A Self-Tuning Proportional-Integral-Derivative Controller for an Autonomous Underwater Vehicle, Based On Taguchi Method

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1 Jounal of Comput Scinc 6 (8): , 2010 ISSN Scinc Publications A Slf-Tuning Popotional-Intgal-Divativ Contoll fo an Autonomous Undwat Vhicl, Basd On Taguchi Mthod M. Santhakuma and T. Asokan Dpatmnt of Engining Dsign, Indian Institut of Tchnology Madas, Chnnai (600036), India Abstact: Poblm statmnt: Convntional Popotional-Intgal-Divativ (PID) contolls xhibit modatly good pfomanc onc th PID gains a poply tund. Howv, whn th dynamic chaactistics of th systm a tim dpndnt o th opating conditions of th systm vay, it is ncssay to tun th gains to obtain dsid pfomanc. This situation has nwd th intst of sachs and pactitions in PID contol. Slf-tuning of PID contolls has mgd as a nw and activ aa of sach with th advnt and asy availability of algoithms and computs. This study discusss slf-tuning (auto-tuning) algoithm fo contol of autonomous undwat vhicls. Appoach: Slf-tuning mchanism will avoid tim consuming manual tuning of contolls and pomiss btt sults by poviding optimal PID contoll sttings as th systm dynamics o opating points chang. Most of th slf-tuning mthods availabl in th litatu w basd on fquncy spons chaactistics and sach mthods. In this study, w poposd a mthod basd on Taguchi s obust dsign mthod fo slf-tuning of an autonomous undwat vhicl contoll. Th algoithm, basd on this mthod, tund th contoll gains optimally and obustly in al tim with lss computation ffot by using dsid and actual stat vaiabls. It can b usd fo th Singl-Input Singl-Output (SISO) systms as wll as Multi-Input Multi-Output (MIMO) systms without mathmatical modls of plants. Rsults: A simulation study of th AUV contol on th hoizontal plan (yaw plan contol) was usd to dmonstat and validat th pfomanc and ffctivnss of th poposd schm. Simulation sults of th poposd slf-tuning schm a compad with th convntional PID contolls which a tund by Zigl-Nichols (ZN) and Taguchi s tuning mthods. Ths sults showd that th Intgal Squa Eo (ISE) is significantly ducd fom th convntional contolls. Th obustnss of this poposd slf-tuning mthod was vifid and sults a psntd though numical simulations using an xpimntal undwat vhicl modl und diffnt woking conditions. Conclusion/Rcommndations: By using this schm, th PID contoll gains a optimally adjustd automatically onlin with spct to th systm dynamics o opating condition changs. This tchniqu found to b mo ffctiv than convntional tuning mthods and it is vn vy convnint whn mathmatical modls of plants a not availabl. Comput simulations showd that th poposd mthod has vy good tacking pfomanc and obustnss vn in th psnc of distubancs. Th simpl stuctu, obustnss and as of computation of th poposd mthod mak it vy attactiv fo al tim implmntation fo contolling of undwat vhicl and it offs a chanc to xtnd th sam tchniqu to th th dimnsional vhicl tacking contol as wll. y wods: Autonomous undwat vhicl, Taguchi s mthod, popotional-intgal-divativ contol, slf-tuning, plana contol INTRODUCTION Modn dvlopmnts in th fild of contol, snsing and communication hav mad incasingly complx and ddicatd undwat vhicl systms a ality. Usd in a highly hazadous and unknown nvionmnt, th autonomy and contol of th vhicl is th ky to mission succss. Though th dynamics of undwat vhicl systm is highly coupld and nonlina in natu, dcoupld lina contol systm statgy is widly usd fo pactical applications. As autonomous undwat vhicl nds intllignt contol systm, it is ncssay to dvlop contol systm that ally taks into account th coupld and Cosponding Autho: T. Asokan, Dpatmnt of Engining Dsign, Indian Institut of Tchnology Madas, Chnnai (600036), India Tl: Fax:

2 non-lina chaactistics of th systm. In addition, most of th AUVs a undactuatd, i.., thy hav fw actuatd inputs than th Dgs Of Fdom (DOF), imposing non-intgabl acclation constaints. A summay of th cnt dvlopmnts in this aa can b found in (Fossn, 1994; Yuh, 2000). Dynamics and contol of AUV in a constaind nvionmnt poss gat challngs to dsigns. This, coupld with th unctainty of hydodynamic paamts, mak th contoll dsign an xtmly tough task. Dsign, modling and simulation of th vhicl a impotant ky issus in contolling th vhicl and som of th cnt woks a summaizd in th litatu (Fossn, 1994). Th contol tchniqus poposd in litatu can b boadly classifid into two majo catgois: adaptiv contol and obust contol (Yuh, 2000; Antonlli, 2007). In adaptiv contol th contoll paamts a automatically vaid to maintain a satisfactoy lvl of pfomanc whn th systm paamts a unknown and/o tim vaying. Robust contol fs to th contol of unctain plants with unknown distubanc signals, unctain dynamics and impcisly known paamts making us of spcial fixd contolls. Among ths, adaptiv contol is considd to b btt fo plant unctainty. Howv, it is computationally intnsiv fo high od systms and quis xact knowldg of th dynamic paamts, apat fom th computation of invs Jacobian matix. Th obust contol schm povids a satisfactoy pfomanc with a simpl contol stuctu, but coms with undsid high contol activity at stady stat. On th oth hand, th commonly usd PID contol (Pi and Canudas-d-Wit, 1996; Santhakuma and Asokan, 2009) dos not qui any infomation of th plant dynamics and has a simpl standad stuctu. Moov, owing to modling unctaintis a mo sophisticatd contol schm is not ncssaily mo fficint than a wll-tund PID contoll. Alongsid th advantags, howv, th poblm of tuning PID contolls has maind an activ sach aa. Tuning is th adjustmnt of th fdback contoll paamts to obtain a spcifid closd-loop spons. In convntional PID contolls, onc wll-tund PID gains a obtaind, ths contolls usually xhibit good pfomanc. Howv, whn th dynamic chaactistics of th systm a tim dpndnt o th opation conditions of th systm vay, it is ncssay that th PID gains must b tund again. Castillon t al. (2006) hav viwd twnty-fou diffnt tuning mthods and has concludd that most of th contolls a tund using fquncy sponss du to th advantags in xpssing th modling os dictly in J. Comput Sci., 6 (8): , th fquncy domain. Howv, fquncy spons mthods a difficult to implmnt in th MIMO systms. Fll and Rddivai (1995), blivd that PID contolls a pooly tund bcaus of taditional mthods of contoll dsign and th tuning to achiv minimum vaianc quis th ngin to cat a closd-fom mathmatical modl of th systm and contoll dynamics. Tuning of contolls using Taguchi mthod was poposd by thm to impov th contoll pfomanc. Though this was found to b vy convnint, th contoll gains w not optimal and nois factos w not considd. Santhakuma and Asokan (2009) hav attmptd tacking contol of undwat vhicl using PID contol. A pliminay ffot was mad by intoducing a obust dsign mthod in th fild of undwat vhicl contol and th ffct of noiss was considd. This study mainly focusd on dpth contol of a topdo shapd undwat vhicl and it also compad oth possibl tuning mthods. Slf-tuning of PID contolls has mgd as a nw and activ aa of sach and dvlopmnt with th advnt and asy availability of algoithms and computs and is civing mo and mo attntion (Astom and Hagglund, 1988; Bobal t al., 1999; Gawthop, 1986; Yu, 2006; Liu, 2007; Huang and Lin, 2007). Slf-tuning mchanism will avoid th timconsuming manual tuning and pomiss btt sults by poviding optimal PID contoll sttings automatically as th systm dynamics o opating points chang. Most of th slf-tuning mthods a basd on fquncy spons chaactistics and sach mthods. In this study, it is poposd to us Taguchi s obust dsign mthod basd slf-tuning schm fo an autonomous undwat vhicl. Th maining pat of th study is oganizd in th following mann: A bif discussion on th modling of AUV is psntd followd by th contoll dsign dtails. A discussion on th poposd slf-tuning schm is psntd in matials and mthods. In th sults and discussion, simulation sults and obustnss of th poposd contoll a psntd fo an xpimntal AUV and a compaison of th sults with that of a convntional PID contoll is also povidd. Finally, concluding maks of th poposd mthod and it s th scop of futu study a psntd. Modling of AUV kinmatics and dynamics: In this study, w hav considd an xpimntal autonomous undwat vhicl as a tst platfom fo ou xpimnts and analysis. This is a topdo-shapd und actuatd AUV, without any sid thusts to contol th sway diction (this is not implmntd bcaus of conomical and wight considations) (Fig. 1).

3 Th dynamic modl of th vhicl on th hoizontal plan is as givn by (3): M νɺ + C(ν)ν + D(ν)ν = τ (3) wh, M-intia matix, C(ν)-Coiolis and Cntiptal matix, D(ν)-Damping matix and τ-input vcto, th componnts of which a as follows: Fig. 1: Body-fixd fam and ath-fixd fnc fam fo AUV Th a only two stn poplls which a offing contol inputs as th foc in th sug diction and th contol toqu in yaw diction in th hoizontal plan (by diffntial mod opation of poplls). Th following assumptions a mad in dvloping th mathmatical modl fo th AUV. Vhicl has an xz-plan of symmty; sug is dcoupld fom sway and yaw; hav, pitch and oll mods and ths axs tms a nglctd. Und ths alistic assumptions, th motion of th vhicl in th yaw plan is dscibd by th following odinay diffntial quations (Fossn, 1994; Santhakuma and Asokan, 2010). Th kinmatics of th vhicl on th hoizontal plan is as givn by (1): m M = 0 m22 m 23, 0 m32 m 33 m = m X,m = m - Y,m = mx Y, 11 uɺ 22 vɺ 23 g ɺ m = I N,m = mx N 33 z ɺ 32 g vɺ 0 0 c13 C(ν) = 0 0 c 23, c13 c23 0 (m23 + m 32) c13 = m22v,c23 = m11u 2 D(ν) = L(ν) + NL(ν) ν l L(ν) = 0 l22 l23, 0 l32 l33 l = X,l = Y,l = Y,l = N,l = N 11 u 22 v v 33 nl NL(ν) = 0 nl22 nl 23, 0 nl32 nl 33 nl = X 11 u u nl = Y,nl = Y 22 v v 23 nl = N,nl = N 32 v v 33 T ( ) τ = τ 0 τ, τ = Bn and n = V V u s p T (4) (x, y) a th sug and sway displacmnts, Ψ is ηɺ = J( ψ) ν (1) th yaw angl in th ath fixd fam, u, v and dnot sug, sway and yaw vlocitis; (m Wh: 11, m 22, m 23, m 32, m T 33, l 11, nl 11, l 22, nl 22, l 23, nl 23, l 32, nl 32, l 33, nl 33 ) > 0 η = x y ψ = Th displacmnt vcto with spct dnot th hydodynamic damping and vhicl intia to intial fam including addd mass, th contols τ u and τ a th T ν = u v = Th vlocity vcto with spct to sug foc and yaw momnt. V s and V p a th thust input voltags of staboad sid thust and potsid body fixd fam thust spctivly. B is th input matix. J( ψ ) = Th tansfomation matix (Jacobian) X u, Y v,y, N v and N a th lina hydodynamic and is givn as: damping focs and momnts on th cosponding axs. X u, Y,Y, N and N A th non-lina u v v v v cosψ -sinψ 0 hydodynamic damping focs and momnts on th J( ψ ) = sinψ cosψ 0 (2) cosponding axs. X uɺ, Y vɺ,y ɺ,Nvɺ and N ɺ a th addd mass ffcts. 864

4 Fig. 2: Poposd yaw plan PID contoll stuctu fo an autonomous undwat vhicl Contoll dsign: Th dsign of sway (yaw plan) contoll fo th AUV to tack a givn fnc sway tajctoy is xplaind blow. Th popotionalintgal-divativ contol law usd h is givn by (5): τ = pyy + iy ydt + dyyɺ + pψψ + i ψ ψ dt + dψψ ɺ (5) wh, p, i and d a th popotional, intgal and divativ gains of th contoll spctivly and th subscipt dnots th o. Th PID contol schm is schmatically dpictd in Fig. 2. Dtaild dsciption and stability analysis of PID contoll fo an undactuatd AUV a givn in (Santhakuma and Asokan, 2010). Th a six contoll gains in th yaw plan contoll. Ths contoll gains a to b tund in such a way that th contoll is optimal in natu. MATERIALS AND METHODS Fig. 3: Block diagam of poposd slf tuning contoll stuctu Taguchi s obust tuning mthod: Th Taguchi s obust paamt dsign is usd to dtmin th lvls of factos and to minimiz th snsitivity to nois. That is, a paamt stting should b dtmind with th intntion that th poduct spons has minimum vaiation whil its man is clos to th dsid tagt. Taguchi s mthod is basd on statistical and snsitivity analysis fo dtmining th optimal stting of paamts to achiv obust pfomanc (Byn and Taguchi, 1986). In stting up a famwok fo obust dsign, th classifications of th quantitis at play in th dsign task a givn blow: Dsign Vaiabls (DV) a thos quantitis to b dcidd by th dsign with th pupos of mting pfomanc spcifications und givn conditions Dsign-Envionmnt Paamts (DEP) is thos quantitis ov which th dsign has no contol and that dfin th conditions of th nvionmnt und which th dsignd objct will opat Pfomanc Functions (PF) a quantitis usd to psnt th pfomanc of th dsign in tms of dsign vaiabls and dsign-nvionmnt paamts Slf-tuning of PID contoll using Taguchi s mthod: Th poposd contoll schm fo th AUV is shown in Fig. 3. Th tajctoy contoll gnats Th sponss at ach stting of paamts a th dsid tajctoy fom th us inputs. Us inputs tatd as a masu that would b indicativ of not consist of stat point, goal point, way points and vhicl only th man of som quality chaactistic, but also spd o tim duation. Ths dsid valus a th vaianc of th sam chaactistic. Th man and compad with th actual valus which a coming fom th vaianc a combind into a singl pfomanc th AUV dynamic modl (snso valus in th al masu known as th Signal-to-Nois (S/N) atio tim). Compaato is giving tacking os and ths (Byn and Taguchi, 1986; Pak, 1996). Taguchi o valus a fd into th PID contoll and classifis obust paamt dsign poblms into contoll is gnating ncssay contol signals, as p diffnt catgois dpnding on th goal of th th contol law. Th slf-tuning block calculats th poblm and fo ach catgoy as follows: optimal valus of th contoll gains to duc th tacking os. Th al-tim calculations of gains a Small th btt: Th tagt valu of y, that is, achivd by implmnting th Taguchi s obust quality vaiabl is zo. In this situation, S/N Ratio optimization mthod. Th vaiations in th input (SNR) is dfind as follows: commands as wll as th tacking o a usd in n aiving at th optimal gains. Th mthodology usd in 1 2 SNR = 10log yi (6) dvloping this slf-tuning contoll is xplaind blow. n i = 1 865

5 Lag th btt: Th tagt valu of y, that is, quality vaiabl is infinit and S/N atio is dfind as follows: n 1 1 SNR = 10log n 2 (7) i= 1 y i Nominal th bst: Th ctain tagt valu (s) is givn fo y valu. In this situation S/N atio is dfind as follows: n 2 y i SNR = 10log 2 (8) i= 1 s In this study, small th btt chaactistic is usd du to th quimnt to minimiz th position tacking o. Taguchi s mthod uss an Othogonal Aay (OA) and analysis of man to study th ffcts of paamts basd on statistical analysis of xpimnts. An OA is a factional factoial matix which assus a balancd compaison of lvls of any facto o intaction of factos. It is a matix of numbs aangd in ows and columns wh ach ow psnts th lvl of th factos in ach un and ach column psnts a spcific facto that can b changd fom ach un. Th aay is calld othogonal bcaus all columns can b valuatd indpndntly of on anoth (Pak, 1996). Th dsign of yaw plan contoll paamts is caid out using this tchniqu. Th a six contoll gains (sway is an unactuatd stat, thfo sway and yaw a combind in od to gt sway motion) and fiv lvls of ach gain a considd fo th analysis, thfo an othogonal aay of L 25 [5 6 ] is chosn fo th analysis (Pak, 1996). Th physical valus of th contoll paamts a chosn by considing xpimntal vhicl actuato and snso systm chaactistics such as tim dlay, satuation limit and dad zon and its physical valus a givn in th Tabl 1. With th hlp of ths physical valus simulation xpimnts a conductd as p L 25 [5 6 ] OA. Objctiv of this analysis is to impov th contoll pfomanc by minimizing th o. In this analysis, masu of systm pfomanc is in th fom of Intgal Squa Eo (ISE) (by intgating th squa of th o ov a fixd intval of tim) and fom th simulations ISE is calculatd and codd as givn in th Tabl 1. Fo xampl, th SNR fo xpimnt 1 is calculatd basd on (6) (using small th btt chaactistics) and as givn by (9): SNR fo xpimnt 1 = 10 log ( ) +80 = 17.33dB (9) J. Comput Sci., 6 (8): , 2010 Tabl 1: Dsign Of Expimnts (DOE) fo yaw plan contol (L 25 [5 6 ]) ISE SNR py dy iy pψ dψ iψ (m 2 ) (db) Tabl 2: Sum of SNR fo diffnt factos and lvls Sum of SNR in db Gains L 1 L 2 L 3 L 4 L 5 Total py dy iy pψ dψ iψ (80 db is addd to avoid ngativ valus fo SNR, to mak compaisons asy). Fo idntifying th optimal paamt combination, sum of th SNR of ach facto and thi ach lvl valus a calculatd as shown in Tabl 2. Fo xampl, th sum of th S/N atio fo lvl 1 of th facto dy (i.., dy = 0.2) is calculatd with th hlp of SNR valus psntd in Tabl 1 as follows: Sum of th SNR fo Lvl 1 of dy = ( ) db = dB (10) Tabl 2 (Sum of SNR valus) givs th optimum lvl of ach paamt (gain). That is, th lvl which contains maximum valu of sum of th SNR is th optimum lvl. Fom Tabl 2, it is found that th optimum lvls (na optimal) of contoll paamts py, dy, iy, pψ, dψ and iψ a 3, 4, 2, 4, 4 and 1 spctivly. Th cosponding physical valus of 866

6 ths paticula lvls a 15, 0.8, 10, 0.8, 0.4 and 1 spctivly. Fo futh fin tuning of th contoll paamts, th sam pocdu can b patd. In this study, discussion is limitd only to illustat th obust mthod fo contoll paamt adjustmnt. Howv th intaction ffct btwn contoll paamts as such is an impotant topic which is kpt opn fo futu sach. Th optimal contoll paamts a incopoatd in th contoll and simulatd th vhicl closd loop bhaviou in od to dmonstat th poposd tchniqu. Th closd loop spons fo this tund contoll is psntd in Fig. 4, which confims that Taguchi mthod tund contoll is giving good tansint and stady stat sults with lss ovshoot, fast spons and lss stady stat o. In od to chck th pfomanc of th contoll, vhicl pfomanc has bn invstigatd und vaious opating conditions such as 2 m stp input, multipl stp, amp and sin inputs. Closd loop sponss of ths conditions a obtaind fom simulations and psntd in Fig. 5. Fom Fig. 5a, it is found that th is an ovshoot of appoximatly 20% fo th 2 m stp input. Simila tnd is sn in th cas of multipl-stp input also. Compad to th unit stp input spons, th sttling tim has also changd with th chang in input command. In th cas of tim vaying inputs such as amp and sin inputs, th sponss (Fig. 5c and d) show that th initial tacking os a high. Ths vaiations a mainly du to th fixd valus of th contoll gains fo vaious input scnaios. Th contoll has to adapt th changs in th woking conditions and/o systm dynamics. Th poposd slf-tuning mchanism is dvlopd using Taguchi s mthod to addss this issu. This is dvlopd by considing fiv diffnt command input scnaios (unit stp, ngativ stp, multipl stp, amp and simpl sin) and finding out th optimal contoll paamts fo ach of ths scnaios using Taguchi s mthod, as dscibd ali. Using lina gssion analysis and cuv fitting, th lationship btwn contoll paamts ( py, dy, iy, pψ, dψ and iψ ) and th sway o (y ) is dvlopd fom th abov valus of optimal paamts. A gssion modl is dvlopd fo ach paamt using a confidnc lvl of 99% and with th hlp of siduals and vaiancs. Fo xampl, th optimal valus of contoll popotional gain py a 15.00, 15.03, , and fo th cosponding input conditions. Applying lina gssion analysis to th abov valus, th modl is divd as givn in (11). Th lationship btwn sway o and popotional gain is also obtaind and is psntd in Fig. 6: py (R 2 = 0.996) = y (11) (a) (c) (b) (d) Fig. 5: Closd loop spons of Taguchi s mthod tund PID Contoll fo diffnt inputs (a) (b) (c) (d) Fig. 4: Closd loop spons of Taguchi s mthod tund PID Contoll 867 Fig. 6: Rlationship btwn sway o to th popotional contol gain (gssion analysis)

7 wh, R 2 is th cofficint of dtmination (goodnss of fit) and it povids a masu of how wll futu outcoms a likly to b pdictd by th modl. In oth wods, R 2 100% givs th pcntag of cooboation and y is th sway position tacking o. Simila pocdu was adoptd to gt th gssion modl fo all oth paamts. Th slftuning mchanism consists of all th contoll paamt modls as givn by (12). As sn fom this quation, th contoll tuning is dictly latd to th tacking o and th paamts a slctd on th basis of th slf-tuning law. Sinc th changs in systm paamts o opating conditions a dictly flctd in th closd loop tacking os, contoll can automatically adapt to any vaiations in ths paamts by suitably adjusting th contoll paamts: = = 2-2 py(r 0.996) y = = dy(r 0.930) y = = 2-2 iy(r 0.965) y = = + 2 pyaw (R 1.000) y = = + 2 dyaw (R 0.923) y = = 0-3 y 2 iyaw (R 0.970) (12) Fig. 7: Hadwa-in-loop simulation stup with Jubil autonomous undwat vhicl Tabl 3: Rigid body and hydodynamic paamts of th JUBILEE AUV Paamt Symbol Valu Unit Mass m kg Rotational Intia I 3.70 kg m 2 Addd mass in sug Addd mass in sway Addd (mass) intia in yaw Sug lina dag Sug quadatic dag Sway lina dag Sway quadatic dag Yaw lina dag Quadatic yaw dag z X ɺ kg u Y ɺ kg v Y ɺ 1.04 kg m ad 1 N ɺ kg m v N ɺ kg m 2 ad 1 X kg sc 1 u X kg m 1 u u Y v kg sc 1 Y 0.12 kg m sc 1 Y kg m 1 v v Y 0.25 kg m ad 1 N v 1.20 kg m sc 1 N kg m 2 sc 1 N 2.24 kg v v N kg m 2 ad Expimntal platfom: Fo this study, Jubil, a tst bd AUV bing dvlopd at IITM, is slctd as an xpimntal st-up. Figu 7 shows th fist pototyp of this AUV and th paamts usd fo th numical simulations a givn in Tabl 3. RESULTS In od to dmonstat and validat th pfomanc and ffctivnss of th poposd schm, typical simulation sults a psntd. Simulation sults fo two input conditions such as 2 and 5 m stp input, with and without slf-tuning a psntd in Fig. 8. Th vaiations of contoll paamts duing slf-tuning a shown in Fig. 9. Fig. 8: Compaison of diffnt stp sponss with and without slf-tuning schm

8 Fig. 9: Tim histoy of gain valus (slf-tund) fo diffnt inputs Fig. 11: Compaison of systm sponss with spct to multipl stp fnc input in th psnc of distubanc Fig. 10: Compaison of systm sponss with spct to non-zo initial condition Th contoll obustnss is dmonstatd by analyzing th pfomanc of th slf-tund contoll und fou diffnt opating conditions i.., unit stp input with non-zo initial o, multipl stps with andom distubancs, multipl stps with paamt unctaintis and tim vaying input (sin) with andom distubancs. Th wll known convntional Zigl and Nichols (1993) mthod tund PID is usd fo th compaison aspcts. On impotant issu in th undwat vhicl contol is th initial o in position and ointation of th vhicl whn th contoll is switchd on. Sinc most of th undwat vhicls a launchd fom th moth ship, th can b considabl amount of o in th position and ointation at th initial stag. Any nw contoll nds to b analyzd fo its ability to act to lag initial os. Th poposd slftuning PID contoll is subjctd to a simulatd initial o tst to analyz its pfomanc. Closd loop sponss fo non-zo initial o: H, an initial o of 0.1 m in sway (y) position is assumd and th closd loop pfomanc compaison of contolls is psntd in Fig. 10. Fig. 12: Compaison of systm sponss with spct to sin fnc input Closd loop sponss fo multipl stp input in th distubd condition: Th closd loop sponss of PID contolls (with and without slf-tuning) fo multipl stp input in th psnc of distubancs a psntd in Fig. 11. H, th ffct of undwat cunt and oth distubing ffcts a assumd to b andom valus in th input sid, with th magnitud of 5 N and ± 5 Nm in th foc and momnt spctivly. Simulation sults fo distubanc jction in th cas of vaying input (sin input) in th psnc of andom distubancs a psntd in Fig

9 Tabl 4: Compaison of Intgal Squa Eo (ISE) valus fo diffnt contolls Intgal Squa Eo (ISE) in m Convntional PID tund by Input typ Zigl-Nichols mthod Taguchi mthod Slf-tuning PID Unit stp input with non-zo initial o Multipl stp input with distubancs Multipl stp input with paamt unctaintis Tim vaying input (sin) with distubancs Fig. 13: Compaison of systm sponss with spct to multipl stp fnc input und paamt unctaintis Closd loop sponss fo multipl stp input with paamt unctaintis: Th closd loop sponss of PID contolls (with and without slf-tuning) fo multipl stp input und paamt ctaintis a psntd in Fig. 13. H, th vhicl paamt vaiations a assumd to b 50% of th actual valus fo all th paamts. A compaison of pfomanc masu of slftuning PID contoll with spct to oth contolls is povidd in Tabl 4. DISCUSSION It can b sn fom th sults psntd in Fig. 8 that th PID contoll tund fo 2 m stp is pfoming wll fo 2 m stp, but shows dtioation in pfomanc fo 5 m stp, with a lag ovshoot and sttling tim. Simila tnd is sn fo 5 m stp also. On th oth hand, slf-tuning PID is pfoming wll in both th stp input conditions (Fig. 8). This is achivd though th tuning of th contoll paamts, as shown in Fig. 9. This confims that th poposd contol schm is adapting wll to th vaiations in opating stat. 870 Th ability of th contoll to ffctivly ovcom th initial o is dmonstatd in th sults psntd in Fig. 10. Th initial os a found to convg to its dsid stat of zo ov a shot piod of tim in th slf-tuning schm. It is obsvd fom Fig. 11 that th poposd contoll has a good tacking pfomanc in th psnc of undwat cunt and oth distubancs. Compad to oth convntional contoll sponss, th ovshoot and is tim hav significantly ducd. Rsults povidd in Fig. 12 show th ability of th contoll to adapt wll to vaying inputs. Th ffctivnss of th poposd contoll in adapting to th paamt vaiations is dmonstatd in Fig. 13. Th sults show that th schm is supio to many oth contol schms. Th compaison sults psntd in Tabl 4 shows that th pfomanc (in tms of ISE) of slf-tuning contoll is much btt than th convntional contolls. Th sults psntd abov confims th fact that th slf-tuning PID schm pfoms wll in tms of smooth tansint spons, quick convgnc of tacking os to zo, obustnss, distubanc jction and adapting to paamt vaiations. CONCLUSION In this study, a nw slf-tuning PID contol schm fo AUV contol using Taguchi s mthod is psntd. By using this schm, th PID contoll gains a optimally and obustly adjustd onlin with spct to th systm dynamics and opating condition changs. This tchniqu is found to b mo ffctiv than convntional tuning mthods and it is vn vy convnint whn mathmatical modls of plants a not availabl. This mthod can b asily xtndd to multiinput and multi-output systms fom basic singl-input and singl-output systms. Comput simulations showd vy good tacking pfomanc and obustnss of th poposd mthod vn in th psnc of distubancs. Th simpl stuctu, obustnss and as of computation of th poposd mthod mak it vy attactiv fo al tim implmntation fo contolling

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