INTERNAL MODEL CONTROL USING NEURAL NETWORK FOR SHIP ROLL STABILIZATION

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1 Journal of Marine Science and Technology, Vol. 5, No. 2, pp (27) 4 Short Paper INTERNAL MODEL CONTROL USING NEURAL NETWORK FOR SHIP ROLL STABILIZATION Fuat Alarçïn Key word: hip roll tabilization, internal model control, and neural network. ABSTRACT In thi paper, a neural network (NN) baed on internal model control (IMC) i developed to adjut control parameter for roll motion of a container hip. Controller architecture, which combine neural network with internal model control, ha been outlined and it effectivene demontrated on the container hip roll tabilizer. The control ignal error i ued with back-propagation algorithm to update the weight of the neural controller. In concluion, the neural network baed on internal model control ytem are analyzed, and compared to claical control reult. A can be een from numerical reult, the NN baed on IMC i implemented uccefully to reduce roll amplitude. INTRODUCTION The roll motion of hip in large amplitude i very difficult to control due to nonlinear dynamic. For thee reaon during the lat decade many reearcher have been making a tudy about roll motion control. The background to the problem of deigning roll tabilization control for hip wa reviewed [] and an overview ha been preented [3]. Fin tabilizer are attractive for roll reduction ince they are highly effective, work on a large number of hip, and are much eaier to control, even for varying load condition and actuator configuration. Therefore, fin tabilizer can be ued in order to provide atifactory roll damping performance. Variou control trategie have been preented for the roll motion control of hip. Proportional-Integrative-Derivative (), which i control claical control ytem, i propoed for roll motion control [6]. The performance of claical optimized given, and Paper Submitted 9/2/5, Accepted /25/6. Author for Correpondence: Fuat Alarcin. alarcin@yildiz.edu.tr *Department of Naval Architecture and Marine Engineering, Yιldιz Technical Univerity, Beikta, Itanbul H-infinity controller are compared in [2, 5, 9]. Becaue of the unpredictable operating environment of hip, conventional control method uch a the controller may not be able to give good damping performance. Hence, reearcher developed internal model control (IMC) ytem in order to provide atifactory performance. IMC concept have found acceptance in indutrial application due to high performance and robutne [6, 7]. A detailed analyi ha been given by []. For the implementation of IMC algorithm, neural network control method i able to adapt on order to improve the IMC performance. The idea of uing neural network for IMC ha been conidered by []. A cited earlier a powerful computational tool neural network technique have been utilized in many dicipline a well a in marine field [4, 4, 9]. Efficiency of the propoed NN adaptive control i tudied by back-propagation algorithm to update weight of the controller. The back-propagation algorithm introduced two main advantage in accelerating both the peed of the learning proce and the peed of the evaluation [7, 8]. In thi paper, neural network i adopted in IMC deign and how good advantage. Applicability of a neural network controller baed on model reference adaptive control i invetigated for deigning roll tabilizer control for a container hip. EQUATION OF MOTION The equation of motion for a container hip ha been obtained from Newton econd law. The dynamic model of the hip i hown Figure [3]. In literature a hip ix degree of freedom dynamic equation are expreed a: Mυ B (υ)υ C (η)=m f M w () with η: poition and orientation of the hip

2 42 Journal of Marine Science and Technology, Vol. 5, No. 2 (27) υ: linear and angular velocity of the hip M: inertia matrix including added ma B: matrix coniting of damping term C: vector of retoring force and moment due to gravity and buoyancy M f : vector of fin control input M w : vector of wave input The mathematical model of a container hip ued in thi tudy i decribed in reference [3]. Three degree of freedom model of the container hip wa developed to deign a roll controller that ue the fin a a control input. (m Y v )v = Y v Y Y p p Y r r Y α α Y w (I x K P )p = K p p K v v K r r mggm K α α K w (I z N r )r = N r r N N p p N v v N α α N w (2) The above decribed mathematical model give a good approximation of the maneuvering behavior of a container hip. Where v i the way velocity; p, r repectively are the roll and yaw rate. Y v, K p and N r indicate the hydrodynamic coefficient of way, roll and yaw moment, repectively; m i the ma of the hip; g i the gravity contant; I x and I z repectively are the moment of inertia about the X-Z axi; and GM i the hip metacentric height, which indicate the retoring capability of a hip in roll motion. The fin angle i repreented by α. The wave lope i. The fin and wave force and moment are repreented by the term Y α, K α, N α and Y w, K w, N w, repectively. The hip inertia matrix for 3 DOF, fin and wave force and moment are given. M f = M w = Y α K α N α (6) Y w K w N w (7). Fin-wave force and moment The force and moment derivative for the pair of fin are a follow: Y α = ρv 2 S f C lα co38 K α = ρv 2 S f C lα R f N α = ρv 2 S f C lα L f co38 (8) The total hip velocity i V and R f i the vertical ditance from the fin center of preure to the roll center of the hip. Lever arm L f i the ditance from the fin center of preure to midhip. The fin angle which i expreed by co38 how the location of the fin from the roll center. The effect of the fin are added into the coefficient matrice depending on the location angle. The wave diturbance wa modeled by an input diturbance. The force and moment generated by the wave acting upon the hip hull have been etablihed uing the reult of JONSWAP pectrum. The wave force and moment are given by Y w, K w, N w and they hould be added to the right-hand ide of the Eq. (2) a [5]. M = m Y v I x N p (3) I z N r Y w = ma S (t ) K w = ml a 2 S (t ) the Corioli matrix, B = Y v Y p Y r K v K p K r (4) N v N p N r N w = ml a 3 S (t ) (9) where Y w i the way force, K w i the roll moment and N w i the yaw wave moment. a, a 2 and a 3 are filter parameter. S(t) i a pectrum for each exciting force the retoring matrix, δ X C = Y mggm N (5) Y θ ψ Z Fig.. Ship coordinate ytem.

3 F. Alarçïn: Internal Model Control Uing Neural Network for Ship Roll Stabilization 43 and moment. STRUCTURE OF ROLL STABILIZATION CONTROL SYSTEM The previou ection about mathematical model i decribed. In thi ection, the controller i deigned to tabilize roll motion of the container hip. Figure 2 how a block diagram of an actual roll tabilization ytem. In thi diagram, i the hip rolling angle and i the angle of the fin. d i repreent and deired roll angle. The tabilizing force will reduce the roll of the containerhip. The deigned ytem ha three degree of freedom tructure uing a IMC and neural network control method. In thi tudy, it i conidered neural network baed on IMC ytem deigned to make the output of the plant track a deired angle.. control for the container hip In the following, the deign of conventional controller will be dicued. In general the control method i employed in the roll control. The control i made by proportioning the fin angle to the rolling angle. Firt controller i conidered. The control ignal of the controller i given by Eq. (). The cloed loop diagram of the feedback ytem i hown in Figure 3. Here, α(t) i the control ignal, d, e and are the deired roll angle, the rolling error and the actual rolling, repectively. control ha been ued in indutry widely and uccefully. The control input α(t) and the roll error are obtained a follow: d e Ship roll controller α Ship roll dynamic α(t )= k p e (t )k d d e (t ) dt k i e (t ) dt () e (t) = d (t) (t) () k p, k i, k d are proportional, integrative and derivative contant. For the controller, parameter have to be tuned. Thee value are obtained by ue of Ziegler- Nichol method [2]. 2. The internal model controller deign In order to control the roll motion of the container hip, an internal model controller i conidered. A baic internal model control i hown in Figure 4. Where G i the proce model of the roll motion and Q() i a regulator. α() denote fin control input, c repreent commanded roll angle, G() i the roll motion tranfer function a follow. G ()= () α() = (2) The IMC and claical feedback tructure are equivalent under the following tranformation [6]. C = Q = Q CG C CG (2) (3) Where C repreent the controller. The main feature of thi control ytem i the way in which it check difference between the output of the proce and of the internal model. Thi difference i fed back into the controller to reject error effect. In order to obtain the internal tability, the mimatch effect between the roll motion and the model of the roll motion hould be minimized. Hence, the controller can include a filter to increae robutne to model mimatch and diturbance. Fig. 2. Containerhip roll control ytem. d Mux e α Ship dynamic c e Regulator Q() α Roll dynamic G() Model G() ~ ~ Filter Controller Fig. 3. Feedback control ytem with PD controller. Fig. 4. Schematic of the IMC cheme.

4 44 Journal of Marine Science and Technology, Vol. 5, No. 2 (27) Q = FG inv (4) Where G inv i an approximation to the invere of the vehicle model G. F() i a low pa function of appropriate order. F ()= ( τ f ) n (5) Where τ f i the filter parameter and n i the order of the filter. Order of the filter are choen in uch away o that the controller tranfer function are proper. 3. Back-propagation neural network The back-propagation algorithm i the mot important algorithm for the upervied training of NN it derive it name from the fact that error ignal are propagated backward through the network on a layerby-layer bai. The neural network i three layer in thi tudy. The network conit of input, hidden and output layer. The network convert the input according to the connection weight. Thee weight are adjuted during the learning proce. To minimize the um of the quared error between the deired output and the network output. A imple neural network repreent in Figure 5. The output layer i given by i net j = Σw ji o i θ j (6) j where w ji repreent the weight between hidden node j and input node i. The output of unit in the hidden and input layer are repreented by o i. The back-propagation algorithm adjut the network parameter in order to minimize the mean quare error. E p = 2 X X 2 X n Σ (t pj o pj ) 2 (7) j output W ji W kj 2 Fig. 5. Neural network diagram. Y Y 2 Y n where t pj i the deired output and o pj actual output. If a igmoid tranfer function i ued in the operation element o pj = Σ j e w ji o pj θ j (8) Uing Eq. (6) and (8), the activity of each unit i propagated forward through each layer of the network. Error for each unit i calculated. δ pj = o pj (t pj o pj )( o pj ) (9) A hidden layer error i back propagated a follow, δ pj = o pj ( o pj )Σ k δ pk w kj (2) The change in each weight i calculated. Thi rule for the adaptation of the weight i known a the generalized delta rule. p w ji (t ) = αδ pj o pi ε p w ji (t) (2) where α i contant that determine the learning rate of the back propagation algorithm, ε determine the effect of previou weight change on the current direction of movement in weight pace. The learning rate ha ued between. to. SIMULATIONS The controller deign objective are to reduce roll amplitude and to evaluate any difference in performance between the and the NN baed on IMC deign. To demontrate effectivene of thi propoed controller a erie of imulation are performed on the container veel. Uing the proce input α and previou output the neural network calculate m which i ued to calculate the error of the neural model e = m ued to adapt the neural mode with back propagation method and to produce feedback ignal. The Neural Network input and output function for the container hip roll tabilizer ytem are given in Figure 6. The figure how the NN plant model and the NN controller. The Neural Network i contituted by an input layer of two neuron, a hidden layer of thirteen neuron and an output layer one neuron. The controller input are the deired roll angle and the actual roll angle. The output i the fin angle, which hould drive the containerhip roll to the deired roll angle. In order to upgrade the NN baed on IMC, the actual error i calculated by back propagation algorithm. A container hip and fin tabilizer whoe main particular are given

5 F. Alarçïn: Internal Model Control Uing Neural Network for Ship Roll Stabilization 45 Table. Container hip main data Container hip Roll fin Length between perpendicular L (m) Profil area f 3.6 m 2 Maximum beam B 32 (m) Lift coeff. lope C Lα /rad Deign draft T.7 (m) Mean pan p 3 m Deign diplacement volume 467 (m 3 ) Mean chord c.2 m Metacenter height GM.83 (m) Section hape NACA 5 d Σ e(t) / e -x / e -x / e -x NNC α (t) Filter Plant NN model (t) Σ (t) m Fig. 6. Neural network a a controller in the IMC approach. in Table. Due to afety reaon, the fin angle i limited in the range of ±3. The wave diturbance may be modeled a an input diturbance, which i generated by Foen [3] in Figure 7. The damping ratio ζ i et to between from.5 to., the encounter frequency i et to between.3 to.3 rad/ec and the wave trength factor i K ω et to. In order to obtain damping ratio, the formula uggeted by reference [8] can be ued. Roll reduction ratio AP RCS Roll reductionratio (%) = (22) AP where AP i the tandard deviation (RMS) of roll amplitude when the fin tabilizer off. RCS i the tandard deviation of roll amplitude while the fin tabilizer i open. Figure 8 and 9 how control performance for and neural network baed on internal model controller. The reult in figure how that the cheme propoed in thi paper ha good repone peedine and robutne. It i oberved that the roll control ytem i capable of attaining the NN baed on internal model controller reult. The roll angle ha been reduced from 8.6 to.5, which correpond to a 94% roll angle reduction with NN baed on IMC. Table 2 ummarize the roll reduction reult. Figure how the fin angle when the urge peed i et equal to 2.7 m/ec. Very good roll reduction i achieved with minimal control effort required with NNIMC. Wave height (m) Roll angle [deg.] Time (ec.) Fig. 7. Wave function. 5 Time (ec.) CONCLUSION No control NNIMC 2 25 Fig. 8. Neural network baed IMC of roll motion. In thi paper an internal model controller of a roll motion tabilizer ytem wa deigned. Controller architecture combine neural network baed on internal model control. Simulation tudie are included to illutrate the effectivene of a neural network control algorithm. Thi lead to the concluion that the NN

6 46 Journal of Marine Science and Technology, Vol. 5, No. 2 (27) Table 2. Controller performance Roll angle (deg.) Roll velocity (deg./ec.) Roll reduction ratio (%) No control NNIMC Roll velocity [deg/ec] Fin [deg.] Time (ec.) Fig. 9. Neural network baed IMC of roll velocity. 5 Time (ec.) Fig.. The correponding fin repone. baed on internal model controller approach i a good alternative to claical controller deign. REFERENCES No control NNIMC 2 25 NNIMC Bhat, N. and Mcavoy, T.J., Ue of Neural Net for Dynamical Modeling and Control of Chemical Proce Sytem, Computer and Chemical Engineering, Vol. 4, No. 4-5, pp (99). 2. Donho, D.C., Deanj, D.S., Katebi, M.R., and Grimble, M.J., Adaptive Controller for Autopilot Application, International Journal of Adaptive Control Signal Proce, Vol. 2, pp (998). 3. Foen, T.I., Guidance and Control of Ocean Vehicle, John Wiley & Son, NY (994). 4. Haddara, M.R. and Xu, J., On the Identification of Ship Coupled Heave-Pitch Motion Uing Neural Network, Ocean Engineeering, Vol. 26, pp (999). 5. Hickey, N.A., Johnon, M.A., Katebi, M.R., and Grimble, M.J., Controller Optimiation for Fin Roll Stabilization, International Conference on Control Application, Hawai, USA (999). 6. Kaltrom, C.G., Atrom, K.J., and Thorell, N.E., Adaptive Autopilot for Tanker, Automatica, Vol. 5, pp (979). 7. Karayianni, N.B. and Venetanopoula, A.N., Fat Learning Algorithm for Neural Network, IEEE Tranaction Circuit and Sytem-II Analog and Digital Sytem Proceeding, Vol. 39, No. 7, pp (992). 8. Karayianni, N.B. and Venetanopoula, A.N., Artificial Neural Network-Learning Algorithm, Performance Evaluation and Application, Kluwer Academic Publiher, pp (993). 9. Katebi, M.R. and Byrne, J.C., LQG Adaptive Ship Autopilot, Tranaction of the Intitute of Meaurement and Control, Vol., No. 4, pp (988).. Lloyd, A.E.J.M., Roll Stabilization by Rudder, Proceeding of the 4 th International Ship Control Sytem Sympoium, Netherland (975).. Morari, M. and Zafirio, E., Robut Proce Control, Prentice-Hall, Englewood Cliff, NJ (989). 2. Ogata, K., Modern Control Engineering, Prentice-Hall, NJ (99). 3. Perez, T. and Blanke, M., Mathematical Ship Modelling for Marine Application (Report No: ØRSTED-DTU: Automation), Univerity of Denmark (22). 4. Raya, T., Gokarna, R.P., and Shaa, O.P., Neural Network Application in Naval Architecture and Marine Engineering, Artificial Intelligence in Engineering, Vol., No. 3, pp (996). 5. Sgobbo, J.N. and Paron, M., Rudder/Fin Roll Stabili-

7 F. Alarçïn: Internal Model Control Uing Neural Network for Ship Roll Stabilization 47 zation of the USCG WMEC 9 Cla Veel, Marine Technology, 36, pp (999). 6. Tzeng, C. and Wu, C., On the Deign and Analyi of Ship Stabilizing Fin Controller, Journal of Marine Science and Technology, Vol. 8, pp (2). 7. Tzeng, C. and Wu, C., A Senitivity Function Approach to the Deign of Rudder Roll Stabilization Controller, Journal of Marine Science and Technology, Vol. 9, pp. -2 (2). 8. Unar, M.A. and Murray-Smith, D.J., Automatic Steering of Ship Uing Neural Network, International Journal of Adaptive Control Signal Proce, Vol. 3, pp (999). 9. Zirilli, A.G.M., Robert, G.N., Tiano, A., and Sutton, R., Adaptive Steering of Containerhip Baed on Neural Network, International Journal of Adaptive Control Signal Proce, pp (2).