A coordinated heave compensation control method and system for a dual-ship-borne lifting arm system

Abstract

The present invention discloses a method and system for coordinated heave compensation control of a dual-shipborne lifting arm system, comprising: based on two longitudinal lifting arms, two transverse lifting arms and a load, the position and speed of each lifting arm are used as state variables, and the attitude angle state variable of the load is represented based on the position and speed of the lifting arm, thereby constructing a dynamic model of the dual-shipborne lifting arm system; based on the dynamic model, the reference compensation trajectory of each lifting arm in the heave motion is tracked as the control target, the minimization of the tracking error is the optimization target, the action constraint of each lifting arm and the position and speed constraint of the lifting arm after the action are used as constraint conditions, and the optimal control strategy is obtained to control the action of each lifting arm. Coordinated heave compensation control under continuous wave disturbance is realized, and the performance of coordinated heave compensation control is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of shipborne crane motion control, and in particular to a coordinated heave compensation control method and system for a double shipborne lifting boom system. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] Ship-borne cranes have been widely used in various fields of offshore facilities such as cargo transportation, offshore drilling platform control, and installation and disassembly of offshore wind power platforms. However, some land crane control technologies are difficult to directly apply to the control of ship-borne cranes. First, the response of waves will be transmitted to the ship, making the movement of the ship very complicated. The six-degree-of-freedom movement of the ship includes movement in three directions (surge, sway and heave) and rotational movement around three axes (roll, pitch and yaw). Second, the dynamic characteristics of ship-borne cranes are more complex and more coupled with the movement of the ship. Continuous wave interference will lead to complex payload swing angles. When lifting, lowering or stabilizing the load at sea, wave compensation control can be used to eliminate the wave movement of the load caused by the ship, thereby decoupling the load movement from the ship movement.

[0004] In recent years, the modeling and wave compensation control of ship-borne cranes have received extensive attention, and many important research results have been published. For example, the wave information measured by the sensor is combined with the Kalman filter algorithm to predict the wave motion within a limited time range, and the feedforward controller uses the predicted motion to compensate for the wave disturbance. For another example, a system decoupling method is designed, and a new ASMC method is developed based on the composite sliding surface formed by the combination of internal coupling dynamics (between actuated variables and non-actuated variables), which includes two adaptive algorithms: switch control and equivalent control.

[0005] Although the motion control of cranes has made great progress, most of the research related to ship-borne cranes is about the anti-sway control of cable cranes, and the application scenario is often the transfer of small and medium-sized loads. For the complete transfer of super-large loads, such as offshore drilling platforms and offshore wind power platforms, the modeling and control of cable cranes is extremely difficult due to the extremely high weight of such loads, complex offshore interference, and the possibility of even two ships and multiple cranes working at the same time. Summary of the invention

[0006] In order to solve the above problems, the present invention proposes a collaborative heave compensation control method and system for a dual-shipborne lifting arm system, which controls the collaborative heave compensation of the dual-shipborne lifting arm system based on an incremental model predictive control algorithm, takes minimizing the tracking error as the optimization goal, tracks the reference trajectory under set constraints, realizes collaborative heave compensation control under continuous wave disturbance, and improves the performance of collaborative heave compensation control.

[0007] In order to achieve the above object, the present invention adopts the following technical solution:

[0008] In a first aspect, the present invention provides a method for controlling coordinated heave compensation of a dual-shipborne lifting arm system, comprising:

[0009] Based on two longitudinal lifting arms, two transverse lifting arms and a load, the position and speed of each lifting arm are taken as state variables, and the attitude angle state variable of the load is represented based on the position and speed of the lifting arm, thereby constructing a dynamic model of the double ship-borne lifting arm system;

[0010] Based on the dynamic model, the control objective is to track the reference compensation trajectory of each lifting arm in the heave motion, the optimization objective is to minimize the tracking error, and the motion constraints of each lifting arm and the position and speed constraints after the lifting arm motion are used as constraint conditions to obtain the optimal control strategy to control the motion of each lifting arm.

[0011] As an optional embodiment, the attitude angle α of the load is expressed based on the position and speed of the lifting arm, specifically:

[0012] The simplified kinetic model obtained is:

[0013]

[0014] M(q i )=N T M(q j )N,

[0015] G(q i )=N T G(q j ),f i =N T f j ;

[0016]

[0017] Wherein, a1, a2, b1, b2 are respectively the first transverse lifting arm stroke, the second transverse lifting arm stroke, the first longitudinal lifting arm stroke, and the second longitudinal lifting arm stroke; are respectively a first transverse lifting arm speed, a second transverse lifting arm speed, a first longitudinal lifting arm speed, and a second longitudinal lifting arm speed; is the partial derivative of the function of the lifting arm stroke and the load attitude angle with respect to a1, b1, b2, a2; q i =[a1,b1,a2,b2] represents the state variable; M(q i ), G(q i ),f i denote the inertia matrix, Coriolis matrix, gravity matrix and control vector respectively; for q i The second-order derivative of for q i The first derivative of .

[0018] As an alternative implementation, the dimension of the state variable is expanded, defined as

[0019]

[0020] The new state equation obtained is:

[0021] in:

[0022]

[0023] g(i)=M(q i ) -1 f i ,i=1,2,3,4;

[0024]

[0025] G=[0 1×4 ;g(1);0 1×4 ;g(2);0 1×4 ;g(3);0 1×4 ;g(4)];

[0026] F∈R 8×1 ,G∈R 8×4

[0027] Among them, F is the state transfer matrix after dimensional expansion, G is the input matrix after dimensional expansion; f(1), f(2), f(3), f(4) are all the row vectors of the matrix f(i); g(1), g(2), g(3), g(4) are all the row vectors of the matrix g(i).

[0028] As an optional implementation, the state equation of the dynamic model is approximately linearized based on the real-time state variables and the real-time action input, and the obtained approximately linearized state equation is:

[0029]

[0030]

[0031] Among them, q t * ,f i * are real-time state variables and real-time action inputs; matrices A and B are both discretized state space model matrices; q t is the state variable; f i is the control vector; Q t The first-order derivative of ; F is the state transfer matrix after dimension expansion, and G is the input matrix after dimension expansion.

[0032] As an optional implementation, the optimization goal is:

[0033]

[0034] Where Δf(k) is the input increment; q a is the state equation considering the input increment; N p is the prediction interval of model predictive control; q a (N p ) indicates that the state variable is in the prediction iteration N p The value after the second; S a ,Q a , R are weight matrices.

[0035] As an optional implementation, the constraint condition is:

[0036]

[0037] Among them, q min ,q max is the maximum and minimum value of the lifting arm position; is the maximum and minimum value of the lifting arm speed; f min , f max Maximum and minimum values ​​entered for lift arm motion; is the changing trend of the state variable; q a (k), q a (k+1) are the state variables at time k and time k+1 respectively considering the input increment; Δf(k) is the input increment; A a ,B a are the state transfer matrix and input matrix of the new state equation respectively; q(k+i) is the state variable at time k+i considering the input increment; Q a(k+i); f(k+i) is the control input at time k+i.

[0038] In a second aspect, the present invention provides a coordinated heave compensation control system for a dual-shipborne lifting arm system, comprising:

[0039] A model building module is configured to build a dynamic model of the double ship-borne lifting arm system based on two longitudinal lifting arms, two transverse lifting arms and a load, taking the position and speed of each lifting arm as state variables, and representing the attitude angle state variable of the load based on the position and speed of the lifting arm;

[0040] The optimization control module is configured to be based on the dynamic model, with tracking of the reference compensation trajectory of each lifting arm in the heave motion as the control target, minimization of the tracking error as the optimization target, and the motion constraints of each lifting arm and the position and speed constraints after the lifting arm moves as constraints, so as to obtain the optimal control strategy to control the movement of each lifting arm.

[0041] In a third aspect, the present invention provides an electronic device comprising a memory and a processor, and computer instructions stored in the memory and executed on the processor, wherein when the computer instructions are executed by the processor, the method described in the first aspect is performed.

[0042] In a fourth aspect, the present invention provides a computer-readable storage medium for storing computer instructions, wherein when the computer instructions are executed by a processor, the method described in the first aspect is performed.

[0043] In a fifth aspect, the present invention provides a computer program product, comprising a computer program, which, when executed by a processor, implements the method described in the first aspect.

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] The present invention proposes a collaborative heave compensation control method and system for a double-shipborne lifting arm system, considers the heave motion of the ship under wave disturbance, establishes a multi-degree-of-freedom nonlinear dynamic model of the double-shipborne lifting arm system, and based on the coupling constraints of the system, expresses the attitude angle of the load by the position and speed of the lifting arm, and expands the dimension of the lifting arm state variable, takes the position and speed of each lifting arm as the state variable, simplifies the nonlinear dynamic model of the system, and facilitates the design and optimization control of the incremental model predictive control algorithm.

[0046] The present invention proposes a collaborative heave compensation control method for a dual-shipborne lifting arm system based on incremental model predictive control. Based on the heave motion prediction algorithm, a reference compensation trajectory of the corresponding lifting arm is obtained. Based on the dynamic model, minimizing the tracking error is used as the optimization goal. The reference trajectory is tracked under the constraints of the lifting arm movement, the position and speed constraints of the lifting arm after the movement. Considering the situation where the actuator is not protected, the capacity of the actuator can be fully utilized while meeting the input saturation constraint requirements, so as to realize collaborative heave compensation control under continuous wave disturbance and improve the performance of collaborative heave compensation control.

[0047] Advantages of additional aspects of the present invention will be given in part in the following description, and in part will become obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0049] Figure 1 A flow chart of a coordinated heave compensation control method for a dual-shipborne lifting arm system provided in Example 1 of the present invention;

[0050] Figure 2 A schematic diagram of a dynamic model of a dual ship-borne lifting arm system provided in Example 1 of the present invention;

[0051] Figure 3 A schematic diagram comparing the tracking reference compensation trajectory 1 and the load swing angle simulation effect provided by Embodiment 1 of the present invention;

[0052] Figure 4 A schematic diagram comparing the tracking reference compensation trajectory 2 and the load swing angle simulation effect provided in Example 1 of the present invention. DETAILED DESCRIPTION

[0053] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0054] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0055] It should be noted that the terms used herein are only for describing specific embodiments, and are not intended to limit exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that the terms "include" and "comprise" and any of their variations are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device comprising a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0056] In the absence of conflict, the embodiments of the present invention and the features of the embodiments may be combined with each other.

[0057] Example 1

[0058] This embodiment provides a method for controlling the coordinated heave compensation of a dual-shipborne lifting arm system. Figure 1 As shown, including:

[0059] Based on two longitudinal lifting arms, two transverse lifting arms and a load, the position and speed of each lifting arm are taken as state variables, and the attitude angle state variable of the load is represented based on the position and speed of the lifting arm, thereby constructing a dynamic model of the double ship-borne lifting arm system;

[0060] Based on the dynamic model, the control objective is to track the reference compensation trajectory of each lifting arm in the heave motion, the optimization objective is to minimize the tracking error, and the motion constraints of each lifting arm and the position and speed constraints after the lifting arm motion are used as constraint conditions to obtain the optimal control strategy to control the motion of each lifting arm.

[0061] The method of this embodiment is described in detail below.

[0062] (1) Based on the Lagrangian method, a five-degree-of-freedom (5-DOF) nonlinear dynamic model of the double-ship-borne lifting arm system is constructed.

[0063] This embodiment proposes to use a rigid lifting arm instead of a cable crane to establish a multi-degree-of-freedom nonlinear dynamic model of a double ship-borne lifting arm system, which consists of two longitudinal lifting arms, two transverse lifting arms and a five-degree-of-freedom (5-DOF) load. According to the constraints between the two longitudinal lifting arms, the dynamic model is simplified, and the two longitudinal lifting arms and the two transverse lifting arms work together to stabilize the large load under wave disturbance, such as Figure 2 As shown, the center of gravity of the first transverse lifting arm, the second transverse lifting arm, the first longitudinal lifting arm, the second longitudinal lifting arm and the load are respectively defined as G a1 ,G a2 ,G b1 ,Gb2 ,G p The intersection points of the first longitudinal lifting arm, the second longitudinal lifting arm and the load are defined as p1 and p2 respectively.

[0064] The ship's own positioning system can compensate for the roll, pitch and yaw caused by control, but cannot compensate for the heave motion of waves. Therefore, the following assumptions are made:

[0065] Assumption 1: The relative lateral positions of the centers of gravity of the two ships are constant and the load mass is evenly distributed.

[0066] Assumption 2: The vertical wave motion of the ship is bounded, and the first-order derivative and second-order derivative of the heave motion satisfy the following inequality requirements:

[0067]

[0068] Among them, u1-u6 are thresholds.

[0069] based on Figure 2 The coordinate system in G a1 ,G a2 ,G b1 ,G b2 ,G p It is expressed as:

[0070]

[0071] Among them, m a ,m b ,m p are the mass of the transverse lifting arm, the mass of the longitudinal lifting arm and the load mass, in t; a1, a2, b1, b2 are the first transverse lifting arm stroke, the second transverse lifting arm stroke, the first longitudinal lifting arm stroke and the second longitudinal lifting arm stroke, in m; L a ,L b are the length of the first lateral lifting arm and the length of the second lateral lifting arm, respectively, in m; h1, h2 are the heave displacement of the first ship and the second ship, respectively, in m; α is the load attitude angle, in rad; D is the distance between the two ships, in m; L is the load length, in m; B is the load height, in m.

[0072] The velocity relationship is obtained by differentiating the coordinates of the center of gravity of the four booms and the effective load (load), and then the kinetic energy and potential energy of the double ship-borne lifting boom system are calculated respectively;

[0073] The kinetic energy includes the kinetic energy of two longitudinal lifting arms, two transverse lifting arms and a payload (load).

[0074]

[0075] Among them, v a1x ,v a1y are the x and y components of the first longitudinal lifting arm velocity, respectively; v a2x ,v a2y are the x and y components of the second longitudinal lifting arm velocity respectively; v b1x ,v b1y are the x and y components of the first transverse lifting arm velocity, respectively; v b2x ,v b2y are the x and y components of the second transverse lifting arm velocity respectively; v px ,v py are the x and y components of the load velocity respectively.

[0076] Similarly, the potential energy is:

[0077]

[0078] Then, based on formulas (3) and (4), the Lagrangian is defined as With q j =[a1,b1,a2,b2,α] as generalized coordinates, i.e., state variables, representing the operating range of the four lifting arms and the angle of the load; the corresponding generalized force is f j =[X1,X2,X3,X4,0], i.e., the four lifting arms control input torque, indicating the action of the four lifting arms;

[0079] The Lagrange equation is as follows:

[0080]

[0081] Among them, X1, X2, X3, and X4 are the control input torques of the four lifting arms respectively.

[0082] Finally, the complete dynamic model of the double ship-borne lifting arm system is obtained, which can be mathematically summarized into a more compact form:

[0083]

[0084] Among them, M(q j ), q,G(q j ),f j denote the inertia matrix, Coriolis matrix, state variables, gravity matrix and control vector respectively.

[0085] The above matrices and vectors can be written as follows:

[0086]

[0087]

[0088]

[0089] The matrix M(q j ) are:

[0090]

[0091]

[0092]

[0093]

[0094] According to M(q j )and The definition of can be obtained through algebraic operations:

[0095] Property 1: The matrix M(q j ) is positive definite.

[0096] Property 2: is obliquely symmetric, that is

[0097]

[0098] These two characteristics will be helpful for the subsequent design and analysis of the controller for the dual-shipborne lifting arm system.

[0099] It can also be proved that:

[0100] (2) Model conversion

[0101] There are certain coupling constraints in the double-ship-borne lifting arm system. Reasonable use of system constraints can simplify the order of the dynamic model and reduce the control difficulty.

[0102] The constraints of the double ship-borne lifting boom system are;

[0103] h1+b1-h2-b2-2Lsinα=0 (8).

[0104] Without loss of generality, assume that the functional relationship between the four lifting arm strokes and the load attitude angle is:

[0105] α=g(a1,b1,b2,a2) (9).

[0106] Based on constraint equations (8) and (9), the partial derivatives of a1, b1, b2, and a2 in (9) are obtained respectively:

[0107]

[0108] Therefore, we only need to differentiate equation (9) with respect to time t and then integrate it to obtain α;

[0109]

[0110] Written in a more compact form:

[0111]

[0112] Then, the simplified kinetic model is:

[0113]

[0114] Among them, q i =[a1,b1,a2,b2] represents the new system state variables, and They represent the second-order derivative and first-order derivative of the new system state variables respectively.

[0115] Add a constraint on the load height variation:

[0116]

[0117] According to formula (11), the matrix N is:

[0118]

[0119] Since the simplification process is similar to making implicit functions (system constraints) explicit, it does not affect the accuracy of the system dynamics model.

[0120] Based on the simplified dynamic model (12), the state space is obtained as:

[0121]

[0122] in,

[0123] Right now

[0124] Expand the dimensions of the state variables to include the travel position and velocity of the lift arm, and define new state variables: Indicates the speed of the four lifting arms.

[0125] According to formula (13), the new system state equation is obtained:

[0126]

[0127] in:

[0128]

[0129] Wherein, F represents the state transfer matrix of the system after dimensional expansion, G represents the input matrix of the system after dimensional expansion; f(1), f(2), f(3), f(4) respectively represent all the row vectors of the matrix f(i) defined in equation (13); g(1), g(2), g(3), g(4) respectively represent all the row vectors of the matrix g(i) defined in equation (13).

[0130] The method of this embodiment is dedicated to the study of coordinated heave compensation control. The system exhibits less nonlinear characteristics, so the new system state equation is centered around the real-time operating point (q t * ,f i * ) is approximately linearized, q t * ,f i * The real-time state variables and real-time actions are input, thereby obtaining a new system state equation.

[0131]

[0132]

[0133] The Model Predictive Control (MPC) algorithm is a model-based discretization method that is widely used in the field of industrial control. It requires a suitable discrete-time linear system to define the system dynamics within the MPC prediction range. The basic idea is to use the current state and constraints of the system to predict the state and input variables for a period of time in the future, and solve a set of optimal control input sequences; then, only the first set of results in the optimal control sequence is selected and applied to the system. At the next moment, the same operation is repeated to obtain a new optimal control input sequence to achieve the control goal.

[0134] The linear time discrete system model is expressed in state space as:

[0135] q(k+1)=Aq(k)+Bf(k)(17)

[0136] Where q∈R 8 , f∈R 4 ; Matrices A and B are both discretized state space model matrices, obtained by the zero-order hold method under a given discretization period Ts:

[0137] (3) Control objectives

[0138] Considering that the lifting arm is rigidly connected to the hull, the movement of the ship is more directly transmitted to the lifting arm and the lifting point. The study shows that based on the wave data measured by the sensor at the previous moment, the corresponding amplitude and phase information estimates are determined using the FFT method and state estimator to predict future wave actions.

[0139] Therefore, the control objectives can be summarized as follows:

[0140] 1) Based on the wave-ship heave motion prediction algorithm, the ship motion trajectory is transformed through the ship-arm attitude transformation matrix to obtain the reference compensation trajectory of the corresponding lifting arm, and the reference trajectory is tracked under the input constraints to perform collaborative heave compensation. Its mathematical expression is: q i (t) = q id (t),i=1,2,3,4;q id (t) is the reference compensation trajectory of each lifting arm during heave motion.

[0141] 2) Consider the case where the actuator is not protected to meet the input limits of the actuator (lift arm):

[0142] |f i |≤|f imax |,i=1,2,3,4;f imax Represents the maximum input that meets the saturation requirement.

[0143] Finally, the optimal control law that meets the control objectives and constraints is obtained.

[0144] (4) Controller design

[0145] Based on the dynamic model and control objectives of the dual-ship-borne lifting arm system, an incremental model prediction algorithm framework is constructed. The reference trajectory of the state variables in the discrete state is expressed as q d (k) indicates that the coordinated heave compensation control is realized under the discrete control input f(k).

[0146] The input increment Δf(k) represents the change in the input during the sampling time and is defined as follows:

[0147] Δf(k)=f(k)-f(k-1) (18).

[0148] Among them, f(k) and f(k-1) are the action inputs at time k and time k-1 respectively. Δf(k) is used as the cost in the performance indicator, which affects the speed change of the control input, thereby generating smoother control inputs and avoiding faster changes in the system.

[0149] Then, substitute formula (18) into formula (17), and we have:

[0150] q(k+1)=Aq(k)+BΔf(k)+Bf(k-1) (19)

[0151] Among them, q(k) and q(k+1) are the state variables at time k and time k+1 respectively.

[0152] The dynamic equation of the control target is:

[0153] q d (k+1)=A D q d (k) (20)

[0154] Among them, A D is the target state transition matrix.

[0155] Define new state variables, state transfer matrix, and input matrix:

[0156]

[0157] According to equations (19)-(21), the new state space equation is:

[0158] q a (k+1)=A a q a (k)+B a Δf(k) (22)

[0159] Among them, q a (k), q a (k+1) are the state variables at time k and time k+1 respectively; A a ,B a are the state transfer matrix and input matrix of the new state equation respectively.

[0160] At time k, the prediction interval N of iterative model predictive control p Trends of internal state variables;

[0161]

[0162]

[0163] Among them, N p is the prediction interval of model predictive control, Iteration N p The matrix A after this time.

[0164] In a more compact form, equations (23)-(24) can be written as:

[0165]

[0166] The state error is defined as:

[0167] e(k)=q(k)-q d (k) = [I 8×8 -I 8×8 0 8×4 ]q a (k) (26)

[0168] Among them, I 8×8 -I 8×8 0 8×4 They are the identity matrix with eight rows and eight columns, the negative identity matrix with eight rows and eight columns, and the zero matrix with eight rows and four columns.

[0169] Defining the Matrix get:

[0170] e(k)=C a q a (k) (27)

[0171] Taking minimizing the tracking error as the optimization objective, as shown in equation (28), the motion constraints of each lifting arm and the position and speed constraints after the lifting arm moves are combined as constraint conditions, as shown in equation (29), and the control law is solved by solving the optimization objective;

[0172]

[0173]

[0174] definition Substitute into formula (28) to obtain the new optimization objective function;

[0175]

[0176] Among them, q a (N p ) indicates that the state variable is in the prediction iteration N p The value after.

[0177] Among them, in formula (29), the first constraint is the position constraint after the lifting arm moves, which limits the operating range of the lifting arm; the second constraint is the speed constraint after the lifting arm moves, which is the limitation on the maximum speed. The lifting speed of the lifting arm is related to the input torque of the actuator. Therefore, by knowing the range of the input torque of the actuator, the equivalent range of the lifting arm speed can be calculated; the third constraint is the input action constraint of each lifting arm; the fourth and fifth are to limit the initial state to be non-zero.

[0178] In Equation (30), the velocity error is tracked to reduce the tracking position error and smooth the response of the lifting system, which helps to ensure optimal trajectory tracking even in the presence of parameter uncertainties and emerging external disturbances in the control process. The weight matrix S in Equation (30) is a ,Q a ,R will balance the final error, running error and control input increment, and select the parameters that meet the tracking performance expectations, while achieving the closed-loop stability of the system under study.

[0179] Incremental model predictive control is a rolling optimization method. The optimal control parameters only affect the control performance and have no effect on the feasibility and stability of the system. Therefore, according to the actual control problem, a direct trade-off can be made between control performance, computational complexity and economy. In the objective function, all target performances are collected and expressed mathematically, and parameters that can achieve both the expected performance and these conditions are selected.

[0180] It is worth noting that in terms of the impact of the above constraints on the optimization objective function, changing each constraint will change the size of the search space of the optimization problem. When the search space for the system to solve the optimal control is too small, the solution will not be optimal, or even unable to obtain control when it is too extreme; and when the system works over a large range, the challenges to the system hardware are also very severe, and may even cause the system to exceed the physical limit, resulting in damage to the system hardware.

[0181] (5) Simulation verification

[0182] In the simulation, the sampling interval is 0.1s, the prediction time domain is equal to the control time domain of 2s, and the weight coefficient is Q = diag{10 2 ,1,10 6 ,1,10 5 ,1,10 2 ,1},S=I8,R=0.1I4. Simulations under different wave conditions are carried out and compared with LQR and PID. The simulation verifies the effectiveness and prominence of the incremental model predictive control.

[0183] The two waves are:

[0184]

[0185] The lifting arm parameters are set as follows:

[0186]

[0187] The response amplitude operator (ROA) of the ship is equivalent to a low-pass filter. Under the same waveform, the heel compensation reference trajectories of the two ships are roughly the same, but there is a certain time lag.

[0188] Figure 3The three algorithms in waveform 1 are shown. When the two ships work together, the lifting arm of ship 1 tracks the reference compensation trajectory and the changes in load angle. Figure 4 The three algorithms in waveform 2 are shown. When the two ships work together, the lifting arm of ship 2 tracks the reference compensation trajectory and the load angle changes. Table 1 shows the root mean square error (RMSE) of the lifting arm tracking the reference compensation trajectory and the load angle change under the two waveforms controlled by the three algorithms. The simulation results show that under different waveforms, IPMC can significantly improve the offshore load stability capability compared with PID and LQR.

[0189] Table 1 Performance indicators of different controllers

[0190]

[0191] This embodiment proposes a collaborative heave compensation control method for a dual-shipborne lifting arm system based on incremental model predictive control (IMPC). First, a DSLAS five-degree-of-freedom (5-DOF) nonlinear dynamic model based on the Lagrangian method is proposed. Then, based on the heave motion prediction algorithm, the reference compensation trajectory of the corresponding lifting arm is obtained. Based on the dynamic model, the reference trajectory is tracked under the input constraint to realize collaborative heave compensation control under continuous wave disturbance, thereby improving the performance of collaborative heave compensation control.

[0192] Example 2

[0193] This embodiment provides a coordinated heave compensation control system for a dual-shipborne lifting arm system, comprising:

[0194] A model building module is configured to build a dynamic model of the double ship-borne lifting arm system based on two longitudinal lifting arms, two transverse lifting arms and a load, taking the position and speed of each lifting arm as state variables, and representing the attitude angle state variable of the load based on the position and speed of the lifting arm;

[0195] The optimization control module is configured to be based on the dynamic model, with tracking of the reference compensation trajectory of each lifting arm in the heave motion as the control target, minimization of the tracking error as the optimization target, and the motion constraints of each lifting arm and the position and speed constraints after the lifting arm moves as constraints, so as to obtain the optimal control strategy to control the movement of each lifting arm.

[0196] It should be noted that the above modules correspond to the steps described in Example 1, and the examples and application scenarios implemented by the above modules and the corresponding steps are the same, but are not limited to the contents disclosed in the above Example 1. It should be noted that the above modules, as part of the system, can be executed in a computer system such as a set of computer executable instructions.

[0197] In further embodiments, there is also provided:

[0198] An electronic device includes a memory and a processor, and computer instructions stored in the memory and executed on the processor, wherein when the computer instructions are executed by the processor, the method described in Embodiment 1 is performed. For the sake of brevity, it will not be described in detail here.

[0199] It should be understood that in this embodiment, the processor may be a central processing unit CPU, and the processor may also be other general-purpose processors, digital signal processors DSP, application-specific integrated circuits ASIC, off-the-shelf programmable gate arrays FPGA or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0200] The memory may include a read-only memory and a random access memory, and provide instructions and data to the processor. A portion of the memory may also include a non-volatile random access memory. For example, the memory may also store information about the device type.

[0201] A computer-readable storage medium is used to store computer instructions, and when the computer instructions are executed by a processor, the method described in Example 1 is completed.

[0202] The method in Example 1 can be directly embodied as a hardware processor, or a combination of hardware and software modules in the processor. The software module can be located in a mature storage medium in the field such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory, or an electrically erasable programmable memory, a register, etc. The storage medium is located in the memory, and the processor reads the information in the memory and completes the steps of the above method in combination with its hardware. To avoid repetition, it is not described in detail here.

[0203] A computer program product includes a computer program, and when the computer program is executed by a processor, the method described in embodiment 1 is implemented.

[0204] The present invention also provides at least one computer program product tangibly stored on a non-transitory computer-readable storage medium. The computer program product includes computer executable instructions, such as instructions included in a program module, which are executed in a device on a real or virtual processor of the target to perform the process / method as described above. Typically, program modules include routines, programs, libraries, objects, classes, components, data structures, etc. that perform specific tasks or implement specific abstract data types. In various embodiments, the functions of program modules can be combined or divided between program modules as needed. Machine executable instructions for program modules can be executed in local or distributed devices. In distributed devices, program modules can be located in local and remote storage media.

[0205] The computer program code for implementing the method of the present invention can be written in one or more programming languages. These computer program codes can be provided to the processor of a general-purpose computer, a special-purpose computer or other programmable data processing device, so that the program code, when executed by the computer or other programmable data processing device, causes the function / operation specified in the flow chart and / or block diagram to be implemented. The program code can be executed completely on a computer, partially on a computer, as an independent software package, partially on a computer and partially on a remote computer or completely on a remote computer or server.

[0206] In the context of the present invention, computer program codes or related data may be carried by any appropriate carrier to enable a device, apparatus or processor to perform the various processes and operations described above. Examples of carriers include signals, computer readable media, etc. Examples of signals may include electrical, optical, radio, acoustic or other forms of propagation signals, such as carrier waves, infrared signals, etc.

[0207] Those of ordinary skill in the art will appreciate that the units and algorithm steps of each example described in conjunction with this embodiment can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this application.

[0208] Although the above describes the specific implementation mode of the present invention in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without creative work are still within the scope of protection of the present invention.

Claims

1. A method for coordinated heave compensation control of a dual-ship-borne lifting arm system, characterized in that: include: Based on two longitudinal lifting arms, two transverse lifting arms and a load, the position and speed of each lifting arm are taken as state variables, and the attitude angle state variable of the load is represented based on the position and speed of the lifting arm, thereby constructing a dynamic model of the double ship-borne lifting arm system; Based on the dynamic model, the control target is to track the reference compensation trajectory of each lifting arm in the heave motion, the optimization target is to minimize the tracking error, and the motion constraints of each lifting arm and the position and speed constraints after the lifting arm motion are used as constraint conditions to obtain the optimal control strategy to control the motion of each lifting arm. Represents the attitude angle of the load based on the position and velocity of the lift arm , specifically: ； The simplified kinetic model obtained is: ； ； ； in, They are respectively a first transverse lifting arm stroke, a second transverse lifting arm stroke, a first longitudinal lifting arm stroke, and a second longitudinal lifting arm stroke; are respectively a first transverse lifting arm speed, a second transverse lifting arm speed, a first longitudinal lifting arm speed, and a second longitudinal lifting arm speed; is a function of the lift arm travel and load attitude angle. The partial derivative of Represents state variables; denote the inertia matrix, Coriolis matrix, gravity matrix and control vector respectively; for The second-order derivative of for The first derivative of ; The optimization goal is: ； in, is the input increment; To consider the state equation of the input increment; is the prediction interval for model predictive control; Indicates that the state variable is in the prediction iteration The value after the second; are all weight matrices; The constraints are: ； in, is the maximum and minimum value of the lifting arm position; is the maximum and minimum value of the lifting arm speed; Maximum and minimum values ​​entered for lift arm motion; is the changing trend of the state variable; are the state variables at time k and time k+1 considering the input increment respectively; is the input increment; They are the state transfer matrix and input matrix of the new state equation respectively; is the state variable at time k+i considering the input increment; for The first derivative of ; is the control input at time k+i.

2. A method for coordinated heave compensation control of a dual-shipborne lifting arm system according to claim 1, characterized in that: The dimension of the expanded state variable is defined as ; The new state equation obtained is: ; in: ； ； Among them, F is the state transfer matrix after dimension expansion, and G is the input matrix after dimension expansion; The matrices are All row vectors of ; The matrices are All row vectors of .

3. A method for coordinated heave compensation control of a dual-shipborne lifting arm system as claimed in claim 1, characterized in that: The state equation of the dynamic model is approximately linearized based on the real-time state variables and real-time action input. The approximate linearized state equation is: in, are real-time state variables and real-time action inputs; matrices A and B are both discretized state space model matrices; is the state variable; is the control vector; for The first-order derivative of ; F is the state transfer matrix after dimension expansion, and G is the input matrix after dimension expansion.

4. A coordinated heave compensation control system for a dual-ship-borne lifting arm system, characterized in that: include: A model building module is configured to build a dynamic model of the double ship-borne lifting arm system based on two longitudinal lifting arms, two transverse lifting arms and a load, taking the position and speed of each lifting arm as state variables, and representing the attitude angle state variable of the load based on the position and speed of the lifting arm; The optimization control module is configured to obtain an optimal control strategy based on the dynamic model, with tracking the reference compensation trajectory of each lifting arm in the heave motion as the control target, minimizing the tracking error as the optimization target, and taking the motion constraint of each lifting arm and the position and speed constraints after the lifting arm motion as constraint conditions, so as to control the motion of each lifting arm; Represents the attitude angle of the load based on the position and velocity of the lift arm , specifically: ； The simplified kinetic model obtained is: ； ； ； in, They are respectively a first transverse lifting arm stroke, a second transverse lifting arm stroke, a first longitudinal lifting arm stroke, and a second longitudinal lifting arm stroke; are respectively a first transverse lifting arm speed, a second transverse lifting arm speed, a first longitudinal lifting arm speed, and a second longitudinal lifting arm speed; is a function of the lift arm travel and load attitude angle. The partial derivative of Represents state variables; denote the inertia matrix, Coriolis matrix, gravity matrix and control vector respectively; for The second-order derivative of for The first derivative of ; The optimization goal is: ； in, is the input increment; To consider the state equation of the input increment; is the prediction interval for model predictive control; Indicates that the state variable is in the prediction iteration The value after the second; are all weight matrices; The constraints are: ； in, is the maximum and minimum value of the lifting arm position; is the maximum and minimum value of the lifting arm speed; Maximum and minimum values ​​entered for lift arm motion; is the changing trend of the state variable; are the state variables at time k and time k+1 considering the input increment respectively; is the input increment; They are the state transfer matrix and input matrix of the new state equation respectively; is the state variable at time k+i considering the input increment; for The first derivative of ; is the control input at time k+i.

5. An electronic device, characterized in that: The invention comprises a memory and a processor and computer instructions stored in the memory and executed on the processor, wherein when the computer instructions are executed by the processor, the method according to any one of claims 1 to 3 is completed.

6. A computer-readable storage medium, characterized in that: Used to store computer instructions, which, when executed by a processor, complete the method described in any one of claims 1 to 3.

7. A computer program product, characterized in that The invention comprises a computer program, which, when executed by a processor, implements the method according to any one of claims 1 to 3.

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