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Fin and rudder hybrid stabilization system
FIN AND RUDDER HYBRID STABILIZATION SYSTEM
Hiroyuki Oda* ,Takashi Hyodo* ,Masamitsu Kanda* Hiroyuki Fukushima** , Keiji Nakamura** Seiichi Takeda*** ,Toshifumi Hayashi*** and Hisato Fujiwara***
* Akishima Laboratories(Mitsui Zosen) Inc.
1-50 Tsutsujigaoka l-chome Akishima, Tokyo, Japan
** Mitsui Engineering & Shipbuilding Co., Ltd. 1-1 tama 3-chome Tamano, Okayama, Japan *** Tokyo University of Marine Science and Technology. 5-7 Konan 4, Minato-ku, Tokyo, Japan
Abstract: Modern roll stabilization system, namely fin, anti-roll tank and rudder action are used respectively or in combination on most passengers and naval ships. This paper proposes the advanced rudder roll stabilization control system with fin control. Fin and rudder multivariate hybrid control system were designed using multivariate autoregressive model with multi-input (yaw and roll motion) and multi-output (rudder and fin angle), named MAFRCS (Multivariate Autoregressive Fin and Rudder hybrid Control System). This paper presents the results of studies which led to the development of performing mode of operation for this hybrid control system which system has full control of rudder while fin automatically reduce the roll motion and keep the yaw motion. The results of full scale experiments and simulations studies were given to illustrate the system performances. Copyright © 2004 IFAC Keywords: Rudder roll stabilization, Fin and rudder hybrid control, Full scale experiment
1. INTRODUCTION
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 fm and the rudder together for reduce the roll motions and maintaining the ship heading (Sgobbo et aI., 1999). The combination of fm and rudder is a highly 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 to control ship's heading as well as rolling motion with fin and rudder together or alternative, this paper proposes the advanced rudder
CAMS 2004
roll stabilization control system with fin control. Fin and rudder multivariate hybrid control system was designed adopting multivariate autoregressive model with mUlti-input (yaw and roll motion) and multi-output (rudder and fin angle), named MAFRCS (Multivariate Autoregressive Fin and Rudder hybrid Control System). In section 2, yaw and roll control with fin and rudder was discussed. In section 3, designing fin and rudder hybrid control system based on multivariate auto-regressive model was summarized. In section 4, defmition of roll reduction is explained. In section 5, results of full scale experiment were performed. In section 6, design and confirm with numerical simulation were discussed. Finally, conclusions and discussions were summarized.
119
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.
2. YAW AND ROLL CONTROL WITH FIN AND RUDDER The ship is steered by her 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 a rudder control surface as shown in Fig.l (Cowley, 1972). On the other hand, roll motion is controlled by fin as shown in Fig.l, 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 shown as white arrow at Fig. l (Kallstrom, 1981). The longer these distances (arm) between them and higher ship speed make the stronger yaw and roll moment. Once the roll has begun, it causes yaw moment. This coupling motion can be explained by longitudinal asymmetry of hull configuration due to roll angle. Sometimes they might induce the so called roll-yaw-rudder-fin instability. Yaw arm (rudder)
3. HYBLID STABILIZATION SYSTEM
3.1 Fin and rudder hybrid controller 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- input and multi-output (M1MO) system, different from the single-input single-output (S1SO) system used for classical piloting or stabilization system. To stabilize the ship on the navigation, the image of hybrid control system has been used as shown in Fig.2. The purpose of fin and rudder hybrid control system is put on roll reduction as well as course keeping using fin and rudder. 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. The block diagram of hybrid control system is shown in Fig.3. The purpose of multivariate hybrid control system is put on roll reduction as well as course keeping using fin and rudder. Hybrid Controller f - - - - - - - - - - - - - - - - - - - -
~
Yaw component of Fin Lift
The motion in the horizontal plane ( Top view) Roll arm (fin)
Yaw component of Fin Lift Roll arm (rudder)
The motion in the vertical plane ( Stern View)
Rudder (Roll & Vaw)
Fig. 1 Yaw and Roll Coupling Motion with Fin and Rudder
Fig. 2 Image of Hybrid Control System
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 mode ling is thus considered in surge, sway, yaw and roll (Oda, et aI. , 1996).
Fin angle
Roll rate dev. Hybrid Controller L -_ _ _- '
~ J f r ;~~rse 1
Roll rate
Gyro
-
~------------~
y
Rudder angle
Roll rate=
x
Surge: m(u - vr) = X " + X p + X R + X F + X E Sway : m (v + ur)
=
Y H + Y p + Y R + Y F + YE
Yaw
: 1 zz
r=
N
+ N
p
Roll
: 1 xx
p=
K" + K
p
H
+ N + K
R
R
+ N F + N £ + KF + K£ (1)
Where m, 1zz and 1xx are mass and turning moment of inertia, u, v, rand p are ship's speed along X, Y
120
Rudder
a
Fin
(c)
Fig. 3 Rudder, Fin and Hybrid Control
CAMS 2004
Table 1 Principal particulars of "UMITAKA MARU"
3.2 Multivariate auto-regressive model The basic control model adopted here for predictions of roll and yaw motion is a control type of Multivariate Auto-Regressive eXogenous model (MARX model) (Oda, et aI., 1992, Oda, et aI., 2003).
X(n)
M
M
m =,,]
m =!
HuU
= IA(m)X(n-m)+ IB(m)Y(n-m)+U(n) (2)
This control law is powerful stochastic model in designing a roll reducible autopilot system (heading control), where X(n) is two-dimensional vector of controlled variable (r) ; yaw and roll. Y (n) is two-dimensional vector of control variable (I) ; rudder and fin angle. U(n) is white noise. The order M of the model is obtained by Ale.
AIC(M) = N · Iog{ det(dr, M)} + 2· r(r + I)(M + I) (3)
Rudder
Fin ART Propeller Engine
Length (Lpp) Breadth Depth Draft Displacement Gross Ton GM Roll Period Area Aspect Slew rate Area Slew rate Type Type Dia. * No. Type Power * rpm
83 .0 (m) 14.9 (m) 8.9 (m) 5.95(m) 4000 (ton) 1886 (ton) 1.32 (m) 10.3 (sec) 9.63 (m**2) 1.45 5 (deg/s) max. 6 (m**2) 20 (deg/s) max Variable Period Cpp 3.8 (m) * 4 Diesel 4489 (KW) * (rpm)
520
Where N is data length and optimal MARX model has the order which takes the minimum value of AlC estimation (MAICE) (Akaike, 1974). This control model is obtained by the MAICE procedure, using the actual data (roll and yaw angle, fin and rudder angle) gained from the preliminary full scale trial for the identification of the fin and/or rudder dynamics. Based on the modem control theory, this model can be transformed to a state space representation. The optimal control law which minimizes the quadratic criterion function 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)
(4)
Photo. 1 The view of "UMITAKA MARU" The optimal problem with the criterion can be solved using the technique of dynamic programming.
4. DEFINITION OF ROLL REDUCTION 4.1 Target ship of experiment To confirm the effectiveness of MAFRCS, full scale experiments were carried out using prototype control system. The experiments were made on the fishery training ship "UMITAKA MARU" of Tokyo University of Fisheries. The principal particulars are shown in Table I. The view of target ship and fin are shown in Photo 1. In order to check the roll-yaw-rudder-fin instability and control law by means of MARX model, preliminary studies were already done using free running model experiment with radio control.
4.2 Definition of roll reduction To confirm the basic performance of roll reduction of MARFCS, full scale experiments were implemented that the cases from forced oscillation to free damping and fin and/or rudder stabilization control. The percentage reduction of roll motion is defined by
REDUCTION
= Mfn(Free) -lvffs(Stabilization) .100(%) Mfn(Free) (5)
The roll amplitude factors denote Mfn(free) and Mfs(stabilization) are calculated by following equation. Mlfa=-r=========~============
CAMS 2004
121
Notations in this equation are follows; co : wave period, con : natural roll period Ca : roll damping factor defined as follows
1 rpn C n =-·loge-27r rpn+l
Table 2 Definition of roll reduction ( Free dump and stabilization ) (a)
1 rpj Cs=-·loge-7r rp j+l
<1>1 -3.3den 3.3d""
<1>3 -l.Sden 1.Sd""
4.2den
il-l
<1>.
<1>4 1.5dea 1.5cteO
.1 3.4den
i
(7)
(a)
<1>2 2.3dea 2.3d""
5.6den
<1>6 <1>5 - 1.3dea I 1.ldw 1.3dea I 1.ldea +2 2.4dea
2.9dea
(b) r-~-=----r-.....,...---r--:::-::--r----':-:----'
roe dumping
(c) Free dumnin(] 0.080 Cn1 0.056 Cn2 Cn3 0.060 Crtmeanl 0.066 Mfi1 7.632
I REDUCTION I 110
130
150
110
190
210
230
250
270
290
If
; . .--
i
~
~
Stabilization
1-0=""=...... == - -=+-===....-i = """~ =-=+=~_L.-
2
~~_=_=~l___:_=~'=_=_=~=_=_=.~=_=_=,E_=_~ _,_=_=_=~_+-=_=~=~=_=_=I
.2
~~=-=-=l-=-==~=-=-+=-=-==-+.~-:-:+-::-:+--+-:=-:+:--~ :
.,
.:..:...:..~:..:..: : ::.J.:..=;:..: - =..,L=:"':' = .::L: = =..:..: = =:..r:. ~..:..:: : :~ : : ..:..l : ~ = ..:..; = =:..:J = ..:..:: = =...:...J =
.6
110
130
150
110
190
210
230
250
210
290
310
Time (sec)
Fig. 4 Example time series of roll angle ( Free dump and stabilization ) Examples of definition of roll reduction are shown in Fig. 4. Fig.4 (a) shows the time series of roll angle at free dumping and Fig4 (b) shows the time series of roll angle at stabilization control (Kallstrom, 1990). Using example data, the calculation flow of roll reduction is shown Table 2. Table 2 (a) shows double amplitude at free dumping (
122
44.83%
310
Time (sec)
(b)
Stabilization Cs1 0.089 Cs2 0.165 Cn3 0.101 Cs'meanl 0.119 Mfs 4.210
The MAFRCS included measurement of roll angle, roll rate, yaw angle by vertical optical fib er gyro and measurement of rudder angle and fin angle by ship's equipment. The performance of roll damping has been measured in different ways. From the scientific point of view, the obvious approach is to measure the roll angle with and without the rolling damping system during exactly the same condition. In order to confirm the basic performance of roll damping and course keeping of MAFRCS, full scale experiments were implemented in the cases from forced oscillation to free damp and MAFRCS. A simple approach is to move the rudder and/or fin in sinusoidal way with a frequency close to ship's natural roll period and measure rudder and/or fin angle and roll motion as shown in section 4.2. 5.1 Roll stabilization and course keeping by rudder andjin Fig. 5 and Fig 6 show the function of rolling reduction and course keeping performance in the condition of navigation under forced oscillation by fin and stabilization by rudder and fin multivariate hybrid control system ( MAFRCS ) in the calm sea. Fig. 5 is the results in the condition of ship speed 16kts and Fig. 6 is the results of ship speed 19kts. In this figure, the first column is rudder angle, the second column is fin angle (starboard), the third column is fin angle (port), the fourth column is roll angle, the fifth column is roll rate and the last column is yaw deviation from set course. 5.2 Summary of measured roll reduction with MAFRCS The percentages of roll reduction of roll angle and roll rate were defined in section 4. Summary of
CAMS 2004
Oscillation
measured roll reduction were performed that roll and heading control with rudder, roll and heading control with fin, roll and heading control with both fm and rudder. The roll reductions with some control mode ofMAFRCS are summarized in Table 3. Oscillation
~~. l
"::""
Sta bilization
0.0
-~- I j~ ~dl o
56
11 2
56
,"
Fina~re(R)
de<]
51.5
103.0
154.5 1
Finangle(L) d'9
: ~~ :: I ! j : f --------,r---------
--15 lO
Stabilization
w:~ - r : 1 1
i ,
.. It
....
I
_
0_0
•
51.5
~ .~' .~"f1¥Ait ~Wtf_ u
~
103.0
1S4.s l
Roll rate
deg /s
I I'' 1 f: _
_
Roll angle d'9 10
~7 1 ~ _ u
~
t- 1 _
_
Ya w.dev.
d'9
Roll angle
sects)
de<]
Fig. 6 Time series of forced oscillation and stabilization ( Sea state lwith speed 19 kts: Control of rudder and fin )
Yaw.dev de9
It can be concluded that in normal conditions a roll sects)
Fig. 5 Time series of forced oscillation and stabilization (Sea state lwith speed 16 kts: Control of rudder and fin )
5.2 Summary of measured roll reduction with MAFRCS The percentages of roll reduction of roll angle and roll rate were defined in section 4. Summary of measured roll reduction were performed that roll and heading control with rudder, roll and heading control with fin, roll and heading control with both fin and rudder. The roll reductions with some control mode ofMAFRCS are summarized in Table 3.
Table 3 Summary of measured roll reduction Control mode of MAFRCS Rudder only Fin only Fin & Rudder
CAMS 2004
Reduction (%) define eq. (5) Roll angle Roll rate 49 31~47 71~73
74~76
67~77
60~80
reduction in the order of 70~80(%) is achievable with MAFRCS ( fin mode and hybrid mode ), but these experiments were carried out without control gain to optimize. Also the heading control by MAFCS can maintain the desired course in allowable limit
6. CONFIRMATION OF HYBRID SYSTEM Simulation techniques are presented as a possible aid in the design of fin and rudder multivariate hybrid control system (MAFRCS). The results of full scale experiment with "UMITAKA MARU" shown in section 5 were confirmed by simulation study. But these simulation studies were carried out without control gain to optimize exactly. Fig. 7 shows the simulation results of rolling reduction and course keeping performance in the condition of navigation under forced oscillation by fin and stabilization by rudder and fin multivariate hybrid control system (MAFRCS). The results of Fig. 7 indicate that the full scale experiment and simulation were well fitted in the function of roll reduction and course keeping. In this figure, solid line shows full scale results and dotted line shows simulation results. Also the first column is rudder angle, the second column is fin angle (starboard), the third column is roll angle and the last column is yaw deviation from set course.
123
The results of dynamic simulation suggested that the simulation techniques were reasonable and useful tool for design and confirm the ship's dynamics and control law of MAFRCS.
60
Time[s)
1 1 11 1<0
60
ACKNOWLEDGEMENT In the full scale experiments described in this paper, YKoike captain, H.Yonemoto chief engineer and crew gave helpful support with especial thanks to "UMITAKA MARU". Helpful suggestions and encouragement were received from Prof. K.Ohtsu of Tokyo University of Mercantile Marine and Mr. S.Ueki and Mr. H.Kanehiro of Mitsui Engineering & Shipbuilding Co., Ltd.
REFERENCES
Time(s)
20
60
20
60
I I I I!
80 Time(s)
100
120
140
80
100
'20
1<0
!
Tim e(s)
~ I:~ I----tlf---+,.j.---+..1--+-1--+-1---+-1---+---111 ~
I 60
Time(s)
Fig. 7 Simulation results of forced oscillation and stabilization driven by rudder and fin 7. CONCLUSIONS This paper presents the advanced rudder roll stabilization control system with fin control. Fin and rudder multivariate hybrid control system were designed using multivariate autoregressive model with multi-input (yaw and roll motion) multi-output (rudder and fin angle). This control system is called MAFRCS (Multivariate Autoregressive Fin and Rudder hybrid Control System). The purpose of this paper is to verify the effectiveness of MAFRCS in simulation and in full scale experiments. From the results of full scale experiments, fin and rudder multivariate hybrid control system reduce the roll motion in the order of 70~80(%) with course keeping. Also the results of dynamic simulation that the simulation techniques with was useful tool for design and confirm the ship's dynamics and control law. Through these studies, it can be expected that the MAFRCS have higher controllability than conventional rudder roll control systems or conventional fin stabilization systems. Hereafter, the authors are going to apply this hybrid control system and advanced rudder roll stabilization system (Oda, et aI. , 1999) to several types of ship to be of great use and to develop good effect of next generation type motion control.
124
1. N. Sgobbo, M. G. Parsons (1999). RudderlFin Roll Stabilization of the USCG WMEC 901 Class Vessel, Marine Technology, Vo1.36, No.3. W. E. Cowley (1972). The Use of the Rudder as a Roll Stabiliser, SCSS'72. C. G. Kallstrom (1981). Control of Yaw and Roll by a Rudder/Fin Stabilization System, SCSS' 81. H. Oda, K. Igarashi, K. Ohtsu (1996). Simulation Study and Full Scale Experiment of Rudder Roll Stabilization System, SCSS'96. H. Oda, K. Ohtsu, M. Sasaki, Y. Seki, T. Hotta (1992). Rudder Roll Stabilization Control System through Multivariate Auto Regressive Model, CAMS '92. H. Oda, T. Hyodo, M. Kanda, H. Fukushima, K. Nakamura, S. Takeda, T. Hayashi, H. Fujiwara (2003). Designing fin and rudder multivariate hybrid control system, SCSS'2003 . H. Akaike (1974). Statistical Analysis and Control of Dynamic System, Kluwer Academic Publishers. C. G. Kallstrom, W. L.Schultz (1990). An Integrated Rudder Control System for Roll Damping and Course Maintenance, SCSS '90. H. Oda, T. Hyodo, K. Ohtsu, M. Ito, N. Hirose, 1.S. Park, H. Sato (1999). Designing Advanced Rudder Roll Stabilization System - High Power with Small Size Hydraulic System and Adaptive Control-, SCSS'99.
CAMS 2004
Hiroyuki Oda* ,Takashi Hyodo* ,Masamitsu Kanda* Hiroyuki Fukushima** , Keiji Nakamura** Seiichi Takeda*** ,Toshifumi Hayashi*** and Hisato Fujiwara***
* Akishima Laboratories(Mitsui Zosen) Inc.
1-50 Tsutsujigaoka l-chome Akishima, Tokyo, Japan
** Mitsui Engineering & Shipbuilding Co., Ltd. 1-1 tama 3-chome Tamano, Okayama, Japan *** Tokyo University of Marine Science and Technology. 5-7 Konan 4, Minato-ku, Tokyo, Japan
Abstract: Modern roll stabilization system, namely fin, anti-roll tank and rudder action are used respectively or in combination on most passengers and naval ships. This paper proposes the advanced rudder roll stabilization control system with fin control. Fin and rudder multivariate hybrid control system were designed using multivariate autoregressive model with multi-input (yaw and roll motion) and multi-output (rudder and fin angle), named MAFRCS (Multivariate Autoregressive Fin and Rudder hybrid Control System). This paper presents the results of studies which led to the development of performing mode of operation for this hybrid control system which system has full control of rudder while fin automatically reduce the roll motion and keep the yaw motion. The results of full scale experiments and simulations studies were given to illustrate the system performances. Copyright © 2004 IFAC Keywords: Rudder roll stabilization, Fin and rudder hybrid control, Full scale experiment
1. INTRODUCTION
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 fm and the rudder together for reduce the roll motions and maintaining the ship heading (Sgobbo et aI., 1999). The combination of fm and rudder is a highly 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 to control ship's heading as well as rolling motion with fin and rudder together or alternative, this paper proposes the advanced rudder
CAMS 2004
roll stabilization control system with fin control. Fin and rudder multivariate hybrid control system was designed adopting multivariate autoregressive model with mUlti-input (yaw and roll motion) and multi-output (rudder and fin angle), named MAFRCS (Multivariate Autoregressive Fin and Rudder hybrid Control System). In section 2, yaw and roll control with fin and rudder was discussed. In section 3, designing fin and rudder hybrid control system based on multivariate auto-regressive model was summarized. In section 4, defmition of roll reduction is explained. In section 5, results of full scale experiment were performed. In section 6, design and confirm with numerical simulation were discussed. Finally, conclusions and discussions were summarized.
119
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.
2. YAW AND ROLL CONTROL WITH FIN AND RUDDER The ship is steered by her 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 a rudder control surface as shown in Fig.l (Cowley, 1972). On the other hand, roll motion is controlled by fin as shown in Fig.l, 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 shown as white arrow at Fig. l (Kallstrom, 1981). The longer these distances (arm) between them and higher ship speed make the stronger yaw and roll moment. Once the roll has begun, it causes yaw moment. This coupling motion can be explained by longitudinal asymmetry of hull configuration due to roll angle. Sometimes they might induce the so called roll-yaw-rudder-fin instability. Yaw arm (rudder)
3. HYBLID STABILIZATION SYSTEM
3.1 Fin and rudder hybrid controller 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- input and multi-output (M1MO) system, different from the single-input single-output (S1SO) system used for classical piloting or stabilization system. To stabilize the ship on the navigation, the image of hybrid control system has been used as shown in Fig.2. The purpose of fin and rudder hybrid control system is put on roll reduction as well as course keeping using fin and rudder. 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. The block diagram of hybrid control system is shown in Fig.3. The purpose of multivariate hybrid control system is put on roll reduction as well as course keeping using fin and rudder. Hybrid Controller f - - - - - - - - - - - - - - - - - - - -
~
Yaw component of Fin Lift
The motion in the horizontal plane ( Top view) Roll arm (fin)
Yaw component of Fin Lift Roll arm (rudder)
The motion in the vertical plane ( Stern View)
Rudder (Roll & Vaw)
Fig. 1 Yaw and Roll Coupling Motion with Fin and Rudder
Fig. 2 Image of Hybrid Control System
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 mode ling is thus considered in surge, sway, yaw and roll (Oda, et aI. , 1996).
Fin angle
Roll rate dev. Hybrid Controller L -_ _ _- '
~ J f r ;~~rse 1
Roll rate
Gyro
-
~------------~
y
Rudder angle
Roll rate=
x
Surge: m(u - vr) = X " + X p + X R + X F + X E Sway : m (v + ur)
=
Y H + Y p + Y R + Y F + YE
Yaw
: 1 zz
r=
N
+ N
p
Roll
: 1 xx
p=
K" + K
p
H
+ N + K
R
R
+ N F + N £ + KF + K£ (1)
Where m, 1zz and 1xx are mass and turning moment of inertia, u, v, rand p are ship's speed along X, Y
120
Rudder
a
Fin
(c)
Fig. 3 Rudder, Fin and Hybrid Control
CAMS 2004
Table 1 Principal particulars of "UMITAKA MARU"
3.2 Multivariate auto-regressive model The basic control model adopted here for predictions of roll and yaw motion is a control type of Multivariate Auto-Regressive eXogenous model (MARX model) (Oda, et aI., 1992, Oda, et aI., 2003).
X(n)
M
M
m =,,]
m =!
HuU
= IA(m)X(n-m)+ IB(m)Y(n-m)+U(n) (2)
This control law is powerful stochastic model in designing a roll reducible autopilot system (heading control), where X(n) is two-dimensional vector of controlled variable (r) ; yaw and roll. Y (n) is two-dimensional vector of control variable (I) ; rudder and fin angle. U(n) is white noise. The order M of the model is obtained by Ale.
AIC(M) = N · Iog{ det(dr, M)} + 2· r(r + I)(M + I) (3)
Rudder
Fin ART Propeller Engine
Length (Lpp) Breadth Depth Draft Displacement Gross Ton GM Roll Period Area Aspect Slew rate Area Slew rate Type Type Dia. * No. Type Power * rpm
83 .0 (m) 14.9 (m) 8.9 (m) 5.95(m) 4000 (ton) 1886 (ton) 1.32 (m) 10.3 (sec) 9.63 (m**2) 1.45 5 (deg/s) max. 6 (m**2) 20 (deg/s) max Variable Period Cpp 3.8 (m) * 4 Diesel 4489 (KW) * (rpm)
520
Where N is data length and optimal MARX model has the order which takes the minimum value of AlC estimation (MAICE) (Akaike, 1974). This control model is obtained by the MAICE procedure, using the actual data (roll and yaw angle, fin and rudder angle) gained from the preliminary full scale trial for the identification of the fin and/or rudder dynamics. Based on the modem control theory, this model can be transformed to a state space representation. The optimal control law which minimizes the quadratic criterion function 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)
(4)
Photo. 1 The view of "UMITAKA MARU" The optimal problem with the criterion can be solved using the technique of dynamic programming.
4. DEFINITION OF ROLL REDUCTION 4.1 Target ship of experiment To confirm the effectiveness of MAFRCS, full scale experiments were carried out using prototype control system. The experiments were made on the fishery training ship "UMITAKA MARU" of Tokyo University of Fisheries. The principal particulars are shown in Table I. The view of target ship and fin are shown in Photo 1. In order to check the roll-yaw-rudder-fin instability and control law by means of MARX model, preliminary studies were already done using free running model experiment with radio control.
4.2 Definition of roll reduction To confirm the basic performance of roll reduction of MARFCS, full scale experiments were implemented that the cases from forced oscillation to free damping and fin and/or rudder stabilization control. The percentage reduction of roll motion is defined by
REDUCTION
= Mfn(Free) -lvffs(Stabilization) .100(%) Mfn(Free) (5)
The roll amplitude factors denote Mfn(free) and Mfs(stabilization) are calculated by following equation. Mlfa=-r=========~============
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121
Notations in this equation are follows; co : wave period, con : natural roll period Ca : roll damping factor defined as follows
1 rpn C n =-·loge-27r rpn+l
Table 2 Definition of roll reduction ( Free dump and stabilization ) (a)
1 rpj Cs=-·loge-7r rp j+l
<1>1 -3.3den 3.3d""
<1>3 -l.Sden 1.Sd""
4.2den
il-l
<1>.
<1>4 1.5dea 1.5cteO
.1 3.4den
(7)
(a)
<1>2 2.3dea 2.3d""
5.6den
<1>6 <1>5 - 1.3dea I 1.ldw 1.3dea I 1.ldea +2 2.4dea
2.9dea
(b) r-~-=----r-.....,...---r--:::-::--r----':-:----'
roe dumping
(c) Free dumnin(] 0.080 Cn1 0.056 Cn2 Cn3 0.060 Crtmeanl 0.066 Mfi1 7.632
I REDUCTION I 110
130
150
110
190
210
230
250
270
290
If
; . .--
i
~
~
Stabilization
1-0=""=...... == - -=+-===....-i = """~ =-=+=~_L.-
2
~~_=_=~l___:_=~'=_=_=~=_=_=.~=_=_=,E_=_~ _,_=_=_=~_+-=_=~=~=_=_=I
.2
~~=-=-=l-=-==~=-=-+=-=-==-+.~-:-:+-::-:+--+-:=-:+:--~ :
.,
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.6
110
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190
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Time (sec)
Fig. 4 Example time series of roll angle ( Free dump and stabilization ) Examples of definition of roll reduction are shown in Fig. 4. Fig.4 (a) shows the time series of roll angle at free dumping and Fig4 (b) shows the time series of roll angle at stabilization control (Kallstrom, 1990). Using example data, the calculation flow of roll reduction is shown Table 2. Table 2 (a) shows double amplitude at free dumping (
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44.83%
310
Time (sec)
(b)
Stabilization Cs1 0.089 Cs2 0.165 Cn3 0.101 Cs'meanl 0.119 Mfs 4.210
The MAFRCS included measurement of roll angle, roll rate, yaw angle by vertical optical fib er gyro and measurement of rudder angle and fin angle by ship's equipment. The performance of roll damping has been measured in different ways. From the scientific point of view, the obvious approach is to measure the roll angle with and without the rolling damping system during exactly the same condition. In order to confirm the basic performance of roll damping and course keeping of MAFRCS, full scale experiments were implemented in the cases from forced oscillation to free damp and MAFRCS. A simple approach is to move the rudder and/or fin in sinusoidal way with a frequency close to ship's natural roll period and measure rudder and/or fin angle and roll motion as shown in section 4.2. 5.1 Roll stabilization and course keeping by rudder andjin Fig. 5 and Fig 6 show the function of rolling reduction and course keeping performance in the condition of navigation under forced oscillation by fin and stabilization by rudder and fin multivariate hybrid control system ( MAFRCS ) in the calm sea. Fig. 5 is the results in the condition of ship speed 16kts and Fig. 6 is the results of ship speed 19kts. In this figure, the first column is rudder angle, the second column is fin angle (starboard), the third column is fin angle (port), the fourth column is roll angle, the fifth column is roll rate and the last column is yaw deviation from set course. 5.2 Summary of measured roll reduction with MAFRCS The percentages of roll reduction of roll angle and roll rate were defined in section 4. Summary of
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Oscillation
measured roll reduction were performed that roll and heading control with rudder, roll and heading control with fin, roll and heading control with both fm and rudder. The roll reductions with some control mode ofMAFRCS are summarized in Table 3. Oscillation
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_
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sects)
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Fig. 6 Time series of forced oscillation and stabilization ( Sea state lwith speed 19 kts: Control of rudder and fin )
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It can be concluded that in normal conditions a roll sects)
Fig. 5 Time series of forced oscillation and stabilization (Sea state lwith speed 16 kts: Control of rudder and fin )
5.2 Summary of measured roll reduction with MAFRCS The percentages of roll reduction of roll angle and roll rate were defined in section 4. Summary of measured roll reduction were performed that roll and heading control with rudder, roll and heading control with fin, roll and heading control with both fin and rudder. The roll reductions with some control mode ofMAFRCS are summarized in Table 3.
Table 3 Summary of measured roll reduction Control mode of MAFRCS Rudder only Fin only Fin & Rudder
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Reduction (%) define eq. (5) Roll angle Roll rate 49 31~47 71~73
74~76
67~77
60~80
reduction in the order of 70~80(%) is achievable with MAFRCS ( fin mode and hybrid mode ), but these experiments were carried out without control gain to optimize. Also the heading control by MAFCS can maintain the desired course in allowable limit
6. CONFIRMATION OF HYBRID SYSTEM Simulation techniques are presented as a possible aid in the design of fin and rudder multivariate hybrid control system (MAFRCS). The results of full scale experiment with "UMITAKA MARU" shown in section 5 were confirmed by simulation study. But these simulation studies were carried out without control gain to optimize exactly. Fig. 7 shows the simulation results of rolling reduction and course keeping performance in the condition of navigation under forced oscillation by fin and stabilization by rudder and fin multivariate hybrid control system (MAFRCS). The results of Fig. 7 indicate that the full scale experiment and simulation were well fitted in the function of roll reduction and course keeping. In this figure, solid line shows full scale results and dotted line shows simulation results. Also the first column is rudder angle, the second column is fin angle (starboard), the third column is roll angle and the last column is yaw deviation from set course.
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The results of dynamic simulation suggested that the simulation techniques were reasonable and useful tool for design and confirm the ship's dynamics and control law of MAFRCS.
60
Time[s)
1 1 11 1<0
60
ACKNOWLEDGEMENT In the full scale experiments described in this paper, YKoike captain, H.Yonemoto chief engineer and crew gave helpful support with especial thanks to "UMITAKA MARU". Helpful suggestions and encouragement were received from Prof. K.Ohtsu of Tokyo University of Mercantile Marine and Mr. S.Ueki and Mr. H.Kanehiro of Mitsui Engineering & Shipbuilding Co., Ltd.
REFERENCES
Time(s)
20
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20
60
I I I I!
80 Time(s)
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1<0
!
Tim e(s)
~ I:~ I----tlf---+,.j.---+..1--+-1--+-1---+-1---+---111 ~
I 60
Time(s)
Fig. 7 Simulation results of forced oscillation and stabilization driven by rudder and fin 7. CONCLUSIONS This paper presents the advanced rudder roll stabilization control system with fin control. Fin and rudder multivariate hybrid control system were designed using multivariate autoregressive model with multi-input (yaw and roll motion) multi-output (rudder and fin angle). This control system is called MAFRCS (Multivariate Autoregressive Fin and Rudder hybrid Control System). The purpose of this paper is to verify the effectiveness of MAFRCS in simulation and in full scale experiments. From the results of full scale experiments, fin and rudder multivariate hybrid control system reduce the roll motion in the order of 70~80(%) with course keeping. Also the results of dynamic simulation that the simulation techniques with was useful tool for design and confirm the ship's dynamics and control law. Through these studies, it can be expected that the MAFRCS have higher controllability than conventional rudder roll control systems or conventional fin stabilization systems. Hereafter, the authors are going to apply this hybrid control system and advanced rudder roll stabilization system (Oda, et aI. , 1999) to several types of ship to be of great use and to develop good effect of next generation type motion control.
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1. N. Sgobbo, M. G. Parsons (1999). RudderlFin Roll Stabilization of the USCG WMEC 901 Class Vessel, Marine Technology, Vo1.36, No.3. W. E. Cowley (1972). The Use of the Rudder as a Roll Stabiliser, SCSS'72. C. G. Kallstrom (1981). Control of Yaw and Roll by a Rudder/Fin Stabilization System, SCSS' 81. H. Oda, K. Igarashi, K. Ohtsu (1996). Simulation Study and Full Scale Experiment of Rudder Roll Stabilization System, SCSS'96. H. Oda, K. Ohtsu, M. Sasaki, Y. Seki, T. Hotta (1992). Rudder Roll Stabilization Control System through Multivariate Auto Regressive Model, CAMS '92. H. Oda, T. Hyodo, M. Kanda, H. Fukushima, K. Nakamura, S. Takeda, T. Hayashi, H. Fujiwara (2003). Designing fin and rudder multivariate hybrid control system, SCSS'2003 . H. Akaike (1974). Statistical Analysis and Control of Dynamic System, Kluwer Academic Publishers. C. G. Kallstrom, W. L.Schultz (1990). An Integrated Rudder Control System for Roll Damping and Course Maintenance, SCSS '90. H. Oda, T. Hyodo, K. Ohtsu, M. Ito, N. Hirose, 1.S. Park, H. Sato (1999). Designing Advanced Rudder Roll Stabilization System - High Power with Small Size Hydraulic System and Adaptive Control-, SCSS'99.
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