Influence of different controllers on ship motion stabilization at applied active fin stabilizer Imed El Fray, Zbigniew Kubik Technical University of Szczecin Department of Computer Science, ul. Zolnierska 49. 71-210 Szczecin, Poland Email: imed_el_fray@ii. tuniv.szczecin.pl Abstract The aim of the presented paper is to compare the fin stabilizer's efficiency depending on the steering method and selected controller adjustment. A digital simulation technique was used in order to evaluate the control methods on reduction of the ship resistance. It was found that the classical controller was more effective than optimal controller, but it can generate a bigger fin angle of attack. Optimal controller and optimal controller with the predictor generated lower fin angles of attack what provided much lower decrease of ship velocity at progressive motion when compared with classical controller characterised by greater decrease of ship velocity. As an effect, the increase of the ship drag caused by classical controller can be observed. 1 Introduction The reduction of the rolling motion can be realised by using special technical devices, eg. passive roll tank stabilisers, active roll tank stabilisers, and fin stabilisers. These stabilisers generate moment that is opposite to the disturbances ^'\ The base of the numerical simulation is the mathematical model of the dynamic sytem : ship and fin stabiliser which is described by the set of differential equations. Using this model the considered parameters as a function of the time were generated. 2 Mathematical Model of Ship Motion With Fin Stabiliser The mathematical model of dynamic ship motion which describes the sway, the surge, and the roll motions, respectively, and the yaw motion can be given in the following eqns. * *: 4-7V + K
282 Marine Technology In the above equation the H-index denotes the hydromechanical reactions, especially the hydromechanical forces and moments acting on a vesel in a seaway (the rudder and the screw motion are not considered). The R-index denotes the forces generated by the rudder, including the hydromechanical forces acting on a vesel when rudder is used. The P-index denotes the propeller's pressure. The aim of presented paper is to show the optimal control of fin stabilization system with preservation of high dampingability of the roll motion by analysing the ship's behaviour on the seaway. The ship drag increment can be caused by the uncorrect fin controll, especially the fin angle attack. The block diagram of the active fin stabilization system is presented on the (Figure 1). M Wave Ship I measuring noise Kalman Filtr White noise Active fin stabiliser ^ *o Controller Figure 1: Block diagram of the active stabilization system The executive mechanism of the fin stabiliser is an inertial nonlinear element. In the case of synthesis of the regulator controling the fin operation, the non-linearity can be negligible. Reguator should be selected in the way that it is impossible to exceed the values of limited angle. The executive mechanism offinstabilizer is shown in a diagramme (Figure 2). Figure 2: Executive mechanism offinstabiliser After simplification of the mathematical model (1) the differential equation of the motion can be written as in *: (2)
Marine Technology 283 where: fift - nondimensional roll damping coefficient, G)jQ- frequency of the roll motion, a g. - effective wave slope, ^F -fin'sangle of attack Presented paper considersthe roll motion stabilization problem, however in order to solve the external disturbance phenomenon, only the most important effect generated by the seaway was considered. The ct (t) in the equation (2) represents the wave slope angle generated by the waved surface of the sea. The height of wave spectrum was calculated according to the ITTC requirements, as: where: _2 173/ii/s r 691 r In the simulations a wave level of encounter hg is generated with a rational spectrum approximation *: *'*' * ll 2coVcos]3/g\ co* + 2(al - J3f)co^ + (CL\ + /3l)~ where: a>e = 0) - co* V / g cos/7 _frequencyof the encounter 1, D - /z.% - variation of the sea wave, as a stationary and ergodic, ' 16 random process with an average zero value, Of, Pf - coefficients of the filter A stochastic process with spectral density * is obtained as an output from thefilterwhen the white noise is applied into the input: where: >/2ab,, = k f - gain coefficient of the filter. g Figure 3 shows the modeling of disturbances using forming filter.
284 Marine Technology Figure 3: Modeling of disturbances using forming filter 3 Results and Discussion The active fin stabiliser provide the most effective stabilization for thevegselstraveling with a high speed on the seaway. The working active fin stabilisers increase also the added resistance of the ship. The most effective roll stabiliser we can consider only in the field of the optimal control. The base for application of another control algorithm is optimal filtering. Moreover, it is important to choose the correct' frequency range for filtering. Investigated algorithms are based (without the classical PDD^ regulator) on the Kalmanfilteringtheory. The classical PDD^ regulator is a base for efficient comparision of the algorithms supported by control theory. The optimal regulator with Kalman filter and the optimal regulator with n-step Kalman's predictor were considered for all experiments. To judge the performance of these controllers, the simulation experiment approach was used. The efficiency of stabilization can be examined at the laboratory by using a nonlinear mathematical model of the ships dynamics. The simplest method for obtaining the performance index which can be usually applied is to take one of the quadratic criterion. The main criteria for fin stabiliser can be expressed as follows: where A, J = J (o* (6) - weighting factor. The ship PA 2124 type was considered ; to compare the experiments simulation tests with used mathematical model. Simulation program was written in FORTRAN programming language. The aim of the numerical simulation was to solve the differential equation using the Runge - Kutta method. The main program require the following input data: length between perpendiculars, width, draft, ship velocity, " resistance as a function of velocity (without stabilizer), cross wave with h^/g= 3.10 m and 5.25 m, T= 7.4 s and 8.5 s. In Figure 4 the results of stabilization for different kind of control systems, namely active fin stabiliser controlled by classic PDD^ controllers (ideal and real), and optimal controller with Kalmanfilter,as well as an optimal controller with predictor (Figure 4) had been compared.
Marine Technology 285 From these results it can be seen, that active fin stabiliser controlled by classical controllers shows better efficiency than optimal controllers. 0 20 40 80 80 100 120 140 20 40 80 80 100 120 140 20 40 60 120 140 160 [deg) 3 finangle of attack 0 20 40 80 80 100 120 140 160 20 40 60 80 100 120 140 160 a - ideal at a sea state of 6 and 8 (the North Pacific) b - real at a sea state of 6 and 8 (the North Pacific) Figure 4: Simulation of roll motion for ship stabilised by classic regulator PDD%:
286 Marine Technology 0 20 40 SO 80 100 120 140 160 0 20 40 60 80 TOO 120 140 160 0 20 40 80 60 100 a - optimal regulator at the sea state of 6 and 8 (the North Pacific) b - optimal with predictor at the sea state of 6 and 8 (the North Pacific) Figure 5: Simulation of roll motion for ship stabilised by : The PDD* regulator exhibit the best efficiency compared with other used controllers. On the other hand, the PDD* regulator generate a very high values of the fin angles of attack (close to maximum) comparing with two other regulators, namely optimal and optimal with predictor. The best efficiency of stabilisation is observed for the North Pacific state of 8. The power spectra presented on Figure 6 confirm a good stabilization by the PDD* regulator. A considerable decreasing of the efficiency of stabilization was observed for lower state of sea.
Marine Technology 287 1. unstabilised ship, 2.stabilised ship with optimal regulator with predictor, 3. stabilised ship with optimal regulator, 4. stabilised ship with real PDD^ regulator, 5. stabilised ship with ideal PDD^ regulator Figure 6: The power spectra of angles for unstabilised and stabilised ship on irregular wave for the state of sea 6 and 8 respectively In Figure 7 the probabilities of exceeding roll angles are presented. For considered two stabilisers the ship roll motions can be decreased up to 40-60% for the state of sea 8 and up to 20-40% for the state of sea 6, respectively. Prob{I<Dl Prob {101 >0>») <D- [deg] 1. unstabilised ship, 2. stabilised ship with optimal regulator with predictor, 3. stabilised ship with optimal regulator, 4. stabilised ship with real PDD^ regulator, 5. stabilised ship with ideal PDD* regulator Figure 7: Probability of exceeding roll angles for unstabilised and stabilised ship on irregular wave for the state of sea 6 and 8 respectively The ideal PDD* regulator has the best efficiency, but high energy consumption by the ships propulsion system due to excessive fins angles of attack (Figure 8). The application of optimal control algorithm causes a decrease in the main value of fins' angles of attack (about 40%). As a result of smaller fins' angles a reduction of added resistance of ship energy consumption by fin actuator is achieved.
288 Marine Technology Prob {151 > 5-} 1. stabilised ship with ideal PDD^regulator, 2. stabilised ship with real PDD^regulator, 3. stabilised ship with optimal regulator, 4. stabilised ship with optimal regulator with predictor Figure 8: Probability of exceeding fin angles for attack on irregular wave for the state of sea 6 and 8 respectively 4 Conclusions The general conclusion is that for the investigated ship the application of the fin stabiliser controlled by classical controller is more effective than optimal controller, but it can generate bigger fin angle of attack. Optimal controller and optimal controller with predictor generate lower fin angles of attack which provide much lower decrease of ship velocity at pregressive motion comparing with classical controller characterised by greater decrease of ship velocity. As an effect, the increase of the ship drag caused by classical controller can be observed. References 1 Dudziak I, Teoria okretu, WM Gdansk, 1988 2. Cox G.G., Lloyd A.R., Hydrodynamic Design Basis for Navy Ship Roll Motion Stabilization, Transaction SNAME, vol. 85, 1977 3. Kawazoe T, Nishikido S., Wada Y.: Effect of Fin Area and Control Methods on Reduction of Roll Motion with Fin Stabilizers. Bulletin of Marine Engineering Society in Japan vol.22, 1994 4. Lloyd A. R: Roll stabilizer Fins. A Design Procedure, Royal Institution of Naval architects, vol.117, 1974 5. Kalstrom G., Ottosson P., The Generation and Controll of Roll Motion of Ships in Close Turns, 4th International Symposium of Ship Operation Automation, Geneva, Italy, Sept 1982 6. El Fray I., Synteza systemu sterowania aktywnym stabilizatorem kolysan bocznych statku w obecnosci wysokoczestotliwosciowych skladowych zaklocen, Technical University of Szczecin, Szczecin 1997 7. Rozenberg L., Parczewski S., Pejace J., Performance Analysis for Ship Roll Stabilisers Simulation Experiment, International Rostocker Schiffstech. Symposium, 1987, p. 107 8. Van Berlekom W. B., Lindgren H., " The SSPA Maritime Dynamics Laboratory. Backround experience and future development.", SSPA International Symposium on Ocean Engineering Ship Handling 1980. Goteberg, Sweden, Proceedings pi: 1.