Academic Journal of Science and Technology 
ISSN: 2771-3032 | Vol. 5, No. 1, 2023 

 

78 

Design	and	Simulation	Analysis	of	Semi-Active	Lifting	
and	Sinking	Compensation	System	

Chuan Wang*, Huachuan Liu, Xueliang Zhang, Chi Huang, Qiufan Chen 

Southwest Petroleum University, Chengdu, China 

* Corresponding author: Chuan Wang 

 

Abstract: The lifting and sinking motion generated by the drilling platform causes large fluctuations in the suspension tension 
of the large hook, which affects the stability of the drilling pressure acting on the rock at the bottom of the well, greatly reduces 
the efficiency of drilling and decreases the service life of the drill bit and the drill column under the action of cyclically varying 
loads, causing an increase in the overall drilling cost. In order to avoid the above situation, a nonlinear model of a semi-active 
lift-sink compensation system is designed and a method to improve the compensation efficiency of the system is proposed. Firstly, 
the relevant physical model of the hydraulic system is established, and then its simulation model is built according to the working 
principle of the semi-active lift and sink compensation system. Then the effects of different factors are added to the simulation 
model of semi-active lifting and sinking compensation, and finally the effects of different factors on the compensation efficiency 
of the active lifting and sinking system are compared. The simulation results show that a regular sinusoidal wave with a peak 
value of 6.5 m and a period of 10 s as the ship's lifting and sinking displacement input will reduce the compensation efficiency 
of the semi-active lifting and sinking compensation system, while the smaller the stiffness of the wire rope, the better the 
compensation effect of the drill column and the higher the compensation accuracy. The proposed method can effectively improve 
the compensation efficiency of semi-active lifting and sinking compensation system. 

Keywords: Lifting and sinking compensation, Simulation, Hydraulic cylinder, Semi-active. 
 

1. Introduction 
At present, the lifting and sinking compensation devices 

used on deepwater floating drilling rigs in China need to be 
imported from abroad at high prices [1], and the relevant 
design and manufacturing technologies of lifting and sinking 
compensation devices are not yet mastered in China. 
Therefore, to carry out in-depth research on the dynamics of 
deep-water drilling systems, find the laws and mechanical 
characteristics of the lifting and sinking motion of the drilling 
column system and the lifting and sinking compensation 
device in the process of deep-sea drilling, and on this basis, 
develop a special overhead crane lifting and sinking 
compensation device for deep-water floating rigs with China's 
own intellectual property rights, is the technical key and 
equipment support for China to realize safe and efficient 
drilling operations in the deep sea. 

The patent proposed by Jones and Cherbonnier in 1990 was 
one of the first active lifting and sinking compensation 
systems using a microprocessor to control it [2]. Professor 
Fang Huachan has conducted many in-depth studies on the 
lift and sink compensation equipment for mother ships in 
offshore drilling and equipment, and discussed the specific 
structure and layout form, system working principle and 
design method of the open-sink compensation device 
installed on the mother ship of offshore drilling [3]. Wu 
Baihai, Xiao Tibing et al. proposed an active lifting and 
sinking compensation system for deep-sea mining equipment 
in 2003 and 2004, and the results of their own simulation and 
simulation tests showed that the system is feasible and has 
high compensation accuracy [4]. Zhou Li et al [5] designed a 
fuzzy predictive control algorithm for the time lag of the 
active compensation system, which improved the stability of 
the system and ensured the anti-disturbance of the system at 
the same time. 

At present, domestic and foreign research on lift-sink 
compensation systems mainly focuses on the improvement of 
mechanical structures and control algorithms [6-9], and few 
consider the nonlinear forces on hydraulic cylinders in 
modeling. In fact, the nonlinear forces on hydraulic cylinders 
can make the system response slower and errors increase 
during use. Nonlinear modeling of hydraulic cylinders can 
improve the accuracy of the modeling of lift-sink 
compensation systems and thus obtain simulation results that 
are closer to reality. This study focuses on modeling the 
nonlinear frictional force and nonlinear spring force applied 
to the hydraulic cylinder, based on which a nonlinear 
modeling method for a semi-active lift-sink compensation 
system is proposed and the effect on the lift-sink 
compensation efficiency is analyzed. 

2. Hydraulic Cylinder Model 

2.1. The kinetic model of hydraulic cylinder. 
The hydraulic cylinder is the execution element pestle of 

the hydraulic system, which transforms the pressure energy of 
the hydraulic pump output liquid into mechanical energy 
output, so as to drive the external load, and its dynamics 
model is shown in Figure 1. 

 

 
Figure 1. Piston cylinder force analysis 

 

Single-piston rod hydraulic cylinder parameters calculation. 
As shown in Figure1 a, the expression of the piston rod 



79 

extension speed is: 

𝑣
4𝑞
𝜋𝐷

The force output from the piston rod is: 

𝐹 𝑝 𝑝
𝜋𝐷

4
𝑝

𝜋𝑑
4

As shown in Figure 1 b, the velocity of the piston rod 
retreating is: 

𝑣
4𝑞

𝜋 𝐷 𝑑

The force output from the piston rod is: 

𝐹 𝑝
𝜋 𝐷 𝑑

4
𝑝

𝜋𝐷
4

As shown in Figure 1c, the force output from the piston rod 
is: 

𝐹 𝑝
𝜋𝑑

4

The piston extends at the velocity of: 

𝑣
4𝑞
𝜋𝑑

2.2. Force analysis of hydraulic piston cylinder 
The pull sub-stiffness of the piston cylinder can be 

calculated using the calculation methods of fluid mechanics 
and fluid-solid coupling theory, but the calculation process 
requires finite element analysis, which is more complicated 
and time-consuming. Considering the error within 7% 
between the stiffness calculation method according to 
compressible fluid and the above finite element calculation 
method, the active cylinder pull-pressure stiffness is 
calculated according to the following formula [9]. 

𝑘
𝐸𝐴
𝐿

Where: 
E——Bulk modulus of elasticity of the hydraulic medium, 

MPa. 
A——area of the end face, m2. 
L——axial length, m. 

2.3. Passive compensated hydraulic spring 
stiffness 

Considering the working gas cylinder as part of the 
accumulator and the gas compression as an isothermal 
process, the liquid-gas spring stiffness of the passive 
compensation part can be calculated from the total volume of 
the accumulator, the average pressure and the piston area 
according to the gas law and the definition of the liquid-gas 
spring stiffness as follows: 

𝑘
𝐴 𝑃

𝑉

Where: 
𝐴 ——Accumulator piston area, m2. 
𝑃 ——Average accumulator pressure, MPa.  
𝑉 ——Total volume of the accumulator, m3. 
Assumptions. 𝑥   is the platform rises and falls in 

displacement. 𝑥   is the displacement of the piston of the 
compensation cylinder, and 𝑚  is the mass of the platform, 
the 𝑚  is the mass of the piston and the piston rod, take a 
small piece of separator at the piston of the compensation 

hydraulic cylinder, when the platform rises on its force 
analysis can be known its force: the liquid gas spring recovery 
force 𝐹 , and its value is 𝑘 𝑥 𝑥  , When the platform 
rises, the storage cylinder gas is compressed, its state for the 
extension, its direction to the right. Compensate the damping 
of the hydraulic cylinder liquid 𝑓   , whose magnitude is 

𝑐  , its direction is opposite to the direction of 

piston movement. Piston rod inertia force 𝐹  .  Its 

magnitude is 𝑚  , and its direction is opposite to the 

piston motion. 
The piston is subjected to a force acting on it by the drilling 

column 𝐹  and its direction is downward.  

Figure 2. Compensating cylinder piston force analysis 

By force analysis, the kinetic equations of the piston and 
the drilling column are obtained as 

𝑘 𝑥 𝑥 𝑐
𝑑𝑥
𝑑𝑡

𝑑𝑥
𝑑𝑡

𝑑 𝑥
𝑑𝑡

𝑚 𝐹  

Letxs be the strain displacement between the lift-sink 
compensator and the drill column, and the tension acting on 
the drill column is 𝐹  and its value is  𝑘 𝑋 , through analysis, 
it is known that the displacement strain of the drilling column 
should be equal to the difference between the rising 
displacement of the platform and the displacement of the 
piston movement: 

𝐹 𝑘 𝑋  

𝑥 𝑥 𝑥  

2.4. Analysis of the force of the wire rope 
According to the size of the drill column under working 

conditions, from the material mechanics, we can get 

𝑘
𝐸𝑆
𝑙

Where: 
𝑘 ——Wire rope stiffness, N/m. 
E——Modulus of elasticity of the drilling column, Pa. 
S——Cross-sectional area of the drilling column, m2. 
𝑙——Wire rope length, m. 

2.5. Longitudinal force analysis of drilling 
column 

Drill column stiffness can be determined based on the drill 
column size and well depth[14]: 

𝑘
𝐴 𝐸
𝐿



 

80 

𝐴 ——Equivalent cross-sectional area of drill string, m2 ; 
𝐿 ——Length of drilling column, m. 
Longitudinal vibration model of drilling column under the 

action of compensation device 
Experience in offshore oil development shows that floating 

rigs drifting more than a few meters from their mooring points 
will result in fatigue damage or outright breakage of the drill 
column, causing unnecessary downtime and significant 
economic losses. For this reason, it is extremely important 
and necessary to compensate for the longitudinal motion of 
the drill column. Although the lifting and sinking 
compensation device greatly improves the working 
environment of the drill bit in the floating drilling system, the 
dynamic load caused by the vibration of the drill column has 
a nonnegligible effect on the effect of the compensation 
device. Therefore, a study of the longitudinal vibration of the 
drill column after the installation of the compensation device 
is a necessary part of improving the efficiency of the lifting 
and sinking compensation device. In this project, based on the 
consideration of the structural characteristics of the active-
passive combined overhead crane lifting and sinking 
compensation device and the knowledge related to the 
dynamics of mechanical system, the vibration model of its 
drill column is established as shown in Figure 2-2. 

 

 

Figure 3. Drill column vibration model 

 

The lifting and sinking motion is a damped vibration 
caused by wave excitation, and the law is similar to a sine 
wave.  

The platform has 6 degrees of freedom of motion, and the 
crane compensation device does not consider the reaction 
force on it. 

The main cylinder block, the driven cylinder block and the 
support structure move together with the derrick and the 
platform, so the above components are considered as rigid 
concentrated masses 𝑀 . 

The floating crane and the lifting and sinking moving parts 
are connected by the piston rod of the compensation cylinder, 
and the piston, piston rod and floating crane are regarded as 
concentrated masses 𝑀 ,  The fluid stiffness of the active 
compensation cylinder 𝑘   ,passive compensation part fluid 
gas spring stiffness 𝑘 , The fluid viscous damping coefficient 
𝑐 . 

The tensioned part of the crane above the neutral point of 
the big hook, top drive and drill column is regarded as the 
concentrated mass 𝑀  , The rigidity of the floating crane, 
which is connected with the floating crane by a wire rope, is 
𝑘  .Drill column equivalent stiffness coefficient 𝑘   The 

coefficient of viscous damping in the mud is 𝑐 . 
The pressurized part of the drill column below the neutral 

point is considered as concentrated mass 𝑀 , and the contact 
stiffness factor of the formation 𝑘 . 

The drilling pressure is the contact force between the drill 
bit and the formation, and its variation value can be estimated 
by the following formula. 

𝛥𝑊𝑂𝐵 𝑥 ⋅ 𝑘  

Where: 
𝑥 ——Displacement of the overhead crane relative to the 

seabed. 
𝑘 ——Effective stiffness between the overhead crane and 

the ground. 

𝑘
1

1
𝑘

1
𝑘

1
𝑘

 

Where: 
𝑘 ——Wire rope stiffness between the overhead crane and 

the travel shop, KN/m. 
𝑘 ——Drill column equivalent stiffness, KN/m. 
𝑘 ——Floor contact stiffness, KN/m 
In the longitudinal vibration model of the drill column 

under the action of the active-passive joint overhead crane 
lifting and sinking compensation device, the drill pipe is 
assumed to be a homogeneous equal diameter elastic rod, and 
the spacer pipe is considered to be vertically downward, with 
no bending deformation of the drill column and no friction 
with the pipe wall. 

In addition, the main differences between this model and 
the vibration model under the action of the rover lifting and 
sinking compensation device are. 

(1) The tensile and compressive stiffness of the active 
compensation part is considered; 

(2) The rigidity of the strata is taken into account, instead 
of considering the drill collar as a rigid body connected to the 
strata; 

(3) The drilling pressure variation calculation is based on 
the effective stiffness between the overhead crane and the 
formation, not just the equivalent stiffness of the drill column. 

Derivation of system transfer functions: 
According to the longitudinal vibration model of the drill 

column under the action of dead rope compensation device, 
the concentrated mass is taken as the separator, and the 
respective equations of motion are established, so as to solve 
the transfer function of the system. Suppose the platform 
lifting and sinking displacement is 𝑥  and the displacement 
of the concentrated mass of the drilling column is 𝑥  and the 
displacement of the lower drilling column is 𝑥 . 

 

 
Figure 4. Force analysis 

 

The separators are taken at each concentrated mass, and the 



 

81 

forces are analyzed separately, and the meanings of each 
conform to the following in Figures4: 

Concentrated mass 𝑀 , hydro-pneumatic spring recovery 
force 𝐹  .The size is the product of the liquid-gas spring 
stiffness coefficient and the absolute deformation, and the 
direction is the same as the direction of platform movement; 
the oil damping force 𝑓  . The size of the fluid viscous 
damping coefficient is the product of the absolute velocity of 
the fluid in the compensation cylinder, and the direction is the 
same as the direction of the platform movement; the friction 
force  𝐹 .  The value of the friction force is complex, 
according to the test, the direction is consistent with the 
direction of platform movement; active cylinder thrust 
𝐹  .The direction is opposite to the direction of platform 
movement; wire rope force 𝐹  , direction downward; inertia 
force 𝐹  , direction downward. 

Concentrated mass 𝑀  , the elastic recovery force of the 
drill column 𝐹   the product of the equivalent stiffness 
coefficient of the drill column and the absolute deformation, 
in the downward direction; mud damping force 𝑓 , the size 
of which is the product of the mud viscous damping 
coefficient and the absolute motion speed of the drill column, 
in the downward direction; wire rope force 𝐹  , direction 
upward; inertia force 𝐹 , direction downward. 

Concentrated mass 𝑀  , the elastic recovery force of the 
drill column 𝐹  , the size of which is the product of the 
equivalent stiffness coefficient of the drill column and the 
absolute deformation, in the upward direction; mud damping 

force 𝑓  , the size of which is the product of the mud viscous 
damping coefficient and the absolute motion speed of the drill 
column, in the upward direction; the formation elastic 
recovery force𝐹  direction down; inertia force 𝐹 , direction 
downward. 

Based on the force analysis, the differential equations of the 
mathematical model of the system are obtained based on 
Newton's law and the force balance equation as follows[10]. 

 

𝑀
𝑑 𝑥
𝑑𝑡

𝑐
𝑑𝑥
𝑑𝑡

𝑘 𝑥 𝐹  

𝑀
𝑑 𝑥
𝑑𝑡

𝑐
𝑑𝑥
𝑑𝑡

𝑘 𝑥 𝑓 𝐹  

Applying the Laplace transform to the above differential 
equation, it is 

𝑀 𝑠 𝑋 𝑠 𝑘 𝑋 𝑠 𝑋 𝑠  

𝑀 𝑠 𝑋 𝑠 𝑐 𝑠𝑋 𝑠 𝑘 𝑋 𝑠 𝑘 𝑋 𝑠 𝑋 𝑠  

𝑀 𝑠 𝑋 𝑠 𝑘 𝑋 𝑠 𝑐 𝑠𝑋 𝑠 𝑘 𝑋 𝑠  

The transfer function model of the longitudinal vibration 
system of the drill column under the lift-sink compensation 
device is derived from the Laplace transform equation and 
modeled in simulink as shown in Figure 5.  

 

 
Figure 5. Matlab--simulink model drilling column equivalent stiffness 

 

2.6. Accumulator pressure and volume 
calculations.  

Considering the gas compression of the accumulator as an 
isothermal process,thgaa hfn -gas spr sess,thgas spring 
stiffness of the passive compensation part can be calculated 
from thetotal volume of the accumulator, the average pressure 
and the piston area. 

𝑘
𝐴 𝑃

𝑉
 

Where: 
𝐴 ——Accumulator piston area (m2); 
𝑃 ——Average pressure of accumulator (MPa); 
Vo——The total volume of the accumulator (m3). 
The static force on the driven cylinder is required to keep 

the load (drill column and drill post) up and the force required 
is 

𝐹
𝐹
2

𝐹
2

 

Where:  

Fcyl——The force acting on the accumulator by the passive 
cylinder, N 
Fw——The role of the load force on the wire rope, N 
Due to the pressure of the nitrogen tank on the mold, a force 

is generated with a magnitude of: 

𝐹 𝐹 𝐹
𝐴
𝐴

𝑀  

𝐹 𝐹 𝐹
𝐴
𝐴

𝐹  

𝑃
𝐹
𝐴

 

Where: 
𝐹CL ——Load force acting on the master cylinder by the 

wire, N (varies withflow) 
𝐹GC——Gravity force on the driven cylinder, N 
𝐴CR——Accumulator piston rod area, mm2 
𝐴 ——Accumulator piston area, mm2 
𝑀AA——Gravity force on the accumulator, N 
The sum of the forces acting on the piston rod of the driven 

cylinder is expressedas follows: 

f2

2

b FFF
dt

xd
M aw

a 



 

82 

𝐹 𝑀 𝑎 𝑓 𝑣 𝐹 𝐹 𝐹 𝐹

𝐹  

Where:  
Fc——all external forces on the driven cylinder, N  
𝑀CR——accumulator piston rod mass, N 
𝑎 ——Accumulator piston rod acceleration, m/s 
𝐹AA——Accumulator force on the driven cylinder, N 
𝐹heave——Force acting on the piston rod by the lifting and 

sinking motion of theplatform, N 
𝐹df——passive cylinder dynamic friction, N 
𝐹sf——static friction of the driven cylinder, N 
𝐹DeltaP——Force generated by the pressure drop in the pipe 

and valve, N 
The equation of motion of the accumulator (neglecting 

nonlinear friction) is [11]: 

1 2

10
1

20
2

ACA AA a p a AA AA cyl N

AA a
AA a

AA a
AA a

F M a B v A P A P F F

V A x
P A v Q

V A x
P A v Q






        

 

  

 

  


i

i

 

el= CR
cyl C D tap

A

A
F F F

A
  

Where. 
𝐹ACA——Accumulator subjected to external force and, N 
MAA——mass of the accumulator as a whole, N 
𝑎  ——Acceleration of the accumulator part with the 

platform motion, m/s2 
𝐵 ——Viscous friction coefficient inside the accumulator 
𝐴 ——Accumulator interface cross-sectional area, mm2 
Va——accumulator inflow/outflow velocity. m/s 
P1、P2——Accumulator piston chamber and rod chamber 

initial pressure, Mpa 
V10 、 V20——Accumulator piston chamber and rod 

chamber initial volume, m3 
Xa—— the distance to the center of the piston in the active 

accumulator, ml 
Q——Accumulator's frontal flow rate, L/s 
𝐹cyl——Force exerted by the piston rod of the driven liquid 

cylinder, N 
Due to the lifting and sinking motion of the platform, there 

are two processes of filling and deflating the accumulator, and 
by the law of conservation of energy there are. 

𝑃𝑉 𝑃 𝑉  

where the pressure fluctuation of the accumulator can be 
expressed as 

0

0 0( )N N N
AA a a

N A N

V
P P P

V A x x

F A P


 

     
  

 

Stiffness factor k1: 
2
2 0

1
0 2

A p
k

V A x



 

Where: 
𝐴 ——working area of auxiliary gas cylinder, m2; 
𝑝  ——initial working pressure of the gas in the 

accumulator, Mpa; 
x——the displacement produced by the piston, m; 
In summary, the parameters of the compensation cylinder 

and accumulator areshown in the table. 

2.7. PID control principle 
Conventional PID control controller is one of the most 

basic and widely used controllers, which has the advantages 
of simple algorithm, good stability and reliability.The 
regulation law of conventional PID controller is very effective 
for quite a number of control objects, especially for linear 
constant systems, and the quality of its regulation process 
depends on the adjustment of each parameter of the PiD 
controller PID is a linear controller, which controls according 
to the given deviation and the amount of its deviation change: 

The form of the continuous equation of the PID control law 
[13]: 

𝑢 𝑡 𝐾 𝑒 𝑡
𝑒 𝑡 𝑑𝑡

𝑇
𝑇

𝑑𝑟 𝑡
𝑑

 

The PID control law is discretized into the form of a 
differential equation: 

𝑢 𝑘 𝐾 𝑒 𝑘 𝐾 𝑒 𝑗 𝑇 𝐾 𝑒 𝑘 𝑒 𝑘 1  

Where: 
u——Controller output signal; 
e——deviation signal:  
𝑇 ——integration time constant. 
𝑇 ——Differential time constant: 
Kp——proportional gain. 
𝐾 ——integral gain 
𝐾 ——Differential gain. 
𝑇——sampling period. 
K——sampling serial number. 
PID regulation is composed of three types of regulation: 

proportional, integral and differential, and their respective 
roles are as follows: 

Proportional regulation P: is proportional to the deviation 
of the response system, once the system deviation, 
proportional regulation immediately produce regulation to 
reduce the deviation. A large proportional role can speed up 
the adjustment and reduce the error, but too large a proportion 
makes the system less stable, and even causes the system 
instability. 

Integral regulation effect I: makes the system eliminate the 
steady-state error and improve the non-differential degree. 
The addition of integral regulation makes the system less 
stable and the dynamic response slower. 

The differential regulation action Dreflects the rate of 
change of the deviation 

signal of the system and can anticipate the trend of the 
deviation change, so it can produce an overshoot control 
effect, which has been eliminated by the differential 
regulation action before the deviation is formed, and can 
improve the dynamic performance of the system. In the case 
of suitable selection of differential time, overshoot can be 
reduced and regulation time can be reduced. The differential 
action has an amplifying effect on noise disturbance, so too 
strong addition of differential regulation is not good for the 
system to resist disturbance. In addition, the differential 
response is the rate of change, and when the input does not 
change, the differential action output is zero. The differential 



 

83 

action cannot be used alone and needs to be combined with 
two other regulation laws to form a PID controller.  

3. Simulation Modeling of Semi-active 
Lift and Sink Compensation 

Compound system sinking compensation compensation 
effect through the hydraulic pump and accumulator part of the 
mutual cooperation, to achieve the reciprocating motion of 
the hydraulic piston rod, to achieve the effect of compensation 
sinking. The rod cavity of the hydraulic cylinder is connected 
to the accumulator and the hydraulic pump, and the 
accumulator and the hydraulic pump provide hydraulic oil 

pressure to the rod cavity to bear the load of the system. When 
the rig moves upward with the wave, the load of the system 
becomes larger, and the force of the wire rope on the overhead 
crane becomes larger, driving the overhead crane downward 
to offset the lifting and sinking movement of the crane. As the 
crane moves down, the oil in the passive compensation 
chamber of the lift and sink cylinder is driven to the 
accumulator, which reduces the volume of the gas inside and 
increases the pressure inside to bear the load of the enlarged 
crane. The joint simulation model based on position feedback 
is shown in Fig. 6, and the mathematical model of position 
feedback in matlab is shown in Fig. 7. 

 

 
Figure 6. Position feadback model 

 

Through the AMEsim software simulation, the signal 
module will move the piston rod speed, acceleration, 
displacement or pressure and the platform signal 
superimposed as the input of PID control, after the control 
module calculates the output to the three-way four-way valve, 

do dlosed-loop PID operation, control the direction of the 
reversing valve, to achieve the purpose of regulating the 
expansion of the active cylinder, its working principle is the 
same as the joint simulation. 

 

 
Figure 7. Mathematical model of longitudinal vibration position feadback of drillingcolumn. 

 



 

84 

 

4. Simulation Results and Analysis 
According to the experimental requirements, the length of 

drilling column is 3500m, the outer diameter of drilling 
column is 168.3mm, the weight of drilling tool is about 450t, 
the mass of top drive is 35t, the modulus of elasticity of 
drilling column material is 2.06*10^5MPa, the density of 
drilling fluid is1.2-1.8 𝑘𝑔⋅ 𝑚3 . The contact stiffnessof the 
formation is 1000Kn/m. 

Amplitude and period of ascending and descending motion 
The lifting and sinking motion of the platform by the action 

of waves and currents is a random vibration whose 
displacement is a function of time, and usually the law can 
only be found by probability statistics. In order to facilitate 
the verification, the platform motion law can be expressed by 
a sine function [11][12]: 

𝐻 𝐴 𝑠𝑖𝑛 𝑤𝑡  

In the formula: 
𝐻  ——the lifting and sinking motion curve of the 

floating platform. 
𝐴——wave height, m. 

 

According to the experimental requirements, the wave 
height is 6.8m/4.8m/2.8m, respectively, and the period is 10s 

(1) The influence of environmental factors” 
 

 
Figure 8. Effect of different sea state on drilling pressure 

fluctuation 
 

 
Figure 9. Effect of different sea states on compensation 

accuracy 

 
Figure 10. Comparson of drilling column and platform 

displacement under different sea conditions 
 

 ه
Figure 11. Effect of mud density on drilling pressure 

fluctuation Figure 
 

 
Figure 12. Effect of mud dansity on compansation accuracy 

 
(2) The influence of internal system parametersI 



 

85 

 
Figure 13. Effect of eylinder diamatar on drilling pressure 

fluctuation 
 

 
Figure 14. Effect of cylinder diameter on compensation 

accuracy 
 

 
Figure 15. The effect of wire rope stiffness on drilling 

pressure fluctuation 
 

 
Figure 16. The effect of wire rope stiffness on compensation 

accuracy 
 

(3) The influence of different control methods 
 

 
Figure 17. Effect of different position control on drilling 

pressure fluctuation 
 

 
Figure 18. Effect of different position control on 

compensation accuracy 
 

Effect of different position feedback methods on 
independent compensation systems: 

The lifting and compensation compound system utilizes 
traditional PID control, which allows the feedback of the 
drilling column moving speed acceleration and displacement 
into the controller, and the normal operation of the hydraulic 
circuit by changing the parameters of P, I and D to achieve the 
control of the hydraulic cylinder piston movement. Different 
control methods, with different degrees of control of the 
hydraulic circuit, lead to different results in the longitudinal 
movement of the drill column. Choosing a wave period of 10s 
and a lift of 6.8m, the displacement curves of the drill column 
with displacement feedback, velocity feedback and 
acceleration feedback of the independent compensation 
system were obtained by the joint simulation model as shown 
in Figure 18, and the compensation efficiency of the three 
position feedback methods were calculated as follows. 

Displacement feedback compensation efficiency 𝑒
1 90.01: 

Speed feedback compensation efficiency 𝑒 1
89.6  

Acceleration feedback compensation efficiency 𝑒 1
84.7 

Then the compensation accuracy of lifting and sinking of 
displacement feedback is about 90.01%, the compensation 
accuracy of lifting and sinking of velocity feedback is about 



 

86 

89.6%, and the compensation accuracy of lifting and sinking 
of acceleration feedback is about 84.7%, then the 
compensation accuracy of velocity feedback is the highest 
and the compensation effect is the best in the composite 
system of lifting and compensation based on position 
feedback. Figure 17 shows the moving speed of the drill 
column of the composite system of lifting and compensation 
based on position feedback, and the drilling pressure 
fluctuation of the three feedback methods is compared, and 
the maximum fluctuation amplitude is 5.02KN, which meets 
the design requirements. 

The wave amplitude and different feedback signals have an 
effect on the compensation effect of the lifting and sinking 
compensation system. In order to study the change law 
between them, different wave amplitudes and feedback 
signals are selected for joint simulation analysis, and the 
results are shown in Figure 10. From Fig.9, it can be seen that 
under the condition of the same feedback signal, the 
compensation effect of the lifting and sinking compensation 
system gradually becomes worse as the wave amplitude 
increases; under the condition of the same wave amplitude, 
different feedback signals correspond to different 
compensation effects. In order to compare the effect of 
different operating water depths on the compensation effect, 
we need to calculate the fluctuation of drilling pressure 
corresponding to the three operating water depths, and then 
determine the effect of different operating water depths on the 
compensation effect by comparing the fluctuation of their 
drilling pressure. 

Figure 9 shows the longitudinal vibration response of the 
drill column corresponding to different wave heights, and the 
analysis results are as follows. When the wave height is 6.8m, 
the fluctuation of the bottom of its drill column is0.95, then 
its compensation effect is90.01%. 

When the wave height is 4.8m, the bottom fluctuation of 
the drill column is0.44, then the compensation effect is 92.4%. 
When the wave height is 2.8m, the fluctuation of the bottom 
of the drill column is 0.21, then the compensation effect is 
93.9%. 

We also compared the difference between position 
feedback, the results are shown in Figure 17-18. Which finally 
resulted in the best compensation effect of 84.3% for velocity 
feedback. 

Simulation results and analysis. 
As shown in Fig. 12, by comparing the influence of 

different mud densities, it is concluded that mud densities 
have little influence on bottomhole pressure fluctuation.  As 
shown in Fig. 13-16, the smaller the straight passage of the 
cylinder, the smaller the stiffness of the wire rope, the smaller 
the vibration amplitude of the drill string, and the smaller the 
fluctuation of bottomhole pressure. 

5. Conclusion 
After comparative analysis, it is concluded that the design 

scheme of lifting and compensation composite system is 
reasonable, which improves the accuracy of control and 
compensation, and it is concluded by comparison that the 
stiffness of wire rope, liquid cylinder diameter and sea 
condition environment have greater influence on the 
compensation effect, while the feedback mode and mud 
density (with or without spacer operation) have less influence 

on the compensation effect.  
Comparing displacement feedback, velocity feedback, and 

acceleration feedback at a wave height of 6.5m yields a higher 
accuracy of 84.3% for velocity feedback and a relatively low 
accuracy of 81.7% for acceleration feedback In the case of 
different wave heights, the comparison wave heights are 6.5m, 
4.8m and 2.8m respectively: as the wave height decreases, the 
frequency of drilling column vibration will also decrease and 
the compensation accuracy will become higher, so we should 
try to choose the operation when the sea condition 
environment is better.  

The smaller the stiffness of the wire rope, the better the 
compensation effect of the drilling column, the higher the 
compensation accuracy, but the stiffness is too small wire 
rope is easy to break, so the selected stiffness should be 
combined with safety issues. 

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