The Preliminary Study of Fin and Rudder Multivariate Hybrid Control System- Advanced Rudder Roll Stabilization System-

IFAC

Copyright © IF AC Control Applications in Marine Systems, Glasgow, Scotland, UK, 2001

C:Cc> Publications www.elsevier.comllocate/ifac

THE PRELIMINARY STUDY OF FIN AND RUDDER MULTIVARIATE HYBRID CONTROL SYSTEM - ADVANCED RUDDER ROLL STABILIZATION SYSTEM -

Hiroyuki Oda* ,Masamitsu Kanda* , Takashi Hyodo* Keiji Nakamura** , Hiroyuki Fukushima** Seiji Iwamoto*** , Seiichi Takeda**** , Kohei Ohtsu*****

* Akishima Laboratories ( Mitsui Zosen) Inc. , ** Mitsui Engineering & Shipbuilding Co., Ltd. *** Kyushu University . **** Tokyo University of Fisheries, ***** Tokyo University of Mercantile Marine Abstract: The combination of fin and rudder seems to be an attractive alternative for roll damping. However fin motions as well as high frequency rudder motions disturb the heading control system. In order to reduce this interaction, this paper proposes the advanced rudder roll stabilization control system with hybrid fin control system. From results of simulation and model experiments, it can be concluded that the fin and rudder hybrid control system is powerful and useful tool for stabilization of roll and course keeping. Copyright ©2001 fFAC Keywords: Rudder roll stabilization, Fin stabilizer, MAR control, Decoupling control

1. INTRODUCTION

2. YAW AND ROLL COUPLING MOTION

Modern roll stabilization system like fin, anti-roll tank and rudder action are used respectively or in combination on most passenger, naval ships. In such systems the low frequency rudder motion is used exclusively to control the heading. The use of rudder roll stabilization is then an attractive option and has received considerable attention in recent research. Some successful applications of rudder roll stabilization system have shown that the adequate roll reduction is only possible with specially designed or constructed ship and rudder system. These unsatisfactory situations have led to use of fin and the rudder together for reduce the roll motions and maintaining the ship heading. The combination of fin and rudder seems to be an attractive alternative for roll damping. However fin motions as well as high frequency rudder motions disturb the heading control system. In order to reduce this interaction, this paper proposes the advanced rudder roll stabilization control system with hybrid fin control system. First, this paper introduces coupling motion for heading and rolling. Next, this paper presents fin and rudder hybrid control system based on multivariate auto-regressive model, decoupling control and optimal regulator. Finally, conclusions and discussions based on results of simulation studies and model experiments are summarized.

When a ship is steered by rudder, the ship heels to inboard side due to the roll moment between the center of gravity and the center of the hydrodynamic force acting on the rudder control surface. On the other hand, when a rolling motion is controlled by fin, the ships heading change due to the yaw moment between the center of gravity and the center of the hydrodynamic force acting on the fin control surface. In this way, this phenomenon can say that yaw, roll , fin and rudder motions couple with each other. . The basic equations of the ship motion can be written in following form . Pitch and heave can generally be neglected if the study concentrate on course keeping and roll damping. Ship motion modeling is thus considered in surge, sway, yaw and roll [I ][2] . Surge: m(u - vr) = X H + X I' + X R + X F + X £ Sway : m (v + ur) = Y 11 + Y /' + Y R + Y F + YE Yaw

: f zz ,: = N

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Where m, Izz and Ixx are mass and turning moment of inertia, u, v, rand p are ship's speed along X, Y axis and rate of turn around Z, X axis. The subscripts H, P, R, F and E denote the hydrodynamic forces from hull, propeller, rudder, fin and external forces .

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Fin stabilizer is a highly attractive device for roll damping. The suitable block diagram for fin stabilizer system is described in Fig.3. The block diagram of hybrid control system is shown in Fig.4. The purpose of multivariate hybrid control system is put on roll reduction as well as course keeping using fin and rudder.

3. HYBRID CONTROL BASED ON MULTIVARIATE OPTIMAL CONTROL As motions of heading and rolling are physically coupled during straight courses and piloting during gyrations, the rudder and fin control laws of control system have a multi variable structure, different from the classical monovariable laws used for classical piloting or stabilization system [3]. To stabilize the ship on the straight course, a multivariate optimal control system has been used as shown in Fig.l .

3.1 Multivariate AR Control (5116] Multivariate Auto Regressive eXogenous model (MARX model) expressed by \I

X(n) =

.\1

A(m)X(n - m)+

B(m)Y(n - m)+ U(n) 111=1

/J/=l

is powerful stochastic model in designing a roll reducible autopilot system, where X(n) IS two-dimensional vector of controlled variable(r); yaw and roll. Y (n) is two-dimensional vector of control variable(l); rudder and fin angle . U(n) is Gaussian white noise . The order M of this model is obtained by Ale. The optimal order in the MARX model is determined by minimizing the value of Ale. Based on the modem control theory, this model can be transformed to a state space representation.

Fig. 1 Hybrid Control System The philosophy behind the rudder roll stabilization system is that the rudder can use as the effectiveness actuator to control both steering and roll reduction [4]. The block diagram of the rudder roll stabilization system is shown in Fig.2.

Z ( n) = (/JZ (n - I) + IT (n - I) + W ( n )

X(n) = HZ(n) where Zen) is the state vector and (/J is the transfer matrix that controls the transition of the state Z( n) . r is the observation vector. In order to evaluate a performance of the control, the quadratic criterion function J optimal in I is considered. Rudder

J, =

Fig.2 Rudder Roll Stabilization System

E{ ' {Z ' (n)Q(n)Z(n)+Y ' (n-I)R(n)Y(n-l}}} 11=1

where Q and R are the weighting function for the controlled and the control variables, respectively. The optimal control law which minimizes J, under constraint of the above state space equation is given by a feedback law with the stationary gain G . Then the optimal control law can be represented by

Yen) = GZ(n) Fig.3 Fin Stabilization System

3.2 Decoupling Control (71 181 Generally every input that is fed into the controlled object has effects on every output in a multivariate system. If the system is divided so as to have an input-output relation of one to one correspondences, it will be easier to design the control system. The state equation and the output equation for time invariant system are given as follows.

Fig.4 Hybrid Stabilization System

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x(t) = Ax(t) + Bu(t)

4. RESULTS OF SIMULATION STUDIES

y(t) = CX(t)

4.1 Multivariate AR Control

where the system has m-input and m-output and is a controllable system. As shown in Fig.! , introducing a new input v and considering the state variable feedback of u(t) = -Fx(t) + Gv(t)

Simulation techniques are presented as a possible aid in the development of fin and rudder hybrid control system. Simulation condition is followings. Ship: Displacement is about 1500 (ton) Speed is 18 (kts). Wave: Significant wave high is 4 (m) Wave period is 12 (sec), direction is beam. Fig.6 shows the simulation results in the case of controlling fin and rudder respectively by MAR Control system. It comes out in the fine line in Fig.6 that yawing and rolling motion without being controlled in the beam sea condition. The dotted line shows the result of controlling fin and the thick line is the result of controlling rudder. These simulation studies were carried out without control gain to optirnize. The reduction of rolling motion and course keeping realized with the result of rudder control of yaw and roll shown in Fig.6. However it is not distinctive in Fig.6 that the fin control of yawing and rolling motion makes up ship's course keeping.

The transfer function matrix of a closed loop system of Fig.5 as Ge(s) = C(sJ - A + BFt' BG Decoupling control is to search for a pair of matrix [ F ,G] to make Gc(s) into the diagonal matrix without zero diagonal elements. Assuming that

7J, = min[j I c, A j - I B

-:t= 0]

is given at the i-th row, the following equation instead of the above equation. u(t) = -B ' - I A' x(t) [c1A ~' , c2A ~~

A' =

+ B'-' y~, (t) , .... , cmA ~"' r'

B' = [c1A ~' - ' B,c2A ~'- ' B, .... , cmA ~"' -' Br'

Then necessary and sufficient conditions for existence of F and G for the decoupling is that B * is nonsingular. It is claimed that F = B'-' A' . G = B'-'

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The new vector v that is the input fed to the closed loop system is introduced in order to decoupling the system. Considering yp,(t) = v(t) the transfer

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function matrix of the closed loop system as the following integrator decoupling system. This system realizes decoupling of the original system. o

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Fig.6 Results of Rudder or Fin Control respectively ( MAR Control)

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Fig. 5 Decoupling Control System

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4.2 Decoupling Control Fig.7 shows the simulation result in the case of controlling combines fin and rudder by decoupling control system. These simulation studies were carried out without control gain to optirnize. In comparison with the result in Fig.6, the hybrid control system of decoupling control seems attractive from the simulation results of both rolling reduction and course keeping in Fig.7. Yaw~

Photo.1 Model Ship UMITAKA-MARU 5.1 M ultivariate AR Control ROI~)

In order to confirm the basic performance of rolling and course keeping of rudder by means of MAR control system, those model experiments were implemented that in the cases from forced oscillation to free damping and the rudder roll control, the results are shown in Fig.8 and Fig.9. Fig_8 shows the function of rolling reduction and course keeping in the condition of navigating under forced oscillation by rudder in the calm sea, replacing rudder in neutral position after 9.5 seconds passed.

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5. RESULTS OF MODEL EXPERIMENTS Roll RatEl:Eg/s) ~

To verify the effectiveness of hybrid control system, model experiments were carried out with radio control system. The model ship as UMITAKA-MARU is a training ship of Tokyo University of Fisheries. The principle particulars of the ship model are shown in Table 1. The model ship of UMITAKA-MARU is shown in Photo. 1.

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Fig.8 Results of forced oscillation and free damp

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Fig.9 shows the function of rolling reduction and course keeping after navigation under forced oscillation by rudder in the calm sea, when 9.5 seconds passed replacing rudder roll control by MAR control. 10

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Fig. 10 Results of forced oscillation and free damp

_; t-V _f\ _V _-A _ - ~_I\_-V_A_-~ _--_ ~ _-_ _ _ - -- --1-

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-«J0'- ; - 1-9--38--5-]--76-T-:-:-~;-1A--13-3-1-52--17-1- -"l O, ' .~ Fig.9 Results of forced oscillation and rudder roll control ( MAR Control)

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From the results ofFig.8 and Fig.9, it is concluded that the reduction of rolling motion by rudder roll control is cleared in comparison with the rudder neutral as well as controlling the course keeping which is a basic function of rudder control.

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5.2 Decoupling Control

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The proposed hybrid control system of decoupling system has been implemented and experimented using scaled model. Fig.1O and Fig.Il show the basic function of the hybrid control system of decoupling fin and rudder when it is implemented in rolling and course keeping. The adjustment of the confirmation and also control gain of fundamental dynamic characteristic adjust it while numerical simulation. In Fig. 10, rolling reduction and course keeping functions are shown in the condition of navigating under forced oscillation occurred by fin and rudder in the calm sea, replacing fin and rudder in neutral position after 25 seconds passed.

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Fig.ll Results offorced oscillation and Hybrid control ( Decoupling Control)

465

Fig.11 shows the rolling reduction and course keeping functions in the same condition when 25 seconds passed controlling by the hybrid control with decoupling fin and rudder control. In these model experiments, the hybrid control of decoupling fin and rudder resulted the attractive control of rolling reduction and course keeping.

6. CONCLUSIONS

This paper presents advanced rudder roll stabilization control system with combined fin system based on MAR and decoupling control. The purpose of multivariate hybrid control system is put on roll reduction as well as course keeping using fin and rudder. The purpose of this paper is to verify the effectiveness of hybrid control system in simulation and in model experiments. From results of simulation studies and model experiments, it can be concluded that the fin and rudder hybrid control system is very powerful and useful tool for stabilization of roll and course keeping navigation at sea. Hereafter, the authors plan to apply this hybrid control system to actual ships to be of great use and to develop good effect of control systems.

REFERENCES

[ I] E.Eda : A degital Simulation Study of Steering Control with Effects of Roll Motions, SCSS'73. 1973. [2] K.Ohtsu and K.Shoji Minimum Time Maneuvering of Ship, MCMC'94, 1994. [3] S.Kummer, G.Hardier and C.Lamber! ; The Cogite System of the Charles de Gaulle Aircraft Carrier, SCSS'99, 1999. [4] H.Oda. K.Ohtsu. M.Sasaki , YSeki and T.Hotta : Rudder Roll Stabilization Control System through Multivariate Auto Regressive Model. CAMS'92. 1992. [5] H.Oda. K.Ohtsu and T.Hotta : Statistical Analysis and Design of Rudder Roll Stabilization System. IFAC Control Engineering Practice. VolA. No .3. 1996. [6] H.Oda. T.Hyodo. K.Ohtsu. M.Ito. N.Hirose. J.s.Park and H.Sato : Designig Advanced Rudder Roll Stabilization System - High Power with Small Size Hydraulic System and Adaptive Control -. SCSS'99. 1999. [7] YOgawara and S.Iwamoto : Studies on the Control System Design of Ship Maneuvering Motion with Decoupling Control. C AMS·98 . 1998. [8] S.Iwamoto. S.Takada. K.Ueno. H.Oda. M.Kanda and T.Hyodo : Control ofYaw and Roll by Rudder and Actiye Stabilizing Fins. Transactions of the West-Japan Society of Naval Architects.2001

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