Pitch Rate Damping of an Aircraft by Fuzzy and Classical PD Controller

Transcription

1 Pitch Rat Damping of an Aircraft by Fuzzy and Classical PD Controllr YASEMIN ISIK Avionics Dpartmnt Anadolu Univrsity Civil Aviation School, 647, Eskishir TURKEY Abstract: - Aircraft dynamics ar in gnral nonlinar, tim varying, and uncrtain. A control systm (classical control systms) dsignd for a flight condition, may not provid th dsird stability and prformanc charactristics in cas of dviation from th quilibrium point. Thr ar numrous studis rgarding flight control in th litratur. On of thm is fuzzy flight control systm. Fuzzy logic controllrs (FLCs) from thir incption hav dmonstratd a vast rang of applicability to procsss whr th plant transfr function is not dfind but th control action can b dscribd in trms of linguistic variabls. FLC's ar also bing usd with improvd prformanc instad of classical" controllrs whr th plant transfr function is known. Most of th applications about th dsign of fuzzy flight control ar in simulation lvl. In this study, th dsign of fuzzy and classical PD controllr for th pitch rat damping systm is analyzd and th rsults for a two-ngind jt fightr aircraft ar valuatd in a MATLAB codd program. Ky-Words: - Aircraft, flight control, pitch rat, classical PD control, fuzzy and fuzzy PD control. Introduction Th aim of a flight control systm (FCS) of an aircraft is to maintain a saf and conomic opration. Thus, th dsird flight missions can b accomplishd vn undr unxpctd vnts. In th arly days of flight, safty was th main concrn of a flight control systm. Sinc th numbr of flights and numbr of popl using plans for travl has incrasd, safty is vn mor important. Aircraft dynamics ar in gnral nonlinar, tim varying, and uncrtain. Gnrally, th dynamics ar linarizd at som flight conditions and flight control systms ar dsignd by using this linarizd mathmatical modl of th aircraft. Howvr, som arodynamic ffcts ar vry difficult to modl rsulting in uncrtaintis in th aircraft dynamics and th dynamic bhavior of an aircraft may chang in a short priod of tim as a rsult of intrnal and/or xtrnal disturbancs. Thus, a control systm dsignd for a spcific flight condition may not b suitabl if th conditions chang from this flight condition. In this cas, th prformanc of th aircraft may b unsatisfactory Morovr, unxpctd situations such as changing wathr conditions and systm failurs ar difficult to modl and thus difficult to translat into appropriat classical control dsigns [,,3]. As th complxity of aircrafts incras, classical mthods bcom unsatisfactory to yild accptabl prformanc [] and com to its limits whn controllrs for MIMO (Multi-Input Multi-Output) systms with high intrnal coupling ar to b dsignd. For a highrnumbr passngr aircraft or a nw suprsonic commrcial transport, powrful and robust tchniqus ar rquird [4]. "Fly by Wir" allows th pilot to control th aircraft stats, as an altrnativ to th convntional dirct control of th ngins and control surfacs. It givs nw opportunitis to incras th ovrall lvl of safty through th flxibility offrd by th control laws. For xampl, rror-tolrant control laws provid flight nvlop protction, and hlp th pilot to rcovr from unusual attituds and succssfully achiv critical manouvrs. Th us of modrn FCS can b bnficial from an conomic point of viw. For crtain typs of aircraft, ful consumption can b rducd by allowing rlaxd static stability, countractd by th application of activ control. Anothr advantag rlatd to ful consumption is that for larg aircraft th wight of Fly by Wir systms is smallr than that of convntional systms. Most importantly, modrn FCS has contributd to improvd dynamical bhavior. For civil aircraft, prformanc can b incrasd by application of activ systms, for xampl to provid gust supprssion and auto-trimming, in ordr to achiv improvd rid quality. Th prformanc bnfits achivd hav th pnalty of trmndous costs involvd in th dvlopmnt of an advancd FCS [4]. Thr ar numrous studis rgarding flight control in th litratur such as adaptiv control [5,6], µ synthsis control [7,8,9], H control [,,], multi ISSN: Issu 7, Volum 5, July

2 modl control [3,4], nural control [5], adaptiv nural control [6,7], gain schduling control [8], control systm with a gntic algorithm optimization procss [9,] and fuzzy control [,]. Ths mthods hav many diffrnt faturs. A common fatur is that ach of thm is dvlopd to achiv advantags ovr classical tchniqus. Th classical approach in which ach mod and flight condition is tratd as a sparat problm has ld to mod prolifration and th nd for complx algorithms. To avoid functional intgration at th nd of th FCS dsign, which is too lat, an all ncompassing and consistnt dsign stratgy is ncssary. Throughout th dsign procss a "systms approach" stratgy should b applid, supportd by good rquirmnts, dsign tools and dsign modls. Application of advancd tchniqus promiss a significant rduction of dsign tim bcaus it would rmov th tim-consuming classical "onloop-at-a-tim" approach and rduc th numbr of dsign points for which a controllr has to b dsignd [4]. Among ths mthods, fuzzy systms hav diffrnt kinds of applications (rgulating th vlocity of a fright train, optimization trip tim and nrgy consumption of a high-spd railway, hlicoptr flight control sytm, control of hating, vntilating and air conditioning systms, hi-tch filming dvics (photo and rcording camras), washing machins, micro wav dvics, industrial control systms, high prformanc mdical instrumnts, railway vhicl control systms, autonomous vhicl control, such as trajctory tracking, or obstacl avoidanc tc.) in many aras [3,4,5,6,7]. Fuzzy control dpnds on th fuzzy algorithm btwn th information of procss and control input. Fuzzy controllrs from thir incption hav dmonstratd a vast rang of applicability to procsss whr th plant transfr function is not dfind but th control action can b dscribd in trms of linguistic variabls. Fuzzy controllrs ar also bing usd to improv th prformanc of a systm whr th plant transfr function is known [8,9]. In th litratur, thr ar diffrnt applications of fuzzy systms in aviation. Most of th applications about th dsign of fuzzy flight control ar in simulation lvl. NASA dvlopd a training simulator whr a fuzzy control is usd for STA (Shuttl Training Aircraft) that is modifid from a Gulf Stram II businss jt. Whn th STA was first dvlopd in 975 convntional linar control systms wr usd. Although ths systms prformd wll, thr wr aras that could b improvd. Th us of fuzzy control was invstigatd with th conclusion that implmnting it in th STA would improv th control systm prformanc. It also allows for a dsign basd on th physical charactristics of th plant, or STA, as opposd to th prvious dsign basd on an approximat mathmatical modl of th plant. This, plus th inhrnt structur of fuzzy control, allows for an asir implmntation of a complx nonlinar control systm. Th nonlinar charactristic of fuzzy control systms is th biggst advantag ovr th old linar control systm. In th nd, th fuzzy control systm s ovrall prformanc is bttr; it is mor than th original linar control systm. Th fuzzy control has improvd th simulation fidlity of th STA and consquntly astronaut training []. An approach basd on a fuzzy logic controllr was implmntd to control and rgulat th atmosphric plasma spray procssing paramtrs (arc currnt intnsity, total plasma gas flow, hydrogn contnt) to th in-flight particl charactristics (avrag surfac tmpratur and vlocity) []. Rsarchrs at th U.S. Burau of Mins, Univrsity of Alabama, and th U.S. Army, hav dvlopd a fuzzy systm for controlling th flight of UH- hlicoptrs through various manuvrs. A gntic algorithm is usd to discovr ruls for ffctiv control of th hlicoptr. Th prformanc of th controllr is tstd both in simulation and in actual flight. Th dvlopd fuzzy controllr architctur is gnral nough to b applicabl to a varity of rotorcraft. Moving th controllr to a nw hlicoptr simply rquirs discovring ruls for th fuzzy controllr [4]. Schram and Vrbruggn, mmbrs of th Group for Aronautical Rsarch and Tchnology in Europ (GARTEUR) dsignd a fuzzy controllr for th landing control of a two-ngin civil aircraft and got succssful simulation rsults [3]. A fuzzy controllr is dsignd for landing of an unmannd aircraft [3]. A fuzzy-logic "prformanc control" systm, providing nvlop protction and dirct command of airspd, vrtical vlocity, and turn rat, was valuatd in a rconfigurabl gnral aviation simulator (configurd as a Pipr Malibu) at th FAA Civil Arospac Mdical Institut. Prformanc of 4 individuals (6 ach of high-tim pilots, low-tim pilots, studnt pilots, and non-pilots) was assssd during a flight task rquiring participants to track a 3-D cours, from tak-off to landing, rprsntd by a graphical pathway primary flight display. Baslin prformanc for ach subjct was also collctd with a convntional control systm. All participants opratd ach systm with minimal xplanation of its functioning and no training. Rsults indicatd that th fuzzy-logic prformanc control rducd variabl rror and ovrshoots, rquird lss tim for novics to larn (as vidncd by tim to achiv stabl prformanc), rquird lss ffort to us (rducd control input activity), and was prfrrd by all groups [3]. ISSN: Issu 7, Volum 5, July

3 Fuzzy PD Control Fuzzy logic is a mthod of rul-basd dcision making usd for xprt systms and procss control that mulats th rul-of-thumb thought procss usd by human bings. Th basis of fuzzy logic is fuzzy st thory which was dvlopd by Lotfi Zadh in th 96s. Dfining a fuzzy controllr, procss control can b implmntd quickly and asily. Many such systms ar difficult or impossibl to modl mathmatically, which is rquird for th dsign of most traditional control algorithms. In addition, many procsss that might or might not b modld mathmatically ar too complx or nonlinar to b controlld with traditional stratgis. Howvr, if a control stratgy can b dscribd qualitativly by an xprt, fuzzy logic can b usd to dfin a controllr that mulats th huristic rul-of-thumb stratgis of th xprt. In othr words, fuzzy controllrs allows imprcis and qualitativ information to b xprssd in a quantitativ mannr. Thrfor, fuzzy logic can b usd to control a procss that a human can control manually with xprtis gaind from xprinc. Th linguistic control ruls that a human xprt can dscrib in an intuitiv and gnral mannr can b dirctly translatd to a rul bas for a fuzzy logic controllr. [5,3] Fuzzy Logic Controllrs can b usd to raliz th closd-loop control actions dirctly, i.. rplac convntional closd-loop controllrs, or thy can complmnt and xtnd convntional control algorithms via suprvision, tuning or schduling of local controllrs [4]. A gnral fuzzy controllr consists of four moduls: a fuzzy rul and data bas, a fuzzy infrnc ngin, and fuzzification /dfuzzification moduls. Th intrconnctions among ths moduls and th controlld procss ar shown in Figur. Most of th systms us fuzzy controllr is PD typ controllr. In this typ controllr, rror and chang of rror knowldgs ar usd in fuzzification and rul bas moduls. Fuzzy PD controllr calculats th appropriat control at th input of th systm according to th rror and chang of rror at th input. Whil dvloping such a systm th most important procss is ncoding th knowldg bas of fuzzy controllr. Th knowldg bas of th fuzzy PD controllr consists of data and rul bass. Mmbrship function distributions of systm input and output variabls ar dfind in data bas. Dtrmining of appropriat knowldg bas is a rathr difficult procss. For most applications, prsonal intuition, logic and xprincs ar usd to constitut knowldg bas. At this point, it is ncssary to hav adquat and propr knowldg. Howvr, in som situations, it is impossibl to gt nough knowldg. At this tim, it can b basd on som algorithmic or logical oprations. Th following list provids som of th mthods dscribd in th litratur to assign mmbrship valus or functions to fuzzy variabls. Intuitions, infrnc, rank ordring, angular fuzzy sts, nural ntworks, gntic algorithms, inductiv rasoning, soft partitioning, mta ruls and fuzzy statistics. Mmbrship functions of rror and chang of rror ar shown in Figur and 3, rspctivly. Mmbrship functions may b slctd as a triangular, trapzoid or othr appropriat forms. Bas valus of ths forms must b intrsctd with ach othr. Th rason of slcting triangular form is that ths mmbrship functions can b idntifid with minimum paramtrs. Ths paramtrs ar th projction of bass and top points of triangl on th and ɺ axs. Th numbr of mmbrship functions changs dpnding on th problm. Th numbr of ths linguistic variabls spcifis th quality of control, which can b achivd using fuzzy controllr. As th numbr of linguistic variabls incrass, th quality of control incrass at th cost of incrasd computr mmory and computational tim. Input + - u Fuzzification Infrnc Dfuzzification Systm Output Data bas Rul bas Fig. Closd loop fuzzy controllr ISSN: Issu 7, Volum 5, July

4 Thrfor, a compromis btwn th quality of control and computational tim is ndd to choos th numbr of variabls. In Tabl, for Sugno typ controllr, as th A, A..A n valus ar ral numbrs and shows rul wight valus, rror and chang of rror mmbrship functions ar dnotd with, C,.C n, D, D,.D n. According th tabl, numbr of ruls will b n [8,33,34,35]. Ths ruls ar; If = C and = D thn = A If = C and = D thn = A n+ If = C n and = D n thn = A n Tabl. Rul wight tabl u 3 Classical PD control PD typ controllr usd in this study bcaus th D ffct nsurs a rapid rspons, incrass damping and dcrass ris tim and sttling tim. As shown in Figur 4 th controllr output is qual to C C C n D A A A n ɺ D A n+ A n+ A n D n A n U( s) = ( K K s) E( s) () p + d µ ( ) C C C n C n C b C a C c C b C c C ( n ) a C ( n ) b C C ( n) a ( n ) c C ( n) b Fig. Error mmbrship functions µ ( ɺ ) D D D n D n D b D D a c D b D c D( n ) a D( n ) b Fig. 3 Chang of rror mmbrship functions D D ( n) a ( n ) c D ( n) b ɺ Input + - E(s) PD controllr U(s) K P + K s Systm d Output Fig. 4 Classical PD Control systm ISSN: Issu 7, Volum 5, July

5 Classical Control mthods ar also rigorously analysabl, and thrfor thy can b radily crtifid, and sinc thy contain rlativly fw componnts, th ffcts of failur of som of thos componnts can b assssd rlativly asily. Thr is a grat dal of xprinc concrning thir us and implmntation availabl within most vndors and airfram manufacturrs. Thir principal disadvantag is th tim takn to prform th dsign procss. It is common in industry for an xisting autopilot dsign to b modifid to suit a nw aircraft, as opposd to a compltly nw dsign bing prformd, and this rducs th dsign tim. A significant amount of knowldg concrning aircraft and thir charactristics is also rquird to support th dsign procdur sinc th optimisation of th controllr dpnds on th knowldg and intuition of th dsignr and not a computr algorithm [4]. 4 Aircraft Pitch Rat Damping Systm Aircraft pitch rat control systm shown in Figur 5. It can b sn from th Figur 5 that, lvator angl δ )(dltac) at th output of th controllr is ( E c calculatd such that th output of systm pitch rat (q) follows th rfrnc pitch rat valu (qd). Th input of actuator provids th chang of lvator angl of th input of aircraft dynamic via actuator transfr function. Controllr calculats th appropriat lvator angl at th input of th actuator. In this study, th dsign of fuzzy and classical PD controllr for th pitch rat damping systm is analyzd and th rsults for a two-ngind jt fightr aircraft ar valuatd in a MATLAB codd program. 5 Fuzzy PD Controllr Application and Simulation Rsults Th proposd fuzzy PD controllr applid to a twongind jt fightr aircraft data. Th flight paramtrs of slctd aircraft ar hight 65 m, Mach no., th dynamic prssur ( q ) 49 Nm -. Also in Figur 5, actuator dynamic is.745, snsor dynamic is 5.73, and aircraft dynamic for th abov flight condition is givn in Equation [36]. () In this study, typ of th dsignd fuzzy controllr is Sugno. So thr ar 5 wight valus. According to intuition mthod, list of linguistic ruls is shown in Tabl. In Tabl, for Sugno typ controllr, as th A, A..A n valus ar ral numbrs and shows rul wight valus, rror and chang of rror mmbrship functions ar dnotd with NVS (ngativ vry small), NS (ngativ small), ZE (zro), PB (positiv big) and PVB (positiv vry big). According th tabl, numbr of ruls will b 5. δ E c q δ E ( s) ( s).73 = s +.76s ( + s.68) Tabl. Rul wight valus NVS NS ZE PB PVB NVS.7.8. ɺ NS ZE PB PVB q d ɺ Fuzzy Controllr δ E c Actuator δ E Aircraft Dynamic q Snsor Fig. 5 Pitch rat damping systm In fuzzy PD controllr, fiv triangular mmbrship function forms for rror and fiv triangular mmbrship ISSN: Issu 7, Volum 5, July

6 function forms for chang of rror ar dtrmind which ar shown in Figur 6 and Figur 7. Bordrs of both function varis btwn ±5 rad/sn. µ ( ) NVS NS ZE PB PVB dltac (rad) Fig.6 Error mmbrship functions µ ( ɺ ) NVS NS ZE PB PVB Fig. 9 tim vs. lvator angl ɺ. Fig.7 Chang of rror mmbrship functions q (rad/sn) -. In codd MATLAB 7. basd program, in fuzzy PD controllr simulation rsults ( ), δ Ec ( dltac)), q), qɺ ) ) shown in th Figurs 8-5 rspctivly ar obtaind in cas of ± rad/sn pitch rat chang Fig. tim vs. pitch rat (rad). chang of q Fig. 8 tim vs. rror Fig. tim vs. chang of pitch rat ISSN: Issu 7, Volum 5, July

7 (r a d ) chang of q dltac (rad) Fig. tim vs. rror Fig. 3 tim vs. lvator angl Fig. 5 tim vs. Pitch rat chang As shown in Figurs 8-5, rsponss obtaind with a fuzzy PD controllr for th pitch rat hav som oscillation, ovrshoot is not short but ris tims and sttling tims of rsponss ar also short. By changing th rul wights in rul tabl and bordrs of mmbrship functions, it is possibl to gt diffrnt rsponss. 4 Classical PD Controllr Application and Simulation Rsults In classical PD controllr K p =-.8 and K d =-.5 ar chosn and th simulation rsults ( ), δ Ec ( dltac)), q), qɺ ) ) shown in th Figurs 6-3 rspctivly ar obtaind in cas of ± rad/sn pitch rat chang q (rad /sn). (rad /sn) Fig. 4 tim vs. pitch rat Fig. 6 tim vs. rror ISSN: Issu 7, Volum 5, July

8 .5 x dltac (rad).5 (rad/sn) Fig. 7 tim vs. lvator angl x -3 Fig. tim vs. rror.4..5 q (rad/sn) -. dltac (rad) Fig. 8 tim vs. pitch rat Fig. tim vs. lvator angl chan g of q q (rad/sn) Fig. 9 tim vs. chang of pitch rat Fig. tim vs. pitch rat ISSN: Issu 7, Volum 5, July

9 chang of q Fig. 3 tim vs. chang of pitch rat 5 Conclusion In this papr, th dsign of fuzzy and classical PD controllr for th aircraft pitch rat damping systm is analyzd and th rsults for an aircraft ar valuatd in a MATLAB codd program. As shown in simulation rsults, rsponss obtaind with fuzzy and classical PD controllr ar a good bit smooth and quit similar in both cass. Furthrmor whn fuzzy PD controllr applid, th sttling tim of rsponss is shortr than classical PD controllr and ovrshoot is smallr. Fuzzy controllrs from thir incption hav dmonstratd a vast rang of applicability to procsss whr th plant transfr function is not dfind but th control action can b dscribd in trms of linguistic variabls. Fuzzy controllrs ar also bing usd to improv th prformanc of a systm whr th plant transfr function is known. Using diffrnt mthods (Intuitions, infrnc, rank ordring, angular fuzzy sts, nural ntworks, gntic algorithms, inductiv rasoning, soft partitioning, mta ruls and fuzzy statistics) in dvloping mmbrship functions and rul wights, prformanc of th fuzzy controllr can b improvd. Rfrncs: [] A. Kahvcioglu, Flight control systm dsign using multi-modl approach and gntic algorithm, PhD Dissrtation, Univrsity of Anadolu,. [] A. Savran, R. Tasaltin and Y. Bcrikli, Intllignt adaptiv nonlinar flight control for a high prformanc aircraft with nural ntworks, ISA Transactions Vol.45, No., 6, pp [3] H.B. Vrbruggn, H.J. Zimmrman, R.Babuska, Fuzzy Algorithms for Control, Kluwr Acadmic Publishrs, 999. [4] Robust Flight Control, A Dsign Challng, Lctur Nots in Control and Information Scincs, Springr Brlin-Hidlbrg, 4/997. [5] K. J. Aström, B. WITTENMARK, Adaptiv control, Lund Institut of Tchnology, Addison Wsly Publishing Company, 989. [6] Exprinc with th X-5 adaptiv flight control systm, 68.pdf [7] D.F. Enns, Robustnss of dynamic invrsion vs. Mu synthsis: Latral-dirctional flight control xampl, Procdings of th AIAA Confrnc on Guidanc, Navigation, and Control, Portland, Orgon, (99). [8] J. R. Hays, D.G. Bats, LFT-basd uncrtainty modling and mu-analysis of th HIRM+RIDE flight control law, Proc. of th IEEE Intrnational Symposium on Computr Aidd Control Systms Dsign (CACSD ), Glasgow,, pp [9] M. F. AI-Malki, D.Wi Gu, Advantags of using µ- synthsis for fault-tolrant flight control systm, IFAC Fault Dtction, Suprvision and Safty of Tchnical Procsss, Bijing, Elsvir IFAC publication (6). [] R.A Nichols, t al, Gain Schduling for H-Infinity Controllrs: A Flight Control Exampl, IEEE Transactions on Control Systms Tchnology, Vol., No., 993, pp [] C. C. Kung, Nonlinar H robust control applid to F-6 aircraft with mass uncrtainty using control surfac invrs algorithm, Journal of th Franklin Institut, Vol.345, 8, pp [] I. Postlthwaita t al, Dsign and flight tsting of various H controllrs for th Bll 5 hlicoptr, Control Enginring Practic, Vol.3, 5, pp [3] Ackrmann, J., Multi-Modl Approachs to Robust Control Systm Dsign, Lctur Nots in Control and Information Scinc, Springr Vrlag,7, 985. [4] Magni, J. F. Multimodl ignstructur assignmnt in flight control dsign, Arospac Scinc and Tchnology, Elsivr Scinc, Vol.3, No.3, 999, pp.4-5. [5] Y. Li, Nuro-controllr dsign for nonlinar Fightr aircraftmanuvr using fully tund RBF ntworks, Automatica, Vol.37,, pp [6] M. Vijaya Kumar, A dirct adaptiv nural command controllr dsign for an unstabl hlicoptr, ISSN: Issu 7, Volum 5, July

10 Enginring Applications of Artificial Intllignc, Vol., 9, pp.8 9. [7] A. Savran, Intllignt adaptiv nonlinar flight control for a high prformanc aircraft with nural ntworks, ISA Transactions, Vol.45, No., 6, pp [8] S. L. Wua t al, Gain-schduld control of PVTOL aircraft dynamics with paramtr-dpndnt disturbanc, Journal of th Franklin Institut, Vol.345, 8 pp [9] C. D. Yang t al, Applications of Gntic-Taguchi Algorithm in Flight Control Dsigns, Journal of Arospac Enginring, Vol.8, No.4, 5, pp.3-4. [] R. Fantinutto t al, Flight control systm dsign and optimisation with a gntic algorithm, Arospac Scinc and Tchnology, Vol.9, 5, pp [] M. Jamshidi, A.Titli, L.Zadh, S. Bovri, Applications of fuzzy logic towards high machin intllignc quotint systms, Prntic Hall PTR, 997. [] A.-F. Kantaa t al, In-flight particl charactristics control by implmnting a fuzzy logic controllr, Surfac & Coatings Tchnology, Vol., 8, pp [3] O. Cordon t al, Tn Yars of Gntic Fuzzy Systms Currnt Framwork and Nw trnds, Fuzzy Sts and Systms, Vol 4, No., 4, pp [4] E. Sanchz, T. Shibata, L.A. Zadh, Gntic Algorithms and Fuzzy Logic Systms, Soft Computing Prspctivs, World Scintific Publishing Co. Pt. Ltd., 997. [5] M.S. Kim, Fuzzy Controllr Dsign with th Dgr of Non-uniformity for th Scald Activ String Tstbd in th Railway Vhicl, Wsas Transactions on Systms and Control, Vol.4, No.7, 9, pp [6] M. C. Popscu, A. Ptrisor, A. Drighiciu, Ptrisor, Fuzzy Control of th Position for th Piston of an Industrial Robot, th Wsas Intrnational Confrnc on Systms, Hraklion, Grc, July -4, 8, pp. -6. [7] I. Susna, G. Vasiliu, A. Filipscu, Ral-tim, mbddd fuzzy control of th Pionr3-DX robot for path following, th Wsas Intrnational Confrnc on Systms, Hraklion, Grc, July -4, 8, pp [8] E. Kiyak, Flight control applications with fuzzy logic mthod, Mastr of Scinc Thsis, Univrsity of Anadolu, 3. [9] S.K. Rotton t al,, Analysis and Dsign of a Proportional Fuzzy Logic Controllr, Dpartmnt of Elctrical Enginring Wright Stat Univrsity, Dayton, Ohio. [3] M. Livchitz, A. Abrshitz, U. Soudak, Dvlopmnt of an automatd fuzzy-logic- basd xprt systm for an unmannd landing, Fuzzy Sts and Systms, Vol. 93, No., 998, pp [3] D. B. Bringr, Applying Prformanc-Controlld Systms, Fuzzy Logic, and Fly-By-Wir Controls to Gnral Aviation, Civil Arospac Mdical Institut Fdral Aviation Administration Oklahoma City,, df [3] N.G. Bizdoaca, A. Ptrisor, E. Bizdoaca, Convntional Control and Fuzzy Control Algorithms for Shap Mmory Alloy basd Tndons Robotic Structur, Wsas Transactions on Systms and Control, Vol.3, No., 8, pp [33] V. Topuz, Fuzzy gntic procss control, PhD dissrtation, Univrsity of Marmara,. [34] T.J. Ross, Fuzzy Logic with nginring applications, McGraw-Hill, 995. [35] M. Duby, N.E. Mastorakis Tunning of Fuzzy Logic Powr Systm Stabilizrs using Gntic Algorithm in Multimachin Powr Systm, Wsas Transactions on Powr Systms, Vol.4, No.3, 9, pp [36] D. McLan, Automatic Flight Control Systms, Prntic Hall, 99. ISSN: Issu 7, Volum 5, July