Numerical considerations regarding the simulation of an aircraft in the approaching phase for landing

Size: px

Start display at page:

Download "Numerical considerations regarding the simulation of an aircraft in the approaching phase for landing"

Damon Sims
5 years ago
Views:

1 INCAS BULLETIN, Volum, Numbr 1/ 1 Numrical considrations rgarding th simulation of an aircraft in th approaching phas for landing Ionl Cristinl IORGA ionliorga@yahoo.com Univrsity of Craiova, Alxandru Ioan Cuza Str. 13, 585 Craiova, Romania DOI: / Abstract This papr dals with numrical considrations rgarding th simulation of th attitud of an aircraft in th approaching phas for landing. Th stat of th art is analyzd in th first sction; th dscription of th procss by mans of which th stady stat vctor of th initial systm, givn in th scond sction, is obtaind in th fourth sction. An improvd systm is givn in th third sction and this systm is furthr nhancd with prturbations, in th fifth sction. Th scond sction dscribs th procss lading to th initial rquird conditions. Th conclusions ar givn in th sixth sction. 1. Stat of th art Th simulation of an aircraft in th approaching phas for landing is important in ordr to nsur th safty of oprations as this stag in flight is a critic on. Various paprs trat this issu, for xampl: [1], [6], [3] tc. Essntially, this particular stag of flight ncssitat mor attntion from th pilot and a bttr coordination in ordr to avoid th so calld PIO phnomnon [].. Th initial systm Th systm (1) is takn from [3]: g z z cos( ) q V g 1 q m mqq m m cos( ) a sin( ) q (1) V a q ( ) Whr w hav: k k k q () p q, if L ( ) (3) L sgn, if L From [4], th following constants of th systm (1) ar usd: z = , z = -.63, m = , m q = , m = , m = -.16, 1

2 INCAS BULLETIN, Volum, Numbr 1/ 1 = rad V m s, L, a 1. 43, g 9.81 s V is th aircraft spd (84.5 m/s) and Rmark 1. is th additiv input valu. is th limit for saturation. Rmark. Th global gains ar: k =.41, k q = 1.84, k p =.51 Howvr, as shown in [5], th output of this systm is not optimal rgarding th ncssary manouvrs in th approaching for landing. In sction thr th systm is improvd in ordr to obtain an improvd output. Also, in sction four, th initial conditions obtaind vrify an auxiliary condition from [3], xprssd by rlation (5). L 3. Th improvd systm Th improvd systm is idntical with rlations (1) and (3), th xcption bing th rlation () which is transformd to (4): k k p k qq (4) From rlation (4), it can b dnotd th fact that a ngativ fdback raction is introducd: -. In ordr to numrically comput th attitud in th simulink languag, th gnral rprsntation of th improvd systm is ndd - shown in Fig. 1. Fig. 1 Th gnral rprsntation of th improvd systm in simulink In Fig. and Fig. 3 th controllr subsystm and, rspctivly th plant subsystm ar shown. Fig. Th controllr subsystm

3 INCAS BULLETIN, Volum, Numbr 1/ 1 Fig. 3 Th plant subsystm Th subsystms from Fig. and 3, with variations will b usd in th systm from sction 5. Th outputs of th systm ar prsntd in Figurs 4, 5, 6 and vs. tim 1 9 [dg] tim [sc] Fig. 4 vs. tim 3

4 INCAS BULLETIN, Volum, Numbr 1/ 1 q vs. tim - q [dg/sc] tim [sc] Fig. 5 q vs. tim 1 vs. tim 5 [dg] tim [sc] Fig. 6 vs. tim vs. tim - [dg] tim [sc] Fig. 7 vs. tim Comparing ths outputs with th ons from [5] th optimality stands out. 4

5 4. Obtaining th initial conditions (from stady-stat) Actually, th computations from prvious sction wr mad using th initial conditions dscribd in this sction. Putting togthr th condition (5) and th conditions from [3] ariss th ncssity for a nw mthodology to stablish th initial conditions. 1 g.4 C T.15 sin( ).35 (5) a V Rmark 3. Th condition (5) is obtaind from [3] and [4]. Rmark 4. is xprssd from th rlation (6). C T INCAS BULLETIN, Volum, Numbr 1/ 1 C T o o.454/ rad, if ( 1, ) o o.157 / rad, if (,15 ) o o.43/ rad, if (15,7 ) (6) In ordr to dtrmin th initial conditions from systm (1) th first two quations ar usd togthr with th rlation (7). cos ( ) sin ( ) 1 (7) Rmark 5. Th first two quations ar considrat homognous and on trigonomtric function is xprssd from th first quation in ordr to b puttd in th scond on. As in [3] th following rlation is obtaind: A B C D (8) Whr A, B, C, D dpnd on th cofficints of systm (1). For rlation (8) in ordr to hav ral solutions, th rlation (9) must b tru. ( B 4AC) 4AD (9) From rlation (9) th rlation (1) is obtaind (.15833,.15833) (1) Th algorithm for computing (, q,, ) consists in itrations ovr, from (1), thn aftr th and. Aftr th itrations ar mad, th following initial point is obtaind (, q,, ) =(.189,,.1, -.15). On can chck that th initial systm vrifis th rlation (5). 5.Th systm with prturbations In ordr to xprss mor clarly th ralitis of flight w us som xtrnal prturbations and on finit input ovr tim. 5

6 INCAS BULLETIN, Volum, Numbr 1/ 1 Fig. 8 Th simulink schm of th systm with prturbations Fig. 9 Th controllr subsystm of th systm wit prturbations Fig. 1 Th plant systm of th systm with prturbations 6

7 INCAS BULLETIN, Volum, Numbr 1/ 1 11 vs. tim 1 9 [dg] tim [sc] Fig. 11 vs. tim of th systm with prturbations q vs. tim - q [dg/sc] tim [sc] 1 Fig. 1 q vs. tim of th systm with prturbations vs. tim 5 [dg] tim [sc] Fig. 13 vs. tim of th systm with prturbations 7

8 INCAS BULLETIN, Volum, Numbr 1/ 1 vs. tim - [dg] tim [sc] Fig. 14 vs. tim of th systm with prturbations Figurs 11, 1, 13 and 14 put in vidnc th fact that th systm is stabl rgardlss th spcifid prturbation. 6. Conclusions Gnrally, th fact that many jt fightrs hav th bar airfram instabl achiving stability through th us of automatic stabilization systms, is known [8]. Following this ida this work is part of a futur implmntation which will us robustnss [7] for achiving stability. REFERENCES [1] BALINT ŞTEFAN, KASLIK EVA, BALINT AGNETA and ACHIM IONIŢĂ, Oscillation Suscptibility Analysis Along Th Path Of Longitudinal Flight, 8, Nonlinar Analysis: Thory, Mthods & Applications. availabl on-lin doi:11.16/j.na [] HESS RONALD, Unifid Thory for Aircraft Handling Qualitis and advrs Aircraft-Pilot, 1997, Journal of Guidanc, Control and Dynamics, Vol., pp No 6. [3] IONIŢĂ ACHIM, BALINT AGNETA and BALINT ŞTEFAN, Limit Cycl Bhaviour in Aircraft Longituinal Trminal Phas, Gnova: S.N., 8. ICNPAA, Mathmatical Problms in Enginring, Arospac and Scinc. [4] IONIŢĂ ACHIM, Prsonal communication to th author, 9. [5] IORGA IONEL CRISTINEL, Th ffct of saturation on th longitudinal command in th approaching phas of flight for landing, Bucharst: INCAS - Institutul National d Crctar- Dzvoltar Arospatiala Eli Carafoli, 9. Procdings of th XXXIInd Caius Iacob National Confrnc on Fluid Mchanics and its Tchnical Applications. pp [6] KLYD, DAVID and othrs, Unifid Pilot-Inducd Oscillation Thory, Volum 1: PIO Analysis with Linar and Nonlinar Effctiv Vhicl Charactristics, Including Rat. s.l.: Air Forc Rsarch Laboratoris, Wright- Pattrson AFB, WL-TR [7] POPESCU DAN, Th analysis and synthsis of th robust systms (in Romanian). CRAIOVA: Editura Univrsitaria, 8. [8] RUNDQUIST L. and HILLGREN R., Phas Compnsation of Rat Limitrs in JAS 39 Gripn, AIAA Atmosfric Flight Mchanics Confrc. pp

Rotor Stationary Control Analysis Based on Coupling KdV Equation Finite Steady Analysis Liu Dalong1,a, Xu Lijuan2,a

204 Intrnational Confrnc on Computr Scinc and Elctronic Tchnology (ICCSET 204) Rotor Stationary Control Analysis Basd on Coupling KdV Equation Finit Stady Analysis Liu Dalong,a, Xu Lijuan2,a Dpartmnt of