Adaptive trajectory tracking control method and system for marine lifting arm based on neural network

Abstract

The present invention relates to the field of electromechanical system control technology, specifically to a method for adaptive trajectory tracking control of a marine lifting arm based on a neural network, wherein a dynamic model of a marine three-degree-of-freedom lifting arm system is established by using the Lagrangian method, and the dynamic characteristics of the marine three-degree-of-freedom lifting arm system are analyzed, wherein the dynamic model includes three driving state quantities, which are the displacements of the lateral, longitudinal and vertical lifting arms. The present invention establishes a dynamic model of a marine lifting arm system by using the Lagrangian method, and designs a nonlinear controller to compensate for the three-degree-of-freedom motion of the ship. By constructing constraint terms, the nonlinear controller effectively limits the motion of the lifting arm within a predetermined range, and the safety of the lifting operation can be ensured even in severe sea conditions. A neural network is used to estimate the parameter / structural uncertainty and nonlinear input dead zone of the lifting arm system, and the neural network update law takes physical constraints into consideration to ensure that the lifting arm operates within a safe range.

Description

Technical Field

[0001] The present invention relates to the technical field of electromechanical system control, and in particular to a method and system for adaptive trajectory tracking control of a marine lifting arm based on a neural network. Background Art

[0002] The marine lifting arm system is a new type of lifting equipment used for dismantling large offshore platforms. Due to factors such as high maintenance costs and environmental degradation, many offshore oil and gas platforms are close to being scrapped and are scheduled to be shut down. The dismantling of the upper part of the offshore platform is an important and challenging task in the decommissioning of the platform. The overall dismantling scheme using the offshore lifting system has attracted the attention of some scholars. This scheme lifts the entire upper deck structure from the jacket structure and transfers it to the transport barge by the offshore lifting system. However, the marine lifting arm system is usually subject to disturbances such as continuous interference from the ship, uncertain dynamics, and physical constraints, which brings major challenges to the controller system design. Therefore, it is meaningful to study an active compensation control system that can stabilize the motion of the offshore lifting arm system.

[0003] In order to study the offshore hull motion compensation control system, many studies have focused on the compensation of the hull's heave motion, and designed heave compensation systems such as anti-disturbance controllers and sliding mode control to offset the impact of the hull's heave motion on the crane load position. However, the hull motion is not just heave motion. Under complex sea conditions, random waves can induce the ship to produce six-degree-of-freedom motion, including translational motion in three directions (surge, roll and heave) and rotational motion on three axes (roll, pitch and yaw). Researchers found that the heave, roll and pitch of the hull are the three most important motions affecting the hull. Therefore, many studies have designed hull motion compensation control systems such as second-order sliding film and adaptive nonlinear for these three main hull motions.

[0004] However, the ship lifting arm system is different from the traditional ship crane. The three degrees of freedom of the lifting arm system are rigid structures and have certain physical limitations. For example, the track length of the lifting arm movement is limited, so the lifting arm is only allowed to move within the specified range of motion. Otherwise, if the lifting arm hits the edge quickly, the track may be damaged, thereby causing a safety accident. In addition, there are uncertain parameters in the lifting arm system. The influence of external disturbances will seriously affect the control effect of the ship lifting control system. Therefore, it is necessary to design a motion compensation control system, which not only positions the lifted waste platform to the desired position, but also meets the physical constraints of the lifting arm system to prevent collision with the edge, and has strong robustness to external interference and parameter uncertainty.

[0005] In view of this, the present application proposes a method and system for adaptive trajectory tracking control of a marine lifting arm based on a neural network. Summary of the invention

[0006] The object of the present invention is to provide a method and system for adaptive trajectory tracking control of a marine lifting arm based on a neural network to solve the above-mentioned problems.

[0007] To achieve the above object, the present invention provides the following technical solutions:

[0008] The method for adaptive trajectory tracking control of a marine lifting arm based on a neural network comprises the following steps:

[0009] Ⅰ. The dynamic model of the three-degree-of-freedom lifting arm system for ships is established by using the Lagrangian method, and the dynamic characteristics of the three-degree-of-freedom lifting arm system for ships are analyzed. The dynamic model includes three driving state quantities, namely the displacement of the lateral, longitudinal and vertical lifting arms;

[0010] II. Designing a nonlinear controller based on a dynamic model of a three-degree-of-freedom lifting arm system for a ship, wherein the nonlinear controller compensates for the three-degree-of-freedom motion of the ship, wherein the three-degree-of-freedom motion of the ship includes heave, roll and pitch motion;

[0011] III. Constructing displacement constraint terms based on the dynamic model of the marine three-degree-of-freedom lifting arm system, the nonlinear controller limits the movement of the three sub-lifting arm mechanisms within a predetermined safety range and decelerates in advance when approaching the safety area. The three sub-lifting arm mechanisms include a transverse lifting arm, a longitudinal lifting arm and a vertical lifting arm;

[0012] IV. The neural network compensation term approximates the uncertain parameters using radial basis function neural network, and estimates the parameter / structural uncertainty and nonlinear input dead zone of the lifting arm system;

[0013] V. Design of neural network update rate considering displacement constraints of three sub-lifting arm mechanisms based on radial basis function neural network.

[0014] Furthermore, in step I, the following steps are included:

[0015] A1. Considering only the three-degree-of-freedom motion of the ship, two right-hand coordinate systems are introduced to describe the dynamic model of the three-degree-of-freedom lifting arm system of the ship, where (o g -x g y g z g ) is the Earth-fixed coordinate system, (o s -x s y s z s ) is the ship coordinate system, the origin of which is located at the rotation center, and the lifting arm system consists of a transverse lifting arm and a vertical arm that move translationally along the track;

[0016] A2. Based on the Lagrangian method, the dynamic model of the marine three-degree-of-freedom lifting arm system is established. When the dynamic equation of the dynamic model is rewritten into a compact matrix-vector form, it is expressed as follows:

[0017]

[0018] Where q = [q1q1q2] · =[d x d y d z ] · Defined as the system state vector, U = [u x u y u z ] · and ΔU=[Δu x Δu y Δu z ]·|,Δu i (i=x,y,z) also includes the influence of friction, F r =[F rx F ry F rz ] · is the disturbance vector caused by the motion of the ship, d x , d y , d z They are the lateral displacement of the lateral lifting arm, the longitudinal displacement of the lateral lifting arm, and the vertical lifting arm displacement;

[0019] A3. There is a dead zone in the driving system of the lifting arm. In order to represent the dead zone, the control force of the lifting arm, i.e., the lateral control force of the lateral lifting arm, f x , lateral lifting arm longitudinal control force f y , vertical lifting arm control force f z , there are the following expressions:

[0020]

[0021] Among them, u x ,u y ,u z are the original control input signals calculated by the lifting arm system controller in the x, y, and z directions, respectively, and b l and b r Respectively represent the upper and lower bounds of the dead zone, g l (·) and g r (·) is an unknown nonlinear function related to the characteristics of the lift arm actuator. For a simple expression, the input with dead zone is usually expressed as f i =u x +Δu i (i=x,y,z), where Δui (i=x,y,z) represents the difference between the controller output and the actual control force.

[0022] Further, in step III, the following steps are included:

[0023] B1. The nonlinear controller limits the displacement of the lifting arm to a preset constraint range. The desired position of the lifted load is defined as the Earth-fixed coordinates in space (o g -x g y g z g ) d y d z d ] · ;

[0024] B2. After calculation, the expected position of the system state variable in the hull coordinates [x sd ,y sd ,z sd ] · , the expression is as follows:

[0025]

[0026] B3. The lifting arm moves within the range of its guide rail, that is:

[0027] q imin <q i <q imax ,(i=1,2,3)

[0028] Among them, q imin and q imax are the upper and lower bounds of the range due to track length limitations.

[0029] A marine lifting arm adaptive trajectory tracking control system based on neural network and a marine lifting arm system control system based on nonlinear controller include a nonlinear control unit, a lifting arm unit, a physical restriction unit and a neural network adaptive parameter unit.

[0030] Further, the lifting arm unit includes the following process:

[0031] C1. Since it is difficult to obtain the accurate values ​​of various variables in the actual application of the offshore lifting arm system, there are unknown parts of the system variables in the dynamic equation of the dynamic model in step A2. Q can be expressed as two parts, namely Q=Q0+ΔQ, where Q0 is the nominal value of Q and ΔQ is the uncertain part of Q. The dynamic equation of the lifting arm system is rewritten as follows:

[0032]

[0033] Where: D≡ΔQU+Q(ΔU+F v +G) represents the external perturbation and parameter uncertainty of the lifting arm system;

[0034] C2. Use neural network to approximate the unknown term D, which can be expressed as:

[0035] D=W * S(x)+ξ(x)

[0036] Where x∈R q is the input of the neural network, W∈R N Represents the weight vector of the neural network, W * represents the optimal weight vector D of the unknown term, ξ(x) is the optimal approximation error, S(x)=[s1(x)s2(x)…s N (x)] * ∈R N is the basis function vector;

[0037] C3,s i (x) is chosen as a Gaussian function, expressed as follows:

[0038]

[0039] Among them, μ i and Represent the width and center vector of the Gaussian function respectively.

[0040] Furthermore, the physical restriction unit includes the following process:

[0041] D1. In order to achieve motion compensation of the lifting arm system without exceeding the preset motion range, a scalar function is defined based on the artificial potential field method to represent a limited state range, which consists of an attractive potential field and a repulsive potential field. The attractive potential is designed as follows:

[0042]

[0043] Among them, Δ1=diag(λ1λ2λ3)∈R 3×3 is the diagonal gain matrix;

[0044] D2. The repulsive potential is related to the distance between the lifting arm and the limit of the restricted range. When the lifting arm approaches the boundary, the repulsive potential increases, and when the lifting arm moves away from the boundary, the repulsive potential decreases. The values ​​of the repulsive potential are as follows:

[0045]

[0046] Among them, k m is a positive gain;

[0047] D3, the tracking error vector of the lifting arm e=(e1e2e3)∈R 3 The definition is as follows:

[0048] e i =q i -q id ,i=1,2,3;

[0049] D4. Combining the gradient and error vector of the artificial potential field method, we get a filter vector r = (r1r2r3)∈R 3 The definition is as follows:

[0050]

[0051] Where Δ2=diag(y1y2y3)∈R 3×3 is a diagonal gain matrix, and is the gradient of the attractive potential function and the repulsive potential function relative to the position vector of the lifting arm. In the above formula, for

[0052] D5. Differentiate r with time and you can get the following results:

[0053]

[0054] in,

[0055] Furthermore, the neural network adaptive parameter unit includes the following process:

[0056] E1. The following control law based on adaptive neural network is proposed:

[0057]

[0058] in, To control the gain, is an estimate vector of weight vectors;

[0059] E2. In order to obtain the optimal weight vector W of the neural network * i , and proposed the following update rule:

[0060]

[0061] in,

[0062] Furthermore, by considering the constraints in the update rule As the arm approaches the upper bound, the update rate of the weight vector increases, and as the arm approaches the lower bound, the update rate of the weight vector decreases.

[0063] Beneficial effects of the present invention:

[0064] 1. In the present invention, a ship lifting arm system is proposed, and a dynamic model of a ship three-degree-of-freedom lifting arm is established by using the Lagrangian method. Based on the dynamic model, the dynamic characteristics of the ship three-degree-of-freedom lifting arm system are analyzed. Based on the dynamic model, a nonlinear controller is designed to compensate for the three-degree-of-freedom motion of the ship. Without linearizing the dynamic model, a lifting arm system trajectory tracking control method is proposed to transfer the payload to the desired position. The controller theoretically guarantees the motion range of the lifting arm by introducing a repulsive force function, and can ensure the safety of lifting operations even in severe sea conditions, thereby ensuring the stability of the closed-loop system.

[0065] 2. In the present invention, a neural network compensation term is designed to approximate uncertain parameters in the presence of unknown continuous interference to the lifting arm, thereby improving the positioning accuracy of the lifting arm. When designing the update rate of the neural network, physical limitations are also taken into consideration, further ensuring that the lifting arm operates within a safe range. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 Schematic diagram of the structure of the marine lifting arm system according to an embodiment of the present invention;

[0067] Figure 2 It is a control system block diagram of the marine lifting arm system described in an embodiment of the present invention;

[0068] Figure 3 1 is a comparison diagram of experimental results of the adaptive lifting arm trajectory tracking control method (dotted line) and the traditional control method (dashed line) at three lifting arm positions under physical constraints in an embodiment of the present invention;

[0069] Figure 4 A comparison diagram of the experimental results of the lifting point position under physical constraints between the adaptive lifting arm trajectory tracking control method (b) described in the embodiment of the present invention and the traditional control method (a);

[0070] Figure 5 1 is a comparison diagram of experimental results of the adaptive lifting arm trajectory tracking control method (dotted line) and the traditional control method (dashed line) at three lifting arm positions when the hull moves faster in an embodiment of the present invention;

[0071] Figure 6 1 is a comparison chart of experimental results of the adaptive lifting arm trajectory tracking control method (b) described in an embodiment of the present invention and the traditional control method (a) at three lifting arm positions when the hull moves faster. DETAILED DESCRIPTION

[0072] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0073] Example 1: Please refer to Figure 1 and Figure 2 , this design proposes an implementation method, a neural network-based marine lifting arm adaptive trajectory tracking control method, comprising the following steps:

[0074] Ⅰ. The dynamic model of the three-degree-of-freedom lifting arm system for ships is established by using the Lagrangian method, and the dynamic characteristics of the three-degree-of-freedom lifting arm system for ships are analyzed. The three-degree-of-freedom motion of the crane ship is considered as disturbance: heave, roll, and pitch. The dynamic model contains three driving state quantities, which are the lateral, longitudinal, and vertical displacements of the lifting arm. Figure 1 It is a schematic diagram of the structure of the marine lifting arm system in a three-dimensional environment. The relevant physical parameters and definitions of the lifting arm system are shown in Table 1:

[0075] Table 1: System parameters

[0076]

[0077]

[0078] The steps include:

[0079] A1. Since the crane ship adopts a dynamic positioning system and is huge, the drift force generated by wind and water flow is ignored. Only the three-degree-of-freedom motion of the ship is considered. Two right-handed coordinate systems are introduced to describe the dynamic model of the ship's three-degree-of-freedom lifting arm system, where (o g -x g y g z g ) is the Earth-fixed coordinate system, (o s -x s y s z s ) is the ship coordinate system, the origin of which is located at the rotation center, and the lifting arm system consists of a transverse lifting arm and a vertical arm that move translationally along the track;

[0080] A2. Based on the Lagrangian method, the dynamic model of the marine three-degree-of-freedom lifting arm system is established. The dynamic equation of the model is as follows:

[0081]

[0082]

[0083] In order to simplify the expression, the kinetic equation of the above kinetic model is rewritten into a compact matrix-vector form as follows:

[0084]

[0085] Where q = [q1q1q2] · =[d x d y d z ] · Defined as the system state vector, U = [u x u y u z ] · and ΔU=[Δu x Δu y Δu z ]·|,Δu i (i=x,y,z) also includes the influence of friction (such as lift arm-track friction), F r =[F rx F ry F rz ] · is the disturbance vector caused by the motion of the ship, d x , d y , d z They are the lateral displacement of the lateral lifting arm, the longitudinal displacement of the lateral lifting arm, and the vertical lifting arm displacement;

[0086] A3. There is a dead zone in the driving system of the lifting arm. In order to represent the dead zone, the control force of the lifting arm, i.e., the lateral control force of the lateral lifting arm, f x , lateral lifting arm longitudinal control force f y , vertical lifting arm control force f z , there are the following expressions:

[0087]

[0088] Among them, u x ,u y ,u z are the original control input signals calculated by the lifting arm system controller in the x, y, and z directions, respectively, and b l and b r Respectively represent the upper and lower bounds of the dead zone, g l (·) and g r (·) is an unknown nonlinear function related to the characteristics of the lift arm actuator. For a simple expression, the input with dead zone is usually expressed as f i =u x +Δu i(i=x,y,z), where Δu i (i=x,y,z) represents the difference between the controller output and the actual control force;

[0089] II. Design a nonlinear controller based on the dynamic model of the ship's three-degree-of-freedom lifting arm system. The nonlinear controller compensates for the ship's three-degree-of-freedom motion, which includes heave, roll and pitch motion.

[0090] III. Constructing displacement constraint items based on the dynamic model of the marine three-degree-of-freedom lifting arm system. The nonlinear controller limits the movement of the three sub-lifting arm mechanisms within a predetermined safety range and decelerates in advance when approaching the safety area to prevent rapid collision with the boundary of the lifting arm. The three sub-lifting arm mechanisms include a transverse lifting arm, a longitudinal lifting arm and a vertical lifting arm, including the following steps:

[0091] B1. The nonlinear controller limits the displacement of the lifting arm to a preset constraint range. The desired position of the lifted load is defined as Figure 1 The space earth fixed coordinates (o g -x g y g z g ) d y d z d ] · ;

[0092] B2. After calculation, the expected position of the system state variable in the hull coordinates [x sd ,y sd ,z sd ] · , the expression is as follows:

[0093]

[0094] B3. To improve the safety of the operation process, the lifting arm moves within the range of its guide rail, that is:

[0095] q imin <q i <q imax ,(i=1,2,3)

[0096] Among them, q imin and q imax are the upper and lower bounds of the range due to track length limitations, respectively;

[0097] IV. The neural network compensation term approximates the uncertain parameters using radial basis function neural network, and estimates the parameter / structural uncertainty and nonlinear input dead zone of the lifting arm system;

[0098] V. The neural network update rate based on the radial basis function neural network is designed considering the displacement constraints of the three sub-lifting arm mechanisms, which further ensures the stability of the system.

[0099] Example 2: Please refer to Figure 1 and Figure 2 This design proposes an implementation method, a neural network-based ship lifting arm adaptive trajectory tracking control system, including a nonlinear control unit, a lifting arm unit, a physical restriction unit and a neural network adaptive parameter unit. An adaptive nonlinear controller designed by the present invention is used to eliminate the continuous external interference of the ship's motion caused by waves, and at the same time limit the displacement of the lifting arm within a preset constraint range; the lifting arm unit includes the following processes:

[0100] C1. In order to describe the controller design process more clearly, Figure 2 The block diagram of the control system is shown. Since it is difficult to obtain the accurate values ​​of various variables in the offshore lifting arm system in practical applications, there are unknown parts of the system variables in the dynamic equation of the dynamic model in step A2. Q can be expressed as two parts, namely Q=Q0+ΔQ, where Q0 is the nominal value of Q and ΔQ is the uncertain part of Q. The dynamic equation of the lifting arm system is rewritten as follows:

[0101]

[0102] Where: D≡ΔQU+Q(ΔU+F v +G) represents the external perturbation and parameter uncertainty of the lifting arm system;

[0103] C2. In order to obtain higher control performance, a neural network is used to approximate the unknown term D, which can be expressed as:

[0104] D=W * S(x)+ξ(x)

[0105] Where x∈R q is the input of the neural network, W∈R N Represents the weight vector of the neural network, W * represents the optimal weight vector D of the unknown term, ξ(x) is the optimal approximation error, S(x)=[s1(x)s2(x)…s N (x)] * ∈R N is the basis function vector;

[0106] C3,s i (x) is chosen as a Gaussian function, expressed as follows:

[0107]

[0108] Among them, μi and Respectively represent the width and center vector of the Gaussian function;

[0109] The physical restriction unit includes the following processes:

[0110] D1. In order to achieve motion compensation of the lifting arm system without exceeding the preset motion range, a scalar function is defined based on the artificial potential field method to represent a limited state range, which consists of an attractive potential field and a repulsive potential field. The attractive potential is designed as follows:

[0111]

[0112] Among them, Δ1=diag(λ1λ2λ3)∈R 3×3 is the diagonal gain matrix;

[0113] D2. The repulsive potential is related to the distance between the lifting arm and the limit of the restricted range. When the lifting arm approaches the boundary, the repulsive potential increases, and when the lifting arm moves away from the boundary, the repulsive potential decreases. The values ​​of the repulsive potential are as follows:

[0114]

[0115] Among them, k m is a positive gain;

[0116] D3, the tracking error vector of the lifting arm e=(e1e2e3)∈R 3 The definition is as follows:

[0117] e i =q i -q id ,i=1,2,3;

[0118] D4. Combining the gradient and error vector of the artificial potential field method, we get a filter vector r = (r1r2r3)∈R 3 The definition is as follows:

[0119]

[0120] Where Δ2=diag(y1y2y3)∈R 3×3 is a diagonal gain matrix, and is the gradient of the attractive potential function and the repulsive potential function relative to the position vector of the lifting arm. In the above formula, for

[0121] D5. Yes r By performing time differentiation, we can obtain the following results:

[0122]

[0123] in,

[0124] The neural network adaptive parameter unit includes the following processes:

[0125] E1. The following control law based on adaptive neural network is proposed:

[0126]

[0127] in, To control the gain, is an estimate vector of weight vectors;

[0128] E2. In order to obtain the optimal weight vector W of the neural network * i , and proposed the following update rule:

[0129]

[0130] in,

[0131] In this embodiment, in many neural networks, the updating rule of the weight vector is only related to the control error, and the physical restriction is an external disturbance to the neural network. Therefore, when the desired position of the lifting arm is set outside the safe area, as the lifting arm approaches the physical boundary, the neural network will tend to reduce the positioning error, and the restriction term will prevent the lifting arm from exceeding the boundary. Therefore, the directions of the two forces will conflict, causing the weight of the neural network to continue to increase and tend to infinity. Therefore, the present invention takes the constraint term into account in the updating rule. As the arm approaches the upper bound, the update rate of the weight vector increases, resulting in a large negative force in the controller. As the arm approaches the lower bound, the update rate of the weight vector decreases, resulting in a large positive force in the controller, further preventing the arm from moving out of the allowed range.

[0132] Stability Analysis: See Figure 3 - Figure 6 In order to prove the stability of the closed-loop control system of the lifting arm system, the following positive definite Lyapunov candidate function is proposed:

[0133]

[0134] in, is the estimated error vector;

[0135] By taking the time derivative of V(t) and using the dynamic model, we can get the following results:

[0136]

[0137] Then, the control law based on the adaptive neural network in step E1 and the update law in step E2 are substituted into the above results to obtain the following formula:

[0138]

[0139] The following inequality holds:

[0140]

[0141] Therefore, the following differential equation is further derived:

[0142]

[0143] in and κ represents the appropriate control gain;

[0144] According to the above differential equation, we can get:

[0145]

[0146] This means:

[0147]

[0148] In the formula express The maximum eigenvalue of

[0149] Then we can get the filter vector of the neural network r and the weight error vector Uniformly eventually bounded, that is:

[0150]

[0151] According to the above formula, we can draw the following conclusions:

[0152]

[0153] It can be clearly seen that as long as the initial position of the lifting arm q i In (q imin ,q imax ) within the preset range, the lifting arm cannot exceed the preset range during the entire control process, otherwise, there must be a moment T c Satisfy q i Close to the preset boundary q imax or q imin This causes V(t) to go to infinity, which is consistent with V(t)∈L ∞ Therefore, the lifting arm will not exceed the preset range in the closed loop system, that is:

[0154]

[0155] From the above derivation, it can be seen that the lifting arm tracking error and speed are ultimately uniformly bounded (UUB), thereby achieving the control target, indicating that the controller designed by the present invention can enable the marine lifting arm system to achieve accurate trajectory tracking and motion compensation of the hull.

[0156] Method validation and comparison: see Figure 3 - Figure 6 In order to ensure the effectiveness of the method of the present invention, it is first compared with the existing control method, in which a restricted area q is set. 3max =0.32m, Figure 3 The figure shows the position comparison of the lifting arm mechanism. It can be seen from the figure that the proposed method achieves excellent tracking performance and significantly reduces the impact of the dead zone on the tracking control performance. In addition, the traditional algorithm does not consider the operation constraints. The red dotted line in the figure is the upper limit of the safety area. When approaching the boundary value, the traditional method does not slow down, but directly impacts the physical limit boundary at a higher speed, which potentially increases the risk of actuator damage. The controller can slow down in advance and ensure that the vertical lifting arm does not collide with the physical limit boundary. Figure 4 The position change of the load position (lifting point) in the inertial coordinate system shows that the load motion range of the proposed method is significantly smaller than that of the traditional controller;

[0157] Then the speed of the ship is increased, and the experimental results are as follows Figure 5 , Figure 6 As shown, it can be seen that since the proposed controller approximates the internal parameter uncertainty and dead zone characteristics through a neural network, the controller of the present invention can effectively cope with more complex ship motions, that is, under different sea conditions, the trajectory tracking accuracy and the load motion range have achieved better performance, and the load movement is in a smaller range. In contrast, traditional controllers often show larger tracking errors when the ship moves faster, and lead to a larger load motion range.

[0158] The present invention proposes a trajectory tracking control method for a marine lifting arm system with an adaptive neural network with state constraints. First, a dynamic model of a marine lifting arm system is established by using the Lagrangian method. Then, a nonlinear controller is designed based on the dynamic model to compensate for the three-degree-of-freedom motion of the ship, including heave motion, roll motion and pitch motion. By constructing constraint terms, the nonlinear controller effectively limits the motion of the lifting arm within a predetermined range, effectively compensates for the motion of the ship under wave disturbance, and can not only position the lifted waste platform to a desired position, but also meet the physical constraints of the lifting arm system to prevent collision with the edge, and ensure the safety of the lifting operation even in severe sea conditions. The neural network is used to estimate the parameter / structural uncertainty and nonlinear input dead zone of the lifting arm system. In particular, the designed neural network update law takes physical constraints into consideration, thereby further ensuring that the lifting arm operates within a safe range. The theoretical stability of the proposed control system is strictly proved by using the Lyapunov technology. Finally, the practicability and effectiveness of the proposed method are verified by experiments. The experimental results show that compared with the existing method, the designed trajectory tracking has higher accuracy and stronger safety.

[0159] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for adaptive trajectory tracking control of marine lifting arms based on neural networks, characterized in that: The following steps are involved: Ⅰ. The dynamic model of the three-degree-of-freedom lifting arm system for ships is established by using the Lagrangian method, and the dynamic characteristics of the three-degree-of-freedom lifting arm system for ships are analyzed. The dynamic model includes three driving state quantities, namely the displacement of the lateral, longitudinal and vertical lifting arms; II. Designing a nonlinear controller based on a dynamic model of a three-degree-of-freedom lifting arm system for a ship, wherein the nonlinear controller compensates for the three-degree-of-freedom motion of the ship, wherein the three-degree-of-freedom motion of the ship includes heave, roll and pitch motion; III. Constructing displacement constraint terms based on the dynamic model of the marine three-degree-of-freedom lifting arm system, the nonlinear controller limits the movement of the three sub-lifting arm mechanisms within a predetermined safety range and decelerates in advance when approaching the safety area. The three sub-lifting arm mechanisms include a transverse lifting arm, a longitudinal lifting arm and a vertical lifting arm; IV. The neural network compensation term approximates the uncertain parameters using radial basis function neural network, and estimates the parameter / structural uncertainty and nonlinear input dead zone of the lifting arm system; V. Design of neural network update rate considering displacement constraints of three sub-lifting arm mechanisms based on radial basis function neural network.

2. The method for adaptive trajectory tracking control of a marine lifting arm based on a neural network according to claim 1, characterized in that: In step I, the following steps are included: A1. Considering only the three-degree-of-freedom motion of the ship, two right-hand coordinate systems are introduced to describe the dynamic model of the three-degree-of-freedom lifting arm system of the ship, where (o g -x g y g z g ) is the Earth-fixed coordinate system in space, (o s -x s y s z s ) is the ship coordinate system, the origin of which is located at the rotation center, and the lifting arm system consists of a transverse lifting arm and a vertical arm that move translationally along the track; A2. Based on the Lagrangian method, the dynamic model of the marine three-degree-of-freedom lifting arm system is established. When the dynamic equation of the dynamic model is rewritten into a compact matrix-vector form, it is expressed as follows: Where q = [q1q1q2] · =[d x d y d z ] · Defined as the system state vector, U = [u x u y u z ] · and ΔU=[Δu x Δu y Δu z ]·|,Δu i (i=x,y,z) also includes the influence of friction, F r =[F rx F ry F rz ] · is the disturbance vector caused by the motion of the ship, d x , d y , d z They are the lateral displacement of the lateral lifting arm, the longitudinal displacement of the lateral lifting arm, and the vertical lifting arm displacement; A3. There is a dead zone in the driving system of the lifting arm. In order to represent the dead zone, the control force of the lifting arm, i.e., the lateral control force of the lateral lifting arm, f x , lateral lifting arm longitudinal control force f y , vertical lifting arm control force f z , there are the following expressions: Among them, u x ,u y ,u z are the original control input signals calculated by the lifting arm system controller in the x, y, and z directions, respectively, and b l and b r Respectively represent the upper and lower bounds of the dead zone, g l (·) and g r (·) is an unknown nonlinear function related to the characteristics of the lift arm actuator. For a simple expression, the input with dead zone is usually expressed as f i =u x +Δu i (i=x,y,z), where Δu i (i=x,y,z) represents the difference between the controller output and the actual control force.

3. The method for adaptive trajectory tracking control of a marine lifting arm based on a neural network according to claim 2, characterized in that: In step III, the following steps are included: B1. The nonlinear controller limits the displacement of the lifting arm to a preset constraint range. The desired position of the lifted load is defined as the Earth-fixed coordinates in space (o g -x g y g z g ) d y d z d ] · ; B2. After calculation, the expected position of the system state variable in the hull coordinates [x sd ,y sd ,z sd ] · , the expression is as follows: B3. The lifting arm moves within the range of its guide rail, that is: q imin <q i <q imax ,(i=1,2,3) Among them, q imin and q imax are the upper and lower bounds of the range due to track length limitations.

4. A marine lifting arm adaptive trajectory tracking control system based on a neural network, applicable to a marine lifting arm adaptive trajectory tracking control method based on a neural network according to any one of claims 1 to 3, characterized in that: A control system for a marine lifting arm system based on a nonlinear controller comprises a nonlinear control unit, a lifting arm unit, a physical restriction unit and a neural network adaptive parameter unit.

5. The neural network-based adaptive trajectory tracking control system for marine lifting arms according to claim 4 is characterized in that: The lifting arm unit includes the following processes: C1. Since it is difficult to obtain the accurate values ​​of various variables in the actual application of the offshore lifting arm system, there are unknown parts of the system variables in the dynamic equation of the dynamic model in step A2. Q can be expressed as two parts, namely Q=Q0+ΔQ, where Q0 is the nominal value of Q and ΔQ is the uncertain part of Q. The dynamic equation of the lifting arm system is rewritten as follows: Where: D≡ΔQU+Q(ΔU+F v +G) represents the external perturbation and parameter uncertainty of the lifting arm system; C2. Use neural network to approximate the unknown term D, which can be expressed as: D=W * S(x)+ξ(x) Where x∈R q is the input of the neural network, W∈R N Represents the weight vector of the neural network, W * represents the optimal weight vector D of the unknown term, ξ(x) is the optimal approximation error, S(x)=[s1(x)s2(x)…s N (x)] * ∈R N is the basis function vector; C3,s i (x) is chosen as a Gaussian function, expressed as follows: Among them, μ i and Represent the width and center vector of the Gaussian function respectively.

6. The neural network-based adaptive trajectory tracking control system for marine lifting arms according to claim 5, characterized in that: The physical restriction unit includes the following processes: D1. In order to achieve motion compensation of the lifting arm system without exceeding the preset motion range, a scalar function is defined based on the artificial potential field method to represent a limited state range, which consists of an attractive potential field and a repulsive potential field. The attractive potential is designed as follows: Among them, Δ1=diag(λ1λ2λ3)∈R 3×3 is the diagonal gain matrix; D2. The repulsive potential is related to the distance between the lifting arm and the limit of the restricted range. When the lifting arm approaches the boundary, the repulsive potential increases, and when the lifting arm moves away from the boundary, the repulsive potential decreases. The values ​​of the repulsive potential are as follows: Among them, k m is a positive gain; D3, the tracking error vector of the lifting arm e=(e1e2e3)∈R 3 The definition is as follows: e i =q i -q id ,i=1,2,3; D4. Combining the gradient and error vector of the artificial potential field method, we get a filter vector r = (r1r2r3)∈R 3 The definition is as follows: Where Δ2=diag(y1y2y3)∈R 3×3 is a diagonal gain matrix, and is the gradient of the attractive potential function and the repulsive potential function relative to the position vector of the lifting arm. In the above formula, for D5. Yes r By performing time differentiation, we can obtain the following results: in, 7. The neural network-based adaptive trajectory tracking control system for marine lifting arms according to claim 6, characterized in that: The neural network adaptive parameter unit includes the following process: E1. The following control law based on adaptive neural network is proposed: in, To control the gain, is an estimate vector of weight vectors; E2. In order to obtain the optimal weight vector of the neural network W * i , and proposed the following update rule: in, 8. The neural network-based adaptive trajectory tracking control system for marine lifting arms according to claim 7, characterized in that: By taking the constraints into account in the update law As the arm approaches the upper bound, the update rate of the weight vector increases, and as the arm approaches the lower bound, the update rate of the weight vector decreases.

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