Shipborne crane anti-swing control method and system

Abstract

The invention relates to the technical field of shipborne crane anti-swing, and discloses a shipborne crane anti-swing control method and system.The method comprises the steps that a ship coordinate system is established, relative kinetic energy of a crane is calculated according to the ship coordinate system, inertia force is added into generalized force of all degrees of freedom, and the relative kinetic energy is obtained; the method comprises the following steps of: analyzing to obtain a dynamic model of suspension arm motion and load swing, constructing self-adaptive sliding mode anti-swing control according to the combination of an RBF neural network model and sliding mode control, analyzing continuous uncertain upper bound disturbance existing in an underactuated shipborne crane load based on the self-adaptive sliding mode anti-swing control, approaching the continuous disturbance of the uncertain upper bound, and carrying out self-adaptive sliding mode anti-swing control on the underactuated shipborne crane load. The dynamic model is simplified, inversion sliding mode control is introduced to compensate the observation error of a nonlinear disturbance observer, the position of a load is judged, and LQR control and self-adaptive sliding mode anti-swing control are switched according to the judgment result. The device has the characteristics of good anti-swing control and dynamic adjustment.

Description

Technical Field

[0001] The present invention relates to the technical field of anti-sway of shipboard cranes, and more particularly, to an anti-sway control method and system for shipboard cranes. Background Art

[0002] The shipbuilding industry is a modern comprehensive and strategic industry that provides technical equipment for water transportation, ocean resource development, and national defense construction. Shipboard cranes are one of the core equipment in the shipbuilding industry, mainly used for tasks such as cargo transfer, underwater tunnel construction, sunken ship salvage, and underwater hoisting operations and underwater replenishment in cross-sea bridge projects. Shipboard cranes usually work under harsh sea conditions, and external disturbances will cause the movement of the ship to be random, which will not only amplify the swing angle of the load, but also be disturbed during the positioning process of the load.

[0003] Currently, many studies have applied non-linear control methods to the anti-sway control of ship cranes. However, traditional control has many set parameters, resulting in amplitude variation and increased positioning error of the load. Moreover, the load can only remain stable within a small range near the equilibrium point and cannot select effective anti-sway control for other positions.

[0004] Therefore, how to provide an anti-sway control method and system for shipboard cranes is an urgent technical problem to be solved by those skilled in the art. Summary of the Invention

[0005] In view of this, the present invention proposes an anti-sway control method and system for shipboard cranes, aiming to solve the problems that traditional control has many set parameters, resulting in amplitude variation and increased positioning error of the load, and the load can only remain stable within a small range near the equilibrium point.

[0006] On the one hand, the present invention proposes an anti-sway control method for shipboard cranes, including:

[0007] Establish a ship coordinate system and calculate the relative kinetic energy of the crane according to the ship coordinate system, add the inertial force to the generalized force of each degree of freedom, and analyze and obtain the dynamic model of the boom movement and the load swing;

[0008] Combining the RBF neural network model and sliding mode control, construct an adaptive sliding mode anti-sway control, and analyze the continuous uncertain upper bound disturbance existing in the load of the underactuated shipboard crane based on the adaptive sliding mode anti-sway control to approximate the continuous disturbance of the uncertain upper bound;

[0009] Simplify the dynamic model, and use a non-linear disturbance observer to observe the total disturbance; introduce backstepping sliding mode control to compensate for the observation error of the non-linear disturbance observer;

[0010] Compare the adaptive sliding mode anti-sway control and the LQR control, judge the position of the load based on the comparison result and the observation of the non-linear disturbance observer, and switch the LQR control and the adaptive sliding mode anti-sway control according to the judgment result.

[0011] Further, when establishing the ship coordinate system and calculating the relative kinetic energy of the crane according to the ship coordinate system, it includes:

[0012] Take the centroid of the ship as the origin of the ship coordinate system, set the bow direction as the positive direction of the x S axis, set the direction perpendicular to the deck upward as the positive direction of the z S axis, the x G axis is parallel to the x S axis, and the z G axis is perpendicular to the ground;

[0013] Establish the ship coordinate system I S ={x S y S z S}, establish the inertial coordinate system I G ={x G y G z G};

[0014] Set the hook and the load as a particle, with a uniform mass distribution of the boom, the cable has strain and the position of the load does not exceed the highest point of the boom, and measure the angle of the boom and the swing angle of the load relative to the z S axis;

[0015] The relative kinetic energy of the crane is obtained from the following formula:

[0016]

[0017] where E represents the relative kinetic energy of the crane, m represents the mass of the boom, P L represents the length of the boom, represents the generalized velocity of the boom, m P represents the mass of the load, represents the row vector from the origin to the payload, dp p represents the column vector from the origin to the payload.

[0018] Further, when adding the inertial force to the generalized force of each degree of freedom and analyzing the dynamic model of the boom movement and the load swing, it includes:

[0019] The generalized force includes the boom gravity, the load gravity, the boom inertial force and the load inertial force;

[0020] Set the elevation angle of the boom, the length of the cable, and the load swing angle as the generalized coordinates, and set the control torque of the boom elevation and the cable tension as the control inputs to construct the dynamic model.

[0021] Furthermore, when constructing the dynamic model, it includes:

[0022] Establish a dynamic model in the generalized coordinates according to the Lagrange equation of the relative kinetic energy of the crane. The dynamic model is obtained from the following formula:

[0023]

[0024] where M(q) represents the inertia matrix, represents the Coriolis centripetal matrix, U c represents the input control vector, represents the vector of the boom inertia force and the load inertia force, f represents the external force disturbance, represents the acceleration of the generalized coordinates, represents the generalized velocity of the generalized coordinates;

[0025] Judge that the shipborne crane is an underactuated shipborne crane according to the dynamic model.

[0026] Furthermore, when constructing the adaptive sliding mode anti-sway control by combining the RBF neural network model and the sliding mode control, it includes:

[0027] The adaptive sliding mode anti-sway control divides the nominal into several sub-nominals, defines the sliding mode surface of each sub-nominal, establishes a hierarchical sliding mode controller on the sliding mode surface of each sub-nominal, and establishes a lumped sliding mode compensator on the last layer of the sliding mode surface. The Lyapunov function is used to determine that any state deviates from the sub-sliding mode surface, and the total switching control input pulls it back to the deviated sliding mode surface. The RBF neural network model is used to approximate the disturbances to the hierarchical sliding mode controller and the lumped sliding mode compensator.

[0028] Furthermore, when simplifying the dynamic model, it includes:

[0029] Establish a new state vector and transform the dynamic model:

[0030] η 1 = φ - α, η 2 = L, η 3 = θ - α;

[0031] η = [η 1 η 2 η 3 T ;

[0032] ​

[0033] where η represents the generalized coordinate, φ represents the angle of the jib, α represents the rotation angle of the ship about the x S axis, L represents the length of the cable, θ represents the swing of the load relative to the z S axis, η 1 , η 2 and η 3 represent the generalized coordinates, [η 1 η 2 η 3 T represents the vector transpose, M t (η) represents the inertia matrix, represents the Coriolis centripetal matrix, G t (η) represents the gravity vector, U c represents the input control vector, f represents the external force disturbance, represents the generalized acceleration of the generalized coordinate, represents the generalized velocity of the generalized coordinate.

[0034] Furthermore, when using a non - linear disturbance observer to observe the total disturbance and introducing backstepping sliding - mode control to compensate for the observation error of the non - linear disturbance observer, it includes:

[0035] Defining the observation error using a non - linear disturbance observer, setting the dynamic characteristics relative to the non - linear disturbance observer, and determining the error dynamic equation of the non - linear disturbance observer;

[0036] Establishing a matrix to exponentially converge the error dynamic equation and converting the observed disturbance into the control quantity of the corresponding input channel;

[0037] Defining the output error vector and taking the derivative, using the Lyapunov function and adopting the adaptive feedback control law, and obtaining the input according to the Lyapunov function.

[0038] Furthermore, when judging the position of the load, it includes:

[0039] Counting the positions of all historical loads and establishing a position set. When the position of the load exists in the position set, it is determined that the position of the load is not corrected, and the position of the load is determined as the target position;

[0040] When the position of the load does not exist in the position set, it is determined that the position of the load is corrected, and the aggregation algorithm is used to aggregate the position set;

[0041] Taking the position set as the data set to be aggregated;

[0042] Determining that the expected number of clusters k is 2 and initializing the parameters of the Gaussian distribution;​

[0043] Calculate the probability that each data in the dataset to be aggregated belongs to each Gaussian distribution to obtain the responsibility value;

[0044] Obtain a dataset according to the responsibility value, and use the dataset as the proximity set;

[0045] Take the average of the positions of all historical loads in the proximity set as the optimization factor, and use the product value of the optimization factor and the position of the load as the target position.

[0046] Further, when switching between the LQR control and the adaptive sliding mode anti-sway control according to the judgment result, it includes:

[0047] Preset a target position distance threshold;

[0048] When the target position is greater than or equal to the target position distance threshold, adopt the adaptive sliding mode anti-sway control;

[0049] When the target position is less than the target position distance threshold, adopt the LQR control.

[0050] Compared with the prior art, the beneficial effects of the present invention are as follows: The calculation of the relative kinetic energy of the crane in the ship coordinate system is introduced, which can accurately describe the dynamic response of the boom and the load, improve the control accuracy and stability of the load movement, establish a dynamic model based on the boom movement and the load swing, clarify the actual situation of each state, and enhance the scientificity and rigor of the anti-sway control of the shipborne crane. The RBF neural network is used to approximate the disturbance and the sliding mode control is introduced to construct an adaptive sliding mode anti-sway control. The adaptive sliding mode anti-sway control can effectively compensate for the hull swing and wind and wave interference according to the changes of external disturbances and movements, ensuring the stable operation of the shipborne crane in a complex environment. The total disturbance is observed by using a nonlinear disturbance observer, the swing trend of the load is identified, and the observation error is compensated through the backstepping sliding mode control. The active control of the load swing is realized, and the swing amplitude of the load in the horizontal and vertical directions is effectively reduced. According to the position of the load and the observation result of the nonlinear disturbance observer, an intelligent switch is made between the LQR control and the adaptive sliding mode anti-sway control. When there are large disturbances or uncertainties, it is switched to the adaptive sliding mode control to overcome the disturbances of the hull in a complex environment, thereby extending the service life of the shipborne crane and reducing the operation cost and maintenance cost.

[0051] On the other hand, the present application also provides a shipborne crane anti-sway control system for applying the above shipborne crane anti-sway control method, including:

[0052] A model establishment unit is configured to establish a ship coordinate system and calculate the relative kinetic energy of the crane based on the ship coordinate system, add inertial forces to the generalized forces of each degree of freedom, and analyze to obtain a dynamic model of the boom movement and load swing;

[0053] An adaptive sliding mode unit is configured to combine an RBF neural network model and sliding mode control to construct an adaptive sliding mode anti-sway control, analyze the continuous uncertain upper bound disturbance existing in the load of the underactuated shipborne crane based on the adaptive sliding mode anti-sway control, and approximate the continuous disturbance of the uncertain upper bound;

[0054] An inversion unit simplifies the dynamic model, observes the total disturbance using a nonlinear disturbance observer; introduces an inversion sliding mode control to compensate for the observation error of the nonlinear disturbance observer;

[0055] A switching unit compares the adaptive sliding mode anti-sway control and LQR control, judges the position of the load based on the comparison result and the observation of the nonlinear disturbance observer, and switches the LQR control and the adaptive sliding mode anti-sway control according to the judgment result.

[0056] It can be understood that the above-mentioned shipborne crane anti-sway control method and system have the same beneficial effects, which will not be elaborated here. Description of the Drawings

[0057] By reading the following detailed description of the preferred embodiments, various other advantages and benefits will become clear to those of ordinary skill in the art. The drawings are only for the purpose of showing the preferred embodiments and are not considered as a limitation of the present invention. Moreover, throughout the drawings, the same reference numerals are used to represent the same components. In the drawings:

[0058] Figure 1 is a flowchart of a shipborne crane anti-sway control method provided by an embodiment of the present invention;

[0059] Figure 2 is a functional block diagram of a shipborne crane anti-sway control system provided by an embodiment of the present invention;

[0060] Figure 3 is a trajectory diagram under adaptive neural network sliding mode control provided by an embodiment of the present invention;

[0061] Figure 4 is a trajectory diagram of each state variable under inversion sliding mode control provided by an embodiment of the present invention;

[0062] Figure 5 is a curve diagram of the input under inversion sliding mode control provided by an embodiment of the present invention. Detailed Embodiments

[0063] Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although the exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided so that the present disclosure can be more thoroughly understood and the scope of the present disclosure can be fully conveyed to those skilled in the art. It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other. The present invention will be described in detail below with reference to the drawings and in combination with the embodiments.

[0064] In some embodiments of the present application, referring to Figure 1 as shown, a sway prevention control method for a shipborne crane includes:

[0065] S100: Establish a ship coordinate system and calculate the relative kinetic energy of the crane according to the ship coordinate system, add the inertial force to the generalized force of each degree of freedom, and analyze to obtain the dynamic model of the boom movement and the load swing;

[0066] S200: Combine the RBF neural network model and the sliding mode control to construct an adaptive sliding mode anti-sway control. Based on the adaptive sliding mode anti-sway control, analyze the continuous uncertain upper bound disturbance existing in the load of the underactuated shipborne crane, and approximate the continuous disturbance of the uncertain upper bound;

[0067] S300: Simplify the dynamic model, and use a nonlinear disturbance observer to observe the total disturbance; introduce an inverse sliding mode control to compensate for the observation error of the nonlinear disturbance observer;

[0068] S400: Compare the adaptive sliding mode anti-sway control and the LQR control, judge the position of the load based on the comparison result and the observation of the nonlinear disturbance observer, and switch the LQR control and the adaptive sliding mode anti-sway control according to the judgment result.

[0069] Specifically, the Lagrange equation is used to conduct dynamic analysis on the load of the shipborne crane. A ship coordinate system is established according to the actual position of the crane on the ship, and the state variables are transformed to obtain the dynamic model of the boom movement and the load swing, laying a foundation for the subsequent research on the anti-sway control of the shipborne crane load. Aiming at the problem of continuous uncertain upper-bound disturbances existing in the underactuated shipborne crane, an adaptive Radial Basis Function (RBF) neural network sliding-mode anti-sway control is established. The dynamic model is converted into a nominal form that conforms to the underactuated characteristics. According to the control law of the sliding-mode control, the uncertainty of the parameters of the underactuated shipborne crane is compensated. The adaptive RBF neural network model approximates and compensates for the disturbances with an uncertain upper bound caused by continuous and non-linear external disturbances in the shipborne crane, realizing the dual control of payload positioning and swing suppression under continuous unknown disturbances. For tracking the position of the load of the shipborne crane, an adaptive backstepping sliding-mode anti-sway control strategy is adopted. For the observable part in the disturbance signal, a non-linear disturbance observer is used for online observation, and the observation error converges exponentially by designing parameters. For constructing a load anti-sway controller using the adaptive backstepping sliding-mode method after introducing the non-linear disturbance observer, the adaptive law is applied to compensate for the disturbances that cannot be observed again, improving the position tracking accuracy of the shipborne crane for the load, overcoming the position uncertainty of the load and external random disturbances, and thus improving the control performance.

[0070] It can be understood that when the load is far from the target position, sliding-mode control is adopted, and when the load is close to the target position, it is switched to LQR (Linear Quadratic Regulator) control, realizing the switching between LQR control and sliding-mode control. Through simulation verification by MATLAB, it is proved that the shipborne crane has uniformly ultimately bounded stability, can obtain low state deviation and output deviation, and at the same time suppresses the swing of the load, having good effectiveness and feasibility.

[0071] In some embodiments of the present application, when establishing the ship coordinate system and calculating the relative kinetic energy of the crane according to the ship coordinate system, it includes: taking the centroid of the ship as the origin of the ship coordinate system, setting the bow direction as the positive direction of the x S axis, setting the direction perpendicular to the deck upward as the positive direction of the z S axis, the x G axis and the x S axis are parallel, the z G axis is perpendicular to the ground, and the ship coordinate system I S ={x S y S z S} is established. The inertial coordinate system I G ={x G yG z G}, set the hook and the load as a particle, and the boom has a uniform mass distribution. The cable has strain and the position of the load does not exceed the highest point of the boom. Measure the angle of the boom and the swing angle of the load relative to the z S axis. The relative kinetic energy of the crane is obtained by the following formula:

[0072]

[0073] where E represents the relative kinetic energy of the crane, m represents the mass of the boom, P L represents the length of the boom, represents the generalized velocity of the boom, m P represents the mass of the load, represents the row vector from the origin to the payload, dp p represents the column vector from the origin to the payload.

[0074] It can be understood that by establishing a ship coordinate system and only considering the lifting motion and rolling motion of the ship in the vertical plane, the complexity of obtaining the dynamic model is reduced. represents the rotation situation between I S and I G , and is represented as the rotation matrix as

[0075]

[0076] where α represents the rotation angle of the ship around the x S axis, S α and C α represent sinα and cosα. Similarly, S φ and C φ represent sinφ and cosφ. The displacement situation of I S relative to I G is represented by P G as:

[0077] p G = [0 p y p z T ;

[0078] d s represents the vector from the origin O S of the ship coordinate system to the base of the crane. d represents the distance from the center of gravity of the boom to the origin O S ;

[0079] d s = [0 d y d z ​​T ;

[0080] The position coordinates of the load in the inertial coordinate system I G are expressed as:

[0081]

[0082] where y represents the y-axis value in the inertial coordinate system I G in y G axis value, z represents the z-axis value in the inertial coordinate system I G in z G axis value, P L represents the length of the boom, φ represents the angle of the boom, θ represents the swing of the load relative to the z S axis, L represents the length of the cable, d represents the distance from the center of gravity of the boom to the coordinate origin O S of, O S the origin of the ship coordinate system, P p represents the displacement vector from O S to the payload, g represents the acceleration due to gravity, m represents the mass of the boom, m P represents the mass of the load. According to transporting the goods to other fixed positions in I G in, the target position (a, b) of the load in the inertial coordinate system I G is set, φ d , L d and θ d respectively represent the expected values of φ, L, and θ at the equilibrium point. Eliminating the swing within the inertial coordinate system, so θ d is equal to the rotation angle α of the ship around the x S axis,

[0083]

[0084] Thus, the relative kinetic energy of the crane is obtained.

[0085] In some embodiments of the present application, when constructing the dynamic model, it includes: establishing a dynamic model in generalized coordinates according to the Lagrangian equation of the relative kinetic energy of the crane, and the dynamic model is obtained from the following formula:

[0086]

[0087] where M(q) represents the inertia matrix, represents the Coriolis centripetal matrix, U c represents the input control vector, represents the vector of the boom inertial force and the load inertial force, f represents the external force disturbance, represents the acceleration of the generalized coordinates, Denote the generalized velocity of the generalized coordinates. According to the dynamic model, it is determined that the shipborne crane is an underactuated shipborne crane.

[0088] It can be understood that q is defined as [q 1 q 2 q 3 T = [φ L θ] T as the generalized coordinates, M(q) ∈ R 3×3 , U c ∈ R 3×1 , f ∈ R 3×1 , the control torque of the boom is M c , the cable tension F L , the friction force f of the boom pitching φ , the friction force f of the cable l , the disturbing force f exerted by the sea breeze on the load θ , and the expansion expression is:

[0089]

[0090]

[0091] U c = [M c F L 0] T ;

[0092]

[0093] f = [f φ f l f θ T ;

[0094] The Lagrange equation of the generalized coordinate q = φ is expanded as:

[0095]

[0096] The Lagrange equation of the generalized coordinate q = L is expanded as:

[0097]

[0098] The Lagrange equation of the generalized coordinate q = θ is expanded as:

[0099]

[0100] According to the dynamic model, it is obtained that the shipborne crane is an underactuated shipborne crane system, which has strong coupling non-linear characteristics and is also disturbed by the ship motion caused by the sea breeze. ​​

[0101] In some embodiments of the present application, when constructing an adaptive sliding mode anti-sway control by combining an RBF neural network model and a sliding mode control, it includes: the adaptive sliding mode anti-sway control divides the nominal into several sub-nominals, defines the sliding mode surface of each sub-nominal, establishes a hierarchical sliding mode controller on the sliding mode surface of each sub-nominal, and establishes a lumped sliding mode compensator on the last-layer sliding mode surface. The Lyapunov function is used to determine that any state deviates from the sub-sliding mode surface, and the total switching control input pulls it back to the deviated sliding mode surface. The RBF neural network model is used to approximate the disturbances to the hierarchical sliding mode controller and the lumped sliding mode compensator.

[0102] It can be understood that the tracking error is defined as:

[0103] e L = L - L d e 1 = φ - φ d e 2 = θ - θ d ;

[0104] Two equivalent inputs u and u L are used to control the tracking desired trajectories of the three states φ, L, and θ. The input u L is used to control L, and the input u is used to control φ and θ simultaneously. The control law of u L is:

[0105]

[0106] k L2 and k L1 represent positive real numbers. The mathematical model composed of φ and θ is written in the form of the following state space expression:

[0107]

[0108] where, is the state variable vector, u is a single control input, d 2 is the upper bound of the uncertainty perturbation received by the payload, d 2 is the perturbation caused by the ship motion received by the payload, g i and b i (i = 1, 2) are non-linear functions of the state variables, and are respectively b 1 (x) = 1, b 2 (x) = -P L S θ-φ / L,

[0109]

[0110] Without considering the uncertainty disturbance, construct the first-layer sliding surface, and each sliding surface is:

[0111] s 1 = c 1 x 1 + x 2 ;

[0112] s 2 = c 2 x 3 + x 4 ;

[0113] where c 1 and c 2 represent positive constants, and the second-layer sliding surface is:

[0114] S = a 1 s 1 + a 2 s 2 ;

[0115] where a 1 and a 2 represent positive constants. Adopt the exponential reaching law:

[0116]

[0117] where k and ε represent positive constants. Establish a lumped sliding mode compensator on the last-layer sliding surface to obtain the lumped sliding mode control law, and the total control input is:

[0118] u = u eq1 + u eq2 + u sw ;

[0119] where u eq1 and u eq2 represent the hierarchical sliding mode control laws of each sub-nominal sliding surface, and u sw represents the switching control for realizing the sliding surface. The total control law is:

[0120]

[0121] Adopt the Lyapunov function, and the Lyapunov function is:

[0122]

[0123] Adopt the RBF neural network model to approximate the disturbance, f = W *T h(x)+δ, h = [h j T represents the output of the Gaussian basis function, δ represents the neural network approximation error, and W * ​Denote the weights of the ideal neural network as, and the external force disturbance as f. According to Adding the total control input u = u eq1 + u eq2 + u sw , and the neural network input is taken as z = [x 1 , x 3 T , we get:

[0124]

[0125] According to the Lyapunov function and LaSalle's invariant set theorem, it can be known that the RBF neural network will continuously approximate the disturbance with an uncertain upper bound, thereby suppressing the swing of the load and improving the anti-swing stability.

[0126] In some embodiments of the present application, when simplifying the dynamic model, it includes: establishing a new state vector and transforming the dynamic model:

[0127] η 1 = φ - α, η 2 = L, η 3 = θ - α;

[0128] η = [η 1 η 2 η 3 T ;

[0129]

[0130] where η represents the generalized coordinate, φ represents the angle of the boom, α represents the rotation angle of the ship around the x S axis, L represents the length of the cable, θ represents the swing of the load relative to the z S axis, η 1 , η 2 and η 3 represent the generalized coordinates, [η 1 η 2 η 3 T represents the vector transpose, M t (η) represents the inertia matrix, represents the Coriolis centripetal matrix, G t (η) represents the gravity vector, U c represents the input control vector, f represents the external force disturbance, represents the generalized acceleration of the generalized coordinate, represents the generalized velocity of the generalized coordinate.

[0131] It can be understood that M t (η) ∈ R​​​3×3 , G t (η) ∈ R 3×1 , U c ∈ R 3×1 , f ∈ R 3×1 , the expanded expression is:

[0132]

[0133]

[0134] U c = [M c F L 0] T ;

[0135]

[0136] f = [f φ f l f θ T ;

[0137] The Lagrangian equation of the generalized coordinate η = η 1 expands to:

[0138]

[0139] The Lagrangian equation of the generalized coordinate η = η 2 expands to:

[0140]

[0141] The Lagrangian equation of the generalized coordinate η = η 3 expands to:

[0142]

[0143] Set the virtual input as u s = [u 1 u 2 u 3 . By transforming the dynamic model, it lays a foundation for observing the total disturbance using a nonlinear disturbance observer later. Set the heave motion p z = 0.4sin(πt), α = π / 36sin(πt) rad. If the load is to reach the target position (4m, 3.5m) without waves and other disturbances, which is equivalent to the crane on land, the expected values of φ, L, and θ are: φ d = 1.04 rad, L d = 1m and θ d ​= 0 rad, considering the situation on the sea surface, the remaining parameters are shown in the following table.

[0144]

[0145] The parameters selected for the adaptive neural network sliding mode control are: c 1 = 1.7, c 2 = 20, a 1 = 1.7, a 2 = 1, k = 10, ε = 0.5. The trajectories of the cable length, the angle of the jib, and the swing angle of the load under the adaptive neural network sliding mode control are verified by simulation in Matlab. Refer to Figure 3 as shown.

[0146] In some embodiments of the present application, when using a nonlinear disturbance observer to observe the total disturbance and introducing an inverse sliding mode control to compensate for the observation error of the nonlinear disturbance observer, it includes: defining the observation error using the nonlinear disturbance observer, setting the dynamic characteristics relative to the nonlinear disturbance observer, determining the error dynamic equation of the nonlinear disturbance observer, establishing a matrix to make the error dynamic equation converge exponentially, converting the observed disturbance into the control quantity of the corresponding input channel, defining the output error vector and taking the derivative, using the Lyapunov function and the adaptive feedback control law to take the law, and obtaining the input according to the Lyapunov function.

[0147] It can be understood that the observation error of the nonlinear disturbance observer is defined as:

[0148]

[0149] where e f represents the observation error, represents the estimated value of f, f represents the external force disturbance. Setting the dynamic characteristics relative to the nonlinear disturbance observer, the process of the shipborne crane being disturbed is defined as slow, then From this, it can be obtained that:

[0150]

[0151] The gain of the given nonlinear observer satisfies:

[0152]

[0153] The error dynamic equation of the nonlinear disturbance observer is obtained:

[0154]

[0155] Establish a matrix ρ 11= ρ and greater than 0, such that the error dynamic equation converges exponentially, and the output of the nonlinear disturbance observer is transmitted to the gain The observed disturbance is converted into the control quantity of the corresponding input channel, and it is obtained that:

[0156]

[0157] By adopting a nonlinear disturbance observer, the external force disturbance f is changed into e f , thereby reducing the influence of the disturbance. By adopting a nonlinear disturbance observer, the form of the state space expression is reorganized:

[0158]

[0159] The output error vector is defined as

[0160] z 1 = η - η d ;

[0161] where η d represents the given position command of the shipborne crane. Taking the derivative of the above formula, it is obtained that:

[0162]

[0163] The Lyapunov function is defined as:

[0164]

[0165] The virtual control quantity a 1 = c 1 z 1 , where c 1 represents c 1 ∈R 3×3 is a symmetric and positive definite constant matrix. Let:

[0166]

[0167] Substitute the z 2 formula into the formula, and it is obtained that

[0168]

[0169] Substitute the above formula into the Lyapunov function V 1 , and it is obtained that:

[0170]

[0171] When z 2 = 0, then V 1 ≤0. The Lyapunov function is defined as:

[0172]

[0173] where \(s = [s 1 s 2 s 3 \) is the sliding mode surface, defined as:

[0174] \(s = k 1 z 1 +\dot{z} 2 ;\)

[0175] where \(k 1 \in\mathbb{R} 3×3 \) is a positive definite symmetric matrix. Differentiating the above formula and combining the formulas gives:

[0176]

[0177] Differentiating the Lyapunov function \(V 2 \) gives:

[0178]

[0179] Define the predicted observation error as which is the estimated value of the observation error of the nonlinear disturbance observer, and we get:

[0180]

[0181] Define the Lyapunov function as:

[0182]

[0183] where \(\gamma\) represents a positive constant. Differentiating the above formula gives:

[0184]

[0185] The adaptive feedback control law is:

[0186]

[0187] where \(\beta, c 2 \) represent positive definite matrices. Similarly, \(\beta 3 \) and \(c 3 \) also represent positive definite matrices. According to the above formula, the adaptation law is taken as:

[0188]

[0189] Define the total sliding mode surface function of \(\eta 1 \) and \(\eta 3 \) as:

[0190] \(S = a1 s 1 +a 2 s 3 ;

[0191] According to the above formula, the Lyapunov function is:

[0192]

[0193] Deriving the above formula gives:

[0194]

[0195] According to the above formula, it is obtained that:

[0196]

[0197] Substitute into the formula, and the input of the shipboard crane as an underactuated shipboard crane system is obtained as:

[0198]

[0199] F L = u 2 ;

[0200] Set m = 10 kg, m p = 1 kg, p L = 0.7 m, g = 9.8 m / s 2 , d = 0.05 m, φ = 0.17 rad, L = 0.1 m and θ = 0 rad, c 1 = 80, c 2 = 25, k 1 = 10, β = 10, γ = 12, verify the backstepping sliding mode control, and the respective state variables and inputs are verified by simulation in Matlab. Refer to Figure 4 and Figure 5 as shown. After introducing a nonlinear disturbance observer in the shipboard crane as an underactuated shipboard crane system, the influence of the disturbance on the output is further reduced, which not only improves the tracking performance of the load position of the shipboard crane but also further eliminates the disturbance.

[0201] In some embodiments of the present application, when determining the position of the load, it includes: statistically analyzing the positions of all historical loads and establishing a position set. When the position of the load exists in the position set, it is determined that the position of the load is not corrected, and the position of the load is determined as the target position. When the position of the load does not exist in the position set, it is determined that the position of the load is corrected. The aggregation algorithm is used to aggregate the position set, and the position set is used as the dataset to be aggregated. The expected number of clusters k is determined to be 2, and the parameters of the Gaussian distribution are initialized. The probability that each data in the dataset to be aggregated belongs to each Gaussian distribution is calculated to obtain the responsibility value. The dataset is obtained according to the responsibility value, and the dataset is used as the similar set. The average value of the positions of all historical loads in the similar set is taken as the optimization factor, and the product value of the optimization factor and the position of the load is used as the target position.

[0202] It can be understood that by statistically analyzing the positions of historical loads and establishing a position set, the reliability of the data source is ensured, and the risk of misjudgment is reduced. The position set represents the reasonable range of the load within a certain range. When a position that has not appeared is judged, there may be artificially set errors. The aggregation algorithm is used for correction to reduce the influence of random fluctuations. The optimization factor dynamically adjusts the position of the load, which not only improves the accuracy of position judgment but also takes into account the ability of real-time correction. It reduces the computational complexity and enhances the robustness.

[0203] In some embodiments of the present application, when switching between LQR control and adaptive sliding mode anti-sway control according to the judgment result, it includes: presetting a target position distance threshold. When the target position is greater than or equal to the target position distance threshold, adaptive sliding mode anti-sway control is adopted. When the target position is less than the target position distance threshold, LQR control is adopted.

[0204] It can be understood that by linearizing the underactuated shipborne crane system near the equilibrium point, an approximate transformation can be made, such that η 1 ≈η 1d ,η 2 ≈η 2d ,η 3 ≈0,sinη 3 ≈η 3 ,cosη 3 ≈1, Expand the formula at the equilibrium point by Taylor series and ignore the high-order terms. Set the target position distance threshold Ω c

[0205]

[0206] Ω c ={x,y<0.17};

[0207] Among them, \(E\) represents the linearization result near the equilibrium point, \(E\) 1 represents the adaptive sliding mode anti-sway control, \(E\) * represents the LQR control. \(x\) and \(y\) represent the target positions. The LQR control is based on minimizing the quadratic performance index of the system state, which is expressed as the weighted sum of the control performance and the state deviation, and is represented by the quadratic function of the system state. The gain matrix is determined by the weight matrices \(Q\) and \(R\). These two weight matrices are used to adjust the system state and the control input. The state weight matrix \(Q\) reflects the degree of emphasis on the state deviation, while the input weight matrix \(R\) reflects the degree of emphasis on the change of the control input. The LQR control considers the optimization of the entire state space. Therefore, when facing system disturbances, its tracking performance hardly changes significantly, and lower state deviations and output deviations can be obtained, thus achieving the effect of suppressing the load swing. The adaptive sliding mode anti-sway control has good robustness and fast response characteristics. By introducing the sliding mode surface, it can quickly respond to and resist external disturbances, ensuring that the shipborne crane remains stable when facing uncertain disturbances. When the disturbance amplitude is large, the tracking performance is likely to decline. Therefore, when pursuing to improve the control accuracy and anti-sway ability, the control can be dynamically selected according to the actual situation, maximizing the characteristics of the two controls.

[0208] In summary, the beneficial effects of the present invention are as follows: By introducing the calculation of the relative kinetic energy of the crane in the ship coordinate system, the dynamic responses of the boom and the load can be accurately described, improving the control accuracy and stability of the load movement. By establishing a dynamic model based on the boom movement and the load swing, the actual situations of each state are clearly shown, enhancing the scientificity and rigor of the anti-sway control of the shipborne crane. Using the RBF neural network to approximate the disturbance and introducing the sliding mode control, an adaptive sliding mode anti-sway control is constructed. The adaptive sliding mode anti-sway control can effectively compensate for the hull swing and wind and wave interference according to the changes of external disturbances and movements, ensuring the stable operation of the shipborne crane in a complex environment. The total disturbance is observed by using a non-linear disturbance observer, the swinging trend of the load is identified, and the observation error is compensated through the backstepping sliding mode control. The active control of the load swing is realized, effectively reducing the swing amplitude of the load in the horizontal and vertical directions. According to the position of the load and the observation results of the non-linear disturbance observer, an intelligent switch is made between the LQR control and the adaptive sliding mode anti-sway control. When there are large disturbances or uncertainties, it switches to the adaptive sliding mode control, overcoming the disturbances of the hull in a complex environment, thereby extending the service life of the shipborne crane and reducing the operation cost and maintenance cost.

[0209] In another preferred embodiment based on the above embodiments, refer to Figure 2As shown, this embodiment provides an anti-sway control system for an on-board crane, which is used to apply the above anti-sway control method for an on-board crane, and includes:

[0210] A model establishment unit, which is used to establish a ship coordinate system and calculate the relative kinetic energy of the crane according to the ship coordinate system, add inertial forces to the generalized forces of each degree of freedom, and analyze and obtain the dynamic model of the boom movement and the load sway;

[0211] An adaptive sliding mode unit, which is used to combine the RBF neural network model and sliding mode control to construct an adaptive sliding mode anti-sway control, and analyze the continuous uncertain upper bound disturbance existing in the load of the under-actuated on-board crane based on the adaptive sliding mode anti-sway control, and approximate the continuous disturbance of the uncertain upper bound;

[0212] An inversion unit simplifies the dynamic model, and uses a non-linear disturbance observer to observe the total disturbance; introduces an inverse sliding mode control to compensate for the observation error of the non-linear disturbance observer;

[0213] A switching unit compares the adaptive sliding mode anti-sway control and the LQR control, judges the position of the load based on the comparison result and the observation of the non-linear disturbance observer, and switches the LQR control and the adaptive sliding mode anti-sway control according to the judgment result.

[0214] It can be understood that the model establishment unit establishes the ship coordinate system as the benchmark for dynamic analysis. Based on this coordinate system, the relative kinetic energy of the crane can be accurately obtained, and the influence of inertial force on the load is considered. It is introduced into the generalized force of each degree of freedom of the crane to establish a dynamic model. Based on the dynamic model, the dynamic relationship between the boom movement and the load swing can be analyzed, so as to obtain an accurate kinematic description, providing a reliable theoretical basis for subsequent control strategies. The adaptive sliding mode unit combines the RBF neural network model and sliding mode control to construct an adaptive sliding mode anti-sway control. This control can adaptively adjust the control parameters to respond to the continuous uncertain upper bound disturbance of the load in real time. During the control process, the adaptive sliding mode unit approximates the disturbance in real time to accurately estimate and compensate the continuous disturbance of the uncertain upper bound, improving the robustness and anti-interference ability of the system, enabling the shipborne crane to operate stably in the complex environment of sea waves and sea winds. The inversion unit realizes the accurate observation of the system through the simplification of the dynamic model and the application of a nonlinear disturbance observer. The nonlinear disturbance observer can accurately evaluate the total disturbance of the system, improving the accuracy of the dynamic response of the load swing and boom movement, and reducing the risk brought by the error accumulation and disturbance uncertainty of the system. The switching unit compares the adaptive sliding mode anti-sway control with the linear quadratic regulator LQR control, and judges the switching of the control strategy according to the observation results of the nonlinear disturbance observer and the load position. When the load swings within the allowable range, the system adopts LQR control to achieve precise positioning and energy consumption optimization; when the load swing exceeds the control range, the system automatically switches to the adaptive sliding mode anti-sway control to ensure the stability of the load, improving the control flexibility of the system and ensuring the safe and efficient operation of the shipborne crane.

[0215] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0216] The present application is described with reference to the flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram can be implemented by computer program instructions, and the combination of processes and / or blocks in the flowchart and / or block diagram can also be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate for implementation in the process Figure 1one or more processes and / or blocks Figure 1 a device for the functions specified in one or more blocks

[0217] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory produce a manufactured article including an instruction device that implements the processes Figure 1 one or more processes and / or blocks Figure 1 the functions specified in one or more blocks

[0218] These computer program instructions can also be loaded onto a computer or other programmable data processing device, such that a series of operational steps are performed on the computer or other programmable device to produce a computer-implemented process, and thus the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in Figure 1 one or more processes and / or blocks Figure 1 one or more blocks

[0219] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications or equivalent replacements can still be made to the specific implementation manners of the present invention, and any modifications or equivalent replacements that do not depart from the spirit and scope of the present invention shall be covered by the protection scope of the claims of the present invention.

Claims

1. A ship-borne crane anti-sway control method, characterized in that: include: Establishing a ship coordinate system and calculating the relative kinetic energy of the crane based on the ship coordinate system, adding the inertial force to the generalized force of each degree of freedom, and analyzing and obtaining a dynamic model of the boom movement and load swing; According to the combination of RBF neural network model and sliding mode control, an adaptive sliding mode anti-sway control is constructed, and based on the adaptive sliding mode anti-sway control, the continuous uncertain upper bound disturbance of the underactuated shipborne crane load is analyzed to approximate the continuous disturbance of the uncertain upper bound; The dynamic model is simplified, and a nonlinear disturbance observer is used to observe the total disturbance; an inverse sliding mode control is introduced to compensate for the observation error of the nonlinear disturbance observer; The adaptive sliding mode anti-sway control and the LQR control are compared, the position of the load is judged according to the comparison result and the observation of the nonlinear disturbance observer, and the LQR control and the adaptive sliding mode anti-sway control are switched according to the judgment result.

2. The anti-sway control method for a shipborne crane according to claim 1, characterized in that: When establishing a ship coordinate system and calculating the relative kinetic energy of the crane based on the ship coordinate system, it includes: The center of mass of the ship is taken as the origin of the ship coordinate system, and the bow direction is set as x S The positive direction of the axis is set as z, with the vertical deck upward direction S The positive direction of the axis, x G Axis and x S Axis parallel, z G The axis is perpendicular to the ground; Establish the ship coordinate system I S ={x S y S z S }, establish inertial coordinate system I G ={x G y G z G }; Assuming the hook and the load as a point mass, and the boom with uniform mass distribution, the cable is strained and the load is not positioned higher than the highest point of the boom, measure the angle of the boom and the load relative to the z S The swing angle of the shaft; The relative kinetic energy of the crane is obtained from the following formula: Where E represents the relative kinetic energy of the crane, m represents the mass of the boom, and P L Indicates the length of the boom, represents the generalized speed of the boom, m P represents the mass of the load, represents the row vector from the origin to the payload, dp p Represents a column vector from the origin to the payload.

3. The anti-sway control method for a shipborne crane according to claim 2, characterized in that: When the inertia force is added to the generalized force of each degree of freedom, the dynamic model of boom motion and load swing is analyzed, including: The generalized forces include boom gravity, load gravity, boom inertia force and load inertia force; The pitch angle of the boom, the cable length and the load swing angle are set as generalized coordinates, and the control torque of the boom pitch and the rope tension are set as control inputs to construct the dynamic model.

4. The anti-sway control method for a ship-borne crane according to claim 3, characterized in that: When building a kinetic model, include: A dynamic model is established in generalized coordinates according to the Lagrange equation of the relative kinetic energy of the crane. The dynamic model is derived from the following formula: Where M(q) represents the inertia matrix, represents the Coriolis centripetal matrix, U c represents the input control vector, represents the vector of the boom inertia force and the load inertia force, f represents the external force disturbance, represents the acceleration in generalized coordinates, represents the generalized velocity of generalized coordinates; According to the dynamic model, it is determined that the shipborne crane is an under-actuated shipborne crane.

5. The anti-sway control method for a ship-borne crane according to claim 4, characterized in that: When constructing adaptive sliding mode anti-sway control based on the combination of RBF neural network model and sliding mode control, it includes: The adaptive sliding mode anti-sway control divides the nominal into several sub-nominals, defines the sliding surface of each sub-nominal, establishes a layered sliding mode controller on the sliding surface of each sub-nominal, and establishes a lumped sliding mode compensator on the last sliding surface. The Lyapunov function is used to determine whether any state is separated from the sub-sliding surface, and the total switching control input pulls it back to the separated sliding surface. The RBF neural network model is used to approximate the disturbance to the layered sliding mode controller and the lumped sliding mode compensator.

6. The anti-sway control method for a shipborne crane according to claim 5, characterized in that: When simplifying the kinetic model, it includes: Create a new state vector and transform the dynamic model: eta1=φ-α, eta2=L, eta3=θ-α; n=[n1n2n3] T ; Among them, η represents the generalized coordinate, φ represents the angle of the boom, and α represents the ship's rotation around x. S The axis rotation angle, L is the cable length, θ is the load relative to z S The swing of the axis, η1, η2 and η3 represent the generalized coordinates, [η1η2η3] T represents vector transpose, M t (η) represents the inertia matrix, represents the Coriolis centripetal matrix, G t (η) represents the gravity vector, U c represents the input control vector, f represents the external force disturbance, represents the generalized acceleration in generalized coordinates, represents the generalized velocity in generalized coordinates.

7. The anti-sway control method for a shipborne crane according to claim 6, characterized in that: When a nonlinear disturbance observer is used to observe the total disturbance and a backstepping sliding mode control is introduced to compensate for the observation error of the nonlinear disturbance observer, the method includes: Using a nonlinear disturbance observer to define an observation error, setting a dynamic characteristic relative to the nonlinear disturbance observer, and determining an error dynamic equation of the nonlinear disturbance observer; Establishing a matrix to converge the error dynamic equation exponentially and converting the observed disturbance into the control quantity of the corresponding input channel; The output error vector is defined and derived, the Lyapunov function and adaptive feedback control law are used to obtain the law, and the input is obtained according to the Lyapunov function.

8. The anti-sway control method for a ship-borne crane according to claim 7, characterized in that: When determining the position of the load, include: The positions of all historical loads are counted and a position set is established. When the position of the load exists in the position set, it is determined that the position of the load is not to be corrected, and the position of the load is determined as the target position; When the position of the load does not exist in the position set, it is determined to correct the position of the load, and the position set is aggregated using an aggregation algorithm; Using the location set as a data set to be aggregated; Determine the expected number of clusters k as 2 and initialize the parameters of the Gaussian distribution; Calculate the probability that each data in the to-be-aggregated data set belongs to each Gaussian distribution, and obtain a responsibility value; Obtaining a data set according to the responsibility value, and using the data set as a similar set; The average of the positions of all historical loads in the similar set is taken as the optimization factor, and the product value of the optimization factor and the position of the load is taken as the target position.

9. The anti-sway control method for a ship-borne crane according to claim 8, characterized in that: When the LQR control and the adaptive sliding mode anti-sway control are switched according to the judgment result, it includes: Pre-set the target location distance threshold; When the target position is greater than or equal to the target position distance threshold, the adaptive sliding mode anti-sway control is adopted; When the target position is less than the target position distance threshold, the LQR control is adopted.

10. A ship-borne crane anti-sway control system, used for applying the ship-borne crane anti-sway control method according to any one of claims 1 to 9, characterized in that: include: A model building unit is used to establish a ship coordinate system and calculate the relative kinetic energy of the crane based on the ship coordinate system, add the inertial force to the generalized force of each degree of freedom, and analyze and obtain a dynamic model of the boom movement and load swing; An adaptive sliding mode unit is used to construct an adaptive sliding mode anti-sway control according to a combination of an RBF neural network model and a sliding mode control, and to analyze the continuous uncertain upper bound disturbance of the underactuated shipborne crane load based on the adaptive sliding mode anti-sway control to approximate the continuous disturbance of the uncertain upper bound; The inversion unit simplifies the dynamic model and uses a nonlinear disturbance observer to observe the total disturbance; The backstepping sliding mode control compensates for the observation error of the nonlinear disturbance observer; The switching unit compares the adaptive sliding mode anti-sway control and the LQR control, judges the position of the load according to the comparison result and the observation of the nonlinear disturbance observer, and switches the LQR control and the adaptive sliding mode anti-sway control according to the judgment result.

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