CN113296499B - Optimal polar region FPSO (Floating production storage and offloading) anchoring dynamic positioning control method based on acceleration feedforward - Google Patents
Optimal polar region FPSO (Floating production storage and offloading) anchoring dynamic positioning control method based on acceleration feedforward Download PDFInfo
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Abstract
The invention provides an FPSO (floating production storage and offloading) anchoring dynamic positioning control method based on acceleration feedforward for an optimal heading polar region. The invention aims to compensate disturbance by using acceleration feedforward, improve the system state estimation precision and keep the FPSO at an expected heading and position. 1. An optimal heading calculation method based on the ice coming direction according to the maximum tension and the second maximum tension of the mooring cable is designed. 2. By adding an acceleration term in the state observer, an acceleration feedforward observer of the FPSO (floating production storage and offloading) mooring dynamic positioning system is established, and the influence of fast-changing ice disturbance on state estimation can be effectively inhibited. 3. An anchoring dynamic positioning controller combining acceleration feedforward and nonlinear model predictive control is designed, the nonlinear characteristic of the original system is reserved, the constraint problem of input and output is considered, and the control of the position and the heading is realized.
Description
Technical Field
The invention relates to the field of dynamic positioning control, in particular to an FPSO (floating production storage and offloading) anchoring dynamic positioning control method based on acceleration feedforward for an optimal heading polar region.
Background
With global warming, resource development and scientific research in arctic regions are gradually developed, wherein a Floating Production Storage and Offloading (FPSO) is a mature device in many ocean resource development systems. Compared with the traditional devices such as an ocean fixed platform, the FPSO has the advantage of good flexibility, and the positioning mode can be flexibly selected according to different sea areas and different sea conditions. The anchoring dynamic positioning combines the advantages of the dynamic positioning technology and the anchoring positioning technology, reduces the complexity of anchoring arrangement and the action frequency of the propeller, thereby reducing the loss of the propeller and ensuring safer, more economic and more efficient resource exploitation.
Resource exploitation in polar regions is more complicated and difficult compared with open water areas, and the FPSO operated in the ice-covered water areas is subjected to external force which is not only wave flow, but also ice load which is rapid in change, various in shape, difficult to calculate and highly nonlinear. In order to overcome the severe environment of the polar region and enable the FPSO to be in a safe working state, the invention provides an optimal polar region FPSO anchoring dynamic positioning control method based on Acceleration feedforward (AFF), which can calculate the optimal heading according to the tension of an anchoring cable, improve the anti-interference capability of a system by using the AFF and finally control the motion state of the FPSO by a Nonlinear Model Predictive Controller (NMPC).
Disclosure of Invention
The invention aims to provide an FPSO (floating production storage and offloading) anchoring power positioning control method based on acceleration feedforward, which is used for calculating an expected heading by using anchoring cable tension, designing an AFF (active flight control) observer to reduce an estimation error of an unknown ice load on a ship state, compensating ice disturbance power by using the AFF, and controlling the heading and the position of an FPSO (floating production and offloading) by using an NMPC (non-volatile memory) to keep the FPSO in an expected state.
The purpose of the invention is realized as follows:
the FPSO anchoring power positioning control method based on acceleration feedforward for the optimal heading polar region specifically comprises the following steps:
step 1: and (4) calculating the tension of the mooring cables by using the mooring system model according to the position of the ship, and designing an optimal heading determining method related to the maximum tension mooring cable and the second maximum tension mooring cable.
Calculating the tension of 8 mooring cables in real time to obtain the maximum tension T a And the next highest tension T b And determining the target heading. Calculating T by equation (1) a Multiplying the angular difference of (2) by the weight to calculate T a The target heading is obtained according to the formula (3).
E＝α 1 -α 2 (2)
α T ＝α 1 +E×R (3)
Wherein R is the proportion of the maximum tension in the sum of the maximum tension and the second maximum tension, E is the angle difference between the maximum tension mooring cable and the second maximum tension mooring cable, and alpha T Is the target heading.
Step 2: and adding an acceleration term in the state observer, designing an AFF observer, estimating the position, heading and speed value of the FPSO, and directly compensating unknown ice disturbance by using the AFF in the controller.
Assuming that gravity and noise of the accelerometer are ignored, and considering the slow variation deviation b (t) of the acceleration self mechanical device, the output model of the accelerometer is as follows:
wherein the content of the first and second substances,
the actual acceleration at the previous moment.
α (t) is an acceleration compensation term, and the expression is as follows:
wherein r is d (t) is the unknown disturbance at the last instant.
And filtering the acceleration compensation term to obtain a final acceleration compensation term as follows:
after finishing, the final AFF observer can be obtained as follows:
wherein, τ is a designed control law, and the expression is as follows:
τ＝μ(t)-τ aff (t) (7)
wherein, mu (t) is a control law, tau, designed by NMPC aff Is an acceleration feedforward term, and the expression is as follows:
and step 3: and (4) applying the estimated position, heading and speed to NMPC design, and combining AFF to obtain a control law of the FPSO mooring dynamic positioning system.
The dynamic positioning system is nonlinear, and after the system is linearized by taylor expansion, when the ship motion deviates from a linearization point, the control precision of the ship can be reduced by a linear model predictive control algorithm, and a divergence phenomenon can occur in the serious case.
The accurate feedback linearization method can obtain a new linear system from the nonlinear system through coordinate transformation, the linear system after feedback linearization keeps the nonlinear characteristic of the original motion mathematical model, and then the prediction control law of the mooring dynamic positioning model is designed through the linear system based on feedback linearization.
Utilizing the concept of plum derivative, relative order and differential homoembryo to linearize the accurate feedback of the FPSO system, and obtaining a state space equation as follows:
wherein y is the system output after precise feedback linearization, v is the control law after precise feedback linearization, and v = a (x) + b (x) u,
discretizing and merging equation (10) into a state space equation with an integrator:
wherein x is a (k)＝[Δz(k) y(k)] T ,
C a ＝[O 3×6 I 3×3 ]
Controller design after accurate feedback linearization:
a prediction model within the optimization window can be obtained by equation (12):
Y＝Fx a (k)+ΦΔV (11)
wherein:
because the external ice environment is fast and transient in the ice resistance generated when the FPSO is acted on, the amplitude change rate of the actuator generated by the controller cannot be too large, otherwise damage to the rigid body would be difficult to predict. This relaxes the position constraint, only the FPSO needs to be kept within a certain range, and the following constraints are obtained:
U min ≤U≤U max (12)
ΔU min ≤ΔU≤ΔU max (13)
Y min ≤Y≤Y max (14)
wherein, U min And U max Respectively minimum and maximum actuator amplitude, deltaU min And Δ U max Respectively minimum and maximum values of the rate of change of the amplitude of the actuator, Y min And Y max Are the minimum and maximum values of the output position and heading.
Finding the relationship of Δ V to Δ U and U:
U＝f(ΔV) (15)
and finally, obtaining a control optimization problem about parameter delta V constraint based on nonlinear model control, wherein the control optimization problem is as follows:
wherein, L and N are constant matrixes respectively.
Therefore, the optimal control input u (k) at the moment k, namely the nominal control law mu (t), can be obtained by solving the nonlinear constraint problem, and the anchoring dynamic positioning control is carried out on the FPSO.
The invention has the following beneficial effects:
1. the invention designs a calculation method of the expected heading, reduces the influence of ice load on an FPSO platform, and increases the safety of operation in polar regions with unstable environmental conditions.
2. Due to the influence of external ice load, the FPSO state estimation generates larger deviation, the designed AFF observer effectively reduces the influence of unknown and rapidly-changed ice load on the system state estimation, and the system state estimation precision is improved.
3. The method has the advantages that an AFF control law capable of directly compensating external ice load disturbance is designed, feedforward control is carried out on the ice load disturbance, the influence of the ice disturbance on a system can be predicted, measures are taken in advance, compared with feedback control, the method is good in real-time performance and free from influence of system lag, and therefore performance of the FPSO mooring dynamic positioning system in the polar environment can be effectively improved.
NMPC is different from a linear model prediction control method, all nonlinear terms of the system are considered, the nonlinear system is accurately linearized through differential homomorphic transformation, and the system error in the linearization process is eliminated; compared with other controllers, the NMPC is more convenient and effective in processing the input amplitude and the change rate of the input amplitude of the execution mechanism and the constraint of the motion state of the ship.
Drawings
FIG. 1 is a block diagram of FPSO mooring dynamic positioning control;
FIG. 2 is a schematic view of a mooring line distribution;
FIG. 3 is a schematic diagram of a target heading calculation method.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
To make the aforementioned objects, features and advantages of the present invention clearer, the present invention will be described in further detail with reference to fig. 1 to 3 and the following detailed description, wherein fig. 1 is a block diagram of FPSO mooring dynamic positioning control; FIG. 2 is a schematic view of a mooring line distribution; FIG. 3 is a schematic diagram of a target heading calculation method.
The purpose of the invention is realized by the following steps:
as shown in fig. 1, the FPSO mooring dynamic positioning control process includes: the method comprises the steps of using a sensor (measuring system) to measure the position, the heading and the measured acceleration (ignoring gravity and noise) of the FPSO to an AFF observer, obtaining estimated values of the position, the heading and the speed of the FPSO to be used for designing an NMPC (non-volatile memory controller), obtaining an NMPC control law, and further combining the AFF control law for compensating ice load to obtain a final control law to realize the dynamic positioning control of the FPSO.
1. Building mathematical model of FPSO and anchoring system
(1) Ship motion mathematical model
Wherein eta = [ x y ψ] T ，υ＝[u v r] T ，τ m The mooring cable acts on the tension of the ship; tau. env Is the disturbing force acting on the FPSO.
Is a coordinate transformation matrix, M is a system inertia matrix, D is a damping coefficient matrix, and the expression is as follows:
(2) Buoy mooring system model
The mooring system is assumed to be composed of 8 symmetrically distributed mooring cables, the inner tower of the FPSO is fixed to the seabed through an anchor, and the horizontal tension expression of the ith (i =1, …, 8) cable is analyzed statically by catenary theory as shown in fig. 2:
wherein L is i Represents the length of the ith cable, T hi Represents the horizontal tension of the ith cable, and the expressions of a, b, c and d are shown in formulas (4) to (7), X i Is L i The projection in the horizontal direction and can be calculated by:
wherein (x) i ,y i ) Represents the i-th cable anchor position and (x, y) represents the coordinates of the turret center in the northeast coordinate system.
Wherein the content of the first and second substances,
representing the angle between the lower end of the j-th section of the mooring line and the horizontal plane,
represents the angle, omega, between the upper end of the j-th section of the mooring line and the horizontal plane j Is the weight per unit length, T, of the j-th section of the mooring line h Is the tension of the mooring line in the horizontal direction.
The horizontal resultant tension of all cables of the whole anchoring system in the northeast coordinate system can be obtained according to the formula (5):
wherein, theta i ＝arctan[(y i -y)/(x i -x)]。
Finally, through the transformation matrix J R (psi) the combined tension and moment in the northeast coordinate system are converted into the hull coordinate system, and the combined tension and moment in the FPSO motion mathematical model can be obtainedτ m ：
Wherein X m 、Y m And N m The resultant force and moment of anchoring cable of anchoring system respectively representing longitudinal direction, transverse direction and heading direction under ship body coordinate system, X all 、Y all And N all Representing longitudinal, transverse and heading mooring system mooring cable resultant forces and moments, respectively, in the northeast coordinate system.
2. Calculating an expected heading
The tension of 8 mooring cables is calculated in real time to obtain the maximum tension mooring cable T a And second-order large tension mooring cable T b Calculating T by equation (13) a Multiplying the weight of the sum of the maximum and the second maximum tensions by the angular difference of (14) to calculate T a The target heading is obtained according to equation (15). The target heading is schematically shown in fig. 3.
E＝α 1 -α 2 (30)
α T ＝α 1 +E×R (31)
Wherein R is the proportion of the maximum tension in the sum of the maximum tension and the second maximum tension, E is the angle difference between the maximum tension mooring cable and the second maximum tension mooring cable, and alpha T Is the target heading.
3. Design acceleration feedforward observer
From the mathematical model of the vessel motion of equation (1), considering the measurement deviation b (t) of the accelerometer itself, which is considered as the wiener process, the following model can be obtained:
wherein r is unknown environmental force and system unmodeled term, and w is zero-mean Gaussian driving noise.
Assuming that gravity and noise of the accelerometer are ignored, and considering the slow variation deviation b (t) of the acceleration self mechanical device, the output model of the accelerometer is as follows:
wherein the content of the first and second substances,
the actual acceleration at the previous moment.
The observer is modeled by equation (16):
wherein, C 1 、C 2 And C 3 Is a matrix to be designed, alpha (t) is an acceleration compensation term, and the expression is as follows:
wherein r is d (t) is the unknown disturbance at the last instant.
Substituting equation (19) into equation (18) can be:
if equation (16) is different from equation (20), the closed-loop dynamic error is expressed as:
wherein the content of the first and second substances,
as can be seen from the closed-loop error dynamic expression, by adding an acceleration feedforward term, the error dynamic quick-action disturbance r (t) of the observer of the nominal system is effectively inhibited, so that the state estimation precision is improved.
And filtering the acceleration compensation term to obtain a final acceleration compensation term as follows:
after finishing, the final AFF observer can be obtained as follows:
wherein, τ is a designed control law, and the expression is as follows:
τ＝μ(t)-τ aff (t) (40)
wherein μ (t) is a control law designed by NMPC, and the specific design is shown in the next subsection. Tau is aff Is an acceleration feedforward term, and the expression is as follows:
4. controlling ship position and heading using NMPC
And (3) utilizing the concepts of plum derivative, relative order and differential homoembryo to accurately feed back and linearize the ship model.
Order to
According to the formula (1-4), the state quantity is an estimated value of the previous section, and is expanded into the following form:
wherein the content of the first and second substances,
writing equation (26) as a standard nonlinear state space model:
wherein the content of the first and second substances,
u＝[τ X +τ mX ,τ Y +τ mY ,τ N +τ mN ] T ,y＝[y 1 ,y 2 ,y 3 ] T ，
the output variable h (x) is solved for Li Daoshu:
due to b 1 (x) All elements in the matrix are zero, b (x) is a non-singular matrix, the relative order of the non-singular matrix is equal to the order of the original system, and accurate feedback linearization can be realized. The new state variable z after the accurate feedback linearization is therefore:
wherein the content of the first and second substances,
finally, the state space equation after accurate feedback linearization is:
wherein y is the system output after accurate feedback linearization, v is the control law after accurate feedback linearization, and
v＝a(x)+b(x)u，
controller design after accurate feedback linearization:
discretizing equation (34) into a discrete-time state-space equation:
wherein z (k + 1) is the state at the moment of k +1 after discretization, z (k) is the state at the moment of k after discretization, v (k) is the control input at the moment of k after discretization, and y (k) is the distanceThe system output at the k time after dispersion, A d 、B d And C d Is a system matrix.
From z (k + 1) = z (k) + Δ z (k + 1), y (k + 1) = y (k) + Δ y (k + 1), and substituting into formula (35), one can obtain:
Δz(k+1)＝A d Δz(k)+B d Δv(k) (52)
y(k+1)＝y(k)+C d A d Δz(k)+C d B d Δv(k) (53)
the above is expressed as a state space equation with an integrator:
wherein x is a (k)＝[Δz(k) y(k)] T ,
C a ＝[0 3×6 I 3×3 ]
Design of controller after accurate feedback linearization:
1) Prediction model
Within an optimization window, the future N can be predicted c N in control time domain p A system output (N) c ≤N p )：
Y＝Fx a (k)+ΦΔV (55)
Wherein:
2) Roll optimization
By optimizing the performance index, a control input Δ v that optimizes the objective function is obtained. The objective function is established as follows:
J＝(R s -Y) T (R s -Y)+ΔV T R'ΔV (56)
wherein R is s Is a desired output and
r w is an adjustment parameter.
By bringing (39) into formula (40), we can obtain:
J＝(R s -Fx a (k)) T (R s -Fx a (k))-2ΔV T Φ T (R s -Fx a (k))+ΔV T (Φ T Φ+R')ΔV (57)
derivation is made for the above equation and let:
then, the optimal input sequence Δ V under the unconstrained condition of the time k can be obtained as follows:
ΔV＝(Φ T Φ+R') -1 Φ T (R s -Fx a (k)) (59)
according to the idea of rolling optimization, the first component Δ V (k) of the solution Δ V of equation (43) is substituted into the system, so that the output value y (k + 1) can be obtained at the time k + 1, and taken as the measured value at the next time, and then Δ V at the next time is calculated, and the expected position under the unconstrained condition can be found by repeating the steps.
3) Feedback correction
Depending on the nature of the ice load, the following constraints exist:
U min ≤U≤U max (60)
ΔU min ≤ΔU≤ΔU max (61)
Y min ≤Y≤Y max (62)
expand U into:
the constraint controlling the input sequence U can be expressed as:
-(P 1 u(k-1)+P 2 ΔU)≤-U min (64)
P 1 u(k-1)+P 2 ΔU≤U max (65)
to link the constraints to Δ V, the constraints on Δ U and Y are translated into constraints on Δ V by the following steps:
by developing the equation (36), the relationship between the state z and the control Δ v after the precise feedback linearization at the time from k +1 to k + m can be obtained:
the above formula is collated to obtain a state expression in an optimization window:
Z＝G+HΔV (67)
wherein the content of the first and second substances,
similar to equation (47), expand V into:
using equation (52) and V = a (x) + b (x) U, a relationship of Δ V to U can be established:
U＝f(ΔV) (69)
using the output constraint of equation (46), the output versus Δ V can be found as:
Y min ≤Fx a (k)+ΦΔV≤Y max (70)
and finally, controlling the control optimization problem about parameter delta V constraint based on the nonlinear model to:
minJ＝(R s -Fx a (k)) T (R s -Fx a (k))-2ΔV T Φ T (R s -Fx a (k))+ΔV T (Φ T Φ+R')ΔV
wherein the content of the first and second substances,
thus, we can solve this nonlinear constraint problem to find the optimal control input at time k:
u(k)＝b(z(k)) -1 [b(z(k-1))u(k-1)+a(z(k-1))-a(z(k))+Δv(k)] (72)
here, u (k) is the nominal control law μ (t), and thus the final FPSO mooring dynamic positioning control law is:
and the final control law tau is utilized to realize that the FPSO anchoring dynamic positioning system in the water area of unknown ice environment keeps the optimal heading and makes the system in a safe working area.
Claims (1)
1. An optimal heading polar region FPS0 anchoring dynamic positioning control method based on acceleration feedforward is characterized by comprising the following steps: the method specifically comprises the following steps:
step 1: calculating the tension of the mooring cable by using the mooring system model according to the position of the ship, and designing an optimal heading determination method related to the maximum tension mooring cable and the second maximum tension mooring cable;
calculating the tension of 8 mooring cables in real time to obtain the maximum tension T a And second maximum tension T b Determining target heading, and calculating T by formula (1) a The ratio of the maximum and the second maximum tension sums is obtained by multiplying the angle difference of (2) by the weight,calculate T a The target heading is obtained according to the formula (3);
E＝α 1 -α 2 (2)
α T ＝α 1 +E×R (3)
wherein R is the proportion of the maximum tension in the sum of the maximum tension and the second maximum tension, E is the angle difference between the maximum tension mooring cable and the second maximum tension mooring cable, and alpha T Is the target heading;
step 2: adding an acceleration item in a state observer, designing an AFF observer, estimating the position, heading and speed value of the FPSO, and directly compensating unknown ice disturbance in a controller by using AFF;
assuming that gravity and noise of the accelerometer are ignored, and slow variation deviation b (t) of the mechanical device of the acceleration is considered, the output model of the accelerometer is as follows:
wherein the content of the first and second substances,
the actual acceleration at the last moment;
α (t) is an acceleration compensation term, and the expression thereof is as follows:
wherein r is d (t) is the unknown disturbance at the previous time instant;
and filtering the acceleration compensation term to obtain a final acceleration compensation term as follows:
after finishing, the final AFF observer can be obtained as follows:
wherein, τ is a designed control law, and the expression is as follows:
τ＝μ(t)-τ aff (t) (7)
wherein, mu (t) is a control law designed by NMPC, tau aff Is an acceleration feedforward term, and the expression is as follows:
and 3, step 3: using the estimated position, heading and speed for NMPC design, and combining AFF to obtain a control law of the FPSO mooring dynamic positioning system;
the dynamic positioning system is nonlinear, and after the system is linearized by using Taylor expansion, when the ship motion deviates from a linearization point, the control precision of the ship can be reduced by a linear model predictive control algorithm, and a divergence phenomenon can occur in the serious condition;
the accurate feedback linearization method can transform a nonlinear system into a new linear system through coordinates, the linear system after feedback linearization keeps the nonlinear characteristic of the original motion mathematical model, and then the mooring dynamic positioning model prediction control law is designed through the linear system based on feedback linearization;
utilizing the concept of plum derivative, relative order and differential homoembryo to linearize the accurate feedback of the FPSO system, and obtaining a state space equation as follows:
whereinY is the system output after precision feedback linearization, v is the control law after precision feedback linearization, and v = a (x) + b (x) u,
discretizing and merging equation (10) into a state space equation with an integrator:
wherein x is a (k)＝[Δz(k) y(k)] T ，
C a ＝[O 3×6 I 3×3 ]
Controller design after accurate feedback linearization:
a prediction model within the optimization window can be obtained by equation (12):
Y＝Fx a (k)+ΦΔV (11)
wherein:
because the ice resistance generated when the external ice environment acts on the FPS0 is rapid and transient, the amplitude change rate of the actuating mechanism generated by the controller cannot be too large, otherwise the damage to the rigid body is difficult to predict; this relaxes the position constraint, only requiring FPS0 to remain within a certain range, thus yielding the following constraint:
U min ≤U≤U max (12)
ΔU min ≤ΔU≤ΔU max (13)
Y min ≤Y≤Y max (14)
wherein, U min And U max Respectively minimum and maximum actuator amplitude, deltaU min And Δ U max Respectively minimum and maximum values of the rate of change of the amplitude of the actuator, Y min And Y max Is the minimum and maximum values of the output position and heading;
finding the relation between the delta V and the delta U and U:
U＝f(ΔV) (15)
and finally, obtaining a control optimization problem about parameter delta V constraint based on nonlinear model control, wherein the control optimization problem is as follows:
min J＝(R s -Fx a (k)) T (R s -Fx a (k))-2ΔV T Φ T (R s -Fx a (k))+ΔV T (Φ T Φ+R′)ΔV
st.LΔV≤N (16)
wherein, L and N are constant matrixes respectively;
thus, the optimal control input u (k) at the moment k, namely the nominal control law mu (t), can be obtained by solving the nonlinear constraint problem, and the anchoring dynamic positioning control is carried out on the FPS 0.
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