Auto landing using fuzzy logic

Transcription

1 6t International PD Worksop on Systems and Control, October 4-8, 25 Izola, Slovenia INTRODUCTION Auto landing using fuzzy logic Pavle Boskoski, Biljana Mileva 2, Stojce Deskoski 3 Faculty of Electrical Engineering Skopje, R Macedonia 2Military Academy General Miajlo Apostolski Skopje, R Macedonia 3Faculty of Tecnical Sciences Bitola, R Macedonia pavleb@mobimakcommk Abstract: Fuzzy logic controllers (FLCs) are increasing its popularity as replacement of te conventional control metods Te FLCs finds teir usage in all kind of processes: industrial, medical, environmental etc Te FLCs are used in tis publication for auto landing of an airplane Landing procedure for any aircraft consists of several parts Tis paper puts stress on te actual descending and touc down pase of te landing During te landing procedure te aircraft goes troug tree pases: te descending, te flare manuvar and te actual touc down Te descending trajectory is steady descend on strait line from a start altitude, down to a several meters from te ground level In tat point te aircraft sould proceed wit a flare manuvar Te flare manuvar is actually canging te attack angle of te aircraft from steep descend to a small elevation Tis manuvar allows te aircraft to decrease its vertical down speed Tis sort manuvar is followed by te actual toucing down of te aircraft Te aircraft used in tis paper is an Unmanned Aerial Veicle (UAV) model given in te Aerosim adds in Matlab Te model of te airplane itself is unstable and before any simulation is made wit it, tere is a need to stabilize it Te stabilization of te Aerosim add model in MATLAB is performed by using conventional tecniques of PI, PD and / or PID controllers In order to remain consistent in te wole publication, te autors of tis publication managed to replace te PID controllers wit suitable FLCs In total, tere are four FLCs tat are used to auto land te Aerosim UAV As input signals to te FLC responsible for te landing of te airplane, only simple triangle and trapezoid membersip functions are used and only 2 rules create te output of te FLC wic actually gives te attack angle of te airplane Tis application sows once again tat te fuzzy logic control wit its simple design and its robust properties can totally replace te conventional tecniques of control management Keywords: Fuzzy Logic Contollers, Autolanding, Aerosim Instrument landing Te landing procedure consists of two major pases Te glide pat pase and te finising flare maneuver Wit te advent of te instrument landing system (ILS), aircraft became able to operate safely in weater conditions wit restricted visibility Te instrument landing system is composed of ground -based signal transmitters and onboard receiving equipment Te ground-based equipment includes radio transmitters for te local-izer, glide pat, and marker beacons Te equipment on te airplane consists of receivers for detecting te signals and indicators to display te information Before addressing te auto landing system, we briefly review te basic ideas beind te ILS equipment To guide te airplane down toward te runway, te guidance must be lateral and vertical Te localizer beam is

2 6t International PD Worksop on Systems and Control, October 4-8, 25 Izola, Slovenia used to position te aircraft on a trajectory so tat it will intercept te centerline of te runway Te transmitter radiates at a frequency in a band of 8-2 MHz Te purpose of tis beam is to locate te airplane relative to a centerline of te runway Tis is accomplised by creating azimut guidance signals tat are detected by te onboard localizer re ceiver Te azimut guidance signal is created by superimposing a 9-Hz signal directed toward te left and a 5-Hz signal directed to te rigt on te carrier signal Figure sows an instrument landing localizer signal Wen te aircraft is flying directly along te projected extension of te runway centerline, bot superimposed signals are detected wit equal strengt However, wen te aircraft deviates say to te rigt of centerline, te 5-Hz signal is stronger Te receiver in te cockpit detects te difference and directs te pilot to fly te aircraft to te left by way of a vertical bar on te ILS indicator tat sows te airplane to te rigt of te runway If te airplane deviates to te left, te indicator will deflect te bar to te left of te runway marker Figure Te glide pat or glide slope beam is located near te runway tresold and radiates at a frequency in te range MHz Its purpose is to guide te aircraft down a predetermined descent pat Te glide slope is typically an angle of 25-3 to te orizontal Figure 83 sows a scematic of te glide pat beam Note tat te glide pat angle as been exaggerated in tis sketc As in te case of te localizer, two signals are superimposed on te carrier frequency to create an error signal if te aircraft is eiter ig or low wit respect to te glide pat Tis usually is indicated by a orizontal bar on te ILS indicator tat moves up or down wit respect to te glide pat indicator Te marker beacons are used to locate te aircraft relative to te runway Two markers are used One, located 4 nautical miles from te runway, is called te outer marker Te second, or inner, marker is located 35 ft from te runway tresold Te beams are directed vertically into te descent pat at a frequency of 75 MHz Te signals are coded, and wen te airplane flies overead te signals are detected by an onboard receiver Te pilot is alerted to te passage over a marker beacon by bot an audio signal and visual signal Te audio signal is eard over te aircraft's communication system and te visual signal is presented by way of a colored indicator ligt on te instrument panel In flying te airplane in poor visibility, te pilot uses te ILS equipment in te following manner Te pilot descends from cruise altitude under direction of ground control to an altitude of approximately 2 ft above te ground Te pilot ten is vectored so tat te aircraft intercepts te localizer at a distance of at least 6 nautical miles from te runway Te pilot positions te airplane using te localizer display so tat it is on a eading toward te runway centerline Wen te aircraft approaces te outer marker, te glide pat signal is intercepted Te aircraft is placed in its final approac configuration and te pilot flies down te glide pat slope Te pilot follows te beams by maneuvering te airplane so tat te vertical and orizontal bars on te ILS indicator sow no deviation from te desired fligt pat Te ILS system does not guide te aircraft all te way to toucdown At some point during te approac te pilot must look away from te instruments and outside te window to establis a visual reference for te final portion of te landing Te pilot may take 5 or 6 seconds to establis an outside visual refer Obviously te pilot must do tis at sufficient altitude and distance from te i so tat if te runway is not visible te pilot can abort te landing Tis gi\ to a "decision eigt," wic is a predetermined eigt above te runway t\ pilot cannot go beyond witout visually sigting te runway

3 6t International PD Worksop on Systems and Control, October 4-8, 25 Izola, Slovenia Figure 2 Te ILS as outlined in te previous paragraps is an integral part of an automatic landing system To be able to land an airplane wit no visual refer to te runway requires an automatic landing system tat can intercept te localizer and glide pat signals, ten guide te airplane down te glide pat to some j selected altitude at wic te aircraft's descent rate is reduced and te air executes a flare maneuver so tat it touces down wit an acceptable sink rate, auto land system comprises a number of automatic control systems, wic inc a localizer and glide pat coupler, attitude and airspeed control, and an automatic flare control system 2 Gliding pat controller Te system uses te output signal from te airborne glide pat receiver as a guidance command to te attitude control system of te aircraft Te loop is closed via te aircraft kinematics wic transforms te pitc attitude of te aircraft into a displacement form tat preferred te gliding pat Te situation is represented on te figure 2 Te glide pat angle is denoted by γ and its nominal value is -25 If an aircraft is flying into an airport, but it is displaced below te gliding by a distance d, tat distance is negative Te geometry is sown on figure 2b If te value of te aircraft s own fligt pat is -25, te displacement is Any angular deviation from te centre-line of te glide pat transmission is measured by te airborne glide pat receiver: tat deviation depends upon bot te displacement, d, and te slant range from te transmitter Since te value of γ is so small it is customary to regard te slant and te orizontal ranges, R and x, as identical Te correct relationsip is: G x = R cos( 25 ) () In tis section x and R are taken as identical Terefore te angular deviation? is defined as: Γ = d / R (2) were? is in radians Te component of te airspeed wic is perpendicular to te glide pat is U sin Γ Tis quantity represents te rate of cange of te displacement, ie: G

4 6t International PD Worksop on Systems and Control, October 4-8, 25 Izola, Slovenia d (3) = U sin Γ = ( U / 573) Γ Figure 3 However, for te situation sown on figure 2 te aircraft s fligt pat angle is less ten 25, terefore? is positive (note tat?= γ 25 ) and d is positive As te initial displacement was negative, and its rate of cange is positive, te situation sown on figure 2c represents te case wen te aircraft is approacing te glide pat from below: d = ( U / 573) ( 25 ) dt = ( U / 573) Γdt γ (4) Te block diagram representing te equation is sown on te figure 3 Γ ref G Glide pat coupled controller Pitc attitude Aircraft kinematics γ 2,5 X(p) Glide pat receiver K Rr Γ 573 R d Figure 4 d U FLARE MANEUVER CONTROLLER Altoug te contribution to development of airplane automatic landing systems as been international, te basis of most of te operational systems in service is te system developed in te UK by te Blind Landing Experimental Unit (now disbanded) of te Royal Aerospace Establisment Te automatic flare control system is arranged to provide a flare trajectory corresponding to tat sown in Figure 4 Te trajectory represents te pat of te aircraft's weels as te landing is carried out During tis flare maneuver, te fligt pat angle of te aircraft as to be canged from - 25 to te positive value

5 6t International PD Worksop on Systems and Control, October 4-8, 25 Izola, Slovenia wic is re commended for toucdown; in oter words, during te flare maneuver te control system must control te eigt te aircraft s eg and its rate of cange suc tat te resulting trajectory corresponds as nearly as possible to te idealized exponential pat sown in Figure 4, wile at te same time causing te aircraft to rotate in a fasion similar to te representation of Figure 4 Te equation wic governs idealized, exponential flare trajectory sown in Figure 4 is t/ τ = e (5) Te distance from, to te point of toucdown depends on te value of, te flare entry eigt, and te approac speed of te aircraft, U Usually te point of toucdown, wic is aimed for, is 3 m from te runway tresold wic is te nominal location of te glide pat transmitter Assuming tat te airspeed does not cange significantly trougout te flare trajectory (a not unreasonable assumption), ten: Figure 5 = U sin γ = U sin( = 25ms 573 O ) (assuming landing speed for CHARLIE-l of 573 m s - ) From eq (6) it can easily be sown tat: (6) = τ e t / τ = τ (7) From eq ( 7): ence: = /τ (8) 5 = /τ (9) 2 From Figure 5, x tan x =, terefore: = τ = (435 / 25)x () Hence, substituting eq (9) in eq () yields:

6 6t International PD Worksop on Systems and Control, October 4-8, 25 Izola, Slovenia x 3 = ( / 25) x x = 753m τ = 3s = 325m () Hence, te ideal flare maneuver is assumed to take 65s to completion Te law wic governs te flare trajectory is given by: = 77 (2) A block diagram of an automatic flare control system is sown in Figure 4 Γ ref Automatic θcomm flare control Pitc attitude θ Aircraft kinematics Radio altimetar 77 Figure 6 Note tat te pitc attitude control system is used: canging G results in a cange in fligt pat angle, and consequently, a cange in eigt Because te eigts involved are very low, an accurate measurement of eigt is necessary for tis control system: a low range altimeter is used Te control law used can be simply: θ comm = K C (3) but, to ensure accuracy, it is usual to add an integral to te proportional term so tat: comm c c 2 θ = K K (4) Te addition of te integral term, and te need to remove, by filtering, any noise from te eigt signal obtained from te radio altimeter tends to destabilize te closed loop system Consequently, it is customary to include a pase advance network wit te feedback terms to improve te stability, ie: K c pt comm K c Kc p pt 2 θ = (5) 2 were p = d/dt and T >> T2 Because te model flare trajectory is exponential it takes infinite time to reac zero eigt te reference eigt is set to be -5m, tereby ensuring tat te weels will touc te runway at a time muc nearer 5τs

7 6t International PD Worksop on Systems and Control, October 4-8, 25 Izola, Slovenia 3 SIMULATION RESULTS For te simulation purposes te UAV 6DOF is used Te model is defined in Aerosim plug-in of Matlab Te controllers used for te glide pat an flare maneuver are fuzzy logic controllers 4 REFERENCES [] S Deskovski: Meanika na letanje, Military Academy General Miailo Apostolski, Skopje, 24 [2] M V Cook: Fligt Dynamics Principles, Arnold, London, 997 [3] R C Nelson: Fligt Stability and Automatic Control, Second Edition, McGraw-Hill, Boston, 998 [4] Kyungmoon No and Rames K Agarwal: Automatic Landing System Design Using Fuzzy Logic, Journal of Guidance, Control and Dynamics, Vol 23, No 2, Marc April 2 [5] Li-Xin Wang: A Course in Fuzzy Systems and control, ISBN [6] Leonid Reznik: Fuzzy Controllers, ISBN [7] K M Passino, S Yurkovic, Fuzzy Conrol, ISBN X [8] AeroSim aeronautical simulation blockset, Version, User s Guide, Unmanned Dynamics, wwwudynamicscom