Pitch Rate Damping of an Aircraft by a Fuzzy PD Controller

Transcription

1 Pitch Rat Damping of an Aircraft by a Fuzzy PD Controllr YASEMIN ISIK Avionics Dpartmnt Anadolu Univrsity Civil Aviation School, 2647, Eskishir TURKEY yaisik@anadolu.du.tr 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. In this study an aircraft pitch rat damping is valuatd by using a fuzzy PD controllr. Ky-Words: - Aircraft, flight control, pitch rat, fuzzy and fuzzy PD control. Introduction Th aim of a flight control systm 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 [,2]. As th complxity of aircrafts incras, classical mthods bcom unsatisfactory to yild accptabl prformanc [2] 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 [3]. Now, svral controllr dsign mthods wr dvlopd to achiv advantags ovr classical tchniqus. Som of th advantags ar: nhancd prformanc, improvd fficincy and simplification of th dsign procss. Thr ar numrous studis rgarding flight control in th litratur such as adaptiv control [4,5], µ synthsis control [6,7,8], H control [9,,], multi modl control [2,3], nural control [4], adaptiv nural control [5,6], gain schduling control [7], control systm with a gntic algorithm optimization procss [8,9] and fuzzy control [2,2]. 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 tc.) in many aras [22,23]. Most of th applications about th dsign of fuzzy flight control ar in simulation lvl. Som of ths studis ar as follow, a fuzzy controllr for landing of an unmannd aircraft, a fuzzy controllr for th landing control of a two-ngin civil-aircraft and hlicoptr flight control systm [23,24,25,26]. 2 Fuzzy PD Control 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 [3]. 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. An xampl of a rul tabl also usd in simulations is shown in Tabl. In Tabl, for Sugno typ controllr, as th A, A2..An valus ar ral numbrs and shows rul ISSN: ISBN:

2 Input + - u Fuzzification Infrnc Dfuzzification Systm Output Data bas Rul bas Fig. Closd loop fuzzy controllr 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 25 [27,28,29]. Ths ruls ar; If = NVS and ɺ = NVS thn u =A If = NVS and ɺ = NS thn u =A 2 If = PVB and ɺ = PVB thn u =A 25 u Tabl. Rul wight tabl NVS NS ZE PB PVB 3 Aircraft Pitch rat damping systm Aircraft pitch rat control systm shown in Figur 2. It can b sn from th Figur 2 that, lvator angl ( )(dltac) at th output of th controllr is calculatd such that th output of systm pitch rat (q) follows th rfrnc pitch rat valu (q d ). Th input of actuator E provids th chang of c 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 PD controllr for th aircraft pitch rat control systm is analyzd and th rsults for a two-ngind jt fightr aircraft ar valuatd in a MATLAB codd program. ɺ NVS A A 2 A 3 A 4 A 5 NS A 6 A 7 A 8 A 9 A ZE A A 2 A 3 A 4 A 5 PB A 6 A 7 A 8 A 9 A 2 PVB A 2 A 22 A 23 A 24 A 25 q d ɺ Fuzzy Controllr Actuator E Aircraft Dynamic q Snsor Fig. 2 Pitch rat damping systm ISSN: ISBN:

3 4 Fuzzy PD Controllr Application and SimulationRsults 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.2, th dynamic prssur ( q ) 249 Nm -2. Also in Figur 2, actuator dynamic is.745, snsor dynamic is 5.73, and aircraft dynamic for th abov flight condition is givn in Equation [3]. q s s.68 = 2 E ( s) s +.76s () In this study, typ of th dsignd fuzzy controllr is Sugno. So thr ar 25 wight valus. According to intuition mthod, list of linguistic ruls is shown in Tabl 2. ( ) Tabl. 2 Rul wight valus ( ) NVS NS ZE PB PVB NVS ɺ NS ZE PB PVB In fuzzy PD controllr, fiv triangular mmbrship function forms for rror and fiv triangular mmbrship function forms for chang of rror ar dtrmind which ar shown in Figur 3 and Figur 4. Bordrs of both function varis btwn ±5 rad/sn. µ ( ɺ ) (ra d / s n ) d lt a c (ra d ) NVS NS -2.5 ZE 2.5 Fig. 5 tim vs. rror 5 PVB Fig.4 Chang of rror mmbrship functions PB ɺ -.2 µ ( ) NVS NS ZE PB PVB Fig. 6 tim vs. lvator angl Fig.3 Error mmbrship functions In codd MATLAB 7. basd program, in fuzzy PD controllr simulation rsults ( f ( t, ), f ( t, Ec ( dltac )), f ( t, q) ) shown in th Figurs 5- rspctivly ar obtaind in cas of ± rad/sn pitch rat chang. q (rad /s n) Fig. 7 tim vs. pitch rat ISSN: ISBN:

4 d lt a c ( r a d ) (r a d /s n ) Fig. 8 tim vs. rror q (r a d /s n ) Fig. 9 tim vs. lvator angl Fig. tim vs. pitch rat As shown in Figurs 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. 5 Conclusion In this papr, th dsign of fuzzy 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 PD controllr ar a good bit smooth. 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, 2. [2] 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.2, 26, pp [3] Robust Flight Control, A Dsign Challng, Lctur Nots in Control and Information Scincs, Springr Brlin-Hidlbrg, 224/997. [4] K. J. Aström, B. WITTENMARK, Adaptiv control, Lund Institut of Tchnology, Addison Wsly Publishing Company, 989. [5] Exprinc with th X-5 adaptiv flight control systm, 68.pdf [6] 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). [7] 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 2), Glasgow, 22, pp ISSN: ISBN:

5 [8] 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 (26). [9] R.A Nichols, t al, Gain Schduling for H-Infinity Controllrs: A Flight Control Exampl, IEEE Transactions on Control Systms Tchnology, Vol., No.2, 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, 28, pp [] I. Postlthwaita t al, Dsign and flight tsting of various H controllrs for th Bll 25 hlicoptr, Control Enginring Practic, Vol.3, 25, pp [2] Ackrmann, J., Multi-Modl Approachs to Robust Control Systm Dsign, Lctur Nots in Control and Information Scinc, Springr Vrlag,7, 985. [3] Magni, J. F. Multimodl ignstructur assignmnt in flight control dsign, Arospac scinc and tchnology, Elsivr Scinc, Vol.3, No.3, 999, pp.4-5. [4] Y. Li, Nuro-controllr dsign for nonlinar Fightr aircraftmanuvr using fully tund RBF ntworks, Automatica Vol.37, 2, pp [5] M. Vijaya Kumar, A dirct adaptiv nural command controllr dsign for an unstabl hlicoptr, Enginring Applications of Artificial Intllignc Vol.22, 29, pp.8 9. [6] A. Savran, Intllignt adaptiv nonlinar flight control for a high prformanc aircraft with nural ntworks, ISA Transactions, Vol.45, No.2, 26, pp [7] S. L. Wua t al, Gain-schduld control of PVTOL aircraft dynamics with paramtr-dpndnt disturbanc, Journal of th Franklin Institut Vol.345 (28) pp [8] C. D. Yang t al, Applications of Gntic-Taguchi Algorithm in Flight Control Dsigns, Journal of Arospac Enginring, Vol.8, No.4, 25, pp [9] R. Fantinutto t al, Flight control systm dsign and optimisation with a gntic algorithm, Arospac Scinc and Tchnology, Vol.9, 25, pp [2] M. Jamshidi, A.Titli, L.Zadh, S. Bovri, Applications of fuzzy logic towards high machin intllignc quotint systms, Prntic Hall PTR, 997. [2] A.-F. Kantaa t al, In-flight particl charactristics control by implmnting a fuzzy logic controllr, Surfac & Coatings Tchnology, Vol.22, 28, pp [22] O. Cordon t al, Tn Yars of Gntic Fuzzy Systms Currnt Framwork and Nw trnds, Fuzzy Sts and Systms, Vol 4, No., 24, pp [23] E. Sanchz, T. Shibata, L.A. Zadh, Gntic Algorithms and Fuzzy Logic Systms, Soft Computing Prspctivs, World Scintific Publishing Co. Pt. Ltd., 997. [24] H.B. Vrbruggn, H.J. Zimmrman, R.Babuska, Fuzzy Algorithms for Control, Kluwr Acadmic Publishrs, 999. [25] 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.2, 998, pp [26] Klli Whitlock, Rsarchrs us fuzzy larning for aircraft control, [27] E. Kiyak, Flight control applications with fuzzy logic mthod, Mastr of Scinc Thsis, Univrsity of Anadolu, 23. [28] V. Topuz, Fuzzy gntic procss control, PhD dissrtation, Univrsity of Marmara, 22. [29] S.K. Rotton t al,, Analysis and Dsign of a Proportional Fuzzy Logic Controllr, Dpartmnt of Elctrical Enginring Wright Stat Univrsity, Dayton, Ohio. [3] D. McLan, Automatic Flight Control Systms. Prntic Hall, 99. ISSN: ISBN: