ANALYSIS OF THE DYNAMICS AND CONTROL OF THE MODIFIED OPTICAL TARGET SEEKER USED IN ANTI-AIRCRAFT ROCKET MISSILES

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1 JOURNAL OF THEORETICAL AND APPLIED MECHANICS 52, 3, pp , Warsaw 2014 ANALYSIS OF THE DYNAMICS AND CONTROL OF THE MODIFIED OPTICAL TARGET SEEKER USED IN ANTI-AIRCRAFT ROCKET MISSILES Daniel Gapiński, Izabela Krzysztofik, Zbigniew Koruba Kielce University of Technology, Faculty of Mechatronics an Machine Design, Kielce, Polan tu aniel The paper presents the concept of programme control of the esigne optical target seeker in the phase of searching the air space. The controlling of the programme movements of the seeker axis has been evelope with simultaneous consieration of the process of scanning of the air space by an optoelectronic system of the evice. Numerical analysis of the ynamics of the propose optical scanning seeker as well as the analysis of selection of velocity an suitable trajectories of the isplacement of its axis were conucte. The results were presente in a graphical form. Keywors: self-guiance, ynamics an control, target seeker, rocket missile 1. Introuction Optical scanning heas of self-guie rocket missiles are evices requiring high accuracy an precision of making(awrejcewicz an Koruba, 2012; Moir an Seabrige, 2006; Siouris, 2004). Structural solutions of those evices are constantly improve because etection an etermination of the location of faster an faster moving air targets in real conitions is aitionally hinere by various thermal isruptions(yanushevsky, 2008). In connection with the above, optical systems an structural solutions of those evices are still improve what is proven by the most recent European an American patents publishe in the years (Barenz et al., 2012; Kröner, 2012; Rueger an Zoz, 2012; Shaffer, 2011; Wellman et al., 2010, Wil an Leavy, 2012). The possibility of using innovative structural solutions is consiere, an the optimization of the process of scanning(searching) of the air space by the esigne scanning seeker is presente in the paper. Innovation an the principle of operation have been presente in the patent escription(gapiński, 2005). The esign of the evelope scanning seeker(gapiński, 2005), incluing the most significant constituents, is shown in Fig. 1. The gyroscope rotor consists of the following elements presente in Fig. 1: 2 primarymirror,3 seconarymirrorguar,4 ajustableseconarymirror,5 seconary mirror roller, 6 pattern boar with electromagnet, 8 retaining ring, 9 fastening li,10 boyofmechanicalgyroscope,11 correctivelenssystem,12 permanentmagnetofrivingmotor,14 aitionalmovablemirror,18 geartransmission,19 snap ring,20 bearing,21 twospacerbushings. The complete inner housing consists of: 1 coilofrivingmotor,15 electricmotorcontrollinginnerhousing,13 twoinfrare raiation receivers, 17 pattern boar with electromagnet, 24 fastening boar, 25 twofibre-opticgyroscopes,26 innerhousing,29 bearingfastening,31 moving axis, 32 bearing.

2 630 D. Gapiński et al. Fig. 1. Structure of the moifie scanning seeker The complete outer housing consists of: 15 electric motor controlling outer housing, 27 outer housing, 29 bearing fastening, 31 movingaxis,32 bearing. 2. Moel of the seeker movement Figure2showsaiagramoftheseeker,incluingtheaoptesystemsofcoorinatesaswellas markings of iniviual angles of rotations of the respective systems in relation one to another. Fig. 2. The iagram of the seeker, incluing the aopte systems of coorinates A gyroscope movement can take place uner the influence of moments of external forces M Z anm W generatebycontrollingmotors(15)aswellasangularmovementsoftherocket missileecketerminewiththeuseofangularvelocities ω xp,ω yp,ω zp causingitsrotation arouniniviualaxesofthesystemox P Y P Z P withtherespectiveanglesα xp,α yp anα zp. The following systems of coorinates(awrejcewicz an Koruba, 2012; Baranowski, 2013; Krzysztofik, 2012) were introuce: OX K Y K Z K systemofcoorinatesconnectewiththeirectionsetinspace, OX P Y P Z P movingcoorinatesystemconnectewiththemissile,

3 Analysis of the ynamics an control of the moifie optical target seeker OX CZ Y CZ Z CZ movingcoorinatesystemconnectewiththeouterhousing, OX CW Y CW Z CW movingcoorinatesystemconnectewiththeinnerhousing, OX R Y R Z R movingcoorinatesystemconnectewiththerotor. The following markings of angles of rotation an the orer of measuring them were aopte: ψ angleofrotationox CZ Y CZ Z CZ inrelationtoox P Y P Z P arounaxisz CZ, ϑ angleofrotationox CW Y CW Z CW inrelationtoox CZ Y CZ Z CZ arounaxisx CW, φ angleofrotationox R Y R Z R inrelationtoox CW Y CW Z CW arounaxisy R. Hence,thelocationofgyroscoperotorinrelationtothesystemOX P Y P Z P isetermine withtheuseofthreeangles:ψ,ϑ,φ. As given quantities the following were aopte: 1.J xcz,j ycz,j zcz momentsofcompleteinertiaoftheouterhousing, 2.J xcw,j ycw,j zcw momentsofcompleteinertiaoftheinnerhousing, 3.J xr,j yr,j zr momentsofinertiaoftherotor, 4.ω P (ω xp,ω yp,ω zp ) missileangularvelocity; 5.M Z momentofmissileforcesinteractingwiththeouterhousing, 6.M W momentofforcesoftheouterhousinginteractingwiththeinnerhousing, 7.M R momentofforcesoftheinnerhousinginteractingwiththerotor, 8.M TR momentoffrictionforcesinrotorbearingsanaeroynamicresistance, 9.M TW,M TZ momentsoffrictionforcesinthebearingsoftheinneranouterhousing, respectively. The equations of seeker(gyroscope) motion have been introuce with the use of Lagrange equations of the II-n kin(awrejcewicz an Koruba, 2012; Baranowski, 2013; Krzysztofik, 2012) where J zcz t ω z CZ +J ycw t (ω y CW sinϑ)+j zcw t (ω z CW cosϑ)+j yr t (ω y R sinϑ) +J zr t (ω z CW cosϑ) (J xcz J ycz )ω xcz ω ycz (J xcw +J xr )ω xcw ω ycz +J ycw ω ycw ω xcz cosϑ (J zcw +J zr )ω zcw ω xcz sinϑ+j yr ω yr ω xcz cosϑ =M Z M TZ J xcw t ω x CW +J xr t ω x CW (J ycw J zcw J zr )ω ycw ω zcw J yr ω yr ω zcw =M W M TW J yr t (ω y CW + φ)=m R M TR (2.1) ω xcz =ω xp cosψ+ω yp sinψ ω zcz = ψ+ω zp ω ycw =ω ycz cosϑ+ω zcz sinϑ M TW =c w ϑ ω ycz = ω xp sinψ+ω yp cosψ ω xcw =ω xcz + ϑ ω zcw = ω ycz sinϑ+ω zcz cosϑ MTZ =c z ψ anc w isthefrictioncoefficientinthebearingoftheinnerhousing,c z frictioncoefficientin the bearing of the outer housing. WeassumethatM R =M TR,thenω yr =ω R =n=const (nistheangularvelocityofthe rotor)anmotionoftheseekeraxisisgovernebyequations(2.1) 1,2.

4 632 D. Gapiński et al. 3. Controlling motion of the seeker axis On contemporary battlefiels, the precise aiming of a missile at a moving air target is unoubtely a ifficult thing to accomplish. The scanning seeker propose in the paper will allow onetoaimthemissileonlyintheirectionoftheforeseenlocationofthetarget.theoptical axis of the seeker performs programme movements(e.g. in a circle) an, simultaneously, the system of mirrors scans the surface on an n-leave rosette with the so calle big scanning angle. It increases the area of searching an, with a suitable selection of velocity of the programme movement of the seeker axis, gives satisfactorily ense scanning of space. At the moment of interceptingthetargetbythescanningseeker,theanglesbywhichtheseekeraxisistobemove sothatitoverlappewiththelineofsight(los)areetermine.itisstilltheprogramme controlwhichcanbecarrieout,e.g.inastraightline.duringthatcontrolphase,theangles ϑ Z,ψ Z eterminetheset(esire)programmemovementwhichshoulbemaebytheaxis of the scanning seeker so that it overlappe with LOS. After intercepting the target an the programme presentation of the seeker axis on LOS, there is the secon phase consisting in the tracking of the target. During that phase, the rocket missile is launche, while the angles ϑ Z,ψ Z areeterminesystematicallybythetargetseekeropticalsystem.atthemomentof finishing the operation by the missile start motor(stabilisation of the trajectory of the missile flight),thereappearsaecreaseintheanglesδ W anδ D whatcausesthenarrowingownof theareaofthescannespace.theangles δ W an δ D areinclinationanglesoftheprimary anseconarymirrorrespectivelyinrelationtotheseekeraxis.theyareshowninfig.1.the selection of those angles is presente in the paper by Gapiński(2013). The passing of the seeker from the searching moe to the tracking moe, an the simultaneous interaction of the rocket missile eck aversely affect the long maintaining with a sufficient precision the programme movement an the tracking through its axis. We eliminate by that the suitably chosen correction system. The control law for the axis of the scanning seeker(awrejcewicz an Koruba, 2012; Blakelock, 1991; Łayżyńska-Kozraś, 2009) can be written in the following way M W =Π(t o,t w )M p W (t)+π(t s,t k )M s W M Z =Π(t o,t w )M p Z (t)+π(t s,t k )M s Z (3.1) wherem p W,Mp Z areprogramcontrolsfortheseekeraxis,ms W,Ms Z trackingcontrolsforthe seekeraxis,π(t o,t w ),Π(t s,t k ) functionsofrectangularimpulse,t 0 momentofthebeginning ofthescanningofspace,t w momentofetectingthetarget,t s momentofthebeginningof thetrackingofthetarget(t s =t w ),t k momentofthefinishingoftheprocessofself-guiance. Theprogramcontrols M p W,Mp Z canbeeterminefromtheepenence(korubaetal., 2010) M p W = k w(ϑ ϑ Z )+k z (ψ ψ Z ) h z ( ϑ ϑ Z ) M p Z = k z(ϑ ϑ Z ) k w (ψ ψ Z ) h z ( ψ ψ Z ) (3.2) whereϑ,ψarerealangleseterminingthelocationoftheseekeraxisinspace,ϑ Z,ψ Z set angleseterminingthelocationoftheseekeraxisinspace,k w,k z,h z controllercoefficients. Thetrackingcontrols M s W,Ms Z canbeeterminefromtheepenence(korubaetal., 2010) M s W= k w (ϑ ε)+k z (ψ σ) h z ( ϑ ε) M s Z = k z(ϑ ε) k w (ψ σ) h z ( ψ σ) (3.3) The angles ε, σ are angles etermining the current location of LOS in space, etermine systematically through the optoelectronic system of the scanning seeker.

5 Analysis of the ynamics an control of the moifie optical target seeker Results Numerical research was conucte for the esigne scanning seeker intene for the close-range surface-to-air rocket missiles Parameters of the seeker The moments of inertia of iniviual elements of the seeker have been calculate in relation to respective axes of the aopte systems of coorinates(shown in Fig. 2). The beginnings of allsystemsofcoorinatesoverlapanareattheintersectionoftheaxisofrotationoftheouter housingwiththeaxisofrotationoftheinnerhousingoftheseeker.themaximumtorquesof iniviual motors controlling the outer an inner housing have been etermine base on the previous analysis of the esigne seeker ynamics. The selection of a suitable gear ratio(18) results from the analysis of the cooperation of iniviual seeker mirrors. Momentsofinertiaoftherotorare: J xr = kgm 2,J yr = kgm 2,J zr = kgm 2 Moments of complete inertia of the inner housing: J xcw = kgm 2,J ycw = kgm 2,J zcw = kgm 2 Moments of complete inertia of the outer housing: J xcz = kgm 2,J ycz = kgm 2,J zcz = kgm 2 Angular velocity of the rotor: n=600ra/s Friction coefficients in the bearing of the inner an outer housing: c w =0.05Nms,c z =0.05Nms Maximum torque of the controlling motors: M max =0.8Nm Figure3apresentsthescopeoftheairspacescannebytheoptoelectronicsystemofthe seekerwithalargetopangleofscanningβ w amountingto3.84egrees,whilefig.3bpresents thescopeofthescannespacewithasmallangleofscanningβ w amountingto0.56egrees, howeverβ x,β y aretheconstituentsofangleβ=β w /2. Fig.3.Scanningofspacebytheoptoelectronicsystemwithalargescanningangle(a)an a small scanning angle(b)

6 634 D. Gapiński et al. Figure 4 shows the irect etection of the air target by the optoelectronic system moving withthevelocityof200m/s,whichis3000mawayfromthefiringposition,wherex C,Y C coorinatesoftargetlocation,x S,Y S coorinatesofthelineofscanning. Fig.4.Directetectionofatarget Thetimeofetectingthetargetamounteto0.168s.Thesetangularcoorinatesofthe locationoftheetectetargetinrelationtotheseekeraxisareasfollows: σ=0.435eg, ε=1.5063eg. Inthecasewhenthetargetisoutsietheareascannebytheoptoelectronicsystemofthe evice, the optical axis of the seeker is aitionally set into programme motion. It increases the area of searching an, with a suitable selection of velocity of the programme movement of the seeker axis, gives satisfactorily ense scanning of space. Controlling the axis of the scanning seeker was checke by setting its movement on the surface ofacircularconeanonthesurfaceoftheunwiningcoil.theparametersofthecontrollerhave been chosen accoring to(awrejcewicz an Koruba, 2012) an assume the following values k w =100 k z = kw h z = 2+4k w Figures 5-9 present the results of computer simulation of the control of the scanning seeker axissettingitsmovementonthesurfaceofacircularconeatthesametimetakingintoconsierationthescanningoftheairspacebytheoptoelectronicsystemoftheevice.thetargetwas movingwiththevelocityof250m/sanwas3000mawayfromthefiringposition.figure5a presentstheiagramofthesetangularvelocity ω O fortheseekeraxismovingonthesurface of a circular cone. In the initial phase of control, the scanning seeker axis accelerates till the moment of achieving the set angular velocity amounting to 360 eg/s. In the further phase of control, the angular velocity of the axis is maintaine at the constant level of 360 eg/s. Figures present the results of computer simulation of the control of the scanning seeker axissettingitsmovementonthesurfaceofanunwiningspiralatthesametimetakinginto consieration the scanning of the air space by the optoelectronic system of the evice. The target wasmovingwiththevelocityof70m/sanwas3000mawayfromthefiringposition. Figure10presentstheiagramofthesetangularvelocityω O fortheseekeraxismovingon the surface of an unwining spiral. In the initial phase of control, the axis accelerates till the moment of achieving the set angular velocity amounting to 180 eg/s. Inthefurtherphaseofcontrol,theangularvelocityoftheaxisismaintaineattheconstant level of 180 eg/s. Figures12an14presentthesearchingoftheairspacebytheseekerantheetectionof the target. In the first of the presente simulations, the time of etecting the target amounte

7 Analysis of the ynamics an control of the moifie optical target seeker Fig.5.(a)Setangularvelocityofcirclingarounacircularconebytheseekeraxis;(b)esirean actualrotationoftheouterhousingarountheaxisz CZ Fig.6.(a)DesireanactualrotationoftheinnerhousingarountheaxisX CW ;(a)trajectoryofthe sett Z anactualt R movementoftheseekeraxis Fig. 7. Moments controlling the outer an inner housing of the seeker Fig. 8. Controlling moments in transitional perios

8 636 D. Gapiński et al. Fig.9.Searchingoftheairspacebysettingtheseekeraxisintoprogrammemovementonthesurface of the circular cone an etecting the air target Fig.10.(a)Setangularvelocityoftheseekeraxisinitsmovementonthesurfaceoftheunwining spiral;(b)esireanactualrotationoftheouterhousingarountheaxisz CZ Fig.11.(a)DesireanactualrotationoftheinnerhousingarountheaxisX CW ;(b)trajectoryof thesett Z anactualt R movementoftheseekeraxis to s, while the set angular coorinates of the location of the etecte target amounte to: σ=3.93eg,ε=10.192eg.intheseconcase,thetimeofetectingthetargetamounteto s, while the set angular coorinates of the location of the etecte target amounte to: σ= eg,ε= 1.88eg. Figures 15 an 16 show the results of computer simulation of controlling the seeker axis by settingitinthefirstphaseinmovementonthesurfaceofacircularcone.whentheseekeroes notetectatarget,itpassestotheseconphaseofcontrolonthesurfaceoftheunwining spiral.atthesametime,thescanningoftheairspacebytheoptoelectronicsystemoftheevice

9 Analysis of the ynamics an control of the moifie optical target seeker Fig.12.Searchingoftheairspacebysettingtheseekeraxisintoprogrammemovementonthesurface of the unwining spiral an etecting the air target Fig. 13.(a) Moments controlling the outer an inner housing of the seeker;(b) controlling moments in transitional perios Fig.14.Searchingoftheairspacebysettingtheseekeraxisintoprogrammemovementonthesurface of the unwining spiral an etecting the air target wastakenintoconsieration.thetargetwasmovingwiththevelocityof70m/sanwas3000m away from the firing position. Figure15apresentstheiagramofthesetangularvelocity ω O fortheseekeraxismoving inthefirstanseconphaseofcontrol.intheinitialphaseofcontrol,thescanningseekeraxis accelerates till it reaches the set angular velocity amounting to 360 eg/s, which is maintaine ataconstantlevelof360eg/suntilafullcirclehasbeenmae,afterwhichtheseconphase ofcontrolfollows.intheseconphaseofcontrol,theangularvelocityofmovinginaspiral ecreases till it reaches the set angular velocity amounting to 180 eg/s.

10 638 D. Gapiński et al. Fig.15.(a)Setangularvelocityoftheseekeraxisinitsmovementonthesurfaceofthecircularcone antheunwiningspiral;(b)trajectoryofthesett Z anactualt R movementoftheseekeraxis Fig. 16. Searching of the air space by setting the seeker axis into programme movement an etecting the air target Figure16presentsthesearchingoftheairspacebytheseekerantheetectionofthetarget. Thetimeofetectingthetargetamounteto5.9s.Thesetangularcoorinatesofthelocation oftheetectetargetareasfollows:σ= 1.707eg,ε=15.137eg. 5. Conclusions an final remarks From the conucte analysis of the ynamics an control of the esigne target seeker, it appearsthattheprogrammecontrolofitsaxisinthephaseofsearchingtheairspaceisone with the precision sufficient for etecting both slowly moving air targets such as helicopters, transport aeroplanes, as well as for etecting targets moving with higher velocities amounting to 1000 km/h. The selection of a suitable trajectory as well as angular velocities of movement oftheseekeraxisepens,amongothers,onthetypeoftheairassaultmeans.thesearching oftheairspaceinthewaypresenteinfig.11bischaracterizebyalargeareaofsearching theraiusofwhichcanexceeeven800mforthescanneplanethatis3000mawayfromthe firing position. However, with such a large scanne area, it is possible to successfully etect the targetwhenitsvelocityoesnotexcee300km/h.whereas,forthewaypresenteinfig.6b, theareaofsearchingissmaller,itsraiusamountsto300mforthescanneplanethatisalso 3000maway,howeverthetimeofscanningismuchshorteruetowhichitispossibletoetect targets moving with higher velocities.

11 Analysis of the ynamics an control of the moifie optical target seeker Arocketmissilecanofcoursebeequippewithaswitchenablingonetochoosethetypeof searching of the air space, however on contemporary battlefiels, because of quick response time require, the automation of such type of processes is simply unavoiable. The way of searching showninfig.15b,inwhichthecontroloftheseekeraxisisoneonthesurfaceofacircular cone, an then when the seeker oes not etect any target, it automatically switches to the seconphaseofcontrolonthesurfaceoftheunwiningspiral,canbeasuggestion. Acknowlegements The work reporte herein was unertaken as a part of the research project supporte by the National Centre for Research an Development over the perio References 1. Awrejcewicz J., Koruba Z., 2012, Classical Mechanics. Applie Mechanics an Mechatronics, Vol. 30, Springer, New York 2. Baranowski L., 2013, Equations of motion of a spin-stabilize projectile for flight stability testing, Journal of Theoretical an Applie Mechanics, 51, 1, BarenzJ.,KorullaH.,EckhartR.,KuppelH.,ThollH.D.,BaumannR.,2012, Verfahren zum Steuern eines Lenkflugkörpers un Suchkopf für einen Lenkflugkörper, European Patent EP A1 4. Blakelock J.H., 1991, Automatic Control of Aircraft an Missiles, John Wiley& Sons, New York 5. Gapiński D., 2005, Optical scanning seeker, Patent PL B1 6. Gapiński D., 2013, Analysis of the optoelectronic system of moifie target seeker(in Polish), Proceeings of 14th Conference ASMOR 2013, Jastrzębia Góra, Polan, KorubaZ.,KrzysztofikI.,DziopaZ.,2010,Ananalysisofthegyroscopeynamicsofan anti-aircraft missile launche from a mobile platform, Bulletin of the Polish Acaemy of Sciences Technical Sciences, 58, 4, Krzysztofik I., 2012, The ynamics of the controlle observation an tracking hea locate on a moving vehicle, Soli State Phenomena, 180, Kröner Ch., 2012, Suchkopf fr einen zielverfolgenen Flugkörper, European Patent EP A1 10. Łayżyńska-Kozraś E., 2009, The control laws having a form of kinematic relations between eviations in the automatic control of a flying object, Journal of Theoretical an Applie Mechanics, 47, 2, Moir I., Seabrige A., 2006, Military Avionics Systems, John Wiley& Sons Lt, Chichester 12. Rueger R., Zoz J., 2012, Infrare seeker hea, Unite States Patent US 2012/ A1 13. Shaffer J., 2011, Scanning array for obstacle etection an collision avoiance, Unite States Patent US B2 14. Siouris G. M., 2004, Missile Guiance an Control Systems, Springer, New York 15.WellmanW.,BorcharJ.F.,AnersonD.,2010,Opticalsystemforwiefielofview staring infrare sensor having improve optical symmetry, European Patent EP B1 16.WilN.R.,LeavyP.M.,2012,Opticaletectionsystem,UniteStatesPatentUSRE43681E 17. Yanushevsky R., 2008, Moern Missile Guiance, CRC Press Taylor& Francis Group, New York Manuscript receive September 19, 2013; accepte for print January 21, 2014