect tato flux oientation To implify the contol we need to make a judiciou choice efeence. Fo thi, we place ouelve in a efeence (d, q) elated to the otating field with an oientation of the flux tato, accoding to the condition of the tato flux oientation. [27] [28] & (5) d q By eplacing (5) in () and (2) we obtain Vd R M d q q q L Vq R q d d Vd R d q * V q R q d d M (6) The toque equation become Whee a a RM LL R a a2 a3 L L M 4 a5 a6 b b2 L L L M b3 LL 2 M LL M R RM LL S L L, L ae tato and oto cyclic inductance, σ i edefined leakage facto. [26] The geneated toque of DFM can be expeed in tem of tato cuent and tato flux linkage a: PM Ce q. id d. iq (3) LS P i numbe of pole pai; n addition the mechanical dynamic equation i given by d J Ce C f (4) dt J, C e, C, and f denote the moment inetia of the moto, the electomagnetic toque, the extenal load toque and vicou fiction coefficient, epectively. Ω i the mechanical peed. C e q Equation (4) wa: d dt PM *. q L (7) S L S (8) PM.. RM q L * * *. Ce V q (9) Accoding to the equation (3) of the tato flux, then: d ( d Md ) L q ( q Mq ) L Fom the elation (2) and (4) (2) ntenational Jounal of ntelligent Engineeing and Sytem, Vol., No.3, 27 DO:.22266/ijie27.63.3
Received: Januay 3, 27 24 M d Vd d d T T M q Vq q q T The elationhip of the oto cuent (2) 2 M M d ( ) d Vd T LT L L L M d ( ) q Vd L LT L 2 M M q ( ) q Vq T LT L L L M d ( ) d Vq L L L The elationhip of the mechanical peed (22) d P. M C (. ) f q d (23) dt J. L J J Whee T = L /R and T = L /R ae tato and oto time-contant epectively. [2] 3. Stato flux etimato n the diect vecto contol tato flux oiented DFM, pecie knowledge of the amplitude and the poition of the tato flux vecto i neceay. n moto mode of DFM, the tato and oto cuent ae meaued wheea the tato flux can be etimated [26]. The flux etimation may be obtained by the following equation l M d d d l M q q q (24) The poition tato flux i calculated by the following equation: n which: (25) (26) dt, dt ω=pω and θ i the electical tato poition, θ i the electical oto poition. 4. Fuzzy liding mode contol of DFM Sliding mode contol i a vaiable tuctue contol (VSC). Baically, VSC include eveal diffeent continuou function which map the plant tate to the contol uface. The witching among thee function i detemined by the plant tate which i epeented by the witching function. [29] 4. Speed contol method To apply the liding mode contol theoy to the peed of DFM, follow the tep in the deign of a liding contol. The peed contol i done by contol the oto cuent d. So the contol law: ef eq q q q (27) The peed eo i defined by: e ef (28) The expeion of the peed contol uface: With S( ) ef (29) S( ) ef (3) Subtituting the expeion of Ὼ equation (23) in equation (3), we obtain: P. M C ( ) (. ) f S ef q d (3) J. L J J By eplacing the cuent d we obtain: S( ) ef PM.. JL. ef d eq q ef PM.. d C f q J. L J J Lyapunov function V defined by (32) ( ) 2 V S (33) 2 ntenational Jounal of ntelligent Engineeing and Sytem, Vol., No.3, 27 DO:.22266/ijie27.63.3
Received: Januay 3, 27 25 V S( ) S( ) (34) bn mn n ze p mp bp Duing the convegence of lyapunov function, the condition Ṽ (Ω) = S (Ω).Ṡ (Ω) < mut be checked. n the liding mode and in pemanent egime, we have S(Ω)=, Ṡ(Ω)=, q=. Whee the equivalent contol i: eq JL. C f q ef ef PM.. J J d Theefoe, the coection facto i given by: q (35) K. Sign S( ) (36) To veify the ytem tability condition, the contant K q mut be poitive. 4.2 Fuzzy liding mode contolle deign The conventional liding mode contolle poduce high fequency ocillation in it output, cauing a poblem known a chatteing. The chatteing i undeiable becaue it can excite the high fequency dynamic of the ytem. To eliminate chatteing, a continuou fuzzy logic contol u f i ued to appoximate the dicontinuou contol K q ign(s(ω)), (Fig. 2). We choe the tiangula and tapezoidal membehip function becaue of the implicity of implementation, when the numbe of the function inceae the tability inceae. The membehip function fo input and output vaiable ae choen in Fig. 3. y d + deied State eal State - e Sliding Suface Figue.2 Fuzzy Sliding Mode contol of the peed q Equivalent Command S FLC u eq + u + u f DFM y.8.6 µ.4.2.8.6 µ.4.2 - -.5.5 e(k) and Δe(k) (a) (b) Figue.3 Membehip function fo the input and the output [3]: (a) input and (b) output Δe(k) bn mn n ze p mp bp.2.4.6.8 q Table. Fuzzy tuning ule fo output e(k) bn mn n ze p mp bp bn bn bn bn bn ze ze ze mn bn bn mn mn ze ze ze n bn bn n n p p mp ze bn mn n ze p mp bp p mn n n p p bp bp mp ze ze ze mp mp bp bp bp ze ze ze bp bp bp bp Table how the linguit ule ued in the Fuzzy Logic Contolle. n thee table, n, p, ze,, m, b epeent negative, poitive, appoximately zeo, mall, medium, and big epectively. Fo example bn mean big negative, and o on. The linguitic ule of FSM contolle ae: if Si i Ai and Si i Bi then u fi i Ci (35) Whee A i, B i and C i ae the fuzzy et coeponding to S i, ΔS i and u fi epectively. ntenational Jounal of ntelligent Engineeing and Sytem, Vol., No.3, 27 DO:.22266/ijie27.63.3
Received: Januay 3, 27 26 Table 2. DFM paamete [25] Definition Symbol Value DFM Mechanical P w 4 kw Powe Stato voltage oto voltage Nominal cuent Un Un n 38 V 22 V 3.8/2.2 A Nominal mechanical n peed 42 pm Nominal tato and n oto fequencie 5 Hz Pole pai numbe P 2 Stato eitance oto eitance Stato elf inductance oto elf inductance R R L L.98 Ω.94 Ω.44 H.556 H mutual inductance M.26 H Moment of inetia J. Kg.m2 fiction coefficient f. S 5. Reult and dicuion n thi ection, imulation eult ae peented to illutate the pefomance and obutne of popoed contol law when applied to the DFM. The paamete value of the moto a hown in Table. 2. The moto i opeated at 57 ad/ unde no load and a load ditubance toque (5 N.m) i uddenly applied at t=.6 and eliminated at t=.6 (-5 N.m), and the oto eitance vaiation (inceae at % of nominal value oto eitance), while the othe paamete ae held contant. 5. Compaion between SMC and FSMC The epone of peed, toque, tato flux and oto cuent ae hown in Figue 4-. The fuzzy logic contol i ued to mimic the hitting contol law to emove the chatteing. Compaed with the conventional liding mode contolle, the fuzzy liding mode contol ytem eult in obut contol pefomance without chatteing. The chatteing fee impoved pefomance of the FSMC make it upeio to conventional SMC, and etablihe it uitability fo the ytem dive. peed (ad/) 6 4 2 8 6 4 2 deied SMC.5.5 2 time () Figue.4 Reult of the peed with Sliding mode contolle peed (ad/) 6 4 2 8 6 4 2 deied FSMC.5.5 2 time () Figue.5 Reult of the peed with Fuzzy Sliding mode contolle toque (N.m) 3 25 2 5 5 C Toque -5.5.5 2 time () Figue.6 Reult of the toque with Sliding mode contolle ntenational Jounal of ntelligent Engineeing and Sytem, Vol., No.3, 27 DO:.22266/ijie27.63.3
Received: Januay 3, 27 27 toque (N.m) 3 25 2 5 5 C Toque tato flux (Wb).5.5 -.5 F-d F-q -5.5.5 2 time () Figue.7 Reult of the toque with Fuzzy Sliding mode contolle The eult of the peed contol have hown that the contol with fuzzy liding mode contolle enue good dynamic pefomance with epect to the contol with liding mode contolle even in the peence of paametic vaiation and extenal ditubance. We emak in the Fig. 7 a net amelioation of the eult of the fuzzy liding mode method compaed with the liding mode method. n fact, the elimination of the chatteing poblem pemit the moothne of the contol law. tato flux (Wb).5.5 -.5 F-d F-q -.5.5 2 time () Figue.8 Reult of the oto cuent with Sliding mode contolle -.5.5 2 time () Figue.9 Reult of the oto cuent with Fuzzy Sliding mode contolle oto cuent (A) 3 2 -.5.5 2 time () Figue. Reult of the tato flux with Sliding mode contolle oto cuent (A) 3 2 -.5.5 2 time () Figue. Reult of the tato flux with Fuzzy Sliding mode contolle ntenational Jounal of ntelligent Engineeing and Sytem, Vol., No.3, 27 DO:.22266/ijie27.63.3
Received: Januay 3, 27 28 6. Concluion and futue wok n thi pape, the peed egulation of DFM with two contolle, liding mode (SMC) and fuzzy liding (FSMC) contolle ha been deigned and imulated. The compaative tudy how that the FSMC contolle can be impove the pefomance of peed of the DFM contol. The imulation eult have confimed the efficiency of the FSMC contolle fo diffeent woking condition. The eult how that the FSMC contolle ha good pefomance, and it i obut againt exteio petubation. n the futue wok we popoe anothe contol technique fo example the type 2 fuzzy liding mode contolle, fuion of neual netwok with fuzzy technique, high-ode liding mode contol and the adaptive inteval type 2 fuzzy contolle of the DFM. Refeence [] P. E. Vidal, Commande non-linéaie d'une machine aynchone à double Alimentation, Doct. Thei, Dept. of Elect. Eng., National Polytechnic ntitute of Touloue, Fance, 24. [2] G. Salloum, Contibution à la commande obute de la machine aynchone à double alimentation, Doct. Thei, Dept. of Elect. Eng, National Polytechnic ntitute of Touloue, Fance, 27. [3] M. S. Vicato and J. A. Tegopoulo, A Doubly-fed induction machine diffeential dive model fo automobile, EEE Tan. Ene. Conv., Vol. 8, No. 2, pp.225-23, 23. [4] Y. Bekaka, D. Ben attou, Speed and flux contol fo DFOC of doubly fed induction machine uing liding mode contolle, Acta Electotechnica et nfomatica, Vol., No. 4, pp.75-8, 2. [5] J. C. Pecott, B.P. Raju, The inheent intability of induction moto unde condition of double upply, n: Poc. of the EE, The ntitute of Electical Enginee Monogaph, Vol. 5, No. 7, pp.39-33, 958. [6] E. Blachke, The pincipe of field oientation a applied to the new tanvecto cloed loop contol ytem fo otating field machine, Siemen Review, Vol. 34, pp.27-22, 972. [7] M. Chaai, M. Soltani, M. Goa, Compaative tudy between the conventional egulato and fuzzy logic contolle: application on the induction machine, ntenational Jounal of Science and Technique of Automatic contol & compute engineeing J-STA, Vol., No. 2, pp.96-22, 27. ntenational Jounal of ntelligent Engineeing and Sytem, Vol., No.3, 27 [8] A. Boucheta,. K. Bouehane, A. Hazzab, B. Mazai, M. K. Fellah, Fuzzy-Sliding Mode Contolle fo Linea nduction Moto Contol, Rev. Roum. Sci. Techn. Électotechn. et Éneg., Vol. 54, No. 4, pp.45-44, 29. [9] A. Bouguea, S. Zeghlache, K. Loukal, D. Saigaa, Fault Toleant Fuzzy Sliding Mode Contolle of Buhle DC Moto (BLDC MOTOR), the Mediteanean Jounal of Meauement and Contol, Vol. 2, No. 2, pp.585-597, 26. [] Y. J. Huang and T. C. Kuo, Robut poition contol of DC evomechanim with output meauement noie, Elect. Eng., Vol. 88, No. 3, pp.223-238, 26. [] P. Guan, X. J. Liu, and J. Z. Liu, Adaptive fuzzy liding mode contol fo flexible atellite, Engineeing Appl. Ati ntelli., Vol. 8, No. 4, pp.45-459, 25. [2] H. S. Choi, Y. H. Pak, Y. S. Cho, and M. Lee, Global liding-mode contol impoved deign fo a buhle DC moto, EEE Contol Sytem Magazine, Vol. 2, No. 3, pp.27-35, 2. [3] M. Zhiwen, T. Zheng, F. Lin, X. You, A New Sliding-Mode Cuent Contolle fo Field Oiented Contolled nduction Moto Dive, EEE nt. Conf. AS, pp.34-346, 25. [4] J. J. Slotine, Applied nonlinea contol, Pintice Hall, 996. [5] V.. Utkin, Sliding Mode Contol Deign Pinciple and Application to Electic Dive, EEE Tan. nd. Elect., Vol. 4, No., pp.23-36, 993. [6] R. J. Wai, Adaptive Sliding-Mode Contol fo nduction Sevomoto Dive, EE Poc. Elec. Powe Appl., Vol. 47, No. 6 pp.553-562, 2. [7] A. J. Kohkouei and A. S.. Zinobe, Sliding mode contolle-obeve deign fo SSO linea ytem, nt. J. ytem Science, Vol. 2, pp.363-373, 998. [8] S. V. Dakunov and V.. Utkin, Sliding mode contol in dynamic ytem, nt. J. Contol, Vol. 55, No. 4, pp.29-37, 992. [9] T. C. Manjunath, Deign of Moving Sliding Suface in A Vaiable Stuctue Plant & Chatteing Phenomena, ntenational Jounal of Mechanical, Aeopace, ndutial, Mechatonic and Manufactuing Engineeing, Vol., No. 9, pp.536-542, 27. [2] M. G. Sawe, M. A. Rafiq and B. C. Ghoh, Sliding Mode Speed Contolle of a D.C Moto Dive, Jounal of Electical Engineeing, The ntitution of Enginee, Bangladeh,Vol. 3, No. & 2, 24. DO:.22266/ijie27.63.3
Received: Januay 3, 27 29 [2] K. M. Aun Paad, A. Unnikihnan, N. Uha, Fuzzy Sliding Mode Contol of a Switched Reluctance Moto, Pocedia Technology, Vol. 25, pp.735-742, 26. [22] Y. Yuntao and L. Yan, A Novel Senole Fuzzy Sliding-Mode Contol of nduction Moto, ntenational Jounal of Contol and Automation, Vol. 8, No. 9, pp.-, 25. [23] Z. Shao, Y. Zhan, Adaptive Fuzzy Sliding Mode Contol fo Buhle Doubly Fed Machine, Second ntenational Sympoium on Computational ntelligence and Deign, Vol. 2, pp.73-77, 29. [24] F. Rahidi, M. Rahidi, H. Amii, An adaptive fuzzy liding mode contol fo powe ytem tabilize, ndutial Electonic Society, the 29 th Annual Confeence of the EEE, Vol., pp.626-63, 23. [25] L. Benalia, Contol of a double feed and double ta induction machine uing diect toque contol, Pof. Moulay Taha Lamchich (Ed.), ntech, pp.3-26, 2. [26] D. Ben Attou and Y. Bekaka, Speed contol of a doubly fed induction moto uing fuzzy logic technique, ntenational Jounal on Electical Engineeing and nfomatic, Vol. 2, No. 3, pp79-9, 2. [27] M. Machmoum, F. Poitie, L. Moeau, M. E. Zaim and E. Le- doeuff, Etude d éolienne à vitee vaiable baée u de machine aynchone (MAS-MADA), Polytechnic ntitute of Nante, Fance, 23. [28] A. Faokh payam, M. Jalalifa, Robut peed enole contol of doubly-fed induction machine baed on input-output feedback lineaization contol uing a liding-mode obeve, ntenational confeence on powe electonic, dive and enegy ytem, Vol., No., pp.392-4, 2. [29] F. Xiang, Block-oiented nonlinea contol of pneumatic actuato ytem, Doctoal thei, Depatment of Machine Deign, Royal ntitute of Technology, Sweden, 2. [3] H. A. Mohammad, C. Abba, Z. Youmin, Fault-Toleant Fuzzy Gain-Scheduled PD fo a Quadoto Helicopte Tetbed in the Peence of Actuato Fault, FAC Confeence on Advance in PD Contol PD'2, pp.28 3, 22. ntenational Jounal of ntelligent Engineeing and Sytem, Vol., No.3, 27 DO:.22266/ijie27.63.3