Modelling and Hybrid Intelligent Control of Submarine Periscope

Transcription

1 The 7th Conference of Irnin A erospce Societ The 7 th Irnin Aerospce Societ Conference Feb. 9-/8, Shrif Universit of Technolog IAS-8-XX-XXXX Moelling n Hbri Intelligent Control of Submrine Periscope Ali Kzem n Mohmm Frrokhi, * Deprtment of Electricl Engineering * Center of Ecellence for Power Sstem Automtion n Opertion Irn Universit of Science n Technolog, Tehrn , Irn Abstrct In this pper, first, the nmic equtions of submrine periscope will be etrcte n verifie with rel t. These t re cquire from n eperimentl setup. Then, using neurl network, hbri intelligent control metho will be pplie to control the periscope moel. This control scheme is combine of proportionl controller with feeforwr neurl network to pt the controller to the nonlinerities n prmeter chnging of the plnt. The neurl network will be trine on-line without n preefine initil weights to cope with the chnges in the sstem prmeters. Simultion results will be compre with the conventionl PID controller, which revels goo performnce of the propose controller. Kewors: Periscope - Moelling - Intelligent control - Stbiliztion Kinemtics. Introuction Line-of-Sight (LOS) stbiliztion hs been wiel use b mn reserchers for vrieties of pplictions []. Periscope, which is n importnt equipment in submrines, is n opticl instrument, which is consiere to be n LOS evice. In periscopes, imge sequences, tken b cmer, must be stbilize for better views b the opertor []. A common periscope structure hs been epicte in Figure. Imge sequences, tken from the se surfce, re reflecte b the mirror to the cmer, n observe insie the submrine b the opertor. The structure of periscope is like the gro mirror LOS stbiliztion [], [4]. Mjor ppliction of periscope is in submrines but tnks use them too. Etrcting nmic equtions of submrine periscopes hs vntges for reserch, computer simultion n moel-bse control esign. The structure of this sstem is like robot mnipultor. Therefore, to obtin the nmic equtions, one cn use the well-known methos like the Newton-Euler or the Lgrnge-Euler methos [5], [6]. In this pper, the ltter metho is emploe. Artificil neurl networks re powerful tools for ientifing n controlling nonliner nmic sstems. In this pper, MultiLer Perceptron (MLP) n proportionl controller re use to control the mirror orienttion of the periscope [7]. The trining of the neurl network is performe on-line. This is minl ue to the fct tht in prctice there re uncertinties, perturbtions, or chnges in the sstem prmeters. The simultion results will be compre with the conventionl PID controller. Forwr Kinemtics To obtin the homogeneous trnsformtion mtrices, the bsic metho is use [6]. Figure shows the link coorinte frmes of the periscope shown in Fig.. The trnsformtion mtrices of three links re efine s follows: c s c s c s s c s c T =, T =, T =. () s c Dnmic Eqution of the Periscope To erive the nmic equtions, the Lgrnge-Euler metho is emploe. Hence, the kinetic n the potentil energ of the ll links must be etermine. Ph.D stuent of electricl engineering, control mjor, li_kzem@hoo.com Associte Professor of electricl engineering, control mjor, frrokhi@iust.c.ir

2 The 7th Conference of Irnin A erospce Societ The 7 th Irnin Aerospce Societ Conference Feb. 9-/8, Shrif Universit of Technolog A. The Potentil n Kinetic Energ of the First Since the bo of periscope is fie to the pltform, the kinetic energ of the first link is just ue to the energ of servomotor. Equtions () n () represent the kinetic n the potentil energ of the first link, respectivel. k = J = Jω, () p = mg, () where J n ω re the moment of inerti n the ngulr velocit of the first link, respectivel, n is the height of periscope (Fig. ). B. The Potentil n Kinetic Energ of the Secon The movement of the secon link is like see-sw. Hence, for fining the kinetic n potentil energ of this link, it is ivie into two prts, with hlf mss on either sie. After fining the kinetic n potentil energ of ech prt, the kinetic energies will be e together n the potentil energies will be subtrcte from ech other, to fin the kinetic n potentil energ of the whole link. The velocit of the secon link is clculte t z = b/ with respect to the first coorinte sstem, where b is epicte in Fig.. The position n of the secon coorinte is, with respect to the zero coorinte sstem, is equl to bcs TT b bss = =. (4) z bc+ The velocit of the upper prt is equl to the velocit of the lower prt v = + + z = b ( ωs + ω ). (5) 4 Therefore, the kinetic energ of the secon link is equl to k = mv + Jω. The potentil energ of the secon link is equl to (6) p = mgz mgz = mgbc. (7) C. The Potentil n Kinetic Energ of the Thir The thir link is trete like the secon link. The position of the right-hlf prt of the mirror coorinte is equl to ( ccs sc ) TT T ( scs cc ) = = + (8) z ss+ Hence, the velocit of this link is equl to v z (9) = + +. An the kinetic n potentil energ of this link is k = mv + Jω, () p = mgz mgz = mgs s. () D. Lgrngin Eqution The Lgrngin equtions for the periscope cn be written s L = k + k + k p p p L L = τ. t Solving () iels nmic equtions s () τ = J + mbs + m ( c cc + c + c ) + + mc + mssc + mb ωω sc + m ( ωω sc + ωω csc + ωω csc ωω s ωω cs ω ccs ωω sc + ωωss ), τ = mssc + J + mb + m + m (ωω ccs ωω sc + ωω ss + ω cs + ω cs ω csc + ωωs + ωω ccs ) mb ω sc mgbs + mgc s,

3 The 7th Conference of Irnin A erospce Societ The 7 th Irnin Aerospce Societ Conference Feb. 9-/8, Shrif Universit of Technolog τ = mc + J + m + mgs c + m ( ωω s ωcsc + ωcs + ωω sc ωω ss ωcs ). () An nmic equtions of servomotors re I = RI kb M + v L τ = J B + k I ( ) M M M M M, (4) where I, R n L re the rmture current, resistnce n inuctnce respectivel, k b n k re motor torque constnt n bck-emf constnt, respectivel, M, τm, B M n J M re the motor rottionl ngle, output torque, mping coefficient n rotor inerti, respectivel, n v is the input voltge to the motor. The motor n plnt prmeters re written in tble n, respectivel. A comprison between the t cquire from n eperimentl sstem (Fig. ) n the propose moel, tking the nmics of servomotor into ccount, hs been epicte for (the w is) in Fig. 4. The moeling error hs been shown in Fig. 5. As this figure shows, the error between the eperimentl t n the propose moel is reltivel smll. The input signl, pplie to the moel n the rel plnt, is shown in Fig. 6. Controller Design Figure 7 shows the close-loop control block igrm for controlling the orienttion of the mirror. The neurocontroller comprises of n MLP neurl network (Fig. 8). Error bckpropgtion trining lgorithm hs been emploe. Simultions The min vntge of the on-line trining metho is its robustness ginst chnges in sstem prmeters. Fig. 9 shows the trcking on the is (the pitch is) with the gin of P controller equl to, while the mping coefficient of the plnt is increse b % t the t= sec. It is obvious tht the controller hs rtionl performnce but cn not pt itself ginst chnges in the sstem prmeters. Moreover, there might be simultneous chnges in sstem prmeters. Hence, to chieve better trcking performnce, some pttion lgorithm in the controller structure is neee. Figure shows the P controller combine with the neurl network to trck the reference signl. The ste stte trcking error is ecrese b this controller n cn pt itself to the chnges in the plnt prmeters. Note tht the computtion time for the neurl network is less thn.5 ms in MATLAB softwre, which inictes tht the propose control metho cn be pplie in rel time. Figs. n show the sme results for the (the roll is) with the P gin equl to. Conclusion In this pper, first, the nmic equtions of submrine periscope were etrcte n verifie with rel t. These t re cquire from n eperimentl setup. Then, using neurl network, hbri intelligent control metho ws pplie to control the periscope moel. This control skim ws comprise of proportionl controller with feeforwr neurl network to pt the controller to the nonlinerities n prmeter chnges of the plnt. The simultion results showe goo performnce of the propose controller. R ( Ω ) L ( mh) Tble - Motor Prmeters mv K b rpm mnm K A (m) Tble - Plnt prmeters m ( kg ) m m ( m ) b (m) (m) References - Y. M. Ling, H. R. Tn, H. Y. M. Lio n S. W. Chen, Stbilizing imge sequence tken b the cmcorer mounte on moving vehicle, pp. 9-95, In: Proceeings of IEEE Interntionl Conference on Intelligent Trnsporttion Sstems, Shnghi, Chin,. - A. Kzem, S. A. Hosseini n M. Frrokhi, Trget-bse line-of-sight stbiliztion in periscopes, 5 th IEEE Meiterrnen Conference on Control n Automtion, Athens, 7. - T. H. Lee, K. K. Tn, A. Mmun, M. W. Lee n C. J. Khoh, Composite control of Gro mirror line of sight stbiliztion pltform esign n uto-tuning, In: Proceeings of r IEEE Worl Congress on Intelligent Control n Automtion, Hefei, P.R. Chin,. 4- B. C. Siew, B. M. Chen n T. H. Lee, Design n implementtion of robust controller for free Grostbilize mirror sstem, In: Proceeings of Americn Control Conference, vol. 4, pp. -5, Philelphi, USA, F. L. Lewis, C. T. Abllh n D. N. Dwson, Control of robot mnipultors, Mcmilln Publishing Compn, J. J. Crig, Introuction to robotics: Mechnics n control, Aison-Wesle Publishing Compn, S. Hkin, Neurl Network: A Comprehensive Fountion, Secon Eition, Prentice Hll, 999.

4 The 7th Conference of Irnin A erospce Societ The 7 th Irnin Aerospce Societ Conference Feb. 9-/8, Shrif Universit of Technolog Figures Mirror Mirror micro motors Cmer Min Servomotor Height of Periscope Periscope evitions Rel t n moel response Rel t Moel output Fig. Structure of periscope Fig. 4. Comprison of the rel n moel responses b z z z Moeling error -.5 Fig. coorinte frmes of the periscope Fig. 5 Moeling error 8 Input signl 6 4 Voltge Fig. The eperimentl setup of periscope Fig. 6 Input signl pplie to the servo motor in the moel n in the rel plnt

5 The 7th Conference of Irnin A erospce Societ The 7 th Irnin Aerospce Societ Conference Feb. 9-/8, Shrif Universit of Technolog r e N. N. + P - + u Plnt nmic equtions.5.5 Trck long Trck Reference Fig. 7 Control block igrm -.5 u u I w ij O w l ( k ) Fig. Trcking long the is with the P controller u i q j I b j O b Fig. 8 Structure of the neurl network.. Trcking error with the propose controllers P Controller Hbri.5 Trck long Plnt Reference Fig.. Trcking error of the hbri controller for the is Fig. 9 Trcking long the is with the P controller Trcking error with the propose controllers P Controller Hbri Fig. Trcking error of the hbri controller for the is