Modeling, Design and Control of a Ship Carried 3 DOF Stabilized Platform

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1 Research Jurnal f Appled Scences, Engneerng and Technlgy 4(19): , 1 SSN: Maxwell Scentfc Organzatn, 1 Submtted: May 8, 1 Accepted: May 9, 1 Publshed: Octber 1, 1 Mdelng, Desgn and Cntrl f a Shp Carred 3 DOF Stablzed Platfrm Leghmz Sad, Lu Sheng, Naem Faruk and Bumedene Latfa Cllege f Autmatn, Harbn Engneerng Unversty, Harbn, Helngjang 151, Chna Abstract: The system fr stablzng platfrm f a shp carred antenna a nd ts cre cmpnent are dscussed n ths study. Relevant mathematcs mdel f these cmpnents are establshed. Thus, the dynamc mdel f the system s deduced ncludng the effects f frctn, nerta and trque mtrs. Usng Sld Wrks, we bult the mechancal structure, ncludng the serv machne f each part f the system. The system under cnsderatn s a system wth strng nteractns between three channels. By usng the cncept f decentralzed cntrl, a cntrl structure s develped that s cmpsed f three cntrl lps, each f whch s asscated wth a sngle-varable cntrller. Frst, PD cntrller was appled; then, Takag-Sugen (TS) fuzzy cntrller was used fr cntrllng the platfrm. Smulatn tests were establshed usng Smulnk f Matlab. The btaned results have demnstrated the feasblty and effectveness f the prpsed fuzzy apprach cmparng t the PD cntrller. Smulatn results are represented n ths study. Keywrds: Decentralzed cntrl, dynamc mdel, fuzzy cntrller, PD cntller, smulnk, sldwrks, Takag-Sugen (TS) NTRODUCTON The stablzed platfrm s the bject whch can slate mtn f the vehcle and can measure the change f platfrm s mtn and pstn ncessantly. t can make the equpment whch s fxed n the platfrm am at and track bject fastly and exactly. n the stablzed platfrm systems, the basc requrements are t mantan stable peratn even when there are changes n the system dynamcs and t have very gd dsturbance rejectn capablty. Snce they began t be utlzed abut 1 years ag, stablzed platfrms have been used n every type f mvng vehcle, frm satelltes t submarnes and are even used n sme handheld and grund-munted devces (Hlkert, 8; Debrun, 8). ts applcatn s qute abrad and t becmes nvestgatve htspt n mst cuntres all the tme. The cnsdered platfrm s a class f multvarable servmechansms wth multple axes. The cntrl f such multvarable servmechansms s, n general, nt a smple prblem, as there exst crss-cuplngs, r nteractns, between the dfferent channels. n addtn, ths system s requred t mantan stable peratn even when there are changes n the system dynamcs. n the stablzed platfrm systems, the basc requrement s t have very gd dsturbance rejectn capablty. Presence f nherent nnlneartes such as strctn, frctn, saturatn f actuatrs, etc., als must be taken nt accunt. Many appraches have been prpsed t cntrl such a cmplex ntercnnected system fr example the decmpstn-crdnatn apprach, the aggregatn apprach, the multtme-scale apprach and the decentralzed cntrl apprach (Lnkens and Nyngesa, 1998; Lee et al., 1995) Snce the decentralzed cntrl apprach s relable and practcal n vew f the mplementatn, t s the mst ppular methd that attempts t desgn cntrl schemes, where each subsystem s cntrlled ndependently based n lcal nfrmatn. Hwever, the decentralzed appraches are restrcted t stablzatn and the dynamcs f each subsystem and the ntercnnectn terms are assumed t be knwn (Ne, 1997; Sh and Sngh, 199). n practce, the mdel f the cnsdered platfrm cntans vast unknwn uncertantes. Snce fuzzy lgc cntrl has been cnsdered as an alternatve t tradtnal cntrl schemes t deal wth system dynamcs uncertanty and btan the best perfrmance f the system. Fuzzy cntrl s adpted as the subject f ths study (Yeh, 1999). The bjectve f ths study s t develp the dynamcs mdel and the 3D desgn f the shp carred stablzed platfrm. Then, apply the PD and Fuzzy cntrllers fr stablzng the platfrm. By usng the decentralzed cntrl cncept, we develped a cntrl structure cmpsed f three separate cntrl channels, each f whch s asscated wth a sngle varable cntrller. The smulatn results n applyng the tw prpsed cntrller t a 3-DOF stablzatn system are presented whch demnstrates the effectveness f the prpsed fuzzy cntrller cmparng t the PD cntrller. Crrespndng Authr: Leghmz Sad, Cllege f Autmatn, Harbn Engneerng Unversty, Harbn, Helngjang 151, Chna 3843

2 (Yaw) (Ptch) (Rll) Fg. 1: The 3-DOF platfrm structure SYSTEM DYNAMCS System descrptn: The cnsdered system n ths study s cmpsed f the platfrm, nner gmbal, uter gmbal and the case (Fg. 1); each member s assumed t be rgd and has ne degree f freedm (Leghmz and Lu, 1). Accrdng t the Euler defntn f the rtatn angles, we defne the angles and rates relatng the fur members f the gmbaled system as fllwng (Barnes, 1971): θ = Relatve angle between the nner gmbal and the platfrm, measured abut the platfrm Y axs (Y p ) = Relatve angular rate between the nner gmbal and the platfrm, measured abut the platfrm Y axs (Y p ) ψ = Relatve angle between the uter and nner gmbals, measured abut the nner gmbal Z axs (Z ) = Relatve angular rate between the uter and nner gmbals, measured abut the nner gmbal Z axs (Z ) = Relatve angle between the case and the uter gmbals, measured abut the uter gmbal X axs (X ) = Relatve angular rate between the case and the uter gmbal, measured abut the uter gmbal X axs (X ) At each member f the gmbaled system we asscate an rthgnal crdnate system (Fg. ) platfrm (X p, Y p, Z p ), nner gmbal (X, Y, Z ), uter gmbal (X O, Y O, Z O ) and case (X C, Y C, Z C ). The cnsdered system platfrm s fxed n the shp. Generally the satellte dsh antenna s based n the back part f the shp presented n Fg. 3. Dynamcs mdel: The mathematcal mdelng was establshed usng Euler thery. The Euler s mment equatns are: M H (1) The net trque M cnssts f drvng trque appled by the adjacent uter member and reactn trque appled by the adjacent nner member: H dh dt mh m H H : nertal dervatve f the vectr H () 3844

3 Fg. : The system tplgy Fg. 3: The case crdnates n the bdy-fxed frames mh : Dervatve f H calculated n a rtatng frame f reference m : Abslute rtatnal rate f the mvng reference frame H : nertal angular mmentum M : External trque appled t the bdy By applyng Eq. () n the dfferent parts f the platfrm system, the system may be expressed as a set f secnd-rder dfferental equatns n the state varables. Slvng ths system f equatns we btan: C B A B (3) C A B B C A C A (4) A B A B 3845

4 C A C B * B B A B p p (5) p p C A B B where, A p sn B p 1 * M MPY C p A cs cs sn z B 1 sn cs z z * M z MZ C z x cs sn A 1 cs B cs sn cs C M * c MCX sn y Fg. 4: The base unt f the platfrm Fg. 5: The uter gmbal Detaled equatns cmputatn s presented n the study (Leghmz et al., 11). ESTABLSHNG THREE DMENSONAL MODEL OF THE STABLZED PLATFORM The desgn f a three-axs platfrm requres a ttal f fur bdes. These bdes nclude the base (case), the nner, uter and platfrm gmbals. The base, shwn n Fg. 4 s desgned t prvde a sld fundatn t the three gmbals that wll be rtatng arund ther respected axs. A rgd base s respnsble fr preventng vbratns that wll cause naccurate mvement and gve unpredctable dynamc respnses. n the rght sectn f the base s attached a serv machne be, shwn n Fg. 8a, respnsble f the rtatn f the uter gmbal. The uter gmbal, shwn n Fg. 5, cntrls the system platfrm rll. The uter gmbal wll be drectly attached t the actuatr munted t the base. When the actuatr s actvated t wll allw the uter gmbal t Fg. 6: The nner gmbal rtate 18. The secnd actuatr be, shwn n Fg. 8b, s cntaned nsde the uter gmbal. The actuatr s frmly attached nsde and s enclsed by a cap. The nner gmbal, shwn n Fg. 6, cntrls the 3- DOF platfrm yaw. The mddle gmbal s rtated by the actuatr hused n the uter gmbal. The mddle gmbal allws the platfrm t rtate 9. The thrd and fnal actuatr, shwn n Fg. 8c, s attached the left sde f the nner gmbal. The platfrm gmbal shwed n Fg. 7 s respnsble fr the platfrm s ptch. The platfrm gmbal des nt nclude husng fr an actuatr as there are n addtnal gmbals t rtate. The platfrm system assembly s represented n Fg

5 Fg. 7: The platfrm gmbal Fg. 8: The machne bes used n the platfrm the system based n these cmplete nnlnear dynamcs s extremely dffcult. t s thus necessary t reduce the cmplexty f the prblem by cnsderng the lnearzed dynamcs (Lee et al., 1996). Ths can be dne by ntng that the gmbal angles varatn are effectvely neglgble and that the shp velctes effect s nsgnfcant. Applyng the abve assumptns t the nnlnear dynamcs, the fllwng equatns are btaned: D c x Fc(sgn ) z F (sgn ) D D x 1 z z 1 p Fp(sgn ) x T T mm (6) (7) 1 (8) T Fg. 9: Fnal assembly f the platfrm Table 1: Platfrm parameters Platfrm nner gmbal Outer gmbal.119 x y.845 y z 1. z 1.1 D p.11 D.6 D c.3 Usng ths sftware we can als calculate the prncpal mments f nerta taken at the center f mass f each part f the platfrm system. These mments f nerta wll be used n the fllwng smulatn sectn. The values fund fr these parameters are gven n Table 1. SMULATON RESULTS AND DSCUSSON The cmplete nnlnear dynamcs fr the stablzed platfrm system was develped n the prevus sectn. Here, t suffces t nte that desgnng a smulatn fr 3847 PD cntrller smulatn: n the 3-D f platfrm we wll apply a decentralzed PD whch cnsste f three PD cntrllers appled t each part f the platfrm separately as shwn n Fg. 1 the PD parameters are calculated fr each part usng the Zegler-Nchls methd (Zegler and Nchls, 194). The btaned parameters are lsted n Table. n rder t see the utcme f the desgned cntrller, we perfrmed a smulatn n clsed-lp mde. Ths smulatn was partcularly useful fr the recgntn f the effect f each PD ceffcent t the respnse f the system. Smulatn results wll be presented t llustrate the gmbals behavr t dfferent PD parameters. They are presented n Fg. 11, whch cntan the step respnse f the platfrm system usng the PD cntrller and n Fg. 1, whch cntan the mpulsn respnse f the platfrm respnse usng the PD cntrller. As shwn n Fg. 11 and 1, the respnses are sgnfcantly acceptable but the respnse characterstcs stll nt well mprved. Fgure 13 llustrates the pstn trackng respnses usng PD cntrller. t can be seen that ths cntrller present bad trackng perfrmance wth bg rsng tme. Ths s due t the nnlneartes f the system that the cntrller can t handle. Fr ths an ntrductn f a nn lnear cntrller s necessary.

6 Fg. 1: PD cntrl fr the 3-DOF platfrm Table : PD parameters K p K K d Gmbals pstn (rad) Platfrm nner gmbal Outer gmbal Fg. 11: Step respnse f the platfrm usng PD cntrller Gmbals pstn (rad) Platfrm nner gmbal Outer gmbal Fg. 1: mpulse respnse f the platfrm usng PD cntrller Gmbals pstn (rad) Platfrm nner gmbal Outer gmbal Reference Fg. 13: Pstn trackng respnse usng PD cntrller Gmbals pstn (rad) Platfrm nner gmbal Outer gmbal Fg. 14: Dsturbance rejectn f the 3DOF platfrm usng PD cntrller 3848

7 Fg. 15: TS fuzzy cntrller fr the 3-DOF platfrm Als, n rder t see the dsturbance rejectn apttude f the PD cntrller, small dsturbance was ntrduced. The njected dsturbance was a pulse f.1rad ampltude and adds t the system nput at tme nstant 3s. The dsturbance rejectn capablty f each part f the stablzed platfrm usng PD cntrller s pltted n Fg. 14 They shw that the cntrller s als unable f dealng wth ths stuatn. Fuzzy cntrller smulatn: n the 3-D f platfrm we wll apply a decentralzed Fuzzy cntrller whch cnsste f three TS-Fuzzy cntrllers appled t each part f the platfrm separately as shwn n Fg. 15. The structure f a cmplete fuzzy cntrl system s cmpsed frm the fllwng blcs: Fuzzfcatn, Knwledge base, nference engne, Defuzzfcatn as shwn n Fg. 3 (Chuen, 199). The general TS fuzzy systems n ths study use nput varables. e θ, e ψ, e and,, are selected as nput varables f each subsystem respectvely and defned as tw varables representng the stuatn. c j s selected as utput f the j th subsystem and defned as a varable representng the actn. Ntce that varables fr θ, ψ,,, and assume lngustc terms as ther values such as pstve-bg, negatve-small and zer, etc. Table 3: Rule base f the fuzzy lgc cntrller e θ \ NB NM NS ZR PS PM PB PB ZR PS PM PB PB PB PB PM NS ZR PS PM PB PB PB PS NM NS ZR PS PM PB PB ZR NB NM NS ZR PS PM PB NS NB NB NM NS ZR PS PM NM NB NB NB NM NS ZR PS NB NB NB NB NB NM NS ZR Usng the Takag-Sugen mdel (Takag and Sugen, 1985), the fuzzy system s characterzed by a set f p f-then rules stred n a rule-base and expressed as R: F e θ s A and s B then: c j p p1e p where, A and B are lngustc terms whch n ths study can be NL, NM, NS, ZR, PS, PL and PB. The rule base f ths cntrller s summarzed n Table 3 fr smplcty; the same unverse f dscurse and the same fuzzy set are adpted fr fuzzy nput varables. The membershp functns f ssceles trangles are used as the fuzzfcatn functn. The Sugen type fuzzy cntrller emply lnear functns f nput varables as rule cnsequent, s the steps f aggregatn and defuzzfcatn f fuzzy rules are smultaneusly and the fnal utput f the system 3849

8 Platfrm pstn (rad) PD TS Fuzzy (a) Outer gmbal pstn (rad) nner gmbal pstn (rad) PD TS Fuzzy (b) PD TS Fuzzy Fg. 16: Step respnse f the platfrm system usng PD and TS Fuzzy cntrller, (a) platfrm, (b) nner gmbal, (c) uter gmbal (c) s the weghted average f all rule utputs, cmputed as: T l N j c 1 N 1 (9) The zer-rder Sugen mdel s appled, the utput level z s a cnstant (p 1 = p = ). The value f p depends n the lngustc term f the utput. Fr example f the utput s NB (accrdng t the rule base) s p = -1. T bserve the perfrmance f the desgned fuzzy cntrller a cmparsn between the step respnse f the platfrm usng PD cntrller and the step respnse f the platfrm usng the fuzzy cntrller was dne. The results f the smulatn nvestgatng pstnng perfrmance cmparsn f platfrm system are shwn n Fg. 16. Fgure 16 (Sld lnes) shws step respnses f the stablzed platfrm system when cntrlled by three separated rder- TS fuzzy cntrllers. Fgure 16 Platfrm pstn (rad) Platfrm respnse Desred trajectry Fg. 17: Pstn trackng respnse f the platfrm (dashed lnes) shws step respnses f the stablzed platfrm system when cntrlled by three separated PD cntrllers. As shwn n Fg. 16 the respnses (sld lnes) were sgnfcantly mprved wth smaller versht, shrter rsng tme. Fgure 17 llustrates the pstn trackng respnses usng TS fuzzy PD cntrller. t can be seen that ths cntrller present gd trackng perfrmance wth mnr rse tme. 385

9 CONCLUSON Our research fcused n the cmmn crdnate, knematcs, dynamcs, cntrl system and sftware desgn fr shp carred stablzed platfrm. Fr that n ths study we develped a dynamcs mdelng f the platfrm and a 3D mdel f the platfrm usng Smulnk and SldWrks. Then, we cnsdered the prblem f cntrllng ths multvarable servmechansm where there exst crss-cuplngs between the channels. A fuzzy PD cntrl strategy usng a Takag-Sugen fuzzy mdel has been prpsed and by cmparng t wth PD cntrller, t has been shwn n the study that unfrmly stable peratn s acheved tgether wth asympttc trackng f the reference cmmand sgnals. n the study, smulatn results n applyng the prpsed TS fuzzy PD cntrller t a 3-Df stablzatn system have been presented whch demnstrates the effectveness f the fuzzy cntrller. Future study s drected t the ptmzatn f the scalng factrs f the fuzzy system and the ntellgent methd t generate an effectve rule base. REFERENCES Barnes, F.N., Stable member equatns f mtn fr a three-axs gyr stablzed platfrm. EEE T. Aer. Elec. Syst., 7(5): Chuen, C.L., 199. Fuzzy Lgc n cntrl systems: Fuzzy lgc cntrller-part,. EEE T. Syst. Man Cy., (): Debrun, J., 8. Cntrl systems fr mble satcm antennas. EEE Cntr. Syst. Mag., 8: Hlkert, J.M., 8. nertally stablzed platfrm technlgy cncepts and prncples. EEE Cntr. Syst. Mag., 8: Lee, P.G., K.K. Lee and G.J. Jen, An ndex f applcablty fr the decmpstn methd f mu1tvarable fuzzy systems. EEE T. Fuzzy Syst., 3: Lee, T.H., E.K. Kh and M.K. Lh, Stable adaptve cntrl f multvarable servmechansms, wth applcatn t passve lnef-sght stablzatn system. EEE T. nd. Elec., 43(1): Leghmz, S. and S. Lu, 1. Knematcs mdelng fr satellte antenna dsh stablzed platfrm. Prceedngs f the 1 nternatnal Cnference n Measurng Technlgy and Mechatrncs Autmatn-Vlume, (CMTMA '1), EEE Cmputer Scety Washngtn, DC, USA, pp: Leghmz, S., R. Fraga, S. Lu, K. Later, A. Ouanezar, et al., 11. Dynamcs mdelng fr satellte antenna dsh stablzed platfrm. nternatnal Cnference n Cmputer Cntrl and Autmatn, May 1-3, pp: -5. Lnkens, D.A. and H.O. Nyngesa, A herarchcal multvarable fuzzy cntrller fr learnng wth genetc algrthms. nt. J. Cntr., 63(5): Ne, J., Fuzzy cntrl f multvarable nnlnear servmechansms wth explct decuplng scheme. EEE T. Fuzzy Syst., 5: Sh, L. and S.K. Sngh, 199. Decentralzed adaptve cntrller desgn fr large-scale systems wth hgher rder ntercnnectns. EEE T. Autmat. Cntr., 37: Takag, T. and M. Sugen, Fuzzy dentfcatn f systems and ts applcatns t mdelng and cntrl. EEE T. Syst., Man Cy., 15: Yeh, Z.M., A systematc methd fr desgn f multvarable fuzzy lgc cntrl systems. EEE T. Fuzzy Syst., 7(5): Zegler, J.G. and N.B. Nchls, 194. Optmum settngs fr autmatc cntrllers. T. ASME., 64: