CONTROL SYSTEM DESIGN OF GUIDED MISSILE

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1 VOL. 6, NO., NOVEMBER 0 ISSN ARPN Journal of Eninrin and Alid Scincs Asian Rsarch Publishin Nwork ARPN. All rihs rsrvd. CONTROL SYSTEM DESIGN OF GUIDED MISSILE Muhammad A. R. Yass, Mohammd Khair Aldn Abbas and Ismail Ibrahim Shabib Elcro-Mchanical Eninrin Darmn, Univrsiy of Tchnoloy, Iraq Mchanical Eninrin Darmn, Al-Nahrain Univrsiy, Iraq E -Mail: mkaskar79@yahoo.com ABSTRACT In h rsn work, analyical rformanc of dynamic moion and ransfr funcion wr calculad in roll mod of flyin body. Th analysis of h conrol circui was mad by usin four mhods, Rouh Cririon o drmin whhr h sysm is sabl or no, Roo-Locus mhod usd o drmin h limiaion of h sabiliy for diffrn valu of ra yro 0. o 0. and diffrn valu of ain o 0, Frquncy Rsons mhod usd o find bs ransfr funcion which hav shors im sin and lss amoun of ovrshoo and las mhod usd h comromisin mhod which was don firs wih ailron dflcion o drmin h limid valu of ain, scondly wih caabiliy acuaor swllin ra. Final ransfr funcion slcd was wih ra of yro qual o 0. and ain qual o 8 for bs sady sa bhavior. Th mhod abov is a rfc soluion for flyin body conrol sysm in all mods and ivs an xclln rsul. Kywords: uidd missil, flyin body conrol sysm, Rouh cririon, Roo-Locus mhod, frquncy rsons mhod. INTRODUCTION I can drmin whhr our dsin of a conrol sysm ms h scificaion if h dsird im rsons of h conrolld variabl drmind. by drivin h dfrnial quaion for h sysm solvin hm an accura soluion of h sysm's rformanc can b obaind, bu his aroach is no fasibl for ohr han siml sysm if h rsons dosn' m h scificaions 'i is no asy o drmin from his soluion jus wha hysical aramrs in h sysm should b chand o imrov h rsons. Th abiliy of rdicion h sysm's rformanc by an analysis ha dos no rquir h acual soluion of h diffrnial quaion. Also, w would lik o indica his analysis radily h mannr or mhod by which his sysm mus b adjusd or comnsad o roduc h dsird rformanc characrisics. Th firs hin ba w wan o know abou a ivn is whhr or no i is sabl. This can b drmind by xaminin h roo obaind from h involvd in drmin h roo can b dious, a simlr aroach is dsirabl. By alyin Rouh s cririon o h characrisic quaion i is ossibl in shor or. Ys i dosn' saisfy us bcaus i dosn' indica h dr of sabiliy of h sysm, i.., h amoun of ovrshoo mus b mainaind, wihin rscribd limi and ransins mus di ou in a sufficinly shor im. Th rahical m holds o b dscribd in his s no only indica whhr a sysm is sabl or no bu, for a sabl sysm also a low dr of sabiliy. Ths ar wo basic mhods availabl o us, w can choos o analyz and inrr h sady sa suicidal rsons of h ransfr funcion of h sysm obains an ida of h sysm's rsons. This mhod is basd uon h inrraion of a SyQus lo. Alhouh his frquncy-rsons aroach dosn' yild an xac quaniaiv rdicion of h sysm's rformanc, i.., h ols of h conrol raio cs/rs can no b drmin, nouh informaion can b obaind o indica whhr h sysm nd o b h sysm should b comnsad. This dals wih h rcord mhod ha roos locus mhod, which incororas h mor dsirabl faurs of boh, h classical mhod and h frquncy - rsons mhod. Th roo locus is a lo of h roo of h characrisic quaion of h closd loo sysm as h funcion of h ain. This rahical aroach yild a clar indicaion of h ffc of ain adjusmn wih solvin small ffor comard wih ohr mhod. Th undrlyin rincil is ha h ols of Cs/Rs ransin rsons ar rlasd o h sourc and ols of h on loo ransfr funcion Gs Hs and also o h ain. An imoran advana of h roo locus mhod is ha h roo of h characrisic quaion of h sysm can b obaind dircly, his rsul in a coml and accura soluion of h ransin and sady sa rsons of h conrolld variabl. Anohr imoran faur is ha an aroxima soluion can b obaind wih a rducion of h work rquird. As wih any ohr dsin chniqu, a rson who has obaind a cofficin xrinc wih his mhod is abl o aly i and o synhsiz a comnsain nwork, if on is rquird, wih rlaiv as. MATHEMATICAL ANALYSIS In h rsn work, h analyical rformanc of dynamic moion and ransfr funcion wr calculad in roll mod of flyin body. Th analysis of h conrol circui was mad by usin four mhods, Rouh Cririon o drmin whhr h sysm sabl or no, Roo-Locus mhod usd o drmin h limiaion of h sabiliy for diffrn valu of ra yro 0. o 0. and diffrn valu of ain o 0, Frquncy Rsons mhod usd o find bs ransfr funcion which hav shors im sin and lss amoun of ovrshoo and las mhod usd h comromisin mhod which was don firs wih ailron dflcion o drmin h limid valu of ain, scondly wih caabiliy acuaor swllin ra. Final ransfr funcion slcd was wih ra of yro qual o 0. and ain qual o 8 for bs sady sa bhavior. Th mhod 6

2 VOL. 6, NO., NOVEMBER 0 ISSN ARPN Journal of Eninrin and Alid Scincs Asian Rsarch Publishin Nwork ARPN. All rihs rsrvd. abov is a rfc soluion for flyin body conrol sysm in all mods and iv an xclln rsul. = AERODYNAMIC ANALYSIS Roll aiud conrol sysm Th non dimnsional Laral quaion [4] 5 Th innr loo ransfr funcion A muli-loo fd-back conrol sysm alid o flyin-body, a main fdback of roll anl an aiud yro and an innr loo of roll ra fd-back [], s Fiur-. 6 = Whil h ovrall ransfr funcion 7 Fiur-. Roll aiud conrol sysm. If h acuaor dynamic includd h rsnaion can b sn in Fiur- h innr loo ransfr funcion R-wri q. = 8 Whil h ovrall ransfr funcion was [8] and Thn Fiur-. Roll aiud conrol sysm wih acuaor. 4 9 L = and L = 0 So s= On loo ransfr funcion K-Roo Locus From on loo ransfr funcion which was qual o [4] So h char- quaion bcam qual o 7

3 VOL. 6, NO., NOVEMBER 0 ISSN ARPN Journal of Eninrin and Alid Scincs Asian Rsarch Publishin Nwork ARPN. All rihs rsrvd. s³ s² GR s = 0 Th clos loo.s which was qual o Dividin quaion by w will s= S³ S² S = 0 Solvin quaion abov for difrn[ k] and [GR] and all h comlx roo found was sudid o drmun h ffc of k. Cols loo anfr funcion GR Roo Locus Divid quaion 5 by s= Also i can b wrin as φ s= φ D By arial fracion D s s s s s i i S S i s i s Th Invrs Lalac Transformaion φ = φ D cos sin 6 Solvin quaion abov for difrn[ k] and [GR] and all h comlx roo found was sudid o drmun h ffc of [GR]. Dynamic rsons of ailron dflcion from quaion φ Kφ = δ TφS a and i can b also wrin as δa s K = T S φ s φ φ 6a By akin h lalac invrs of quaion 6a oo δa s K = φ Tφφ φ Dividd quaion 6b by φ 0 S φ D a k φ From quaion.6b φ = T φ0 φ oo φ φ 0 φ φ D = sin P sin cos cos P sin cos P cos sin Sa φd = cos sin - P sin cos φ cos sin sin cos sin cos cos sin By varyin im i can b solv for Ailron dflcion. Acuaor slwin ra I is h im rquird for acuaor o dflc h ailron. 6 8

4 VOL. 6, NO., NOVEMBER 0 ISSN ARPN Journal of Eninrin and Alid Scincs Asian Rsarch Publishin Nwork ARPN. All rihs rsrvd. 9 By diffrnia quaion 6. [ = cos sin sin cos cos sin sin cos cos sin sin cos sin cos cos sin cos sin sin cos T k a S D φ φ φ So by solvin h abov quaion a diffrn GR, K and a = 0, bcom max acuaor slwin ra which occurs a = 0, w will diffrn acuaor slwin ra a diffrn combinaions of GR and K. RESULTS AND DISCUSSIONS DISCUSSIONS Th uros of his dsin o obain lars ain aainabl rquird and h smalls ak ovrshoo and shors im sin. From Tabl- and Fiurs and, GR = 0., maximum K is qual o 4 and for mor han ha h sysm is no sabl. I can b obsrv from Tabl- ha by incrasin K a consan valu of GR, h ral ar of comlx roo will dcras and h imainary ar will incras, his man ha h ovrshoo will incras oo and sin im will also incras, so i mus hav a choos bwn h lars ain aainabl, shors ak ovrshoo and shors im sin. Also by incrasin a consan K h ral ar of comlx roo will incras and imainary ar will incras oo and ha incras h ak ovrshoo and br sabiliy. S Fiurs -0 I can b obsrvd from Tabl- and ailron dflcion curv Fiurs o 0 ha by incrasin K a consan GR, ailron dflcion will also incras bu i dcras by dcasin incrasin GR a consan K. So i can o byond GR = 0. and K = 8 bcaus i is limid by ailron dflcion and cas sudy dsin daa which was qual o 5 rad. Afr comromisin all h valus of K and GR sarchin for our dsin rquirmn which is ivn abov, i is found ha GR = 0., K = 8 is h bs slcion which mus b chckd wih acuaor slwin im im of acuaor o dflc. From Tabl- i can b noic ha h maximum valu of acuaor slwin ra a GR = 0. and K = 0 was qual o rad /sc and h dsin valu of acuaor slwin ra is qual o 90 rad/sc, ha man ha h slcion valu was wihin h limi. Also i can b obsrvd ha as K incrass h acuaor slwin im will also incras and for incrasin GR a consan K h acuaor slwin im rmains h sam.

5 VOL. 6, NO., NOVEMBER 0 ISSN ARPN Journal of Eninrin and Alid Scincs Asian Rsarch Publishin Nwork ARPN. All rihs rsrvd. CONCLUSIONS I can conclud ha h rsons of a conrol sysm is xamind by roo locus mhod and i dnd on ral roo of h characrisic quaion of clos loo ransfr funcion and his roo dnd on K and GR so by incrasin K h roo shif o rih of roo locus which dcras h sabiliy bu by incrasin GR h roo shif o h lf which incrass h sabiliy also incrasin K and GR dnd on max ailron dflcion. REFERENCES [] Roskam J. 97. Mhods for Esimain Sabiliy and Conrol Drivaivs of Convnional Subsonic Airlans. Roskam Aviaion and Eninrin Cororaion, Lawrnc, Kansas. [] Hoak D.E. al USAF Sabiliy and Conrol DATCOM, Flih Conrol Division. Air Forc Flih Dynamics Laboraory, WPAFB, Ohio. [] Tornbk E. 98. Synhsis of Subsonic Airlan Dsin, Dlf Univ. Prss, Dlf, h Nhrlands. [4] Hank C.R. 97. Th Simulaion of a Lar J Transor Aircraf. Vol. I: Mahmaical Modl. NASA CR-756, March. [5] Abbo I.H. and von Donhoff A.E Thory of Win Scions, Dovr, Nw York. [6] Nlson R. C Flih Sabiliy and Auomaic Conrol. McGraw-Hill, Nw York. [7] Mac Millin P.E., Golovidov O.B., Mason W.H., Grossman B. and Hafka R.T Trim Conrol and Prformanc Effcs in Variabl-Comlxiy Hih- Sd Civil Transor Dsin, MAD , July. [8] Hffly R.K. and Jwll W.F. Aircraf Handlin Qualiis Daa, NASA CR. 40

6 VOL. 6, NO., NOVEMBER 0 ISSN ARPN Journal of Eninrin and Alid Scincs Asian Rsarch Publishin Nwork ARPN. All rihs rsrvd. Tabl-. Roll anl rsons a diffrn valus of K and GR. GR K Characrisics quaions Ral roo Sady im Max ak ovr shoo sabiliy ±.05j sabl -4.7±7.6j sabl -.60±.4j Imainary roo ±4.056j ±6.9j ±8.4j ±9.9j ±.444j ±.84j ±4.6j ±5.88j ±7.668j ±5.54j sabl ±7.557j sabl ±9.66j sabl ±.496j sabl ±.4j ±4.59j ±5.96j ±7.77j ±7.04j ±6.05j ±5.9j ±5.8j ±5.778j Sabl ±6.666j sabl ±7.75j sabl ±8.80j sabl ±8.80j sabl ±9.88j sabl ±45.6j ±45.06j ±44.5j ±44.49j ±4.97j ±44.007j ±44.5j sabl ±44.66j sabl ±45.0j sabl ±45.87j -.97±5.5j -.88±5.j -.76±5.958j -0.5±5.640j -9.76±5.40j ±5.6j -6.67±5.0j -5.60±54.084j ±54.87j -.8±55.556j sabl sabl sabl S50s455.9s690.6 S50s455.9s80.7 S50s455.9s S50s455.9s S50s455.9s S50s455.9s S50s455.9s S50s455.9s S50s455.9s6.4 S50s455.9s

7 VOL. 6, NO., NOVEMBER 0 ISSN ARPN Journal of Eninrin and Alid Scincs Asian Rsarch Publishin Nwork ARPN. All rihs rsrvd. Tabl-. Roll anl rsons a diffrn valus of K and GR. GR Gain K Ovrshoo rad Tim ris sc Sady sa im sc Mor han Mor han 0. 4 Ovr damin Ovr damin Tabl-. Rsul of maximum ailron dflcion rquird for diffrn valus of K and CR. GR K max max rad

VOL. 6, NO., NOVEMBER 0 ISSN 89-6608 ARPN Journal of Eninrin and Alid Scincs 006-0 Asian Rsarch Publishin Nwork ARPN. All rihs rsrvd. www.arnjournals.com Tabl-4.

8 VOL. 6, NO., NOVEMBER 0 ISSN ARPN Journal of Eninrin and Alid Scincs Asian Rsarch Publishin Nwork ARPN. All rihs rsrvd. Tabl-4. Rsul of maximum acuaor slwin ra rquird for diffrn K and CR. GR K max /Sc max rad/sc

9 VOL. 6, NO., NOVEMBER 0 ISSN ARPN Journal of Eninrin and Alid Scincs Asian Rsarch Publishin Nwork ARPN. All rihs rsrvd. Roll Anl Rsons GR= Transin Tim Fiur-. Rollin rsons vrss im rsons for GR = 0. and diffrn ain valu K= K= K= K=4 K a consan GR K=5 K=7 K=9.40 Roll Anl Rsons Transin Tim Fiur-. Rollin rsons vrss im rsons for GR = 0. and diffrn ain valu. 44

10 VOL. 6, NO., NOVEMBER 0 ISSN ARPN Journal of Eninrin and Alid Scincs Asian Rsarch Publishin Nwork ARPN. All rihs rsrvd. K a consan GR K=6 K=8 K=0.40 Roll Anl Rsons Transin Tim Fiur-. Rollin rsons vrss im rsons for GR=0. and Diffrn Gain valu Roll Anl Rsons 0.0 K=------GR=0. K=------GR=0. K=------GR= Transin Timsc Fiur-4. Rollin rsons vrss im rsons for GR = 0. and diffrn ain valu. 45

11 VOL. 6, NO., NOVEMBER 0 ISSN ARPN Journal of Eninrin and Alid Scincs Asian Rsarch Publishin Nwork ARPN. All rihs rsrvd Roll Anl Rsons K= GR=0. K= GR=0. K= GR= Transin Timsc Fiur-5. Rollin rsons vrss im rsons for GR = 0. and diffrn ain valu Roll Anl Rsons K= GR=0. K= GR=0. K= GR=0. K= GR= Transin Timsc Fiur-6. Rollin rsons vrss im rsons for GR = 0. and diffrn ain valu. 46

12 VOL. 6, NO., NOVEMBER 0 ISSN ARPN Journal of Eninrin and Alid Scincs Asian Rsarch Publishin Nwork ARPN. All rihs rsrvd Roll Anl Rsons GR=0. K= 0.0 K= K= K= Transin Tim Fiur-7. Rollin rsons vrss im rsons for GR = 0. and diffrn ain valu Roll Anl Rsons.00 GR= Transin Tim Fiur-8. Rollin rsons vrss im rsons for GR = 0. and diffrn ain valu. K=5 K=6 K=7 47

13 VOL. 6, NO., NOVEMBER 0 ISSN ARPN Journal of Eninrin and Alid Scincs Asian Rsarch Publishin Nwork ARPN. All rihs rsrvd Roll Anl Rsons.00 GR= Transin Tim Fiur-9. Rollin rsons vrss im rsons for GR = 0. and diffrn ain valu..000 K=8 K=9 K=0.00 Roll Anl Rsons 0.0 GR= Transin Tim Fiur-0. Rollin rsons vrss im rsons for GR = 0.4 and diffrn ain valu. K= K= K= K=4 48

14 VOL. 6, NO., NOVEMBER 0 ISSN ARPN Journal of Eninrin and Alid Scincs Asian Rsarch Publishin Nwork ARPN. All rihs rsrvd. Roll Anl Rsons GR= Transin Tim Fiur-. Rollin rsons vrss im rsons for GR=0.4 and diffrn ain valu K=5 K=6 K= Roll Anl Rsons GR= Transin Tim Fiur-. Rollin rsons vrss im rsons for GR = 0.4 and diffrn ain valu. K=8 K=9 K=0 49

15 VOL. 6, NO., NOVEMBER 0 ISSN ARPN Journal of Eninrin and Alid Scincs Asian Rsarch Publishin Nwork ARPN. All rihs rsrvd Roll Anl Rsons GR= Transin Tim Fiur-. Rollin rsons vrss im rsons for GR=0.5 and diffrn ain valu K= K= K= K= Roll Anl Rsons GR= Transin Tim Fiur-4. Rollin rsons vrss im rsons for GR = 0.5 and diffrn ain valu. K=5 K=6 K=7 50

16 VOL. 6, NO., NOVEMBER 0 ISSN ARPN Journal of Eninrin and Alid Scincs Asian Rsarch Publishin Nwork ARPN. All rihs rsrvd Roll Anl Rsons GR= Transin Tim Fiur-5. Rollin rsons vrss im rsons for GR = 0.5 and diffrn ain valu GR=0. K=8 K=9 K= K= K=4 K=6 Ailron Dflcion Rad Tim Rsons sc Fiur-6. Ailron dflcion vrss im rsons for GR = 0. and diffrn ain valu. 5

17 VOL. 6, NO., NOVEMBER 0 ISSN ARPN Journal of Eninrin and Alid Scincs Asian Rsarch Publishin Nwork ARPN. All rihs rsrvd GR= K=8 K= Ailron Dflcion Rad Tim Rsons sc Fiur-7. Ailron dflcion vrss im rsons for GR = 0. and diffrn ain valu GR= K= K=4 K=6 Ailron Dflcion Rad Tim Rsons sc Fiur-8. Ailron dflcion vrss im rsons for GR = 0. and diffrn ain valu. 5

18 VOL. 6, NO., NOVEMBER 0 ISSN ARPN Journal of Eninrin and Alid Scincs Asian Rsarch Publishin Nwork ARPN. All rihs rsrvd GR = 0. K= K=4 K=6 Ailron Dflcion Rad Tim Rsons sc Fiur-9. Ailron dflcion vrss im rsons for GR = 0.. GR= K=8 K= Ailron Dflcion Rad Tim Rsons sc Fiur-0. Ailron dflcion vrss im rsons for GR = 0. and diffrn ain valu. 5

19 VOL. 6, NO., NOVEMBER 0 ISSN ARPN Journal of Eninrin and Alid Scincs Asian Rsarch Publishin Nwork ARPN. All rihs rsrvd GR = 0. K=8 K= Ailron Dflcion Rad Tim Rsons sc Fiur-. Ailron dflcion vrss im rsons for GR = 0. and diffrn ain valu GR= K= K=4 K=6 Ailron Dflcion Rad Tim Rsons sc Fiur-. Ailron dflcion vrss im rsons for GR = 0.4 and diffrn ain valu. 54

20 VOL. 6, NO., NOVEMBER 0 ISSN ARPN Journal of Eninrin and Alid Scincs Asian Rsarch Publishin Nwork ARPN. All rihs rsrvd GR= K=8 K= Ailron Dflcion Rad Tim Rsons sc Fiur-. Ailron dflcion vrss im rsons for GR = 0.4 and diffrn ain valu GR=0.5 K=.0000 K=4 K=6 Ailron Dflcion Rad Tim Rsons sc Fiur-4. Ailron dflcion vrss im rsons for GR = 0.5 and diffrn ain valu. 55

21 VOL. 6, NO., NOVEMBER 0 ISSN ARPN Journal of Eninrin and Alid Scincs Asian Rsarch Publishin Nwork ARPN. All rihs rsrvd GR= K=8 K=0 Ailron Dflcion Rad Tim Rsons sc Fiur-5. Ailron dflcion vrss im rsons for GR = 0.5 and diffrn ain valu. Andix A Fiur-A. Conrol sysm dsin simulaion usin Malab. 56

22 VOL. 6, NO., NOVEMBER 0 ISSN ARPN Journal of Eninrin and Alid Scincs Asian Rsarch Publishin Nwork ARPN. All rihs rsrvd. Fiur-A. Conrol sysm dsin rsul usin Malab, Gr = 0. K = 8. 57

MEM 355 Performance Enhancement of Dynamical Systems A First Control Problem - Cruise Control

MEM 355 Performance Enhancement of Dynamical Systems A First Control Problem - Cruise Control MEM 355 Prformanc Enhancmn of Dynamical Sysms A Firs Conrol Problm - Cruis Conrol Harry G. Kwany Darmn of Mchanical Enginring & Mchanics Drxl Univrsiy Cruis Conrol ( ) mv = F mg sinθ cv v +.2v= u 9.8θ