mining system subject to irregular-wave excitation. A novel active-controlled heave compensation system based on dynamic vibration absorber for the deep-sea ...
Proceedings of the 2009 IEEE International Conference on Mechatronics and Automation August 9 - 12, Changchun, China
Modeling and Simulation of Active-Controlled Heave Compensation System of Deep-sea Mining based on Dynamic Vibration Absorber* Liujun Li and Shaojun Liu College ofMechanical and Electrical Engineering Central South University Changsha, Hunan410083, China {liliujun & liushaojun}@mail.csu.edu.cn
Abstract - The heave compensation system is of great importance to the safety and operation efficiency of the deep-sea mining system subject to irregular-wave excitation. A novel active-controlled heave compensation system based on dynamic vibration absorber for the deep-sea mining system was proposed in this paper. The three-degree-of-freedom dynamic models of active heave compensation system based on dynamic vibration absorber in sinusoidal wave are established. An optimal controller was designed for the proposed system by using Linearquadratic optimization technique. The performance of the active heave compensation system based on dynamic vibration absorber was computed and analyzed. It is indicated that the heave compensator based on dynamic vibrator absorber with the optimal controller can have the best performance of heave compensation and it is practical to isolate the lift pipe and its support platform from the significant vibration of the ship motion induced by the sinusoidal wave.
special support or gimbal joint similar to the gyroscope [4], the surge and sway can be reduced by a combination of mooring constrains and thrusters associated with dynamic positioning [5]. Therefore, the heave compensation system becomes greatly important to the reliability and performance of the deep-sea mining system. Hydraulic ram and air accumulator were successfully applied in the compensated platform of 7,500 tons, which is a passive system and can release the bending load from the mining ship in some extent [4]. The dynamic vibration absorber was widely applied in the engineering design of vibration isolation and vibration absorber. It was found that the motion of a harmonically excited oscillator can be absorbed by attaching another, specially chosen, oscillator to it [5]. And Wang proposed an integrated isolation and absorber system for the complex mechanical-electric system on board [6]. This paper proposed a novel active-controlled heave compensation system based on dynamic vibration absorber to isolate the lift pipe and its support platform from the significant vibration of the ship motion induced by the sinusoidal wave. The three-degree-of-freedom dynamic models of active-controlled heave compensation system based on dynamic vibration absorber are established. An optimal controller was designed for the proposed system by using Linear-quadratic optimization technique. The performance of the active heave compensation system based on dynamicvibrator-absorber was computed and analysed in time-domain.
Index Terms - Dynamic Vibration Absorber(DVA), ActivecontrolledHeave Compensation System (AHCS), Optimal Controller, Deep-sea Mining System I. INTRODUCTION
With the deceasing of the mineral resources in the land and the continual development of the world economic, the deep-sea mining has been round the corner. Nautilus is planning to mining the seafloor massive sulphide in the PNG licensed mining area in 2009[1]. It is noted that the deep-sea mining technology has greatly improved as the oil industry moves offshore and the hydraulic lifting mining will be the development trend [2].Generally speaking, the deep-sea mining system is proposed to be mainly composed of the floating manipulation system and underwater operating system as well as the lift pipeline between them[3]. The characteristic of such system is of big inertia and strong randomicity and larger disturbance. As is known to us, the long lift pipe with several thousand meters will be influenced by the vibration of the ship motion induced by the irregular wave, which is tremendous adverse to the safety and operation efficiency of the deep-sea mining system. Therefore, it is important to isolate the lift pipe and its support platform from the bending loads induced by the irregular wave. It was discovered that the motion of the roll and pitch direction can be compensated by the gimbaled bearing and
II. MODELING OF THREE-DEGREE-OF-FREEDOM ACTIVECONTROLLED HEAVE COMPENSATION SYSTEM BASED ON DYNAMIC VIBRATION ABSORBER
As is known to us, the dynamic vibration absorber is generally applied in the multi-degree-of- freedom vibratory systems specially to absorb the motion of a prescribed mass in a multiply connected mass-spring system by attaching an appropriately chosen system to it due to its design flexibility and no re-installation of the target system. It is shown that if an un-damped spring-mass system is coupled with a second oscillating system being excited by a sinusoidal external force, then there must exists an excitation frequency at which the second mass will remain stationary for any magnitude of excitation [7]. In order to exploit active heave compensation system to stabilize the heave platform from the mining ship in
* Thanks for the support to this project by the national Science foundation of China (No. 50675226). 978-1-4244-2693-5/09/$25.00 ©2009 IEEE
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the sinusoidal wave, we propose such a system as shown in Fig.I. In this study, the oscillator to be maintained is a springsupported heave platform Me from which the lift pipe is deploying and retrieving, which is supported on the springloaded vertical guides and driven vertically from the derrick by a pair of linear actuators. The mining ship with Mass Ms forms another oscillator, while the third oscillator is the dynamic vibrator absorber of an un-damped mass Mm (Cm=O) , which is to be controlled by a linear actuator from Mc using feedback in such a way that the heave platform remains stationary over a large frequency range. The physical model of the active heave compensation system based on DVA is shown as Fig.l. The feedback of the three oscillations can be obtained by mounting the accelerometers on the Mm, Me and Ms respectively. Vertical acceleration of the ship can be sampled by averaging the measurements of four accelerometers fixed to the derrick of the mining ship near the actuators driving Me and distributed so as to average out the effects of any small roll and pitch of the ship. These three masses Ms, Me, Mm are assumed to move primarily vertically. This research aims to propose an active-controlled heave compensation system for the deep-sea mining system based on dynamic vibration absorber and investigate the feasibility of its application. In order to investigate the heave compensation effect of the dynamic-vibration-absorber based active heave compensation system and the performance of the active controller, the dynamic model was simplified as Fig.2 based on a number of simplified assumptions below: (1) The deep-sea mining ship is moving primarily in heave, and other motions are considered small in comparison as the surge and sway of the ship can be reduced by a combination of mooring constraints and thrusters associate with dynamic positioning. (2) All oscillations are assumed to be feasible to justify use of linear differential equations. The masses Mm and Me
In this work, we are to verify the possibility of dynamic vibration absorber for the heave compensation system and its active control method, so the disturbance input of the deepsea mining ship induced by the sinusoidal wave can be represented by q(t) =A sin(2lit / T) with the peak amplitude of 205m and the peak period of lOs according to the typical operation condition of the China's mining area. Taking the Chinese ocean poly-metallic pilot mining system designed by China Ocean Mineral Resources R&D Association to service for l000m Chinese ocean trial as the prototype, which has the length of 140m, the width of 30m, the depth of 1305m by approximation of rectangle cylinder and the displacement of 12625tons [8]. The mass of the deep-sea mining ship is taken to be 13000t in this paper. The hydrostatic spring stiffness coefficient Ks and damping coefficient Cs assumed constant for small ship motions and can be calculated by the assumption that the vibration transmission ratio of the sinusoidal wave is 0.3. Kc and KIn are the stiffness coefficients of the actuators, and Cc is the damping rate along the vertical guides. The control forces fm and fc are applied on Mm and Me by their respective linear actuators. The vertical wave-force for a lift pipe of the chosen diameter is found negligibly small. The parameter of the proposed physical system is listed as followed: Ms= 13000.0ton, Mc=200.0ton, Mm=I.Oton. According to Newton's law and free-body method, the dynamic model of the three-degree-of-freedom activecontrolled heave compensation system based on dynamic vibration absorber is discussed below: The motion equations of the dynamic vibration absorber Mm, the heave platform Mc and deep-sea mining ship Ms are: Mill
Mkm) t
L... C,
s....... " .. . . .
Mc(Xc)
j
q(t)
Fig.2 The dynamic modelof the active heave compensation system M m xm =-Km(x m -Xc)-Cm(Xm-X c ) + t;
t
(1)
Me x, = Km(x m -x.)+Cm(X m-xc)-Ke(x c -Xs)-Ce (Xc-X s)- I; + I; (2)
q (t)
M,;, = Ke(x, -x,)+ Ce(~,-x,)-K,(x, -q(t»- C,(x,-q(t»- Ie
Fig.1 The schematicof the active heave compensation system based on DVA
(3)
Where, xm ' xc e x.: x x x.: x x, xs are the displacement, s ' m ' c e s ' m' c
oscillate in air as opposed to on the air-water free surface. Thus the mass, stiffness, and damping coefficients for the oscillators (Mm, KIn) and (Me, Cc, Kc) are independent of frequency. (3) The current velocities are assumed to be small enough to allow horizontal oscillation of the lift pipe to be discount. (4) The exciting force was represented by a sinusoidal wave excitation with the peak period T of lOs and the peak magnitude A of 205m on the ship Ms because the irregular wave can be represented by a sum of sinusoids at different frequencies, amplitude and phases.
the velocity and acceleration of the dynamic vibration absorber, the heave platform and the deep-sea mining ship respectively. Modeling
State variable x=[xm-Xc'Xc -Xs'Xs -q,xm,xc,xsf Input vector u = [1m' fc] Disturbance vector
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w = q(t)
Take the velocity of the active heave compensation system as the output vector
The optimal control law which minimizes the equation (6) is given by [9]: u(k) =-koptx(k) (9)
y = xc The mathematical modelling described in the above may be approximated by X = Aox(t) + Bou(t) + Eow
And the feedback matrix is k opt =(R+BTpB)-IBTpA
(4)
{ Y = Cox(t) + Du(t)
Where P is the positive definite solution of the Riccati equation below p-ATPA+ATpB(R+BTpBrlBpTA-Q=O (10)
Where,
o o o _ Km Mm
A",=
o o o o
0
0 0 0
Km
-I
o
1
s: M
IV. TIME DOMAIN SIMULATION OF ACTIVE CONTROLLED HEAVE COMPENSATION SYSTEM BASED ON DYNAMIC VIBRATION ABSORBER
o
-(Cm+c ,)
o o
M,
o
0
o
0
Eo = [0
0
In order to investigate the performance of the active heave compensation system based on dynamic vibration absorber, the velocity response of the active heave compensation system with optimal controller and the passive system (without control) was simulated in time-domain based on the model (4). As shown in Fig.3, where the input is the velocity of the sinusoidal wave q(l) and the output is the vertical velocity of the heave platform, the displacement of the heave platform then can be integrated from the velocity of heave platform, therefore the heave compensation effect may be obtained in the active controlled heave compensation system with optimal controller. The peak of velocity response of the active heave compensation system with the optimal controller may provide a better heave compensation efficiency with the heave compensation ratio of 84%, which reaching and beyond the designed level by COMRA [10]. It can also be seen that the response of the heave platform and the dynamic vibration absorber is almost identical and a little lagging behind that of deep-sea mining ship due to the dynamics appears mainly predominated by the greatest mass, namely the mining ship as in Fig.4.
M,
_£..
o
Co =
o
1
m
M,
B• • [:
-I
s: M,
o -I
0
0
or
[~ ~ ~ ~ ~ ~] 000001
D =0 Further, the state space equation of a discrete system may be written as x(k
+ I) =Ax(k) + Bu(k) + Ew(k)
(5)
y(k) = Cx(k)
Where, the system (C, A) is observable and (A, B) is controllable . III. DESIGN OF OPTIMAL CONTROLLER
Response of Active Heave Compensated Platform
The design problem of the optimal controller is to determine the optimal control signal which minimizes a performance index [9] J = L[xT (k)Qx(k)+u T (k)Ru(k)]
0.8
(6)
~
OA
~
0.2
i
k =O
8.
~
For the proposed system, by the "trial and error method",
0
.~
Q and R were selected and determined respectively as
~ -0.2
>
100 10
-0.6
(7)
Q=
-o.SO: -----:':,0,--------;2!:-O-
10
°
0] 0.08
-!.SO:---6':c 0-
-:!70: ------:!80
Time (s)
8e13
R =[0.009
-::';30,------ .':c 0-
Fig.3 The responseof the heave platformwith controland W/O control
It can be seen obviously from Fig.5 that the variation trend of the displacement response the mining ship Ms and heave compensation platform Me and dynamic vibration absorber Mm is almost identical in the peak period of the wave. It proves that the heave compensation system with a dedicated design dynamic vibration absorber and adopting proper control strategy can have a perfect heave compensation
(8)
In which the control process was simulated using mathematical model in different Q and R, then the simulation results were compared.
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effect over traditional heave compensation method. It should be emphasized that the aim here is to control the motion of the heave platform supported on board the deep-sea mining ship and not the motion of the deep-sea mining ship itself. The response of the mining ship was not influenced by the control, which can be concluded by comparison of the displacement response curve of the mining ship without control and with active control in Fig.4 and Fig.5. The control has the minimal effect on the motion of the ship itself, which is of great importance to the compliance of high waves. However, it can be seen from Fig.5 that the action of active controlled heave platform and the dynamic vibration absorber is a little forward than that of the deep-sea mining ship. This shift is most likely because the coupling effect among the three masses becomes appreciable under control. It can be further inferred from this figure that the optimal control can achieve the expected result in this simulation .
heave platform was greatly reduced with the percentage of 84% under the active control. The required actuation can be provided by linear motors or hydraulic rams with the feedback from the three parts of the system by the delicate layout of accelerometer. It can be seen from Fig.6 that the active force curve goes up suddenly in the beginning due to the lagging reaction of the actuator to the motion response of the heave platform transmitted from the deep-sea mining ship. The active control force on heave platform is only 500KN, which is much less than that weight of the heave platform 200t. The optional hydraulic actuator can be of 280mm hydraulic cylinder diameter and 150mm piston-cylinder diameter with the hydraulic pressure system of 16MPa. Meanwhile, the active control force on the dynamic vibration absorber is 25KN, the corresponding optional hydraulic actuator can be of 60mm hydraulic cylinder diameter and 35mm piston-cylinder diameter with the hydraulic pressure system of 16MPa. This indicated that the novel active heave compensation system can gain perfect heave compensation effect by less energy consumption over traditional way and the dynamic vibration absorber can be designed off the site specific to the vibration control target.
Response of DVA-HCS
1.5i - ,---- ,---- ,-- ,---r== = = = = ==i'l - - Deepsea Mining Ship - - OVA - - Heave platform
Response of Actbe Heave Compensated Platform
-0.5
10
30
40 lim e(s )
50
60
70
80
Fig. 4 The displacement responseof the passive heave compensation system Respon se of DVA -HCS with Opt imal Cont rol
1.5i - :-- :-- :-- -:-r== ==== =:=:r:::::::===il Deepsea Mining Ship - - OVA -
Heave platform I
I
I
I
I
I I - 1- - -
10
I I I I
---':-10
---':-20
---':-30
---:'::-40
---:':-50
---:':-60
---:':-70
30
40 lime (s)
50
60
70
80
Fig.6 The active force of the Active heave compensation system
The proposed heave compensation system based on dynamic vibration absorber is controlled so that the motion of the heave platform supporting the lift pipe/riser is effectively compensated in the sinusoid wave. The active controlled heave compensation system based on dynamic vibration absorber with optimal controller has an increased effectiveness over traditional heave compensation methods with two-degree-of-freedom system [10], which is meaningful to better regulate the tension on the lift-pipe/riser and reduce the fatigue loads on the lift-pipe/riser in sinusoid waves even in irregular waves. Therefore , the dynamic vibration absorber can move in reasonable amplitude to effectively absorber the vibration of the heave platform induced by the motion of the deep-sea mining ship in the irregular wave. In a word, when heave is the dominant ship motion and current velocities are small, the proposed heave compensation will be effective both during deployment or re-entry of the lift pipe and during mining. Such a heave compensation system could be of great value and in principle used on the deep-sea mining ship where
-0.5
. 1 ':- 0
20
----:' 80
Tlmets)
Fig.SThe responseof the active heavecompensation systemwith optimal controller
It can conclude that the motion of the heave platform transferred from the deep-sea mining ship induced by the sinusoid wave can greatly be absorbed by the dynamic vibration absorber under control. By means of two active control force fm and (, the heave compensation effect of the system on the basis of dynamic vibration absorber can be extended . In the system, force fm brings about the actual cancellation of xc' while force fc restricts the motion of Mm in the presence of fm. By comparing Fig.4 and Fig.5, we can see no significant change observed in the displacement response of the mining ship Ms, while the velocity response of the
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the heave motions with large bandwidth may be a problem as the commercial deep-sea mining is to be on the verge.
well as pitch and roll direction to ensure the operation safety in high waves.
V. RESULTS AND DISCUSSION
ACKNOWLEDGMENT
On the basis of a physical phenomenon resulting from interaction between coupled mechanical oscillators, a novel active-controlled heave compensation system based on dynamic vibration absorber was proposed in this study. The performance of the active-controlled heave compensation system based on dynamic vibration absorber was investigated in time domain by applying the optimal control method. It proved that the active-controlled heave compensation system based on dynamic vibration absorber can effectively reduce the motion of the heave platform supporting the lift-pipe/riser over traditional ways, which is desirable and beneficial to isolate the lift pipe and its support platform from the significant vibration of the ship motion induced by the sinusoid wave. To apply the proposed system in the actual deep-sea mining system, the work to be done in the future will include: 1) Establish a more dedicate three-dimensional virtual prototype of the active heave compensation system combining hydraulic element and active controller to verify the performance of the proposed system. 2) Considering more intelligent and advance control strategy on the basis of the characteristic of strong randomicity and big inertia as well as the large disturbance of the deep-sea mining system by combination of the below water-surface so that the mining efficiency and operation safety was easily improved. 3) Investigate the coupling effect of the three masses and the influence of underwater lift pipe and ore miner under the environmental load and resulting motions and the compensation performance of the heave compensation system with dynamic vibration absorber in the heave as
The author sincerely appreciated the support to this project by the National Science Foundation of China (No. 50675226). REFERENCES [I] Steven D. Scott, "The Dawning of Deep Sea Mining of Metallic Sulphides: The Geologic Perspective", ISOPE Ocean Mining Symposium, Lisbon, pp65-70,2007 [2] Chung, Jin S, "Deep-Ocean Mining Technology: Learning Curve I", Proceedings of the Fifth (2003) Proceedings of The Fifth (2003) Ocean Mining Symposium, pp1-6,2003 [3] YaH Feng, Haoran Li, "Wenming Zhang. Future Trends of Deep Sea Bed Mining Technology", Journal of University of Science and Technology Beijing (English Edition), vol.6, no.1, pp7-10,1999 [4] McNary, J.F.; Person, A.; Ozudogru, Y. H, "7,5OO-ton-capacity, shipboard, completely gimbaled and heave-compensated platform," Journal of petroleum technology, vo129,pp439-448,1978 [5] Umesh A. Korde., "Active heave compensation on drill-ships in irregular waves," Ocean engineering, vo125,N07, pp541-561,1998 [6] WANG Quanjuan, Xia Songhu, Huang Wenbu, "Optimum design of dynamic vibration absorbers of the continuous parameters system based on power flow," Acta Acustica, vo128,n03, pp267-27 1,2003 [7] Meirovitch, L. Elements of Vibration Analysis, 2nd Ed., Chapters 3-6. McGraw-Hill, New York. [8] China Ocean Mineral Resources R&D Association, "Overall design of Chinese ocean poly-metallic pilot mining system 1000m sea trial system". In Press. [9] Liu Shaojun, Zhong Jue, Li Qingchun, Hironao Yamada and Yoshikazu Suematsu, "Optimal control of an active suspension system employing high speed ON/OFF solenoid valve", Journal of Central South University of Technology, volA, no.2, ppI37-140, 1997 [IO]Xiaoyan Tang, Shaojun Liu, Kai Huang, "Design and Simulation Study on a Virtual Prototype of an Active Heave Compensation System for Deep-ocean Mining," Proceedings of The Sixth (2005) ISOPE Ocean Mining Symposium, pp71-75,2005
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