DESIGN OF SHIP CONROLLER AND SHIP MODEL BASED ON NEURAL NEWORK IDENIFICAION SRUCURES JASMIN VELAGIC, FACULY OF ELECRICAL ENGINEERING SARAJEVO, BOSNIA AND HERZEGOVINA, asmin.veagic@etf.unsa.ba ABSRAC his paper proposes a computationay efficient artificia neura network modes for identification of both fuy ogic ship controer and noninear ship mode. he first obective demonstrates how to use noninear network to identify fuy controer and compare contro surfaces of these two controers as we as performance indices. he second obective is to use a noninear network to identify noninear pant in recursive on-ine mode and the third one is to integrate designed two neura networks in one contro scheme to test resuting system response in cosed oop system. KEYWORDS: Ship dynamics, fuy ogic controer, neura networks, course-keeping, traectory tracking, identification, adaptive earning rate.. INRODUCION In the ast few years the new methods has been deveoped which appy artificia neura networks to the tasks of identification and contro of dynamic systems []. hese works are supported by two of the most important capabiities of neura networks; their abiity to earn [2] and their good performance for the approximation of noninear functions [3]. At present, most of the works on system identification using neura networks are based on mutiayer feedforward neura networks with backpropogation earning or more efficient variations of this agorithm [4]. hese methods have been appied to rea processes and they have shown an adequate behavior. In this paper we demonstrated the appication of neura networks in both off-ine and on-ine identifications. he neura network controer that wi be mimic fuy controer in off-ine mode is first designed. his equivaent neura controer shoud have the same (or as simiar as possibe) contro surface as a fuy autopiot. For purpose of on-ine identification on noninear system the backpropagation agorithm with fixed earning rate is not appropriate [5]. he most of the pubications on neura net modes have been restricted to mode identification under open-oop conditions. But in many practica appications, cosed-oop identification is preferred, especiay in on-ine []. his paper presents the usage of BP neura network with adaptive earning rate to identify a noninear mode of ship in on-ine mode during guidance ship on the compex path with fuy controer in a cosed oop. A significant probem with a ship steering contro system is that the parameters of the system change with operating conditions (such as forward speed of the ship, depth of water, etc.) as we as environmenta disturbances (waves, wind, sea currents, etc.) [6]. Aso, additiona noninearities are introduced in system by the steering gear servo system which contains two noninearities: histeresis and saturation. Identification and contro of compex noninear system, ship pus steering gear system are chaenging probems. 2. CONROL SYSEM FOR COURSE AND RACK KEEPING In this section the structures of the contro system for the ship course and track keeping are described. he course-track contro system consists of the fuy controer, the steering gear servo system, the ship and necessary sensors (Fig. ). A ship s track-keeping system can be designed from the course-keeping system by incuding an additiona position feedback.
It is assumed that the dynamics of the gyrocompass and of the rate gyro are negigibe compared with other components of the contro system with more significant infuence on the dynamics of the cosed-oop system. Way points X d, Y ) ( d Xd Yd Disturbances Cacuating desired yaw ange X Y Ψ d _ Ψ e r Fuy Controer c Rate Gyro Steering Machine Ship Gyrocompass Figure. Bock diagram of the fuy contro system for the track-keeping. he main obective of this paper is how to obtain the neura network contro system (Fig. 2) from the system shown in Fig.. Way points X d, Y ) Xd ( d Yd Disturbances Cacuating desired yaw ange X Y Ψ d _ Ψ e r Neura Controer Rate Gyro c Neura mode of ship and steering machine Gyrocompass Figure 2. Bock diagram of the neura network contro system for the track-keeping. 2.. Ship Dynamics and Steering Gear Servo System In our studies we used the noninear mathematica mode which reates the yaw (Ψ ) with the rudder ange () of the ship. he noninear ship mode of a Mariner Cass ship is taken from []. he steering gear servo system consists of two eectrohydrauic steering subsystems: teemotor position servo and rudder servo actuator. he input of the steering gear servosystem originates from the autopiot and is caed the commanded rudder ange ( c ). he output is the actua rudder ange (). he noninear steering gear mode is described in [7]. 2.2 he urning Concept for rack-keeping he desired route is most easiy specified by way points (P,..., P n ) with coordinates P i =(x i, y i ). It is assumed that ship moves on a straight ine between the way points. During the maneuver, the ship is crossing from one to another ine aong a circuar arc. In this paper the turning concept where the ship is circuary moving with a way point outside the circe is used. his concept is competey described in [2] and [8]. 2.3he Base Fuy Controer he course-keeping fuy Sugeno controer (FLC) [2], [3], contains two contro inputs: heading error e=ψ d -Ψ and yaw rate r= dψ/dt. he contro action generated by the controer is the command rudder ange c. 3. NEURAL NEWORK ARCHIECURE he neura networks used in this paper are mutiayered neura networks with backpropagation earning agorithm. Neura network with one hidden ayer is used for identification of ship. In the case of identification of fuy ogic controer, neura network with two hidden ayer is
investigated. he synaptic weights and biases of a typica neura network with one hidden ayer based on backpropagation agorithm are updated as foows. Weights w and biases b of the output ayer: w ( k + ) = w + η y, () b ( k + ) = b + η. (2) Weights w i and biases b of the hidden ayer: wi ( k + ) = wi + η xi, (3) b ( k + ) = b + η, (4) where the error terms for the output and hidden units are respectivey: = ( yr y ) f ( x ). (5) ( k ) = ϕ ( x ) w. (6) he functions φ and f are sigmoid and inear activation functions of neurons in hidden ayer, respectivey, and x and y are input and output of the corresponding neura ayer. he parameter η represents the earning rate. he tota error for each output from the output ayer units is cacuated in the foowing manner: P m E(w, = ( yr y ). (7) 2 p= = where y r and y are desired and actua outputs of the -th neuron in output ayer. If the error is ess than the minimum vaue that has been set, the training process is finished. 4. NEURAL IDENIFICAION OF SHIP CONROLLER We used a three-ayered neura network trained by the backpropagation (BP) agorithm. his neura network consists of an input ayer with input vector x, two hidden ayers and the output ayer with output vector y. In Section 2 the Sugeno type fuy controer for course-keeping that is robust and has good performance is designed. his controer can be approximated by the neura network. he aim is to design equivaent neura controer that wi have the same (or as simiar as possibe) contro surface as a fuy controer. 4. Neura Network Design he proposed neura network has ten neurons in both hidden ayers and one neuron in an output ayer. he seection of input-output training patterns is very important for design neura network. he set of admissibe input vaues of fuy controer [2] is square K=[-3,3] x [-3,3]. We adopted Q=36 input vectors for training neura network, which are propery seected under the whoe contro surface over the set of admissibe vaues. Input signa errordot is periodic with period =6s and an error signa has period =36s. Figure 3 presents the start and the end of signas. hree dots are remarking the parts of signas that are not shown. he quaity of approximation depends on vaues of Q. Sma number of Q produced a ess precise approximation, whie arge number of it gives more compicated cacuation and requires more time for training. error-, errordot -- 3 2 - -2-3 2 3 4 5 6 t[sec]... error-, errordot -- 3 2 - -2-3 3 3 32 33 34 35 36 t[sec] Figure 3. ime diagram of input signas.
he difference between contro surfaces of fuy and neura controers is given in Figure 4. Figure 4. Error contro surface. he contro surface describes the dynamics of the controer and is a generay a time-varying noninear surface. Artificia NNs are based on anaogica earning and try to earn noninear decision surface of fuy controer through adaptive and converging techniques, based on numerica data avaiabe from input-output measurements of the system variabes and some performance criteria. 4.2. Simuation Resuts he performance of the contro system is based on the foowing performance indices, [3]: 2 2 2 I = im [ Ψd Ψ ] dτ = im e ( τ ) dτ, J = im ( τ ) dτ (8) where: e = heading error (deg) = rudder ange (deg). he smaer vaues of both I and J points out that better performance of the contro system is obtained. In Figure 5, the comparison between neura network and fuy controers is presented. Heading time response psi_d, psi [deg] 3 2 desired signa fuy controer neura controer 2 4 6 8 2 4 6 8 2 4 Command ruder ange time response deta_c [deg] 2 fuy controer neura controer -2 2 4 6 8 2 4 6 8 2 t[sec] Figure 5. he simuation resuts comparison obtained by neura network and fuy controers. It can be seen that the heading time responses for both controers (fuy and neuro) controer are without overshoot and osciation during transient response. It is aso noticed that the responses of the rudders are smooth and coincides quite we with desired command rudder ange. he response of the command rudder is smoother in the case of NN type controer. he initia rudder overoad (initia vaues of rudder ange) is arger with fuy than with NN controer (smaer vaue of J). It can be seen that the heading time responses are amost the same in both cases. he vaues of J and I indices for fuy controer scheme (I 2 = 3.725 and J 2 =69.4386) and NN controer scheme (I 2 = 3.9256 and J 2 =67.6667) are insignificant different.
5. NEURAL IDENIFICAION OF PLAN In conventiona BP agorithm, it is often used to choose a proper earning rate using tria-anderror method. Once chosen, the earning rate stays fixed during the whoe process of training. herefore, its convergence tends to be very sow, and it often produces suboptima soutions. o improve the performance of the BP agorithm a earning rate is adaptive at each iteration. he improving of identification capabiities, especiay for on-ine mode in cosed oop fuy contro system, using the time-varying earning rate for the neura network parameters update is proposed in this paper. he neura network mode is paced in parae with pant and the error between the pant and the network outputs is used as the training signa (on-ine identification). he pant is described by the foowing noninear discrete time difference equation: q = f ( q( k ),..., q( k n); c,..., c ( k m)). (9) hus, the pant output q=[ψ x y] at time k depends on the past n output vaues and on the past m vaues of the input c. Denoting the output of the network by q n we obtain the foowing equation: qn( w, = fn( qn( k ),..., qn( k n); c(,..., c( k m)). () where q n =[Ψ n x n y n ]. he mapping f n represents the noninear input-output map of the network that approximates the function f. he neura network used in this paper is composed of one hidden static ayer with feedback (Figure 6). he feedback signas are ship outputs (Ψ, x, y). he output and hidden ayers consist of neurons with inear and sigmoid activation functions, respectivey. c( Mux From ship output ψ( x( y( Demux Ψ n( x{} y{} x n( y n( wo-ayered static neura network ime Deay Figure 6. he simuink mode of dynamic NN. he adaptive BP earning agorithm is used to find optima vaues of the network weights and biases. 5.. BP with Adaptive Learning Rate For on-ine identification equation (7) can be rewritten as: m E(w, = ( y r y ). () 2 = For this purpose we define reationship between E(w, and E(w, as the reative factor χ(: E( E( -E( k ) χ = =. (2) E( E( And then, we determine how to adust earning rate term according to this reative factor χ. he adustment of the earning rate is given as foowing: χ ( k ) η( k + ) = η( [ sgn( χ( ) υ e ], υ (,). (3) he proposed agorithm is based on the conventiona BP agorithm by empoying an adaptive earning rate, where the earning rate is adusted at each iteration. he agorithm proceeds as foows. First, we seected number of neurons in hidden and output ayers, initia vaue of earning
rate and parameter υ. hen training process in cosed contro oop was performed for various vaues of parameter υ, υ [,]. he vaue of υ for which the best identification and contro performance was achieved, we choose as the best. 5.2 Simuation Resuts In order to evauate the earning performance of the proposed adaptive earning agorithm, two experiments wi be discussed. he first experiment presents the comparison between standard and adaptive BP agorithms in two ayered neura networks for identification of noninear mode of ship. In the second experiment the adaptive neura network is used for on-ine identification of ship during norma contro process. After identification procedure, neura network was embedded in contro system, instead of ship mode, and contro performance are compared for both neura networks ike mode (with neura controer) and ship mode (with fuy controer). he effectiveness of proposed neura-neura architecture (Figure 2) in comparison with the starting architecture with fuy controer (Figure ) was anayed for course-keeping and track-keeping probems. A the simuation resuts were generated using the MALAB neura network toobox. 5.2. Comparison between standard and adaptive neura network he training set for off-ine identification was obtained from input/output ship+steering machine data. he input signa is sinusoida shaped. Neura network contains 8 tansig neurons in hidden ayer and 3 purein neurons in its output ayer. he adaptive BP agorithm started from the same initia earning rate η=.4 for both ayers (hidden and output). he satisfactory resuts were obtained with υ=.8. Figure 7 shows the earning process for neura network with standard and adaptive backpropagation agorithm in off-ine mode. his iustrates the reation between the average error and epochs of the earning agorithms. hese resuts indicate that adaptive agorithm is faster than standard and it has a superior convergence speed. he conventiona BP method requires a arger number of iterations (28) for achieving the same contro performance than adaptive BP method (85 iterations). 4 3 Average error 2 85 Epochs, adaptive BP 28 Epochs, standard BP 5 5 2 25 Epoch Figure 7. he comparison of traditiona and adaptive BP neura network identification architectures. 5.2.2 On-Line Identification For the on-ine identification of noninear mode ship and steering gear system the neura network with adaptive earning rate is appied. he satisfactory resuts were obtained with the neura network with inputs, 8 neurons in hidden ayer and 3 neurons in output ayer. his network starts with the random initia weights and random initia bias using initia condition η=.5. he best traectory-tracking resuts were obtained with υ=.8. After training network with adaptive BP agorithms, the same is repacing the noninear mode of ship and steering gear system in course and track keeping contro systems. he good resuts are obtained using neura controer with neura ship mode (neura-neura system) in comparison with system that incuded the fuy controer and exacty ship mode (Figures 8 and 9).
Heading time response psi, psi_d [deg] 3 2 ψ d ψ desired fuy contro neura contro 2 4 6 8 2 4 6 8 2 t [sec] Figure 8. Course changing maneuver with fuy type controer and neura identificator. 25 2 rack-keeping P P3 2 P 4 Y [m] 5 5 S P Fuy system Neura-neura system P 5-5 P 6-5 5 2 25 3 35 4 45 X [m] Figure 9. raectory tracking with fuy type controer and neura identificator. 6. CONCLUSIONS In this paper, we have presented identification schemes of neura networks that ensure identification of noninear dynamica systems. wo types of NN identification are presented. In the first case, the aim is to design equivaent neura controer that wi have the same (or as simiar as possibe) contro surface as the existing fuy controer. he second probem in the paper is identification of pant (servo and ship system). For this purpose we proposed the new agorithm, which is based on the conventiona BP agorithm by empoying an adaptive earning rate, where the earning rate is adusted at each iteration. he standard BP agorithm and BP agorithm with adaptive earning rate were considered and compared in neura network identification of noninear mode of ship and steering gear system in off-ine mode. Simuation resuts demonstrate the effectiveness of the proposed adaptive strategy and superiority in training and convergence speed. 7. REFERENCES []. I. Fossen, Guidance and Contro of Ocean Vehices,. John Wiey & Sons, Chichester, 994. [2] J. Veagic, Z. Vukic and E. Omerdic, "Adaptive Fuy Ship Autopiot for rack-keeping," Contro Engineering Practice, Vo, No. 4, 23, pp. 433-443. [3] Z. Vukic and J. Veagic, "Comparative Anaysis of Mamdani and Sugeno ype Fuy Autopiot for Ships," Proc. Fifth European Contro Conference (ECC 99), Karsruhe, Germany, 999, pp. 57(-6). [4] S. Haykins, Neura Networks, a Comprehensive Foundation, Prentice-Ha, Engewood Ciffs, NJ, 999. [5] R.J. Schakoff, Artificia Neura Networks., McGraw-Hi, New York, 997. [6] K.S. Narendra nad Parthasarthy, "Identification and contro of dynamica systems using neura networks, " IEEE rans. Neura networks, Vo., No., 99, pp. 4-26. [7] R. Reid, M. Youhanaie, M. Banke and J.C. Nørtoft homsen, "Energy osses due to Steering Gear Instaations on Merchant Ships," Proc. Ships Cost and Energy Symposium, New York, USA, 984. [8]. Hohueter and D. Schute, "Operating experience with a high precision track controer for commercia ships," Proc. hird IFAC Workshop on Contro Appications in Marine Systems, rondheim, Norway, 995, pp. 27-278.