FUZZY LOGIC IN FIRE CONTROL SYSTEMS FOR AIR DEFENCE. Military Academy General Mihailo Apostolski, MK-1000 Skopje, Rep.

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1 Copyright 2007 IFAC Th 5 th IFAC DECOM-TT Workshop Csm - Izmir, Rpublic of Turky, May 17-20, 2007 FUZZY LOGIC IN FIRE CONTROL SYSTEMS FOR AIR DEFENCE Saso Glv 1, Zoran Gacovski 2, Jia-h Xu 3, Yuan-wi Jing 3, and Stojc Dskovski 4 1 Military Acadmy Gnral Mihailo Apostolski, MK-1000 Skopj, Rp. of Macdonia 2 Europan Univrsity-Skopj, MK-1000 Skopj, Rp. of Macdonia 5 Northastrn Univrsity, School of Info. T&E,.Shnyang, , P. R. of China 4 Tchnical Faculty, St. Clmnt Univrsity, MK-7000 Bitola, Rp. of Macdonia s: sasoglv@yahoo.com; zgacovski@yahoo.com; llipsis@163.com; stods@mt.nt.mk Abstract: It is th ncssity dfns combat against modrn offnsiv wapons from th air to apply th bst and most fficint dfns tactics and tchnology. Th problms of shooting targts in air spac ar solvd by appropriat dsign of a fir control systm, and th latst dvlopmnts mploy computational intllignc modls and tchniqus. In this papr, a fuzzy-logic knowldg-bas systm in th fir control systm for missil basd air dfns has bn invstigatd. Th aim of this papr is to provid a quality guidanc procss with minimum numbr of masurmnts, and to us th rsults for modification of th xisting air dfnc systms, which ar prsnt in our Army (Strla 10). Th novlty is in dfining fuzzy logic variabls for th approaching vlocitis btwn targt and missil drf and th angl of lad whn th missil is still on th launchr ksif. This fuzzy logic basd tchniqu rducs th dmand for dtrmining of th paramtrs usually calculatd using provisional stimats and mployd in missil s homing guidanc. It is dvlopd by using Fuzzy Toolbox of Matlab. Simulation modl in th vrtical plan is dvlopd by using Matlab/ Simulink platform. Copyright 2007 IFAC Kywords: Air dfnc systms; angl of lad; fuzzy logic; homing guidanc; missil; incoming-laving rgim. 1. INTRODUCTION Modrn combat against air-attacking nmy is most complicatd bcaus th modrn wapons for offnsiv from th air hav high manuvring capabilitis and mov with high vlocity. Thus th problm of shooting airborn nmy targts whil ths ar in th air is vry complicatd too. In missil systms for air dfns, this problm is to b solvd by fir control (sub)systm, and morovr always according to th tchnology of air-attacking nmy. * Th authors acknowldg with gratitud th substantial contribution mad by Profssor Gorgi M. Dimirovski, who is with both Dogus Univrsity of Istanbul, Rp. of Turky, and SS Cyril and Mthodius Univrsity of Skopj, Rp. of Macdonia. Th motivation for this papr aros from th rsarch projct /4 at th Military Acadmy Gnral Mihailo Apostolski Skopj and th Faculty for Elctrical nginring - Skopj titld Dvlopmnt and implmntation of algorithms for guidanc, navigation and control of mobil objcts. Th aim of this papr is to provid a quality guidanc procss with minimum numbr of masurmnts, and to us th rsults for modification of th xisting air dfnc systms, which ar prsnt in our Army (Strla 10). In this papr th homing guidanc systm is assumd to b mployd as built-in subsystm of th airdfnc systm. Functional schmatic of th homing guidanc systms (among which th activ, smiactiv, and passiv ar distinct) is shown in Figur 1.

2 Rsolving th problms of fir control involvs: - Dtction and idntification of th nmy targt; - Calculation of th targt s motion paramtrs; - Solution for shooting targt and dircting of th launchr accordingly; -Launch of th missil and controlling its motion as a function of th applid guidanc law. Th missil guidanc law has so crucial impact as to impos ssntial distinction among air dfnc systms (.g. systm such as Lin-of-sight; Homing; Navigational; and Compound guidanc). Fig. I. Schmatic of homing guidanc missil bas air dfnc systm. Fig. II. A Matlab/ Simulink implmntation modl of th air dfnc systm in Figur I. 2. HOMING-GUIDANCE SYSTEM IN THE ERTICAL PLANE For th purpos of ralization of th invstigation rportd in this papr th simulation modl of homing-guidanc missil systms for air dfns in vrtical plan (Davis t al. 1958; Dskovski, Dskovski t al., 2003; Dimirovski, t al. 2004; Siouris, 2004). Simulation modl in th vrtical plan is implmntd in th Matlab/ Simulink computing nvironmnt. Th motion of th targt in th vrtical plan is dscribd by quations: whr a x a x z g cos z sin a x (t) and z g (1) a (t) ar th acclrations of targt s cntr of th mass, (thy rprsnt th dynamics and manuvring proprtis of th targt), and ar vlocity of targt and pitch of targt s trajctory, (thy ar part of th quation for

3 rlativ motion), x g and z g ar th coordinats of targt s cntr of th mass. In homing-guidanc modl, w hav dfind th block Targt kinmatics. Th motion of missil in th vrtical plan is dscribd by th quation: a g g xk a zk x cos z sin (2) In th homing-guidanc modl, w hav dfind th block Missil dinamic+kinm. Th kinmatics quations of homing-guidanc in th vrtical plan ar: r cos( ) cos( ) r sin( ) sin( ) (3) In this simulation modl of homing guidanc, th mthod for proportional navigation has bn applid (Nupokov, 1970, Prsada, 1973, Dskovski, 2004).. In this mthod, th angl vlocity of targt s trajctory must b proportional with th angl vlocity of targt s lin of sight, that is: K (4) Th idal rlation in this cas is givn with: K 0 (5) In th givn, implmntd modl, ths guidanc laws ar usd as follows: - Classical proportional navigation: in this cas - only vlocity on lin of sight of th taggt dfi/dt is masurd; - Classical proportional navigation: in this cas - vlocity on lin of sight on targt dfi/dt and vlocity of approach btwn targt and missil dr/dt, ar masurd. - Improvd proportional navigation; in this cas - vlocity on lin of sight of targt dfi/dt, vlocity of approach btwn targt and missil dr/dt, and acclration normal to th targt s lin of sight an, ar masurd. - Optimal proportional navigation: in this cas - ths paramtrs ar masurd: vlocity of lin of sight of th targt, vlocity of approach btwn targt and missil, acclration of targt normal to th lin of sight and initial angl of lad. - Classic proportional navigation with fuzzy dtrmind angl of lad ksif and vlocity of approach btwn targt and missil drf: in this cas, w don t nd th masurmnt of vlocity of approaching btwn targt and missil dr/dt, and th angl vlocity of targt s lin of sight dfi/dt. 3. APPLICATION OF FUZZY LOGIC IN FIRE CONTROL SYSTEMS Enginring a fuzzy control systm uss many idas from th so-calld convntional and modrn control nginring mthodologis, xcpt that in fuzzy control it is oftn said that a formal mathmatical modl is assumd unavailabl so that a thorough mathmatical analysis is impossibl (Dimirovski, 1995, Dimirovski, 2002). Whil it is oftn th cas that it is difficult, impossibl, or cost-prohibitiv to dvlop an accurat mathmatical modl for many procsss, it is almost always possibl for th control nginr to spcify som typ of approximat modl of th procss (aftr all, w do know what physical objct w ar trying to control). Indd, it has bn our xprinc that most oftn th control nginr dvloping a fuzzy control systm dos hav a mathmatical modl availabl. In this papr, fuzzy logic is applid for guidanc law of a homing missil(dskovski, 2004). For this purpos, th following variabls ar fuzzifid: th approaching vlocity of th targt and missil drf, and th initial angl of lad on th launchr ksif. For dtrmining of ths fuzzy variabls, thr hav bn dfind and constructd 4 fuzzy logic controllr infrnc systms (FLC): two FLC ar usd for dtrmining of drf, and two for dtrmining ksif. Input paramtrs of th FLC, which ar usd for dtrmining of drf, ar: vlocity of targt, angl of orintation (2 rgims: targt laving or targt arriving) gama, and angl of lvation of th targt - fi. Fig. III. FLC for dtrmining th drf. Whn th targt is in arrival rgim, it is th following fuzzy-rul knowldg-bas infrnc that dtrmins th drf as a function of th input paramtrs stablishd: IF is mf1 and fi0 is low THEN IF is mf1 and fi0 is mdium THEN IF is mf1 and fi0 is high THEN output1 is mf7

4 IF is mf1 and fi0 is vry high THEN output1 is mf8 IF is mf2 and fi0 is low THEN output1 is mf5 IF is mf2 and fi0 is mdium THEN IF is mf2 and fi0 is high THEN output1 is mf7 IF is mf2 and fi0 is vry high THEN output1 is mf8 IF is mf3 and fi0 is low THEN output1 is mf4 IF is mf3 and fi0 is mdium THEN output1 is mf5 IF is mf3 and fi0 is high THEN output1 is mf7 IF is mf3 and fi0 is vry high THEN output1 is mf9 IF is mf4 and fi0 is low THEN output1 is mf3 IF is mf4 and fi0 is mdium THEN output1 is mf4 IF is mf4 and fi0 is high THEN IF is mf4 and fi0 is vry high THEN output1 is mf9 IF is mf5 and fi0 is low THEN output1 is mf2 IF is mf5 and fi0 is mdium THEN output1 is mf4 IF is mf5 and fi0 is high THEN IF is mf5 and fi0 is vry high THEN output1 is mf9 IF is mf6 and fi0 is low THEN output1 is mf1 IF is mf6 and fi0 is mdium THEN output1 is mf3 IF is mf6 and fi0 is high THEN IF is mf6 and fi0 is vry high THEN output1 is mf10 Whn th targt is laving, th rul bas is vry small (16 ruls), bcaus in th laving rgim targts with vlocity largr than 300 m/s cannot b shoot. Th appropriat choic of 6 mmbrship function dgrs for variabl hav bn dfind. Similarly, For variabl fi0, thr ar dfind 4 mmbrship function dgrs, and for th angl it is low, mdium, high, and vry high. Mmbrship function dgrs of th variabls and fi0 ar triangl contours with linguistic valus as follows: {mf1,mf 2,mf3,mf 4,mf5,mf 6} fi0 {low, mdium, high, vry high}, Th fixd sts of thirs valus ar within in th nxt prsntd intrvals: [100, 400m/ s], fi0 [0,1.507rad] W hav shown in our cas study th application of fuzzy systm basd dsigns for control, guidanc and suprvision of missils and combat scnarios that us fuzzy infrnc dcision and control and which is hybrid combind with math-analytical plus fuzzy soft-computing tchniqus(yn t. al. 1998). Of cours, this has to b don in a mod nsuring thir consistnt compatibility. Scondly, w hav shown in our application that thr is a limitd bnfit on prformanc of ths systm nginring dsigns according to th ral-world facts that to som tasks fuzzy systm tchniqus ar bttr suitd whil to othrs math-analytical tchniqus ar mor fruitful. And thirdly, it is rathr important to not that indd mploying som soft-computing formalism and tchniqu, such as fuzzy systms in hr, lads to crating tchnological systms with highr quotint of machin intllignc and simultanously improving or simplifying nginring structur of th dsignd systm. Fig. I. Fuzzy variabl for th vlocity c. Fig.. Fuzzy variabl for th vlocity fi0 4. SIMULATION RESULTS With computational simulation of th systm sown in Figur 2 for svral initial conditions, w can xcut diffrnt simulation xprimnts for various anti-air combat scnarios. In particular, in hr our intrst is focusd on th rsults obtaind by simulation whn fuzzy logical law for guidanc is applid for th scnario of approaching intrcption and of laving intrcption. In Figurs I and II, th motion of th targt and th missil along with th instantanous miss ar

5 rprsntd for th first scnario; th initial conditions ar: altitud of targt H=1500m, vlocity of targt =250m/s, and th targt is coming, gama=180. For th scond scnario, Figurs III and IX th motion of th targt and missil along with th instantanous miss ar rprsntd; th initial conditions ar: altitud of targt H=1000m, vlocity of targt =250m/s, and th targt is outgoing, gama=0. It is sn from th trajctoris in ths simulations, for two diffrnt scnarios, that th systm functions proprly and th contact missil-targt is obtaind in both cass. During th volution of th instantanous miss at th contact tim and considrably bfor th contact, th miss rachs rabidly valu zro. Fig. IX. Evolution of th instantanous miss. 5. CONCLUSION Fig. I. Trajctoris of th missil and th targt. In this papr, th application of a fuzzy-logic rul knowldg bas to th fir control systm (homing missil guidanc) for air dfnc systms has bn drivd. It is dvlopd by using Fuzzy Toolbox of Matlab. W hav usd th fuzzy logic for dtrmining th approaching vlocity btwn th missil and th targt as wll as th lading angl, which will b takn on th launching station sttings. Ths two paramtrs ar usd in th law for homing guidanc of th missil. With this mthod, th ncssity for calculation of ths paramtrs, which ar normally obtaind by using som prvious stimation, has bn amlioratd. Th simulation modl in th vrtical plan was dvlopd in Matlab/ Simulink programming platform. Th aim of this papr is to provid a quality guidanc procss with minimum numbr of masurmnts, and to us th rsults for modification of th xisting air dfnc systms, which ar prsnt in our Army (Strla 10). Fig. II. Evolution of th instantanous miss. Th contributions of this papr ar th dcrasd numbr of snsors which ar usd in th convntional dsign. W hav obtaind th improvd manouvring missil potntial. Th third advantag is that w hav dcrasd th ncssary hardwar mountd on th missil and th dstroying missil capability is incrasd. Th dvlopd simulation programs and obtaind simulation rsults gav us an opportunity to pursu th implmntation of th fuzzy logic in th fir control systm whn th whol 3D spac is takn into considration. This is th topic for th futur rsarch. Fig. III. Trajctoris of th missil and th targt.

6 REFERENCES Brnji, H. R. (1991). Fuzzy logic controllrs. In: R. R. Yagr and L. A. Zadh, ditors, An Introduction to Fuzzy Logic Applications in Intllignt Systms, Kluwr Acadmic Publishrs. Nw York, US. Davis, L. Jr., J. W. Follin Jr., and L Blitzr (1958). Th Extrior Ballistics of Rockts. D. an Nostrand Co., Princnton, NJ US. Dskovski, S. (2004). Homing Guidanc and Missil Systms for Air Dfnc. MA of ARM, Skopj, MK (in Macdonian). Dskovski, S., Z. Gacovski, and G. Dimirovski (2003). Homing guidanc laws using applid fuzzy systms. In: Procdings of th 1 st Intrnational Confrnc on Rcnt Advancs in Spac Tchnologis (RAST03), Istanbul, Nov , pp Turkish Air Forc Acadmy, Istanbul, TR. Dimirovski, G. M. (1995). Foundations of Digital Fuzzy-knowldg Basd Control, Lctur Nots of IASE. FEE of EE SS Cyril and Mthodius Univrsity, Skopj MK (in Macdonian). Dimirovski G. M. (2002). Nw Trnds in Missil Control and Guidanc using Fuzzy Systms (Kynot Lctur). In: First Symposium for Explosiv matrials, Wapons and Military Tchnology, Sptmbr 25-28, Ohrid, Rp. of Macdonia. MA-ARM, Skopj, MK. Dimirovski, G., S. Dskovski, and Z. Gacovski (2004). Classical and fuzzy-systm guidanc laws in homing missil systms. In: Procdings of th 2004 IEEE AESS Intrnational Arospac Confrnc, March 6-13, Big Sky, Montana, pp (1-18). Th IEEE, Piscataway, NJ, and IEEE Arospac Confrncs Offic, Manhattan Bach, CA, USA. Glv, S., S. Dskovski, and Z. Gacovski (2003). Simulation modl for dtrmining th launching zons for missil systms for air dfnc. In: Procdings of th 6 th National Confrnc ETAI 2003 with Intrnational participation, Ohrid, pp. A63-A68. Socity for ETAI, Skopj, MK. Glv, S., S. Dskovski, and Z. Gacovski (2005). Simulation modl for arly warning for air dfnc missil. In: Procdings of th 7 th National Confrnc ETAI 2005 with Intrnational participation, Ohrid, pp. A117- A122. Socity for ETAI, Skopj, MK. Klir, G. J., and Bo Yuan (1995). Fuzzy Sts and Fuzzy Logic Thory and Applications. Prntic Hall PTR, Uppr Saddl Rivr, NJ. Knzvic, S. (1980). Thory of Guidd Ground-toair Missils. Military Publishing Co., Blgrad, SR (in Srbo-Croat). Malygin, A. S. (1978). Fir Control of Missil Systms for Anti-aircraft Combat. onno Izdatlstvo MO SSSR, Moskva, RU (in Russian). Mohnski, D, G. Dimirovski G., and S. Dskovski (2000). Fuzzy rul-basd systm for dtrmining th launching zons for light anti-aircraft missils. In: Procdings of th 5 th National Confrnc ETAI 2000 with Intrnational Participation, Ohrid, MK, pp. A-94-A99. Socity for ETAI, Skopj, MK. Nupokov. F. K. (1970). Shooting by Znith Rockts onno Izdatlstvo MO SSSR, Moskva, RU (in Russian). Prsada. S. A. (1973). Horizon Znith Rockt Complxs. onno Izdatlstvo MO SSSR, Moskva, RU(in Russian). Ross, T. J. (2004). Fuzzy Logic with Enginring Applications. J. Wily & Sons, Ltd., Chichstr, England, UK. Siouris, G. M. (2004). Missil Guidanc and Control Systms. Springr-rlag, Nw York, US. Xu, L.-H., Y.-W. Jing, G. M. Dimirovski, and L.-D. Shi (2006). On UKF Basd Filtr in INS/GPSS Intgratd Navigation Systms: Pt I Thory; Pt II Applications (Joint Rsarch Rport). ICS- SIS&T of Northastrn Univrsity, Shnyang, P.R. of China, and DCE-FE of Dogus Univrsity, Istanbul, TR. Yn, J., and R. Langari (1998). Fuzzy Logic: Intllignc, Control, and Information. Prntic Hall, Uppr Saddl Rivr, NJ US. Zadh, L. A. (1983). Th rol of fuzzy logic in th managmnt of uncrtainty in xprt systms. Fuzzy Sts and Systms, vol. 11, pp (Elsvir Scinc Publishrs BM North-Holland).