Anti-swing control method and system for bridge crane

Abstract

The application relates to a bridge crane anti-swing control method and system, which comprises the following steps: constructing a bridge crane system dynamics model containing the friction of a trolley, a bridge and a lifting rope based on the physical parameters of the trolley, the bridge, the lifting hook and the load, and setting a control target; obtaining an energy function based on the bridge crane system dynamics model, and obtaining an anti-swing controller according to the friction of the trolley, the bridge and the lifting rope, the energy function and the control target; and realizing anti-swing control of the bridge crane according to the driving force of the trolley, the bridge and the lifting rope output by the anti-swing controller.

Description

Anti-sway control method and system for bridge cranes Technical Field

[0001] This invention relates to the field of electromechanical system control technology, specifically to a method and system for preventing swaying of bridge cranes. Background Technology

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

[0003] Bridge cranes are commonly used lifting equipment. Their control system is a typical multi-input multi-output and underactuated electromechanical system. The control input of a bridge crane is less than the degree of freedom of the system output. When the trolley and the bridge frame move simultaneously to lift large structural loads, the hook and load will swing in two stages in three-dimensional space, exhibiting complex double-spherical pendulum characteristics.

[0004] To improve operational efficiency, the length of the lifting rope changes during the movement of the trolley and bridge to complete the load lifting operation. At this time, the bridge crane has three control inputs (trolley controller, bridge controller, lifting controller) and seven output degrees of freedom (trolley displacement, bridge displacement and lifting rope length, and the swing angle of the hook and load in three-dimensional space).

[0005] Existing technologies have proposed various control methods for bridge crane systems. Based on whether or not system motion state feedback signals are included, these methods can be divided into open-loop control and closed-loop control. Open-loop control methods include trajectory planning, input shaping, and smoothers. Closed-loop control methods include adaptive control, energy-analysis-based (EAB) control, sliding mode control, and fuzzy control.

[0006] The inventors discovered that existing bridge cranes only consider six degrees of freedom (trolley movement, bridge frame movement, hook spherical oscillation, and load spherical oscillation), while ignoring the change in the length of the lifting rope. The dynamic modeling and controller design of a seven-degree-of-freedom bridge crane with double spherical pendulum and variable rope length characteristics still need further improvement.

[0007] Moreover, most existing technologies neglect the friction of actuators (trolley, bridge, lifting rope). In actual crane systems, friction is usually difficult to measure directly, and uncertain friction models can affect the positioning accuracy of bridge cranes.

[0008] Furthermore, existing technologies do not consider the overshoot problem of actuators. When the controller gain is not properly selected, the actuator may overshoot or even oscillate back and forth at the target position, causing large load swings and affecting the safety performance of the crane. Summary of the Invention

[0009] To address the technical problems mentioned above, this invention provides a method and system for anti-sway control of bridge cranes, enabling a seven-degree-of-freedom bridge crane to achieve positioning, anti-sway, variable rope length, friction estimation, and overshoot constraints. A three-dimensional dynamic model of the bridge crane's double-spherical pendulum and variable rope length is established using the Lagrangian method without any linearization operations. Based on the system energy function, and combining overshoot constraint terms, adaptive terms, and anti-sway terms, an increasingly coupled closed-loop adaptive controller is designed. The system stability is analyzed using the Russell invariance principle and Lyapunov theory. Experiments verify the effectiveness and robustness of the proposed adaptive anti-sway controller.

[0010] To achieve the above objectives, the present invention adopts the following technical solution:

[0011] The first aspect of the present invention provides a method for anti-sway control of a bridge crane, comprising the following steps:

[0012] Based on the physical parameters of the trolley, bridge, hook, and load, a dynamic model of the bridge crane system containing the frictional forces of the trolley, bridge, and lifting rope is constructed, and control objectives are set.

[0013] Based on the dynamic model of the bridge crane system, the energy function is obtained. Based on the friction of the trolley, bridge frame and hoisting rope, the energy function and the control target, the anti-sway controller is obtained.

[0014] Anti-sway control of the bridge crane is achieved by using the driving force of the trolley, bridge frame and hoisting rope output by the anti-sway controller.

[0015] Construct a dynamic model of the bridge crane system, including:

[0016] Determine the displacement of the trolley and cable tray, the mass of the trolley, cable tray, hook and load, the length of the lifting rope and rigging, and the position and swing angle of the hook and load in the three-dimensional coordinate system;

[0017] Based on the Lagrangian function, the dynamic equations for the trolley displacement, bridge displacement, rope length, hook swing angle, and load swing angle are established, as well as the friction equations for the trolley, bridge, and rope, and converted into matrix form.

[0018] Control objectives include:

[0019] Positioning, trolley displacement, and bridge frame displacement reach the target values, and the length of the suspension rope changes to the target value;

[0020] Anti-sway function; hook sway angle and load sway angle are eliminated.

[0021] The energy function is obtained by differentiating the mechanical energy function derived from the dynamic model of the bridge crane system.

[0022] The energy of a bridge crane system is attenuated through the speed of the trolley, the speed of the bridge frame, and the speed of the hoisting rope.

[0023] The anti-sway controller is shown in the following formula:

[0024]

[0025]

[0026]

[0027] Among them, F xa ,F ya and F za These represent the driving forces of the trolley, bridge, and suspension rope, respectively. x =xx d ,e y =yy d and e z =l1-l 1d Let x and y represent the positioning errors of the trolley, cable tray, and lifting rope, respectively; let l1 and l2 represent the displacements of the trolley and cable tray, respectively; and let k represent the lengths of the lifting rope and rigging rope, respectively. px ,k dx ,k py ,k dy ,k pz ,k dz ,k λ ,k wx ,k wy Indicates control gain. This is the maximum allowable overshoot of the actuator. They represent ω respectively x ,ω y ,ω z The estimated value.

[0028] A second aspect of the present invention provides a system for implementing the above-described method, comprising:

[0029] The control target module is configured to: construct a dynamic model of the bridge crane system containing the frictional forces of the trolley, bridge, and lifting ropes based on the physical parameters of the trolley, bridge, hook, and load, and set the control target;

[0030] The anti-sway control module is configured to: obtain the energy function based on the dynamic model of the bridge crane system, and obtain the anti-sway controller based on the friction of the trolley, bridge frame and hoisting rope, the energy function and the control target;

[0031] The anti-sway actuator module is configured to: realize anti-sway control of the bridge crane based on the driving force of the trolley, bridge frame and hoisting rope output by the anti-sway controller.

[0032] A third aspect of the present invention provides a computer-readable storage medium.

[0033] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the bridge crane anti-sway control method described above.

[0034] A fourth aspect of the present invention provides a computer device.

[0035] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps in the bridge crane anti-sway control method described above.

[0036] Compared with existing technologies, one or more of the above technical solutions have the following beneficial effects:

[0037] 1. The dynamic effects and state constraints of the double spherical pendulum of the bridge crane are fully considered. A dynamic model is constructed using seven degrees of freedom: trolley displacement, bridge frame displacement, hoisting rope length, hook swing angle, and load swing angle. The friction of the actuators (trolley, bridge frame, hoisting rope) is also considered in the dynamic model, thereby improving the positioning accuracy of the bridge crane in anti-swing control.

[0038] 2. The constructed dynamic model includes three driving state variables: trolley displacement, bridge displacement, and rope length; and four non-driving state variables: the swing angle of the hook and load in three-dimensional space, and the friction of the actuators (trolley, bridge, rope). This allows the anti-sway controller to consider more output degrees of freedom and more complex dynamic characteristics of the double spherical pendulum and variable rope length.

[0039] 3. The controller comprises four parts. The first is the proportional-derivative term, which tracks the target trajectory of the trolley / bridge movement and changes in the length of the lifting rope. The second is the overshoot limiting term, which ensures that the actuator's overshoot is always within the set range and quickly reduces to zero. The third is the adaptive term, used to estimate friction parameters. The last part of the trolley and bridge controller is the anti-sway term, enhancing sway control performance. The last part of the lifting rope controller is the gravity compensation term, which is related to the sum of the hook mass and the loaded mass.

[0040] 4. The controller is designed based on the original complex dynamic model. Through closed-loop system stability analysis, it can be seen that there is no need to make small-angle approximations to the dynamic model. This means that even if the non-driven swing angle deviates from the equilibrium point under the action of disturbance, the proposed controller can still maintain good control performance.

[0041] 5. The adaptive term can be used to estimate the uncertain friction force of the actuator online, effectively eliminating the positioning errors of the trolley, bridge and suspension rope. Furthermore, the adaptive term can estimate the uncertain friction force parameter model online during the movement of the trolley and bridge and the lifting and lowering of the load, without the need for offline calibration. Attached Figure Description

[0042] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0043] Figure 1 is a schematic diagram of a seven-degree-of-freedom bridge crane structure provided by one or more embodiments of the present invention;

[0044] Figure 2 is a schematic diagram of the control system of a bridge crane provided in one or more embodiments of the present invention;

[0045] Figures 3(a)-3(j) are comparative experimental results of the adaptive anti-sway control method (Proposed controller), energy analysis-based controller (EAB), and smoother (Smoother) provided by one or more embodiments of the present invention;

[0046] Figure 4 is a schematic diagram of the online estimation results of friction parameters by the adaptive anti-sway control method (Proposed controller) provided by one or more embodiments of the present invention;

[0047] Figure 5(a) is a side view of the load trajectory under the control of an energy analysis-based controller (EAB) provided in one or more embodiments of the present invention;

[0048] Figure 5(b) is a side view of the load trajectory under smoother control provided by one or more embodiments of the present invention;

[0049] Figure 5(c) is a side view of the load trajectory under control based on the adaptive anti-sway control method (Proposed controller) provided by one or more embodiments of the present invention;

[0050] Figure 5(d) is a top view of the load trajectory under the control of the three control methods shown in Figures 5(a)-5(c) provided in one or more embodiments of the present invention. Detailed Implementation

[0051] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0052] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0053] The following embodiments present a method and system for anti-sway control of a bridge crane, enabling a seven-DOF bridge crane to achieve positioning, anti-sway, variable rope length, friction estimation, and overshoot constraints. A three-dimensional dynamic model of the bridge crane's double-spherical pendulum and variable rope length is established using the Lagrangian method without any linearization operations. Based on the system energy function, and combining overshoot constraint terms, adaptive terms, and anti-sway terms, an increasingly coupled closed-loop adaptive controller is designed. The system stability is analyzed using the Russell invariance principle and Lyapunov theory. Experiments verify the effectiveness and robustness of the proposed adaptive anti-sway controller.

[0054] Example 1:

[0055] The anti-sway control method for bridge cranes includes the following steps:

[0056] A dynamic model of a bridge crane system with double spherical pendulum and variable rope length effect was established and analyzed based on the Lagrange method. The model includes three driving state variables: trolley displacement, bridge frame displacement and rope length, and four non-driving state variables: the swing angle of the hook and load in three-dimensional space, for a total of seven degrees of freedom.

[0057] Based on the system energy function, and incorporating overshoot limiting, adaptive, and anti-sway terms, an enhanced-coupling closed-loop adaptive controller is designed. Then, the system stability is rigorously analyzed using the Russell invariance principle and Lyapunov theory.

[0058] The adaptive anti-sway control method enables precise positioning and sway elimination control of the bridge crane, while simultaneously estimating friction parameters online to suppress actuator overshoot.

[0059] Specifically:

[0060] (1) Dynamic model and analysis:

[0061] As shown in Figure 1, a seven-degree-of-freedom bridge crane system is constructed in three-dimensional space. The relevant physical parameters and definitions of the bridge crane system are shown in Table 1.

[0062] Table 1: System Parameters

[0063] Parameters Physical Meaning Unit M1 Trolley mass kg M2 Sum of trolley and cable tray mass kg m1, m2 Hook and load mass kg x, y Trolley and cable tray displacement ml1, l2 Lifting rope and rigging rope length m θ1, θ2, θ3, θ4 Hook and load three-dimensional spatial swing angle deg Fx ,F y ,F z Trolley, cable tray, and suspension rope control force (Ng) and gravitational acceleration (ms) 2 surface

[0064] Based on the Lagrange method, the dynamic equations of a seven-degree-of-freedom bridge crane are established. The dynamic equations related to the driving state variable, trolley displacement x, are as follows:

[0065]

[0066] The dynamic equations related to the driving state quantity, bridge displacement y, are as follows:

[0067]

[0068] The dynamic equations related to the driving state variable, the length of the suspension rope, l1, are as follows:

[0069]

[0070] in F xa ,F ya and F za These represent the driving forces of the trolley, bridge frame, and suspension rope, respectively. F xf ,F yf and F zf Let F represent the frictional forces of the trolley, the bridge frame, and the suspension rope, respectively, and their expressions are as follows:

[0071]

[0072] Where f x0 ,f y0 ,ε x ,ε y ,k xr ,k yr ,d z This represents parameters related to friction.

[0073] The dynamic equations related to the non-driven state variable, hook swing angle θ1, are as follows:

[0074]

[0075] The dynamic equations related to the non-driven state variable, hook swing angle θ2, are as follows:

[0076]

[0077] The dynamic equations related to the non-driving state variable load swing angle θ3 are as follows:

[0078]

[0079] The dynamic equations related to the non-driving state variable load swing angle θ4 are as follows:

[0080]

[0081] To simplify the expression, the above dynamic equations (1)-(8) can be rewritten in the following matrix form:

[0082]

[0083] in:

[0084]

[0085] G(q)=[0 0 g 31 g 41 g 51 g 61 g 71 ] T ;

[0086] q=[xy l1θ1θ2θ3θ4] T ;

[0087] U = [F x F y F z 0 0 0 0] T ;

[0088] m 11 =M1+m1+m2; m 13 = (m1+m2)sinθ1cosθ2; m 14 = (m1+m2)l1cosθ1cosθ2;

[0089] m 15 =-(m1+m2)l1sinθ1sinθ2;m 16 =m2l2cosθ3cosθ4;m 17 = -m2l2sinθ3sinθ4;

[0090] m 22 =M2+m1+m2; m 23 = (m1+m2)sinθ2; m 25=(m1+m2)l1cosθ2;m 27 =m2l2cosθ4;

[0091] m 33 =m1+m2;m 36 =m2l2cosθ2cosθ4sin(θ1-θ3);

[0092] m 37 =m2l2[sinθ2cosθ4-cosθ2sinθ4cos(θ1-θ3)];m 44 =(m1+m2)l1 2 cos 2 θ2;

[0093] m 46 =m2l1l2cosθ2cosθ4cos(θ1-θ3);

[0094] m 47 =m2l1l2cosθ2sinθ4sin(θ1-θ3);m 55 =(m1+m2)l1 2 ;m 56 =-m2l1l2sinθ2cosθ4sin(θ1-θ3);

[0095]

[0096]

[0097]

[0098]

[0099]

[0100]

[0101]

[0102]

[0103]

[0104]

[0105]

[0106]

[0107]

[0108]

[0109]

[0110]

[0111]

[0112]

[0113]

[0114]

[0115]

[0116]

[0117]

[0118] g 31 =-(m1+m2)gcosθ1cosθ2;g 41 =(m1+m2)gl1sinθ1cosθ2; g 51 = (m1+m2)gl1cosθ1sinθ2;

[0119] g 61 =m2gl2sinθ3cosθ4; g 71 =m2gl2cosθ3sinθ4;

[0120] Based on the fact that the swing angle of the hook and load is relatively small, the following reasonable assumptions are made:

[0121] θ i∈(-π / 2,π / 2),i=1,2,3,4. (10)

[0122] (2) Control objectives

[0123] For a seven-freedom bridge crane system, the control objective of this embodiment is as follows:

[0124] 1) Positioning. The driving state quantities, trolley displacement x(t) and bridge displacement y(t), accurately reach the target values, and the suspension rope length l1(t) changes to the target value, i.e.:

[0125] x(t)→x d ,y(t)→y d ,l1(t)→l 1d (11)

[0126] Where x d and y d These represent the target displacements of the trolley and the bridge, respectively. 1d Indicates the target length of the suspension rope.

[0127] 2) Anti-sway. The non-drive state quantities of hook sway angles θ1(t), θ2(t) and load sway angles θ3(t), θ4(t) are eliminated, that is:

[0128] θ1(t)→0, θ2(t)→0, θ3(t)→0, θ4(t)→0; (12)

[0129] (3) Adaptive anti-sway controller design

[0130] To more clearly illustrate the controller design process, Figure 2 shows a block diagram of the control system;

[0131] The mechanical energy of a seven-degree-of-freedom bridge crane system can be described as follows:

[0132]

[0133] Differentiating (13) yields:

[0134]

[0135] As can be seen from equation (14), the seven-degree-of-freedom bridge crane system is passive, and the system's energy can be transmitted through the trolley speed. Cable tray speed and the speed of the hoisting rope attenuation.

[0136] Substituting (4) into (14) yields:

[0137]

[0138] Where φ x ,φ y ,φ z All are measurable regression vectors, ω x ,ω y ,ω z These are all friction parameter vectors, and their relevant definitions are as follows:

[0139]

[0140]

[0141] To address issues such as drive state overshoot, non-drive sway angle suppression, and friction uncertainty, an adaptive anti-sway controller is proposed based on equation (15):

[0142]

[0143]

[0144]

[0145] Where e x =xx d ,e y =yy d and e z =l1-l 1d These represent the positioning errors of the trolley, bridge, and suspension rope, respectively. d and y d These represent the target displacements of the trolley and the bridge, respectively. 1d Indicates the target length of the suspension rope. k px ,k dx ,k py ,k dy ,k pz ,k dz ,k λ ,k wx ,k wy Both represent control gain. This is the maximum allowable overshoot of the actuator. These represent the friction parameter vector ω. x ,ω y ,ω z The estimated value, The adaptive law is:

[0146]

[0147] Where Γ x =diag{γ x1 ,γ x2}, Γ y =diag{γ y1 ,γ y2} represents updating the gain matrix, Γ z This indicates an update gain.

[0148] The controller in equations (18)-(20) consists of four parts. The first term is the proportional-derivative term, which tracks the target trajectory of the trolley / bridge movement and the change in the length of the suspension rope. The second term is the overshoot limiting term, which ensures that the overshoot of the actuator is always within the set range and quickly drops to zero. The third term is the adaptive term, which is used to estimate friction parameters. The last term of the trolley and bridge controller is the anti-sway term, which enhances the sway control performance. The last term of the suspension rope controller is the gravity compensation term, which is related to the sum of the hook mass and the loaded mass.

[0149] (4) Stability analysis of closed-loop system

[0150] Theorem 1: The adaptive anti-sway controller (18)-(20) proposed in this embodiment can suppress the non-driven sway angle while ensuring that the trolley, bridge and suspension rope lengths reach the required positions, that is:

[0151]

[0152] Proof: Step 1, based on Lyapunov stability analysis. The following Lyapunov candidate functions are selected:

[0153]

[0154] in and Let represent the estimation errors of the friction parameters, and define them as follows:

[0155]

[0156] Differentiating equation (23), and then using equation (15) and equation (18) minus equation (20), we can obtain:

[0157]

[0158] From equations (23) and (25), it can be seen that the closed-loop system is Lyapunov stable. Furthermore, we can obtain:

[0159]

[0160] The second step is to prove the asymptotic stability of the system using Russell's invariance theorem. A set Ω is defined as follows:

[0161]

[0162] Where set Φ is the largest invariant set in set Ω. According to (25), in set Φ we can obtain:

[0163]

[0164] From equation (28), we can obtain the following equation:

[0165]

[0166] Where λ x ,λ y and λ z It is a constant to be determined.

[0167] Combining equations (18)-(20), (28), and (29), we obtain:

[0168]

[0169]

[0170]

[0171] Substituting equations (28)-(30) into equation (1), we get:

[0172]

[0173] Integrating equation (33) yields

[0174]

[0175] Where λ1 represents a constant to be determined. Assume λ x ≠0, as t→∞, then

[0176]

[0177] At this point, (35) contradicts equation (26), therefore the assumption is invalid, λ x =0. Equation (34) can be rewritten as follows:

[0178]

[0179] λ x Substituting 0 into equations (29) and (30), we get:

[0180] e x =0,x=x d ,F xa =0. (37)

[0181] Similarly, substituting equations (28), (29), and (31) into equation (2) yields:

[0182]

[0183] Integrating equation (38) yields:

[0184]

[0185] Where λ² represents a constant to be determined. Assume λ... y ≠0, as t→∞, then:

[0186]

[0187] At this point, (40) contradicts equation (26), therefore the assumption is invalid, λ y =0. Equation (39) can be rewritten as follows:

[0188]

[0189] λ y Substituting 0 into equations (29) and (31), we get:

[0190] e y =0, y=y d ,F ya =0. (42)

[0191] Substituting equations (28) and (29) into equations (4)-(7) and eliminating like terms, we get:

[0192]

[0193]

[0194]

[0195]

[0196] By performing calculations (43)×cosθ1-(33) and (44)×cosθ2-(38) respectively, we can obtain:

[0197]

[0198]

[0199] Based on the assumption condition (10), we know that: sinθ i ∈(-1,1),cosθ i ∈(0,1], i=1,2,3,4. Therefore, from equations (47) and (48), we can obtain:

[0200]

[0201]

[0202] Substituting equation (50) into equation (41), we get:

[0203]

[0204] Integrating both sides of equation (51), we get:

[0205] m2l2sinθ4=λ2t+λ3; (52)

[0206] Where λ3 is a constant to be determined. Assuming λ2 ≠ 0, as t → ∞, then:

[0207] sinθ4→∞; (53)

[0208] Equation (53) contradicts the fact that sinθ4∈(-1,1), therefore the assumption is invalid and λ2=0;

[0209] Substituting λ2=0 into equation (51), we get:

[0210]

[0211] Substituting equations (49) and (50) into (36), we get:

[0212]

[0213] The analysis process is similar to that in (52)-(54), so we can conclude that:

[0214]

[0215] Substituting equations (49), (50), (54), and (56) into equations (45) and (46) respectively, and eliminating redundant terms, we obtain:

[0216]

[0217] Substituting equations (28)-(29), (32), (49)-(50), (54), and (56)-(57) into equation (3) yields the following:

[0218]

[0219] Combining the results of equations (28)-(29), (37), (42), (49)-(50), (54), (56)-(58), Theorem 1 is proved using the Russell invariance principle.

[0220] (5) Experimental verification

[0221] To demonstrate the effectiveness of the adaptive anti-sway control method proposed in this embodiment, a bridge crane experimental platform is used to verify the effectiveness of the control method involved.

[0222] The system of the bridge crane experimental platform is as follows:

[0223] M1=3kg, M2=10kg, m1=0.5kg, m2=1.5kg, l2=0.2m;

[0224] The initial and target values ​​for trolley displacement, bridge frame displacement, and suspension rope length are set as follows:

[0225] x0 = 0m, y0 = 0m, l 10 =0.1m,x d =0.5m,y d =0.5m,l 1d =0.5m;

[0226] To ensure a smooth start-up of the drive, the following S-shaped smooth trajectory is selected as the target displacement of the seat trolley and the bridge, and the target length of the suspension rope:

[0227]

[0228] Where k1 = 2k a / kv , k v =0 . 4m / s,k a =0 . 4m / s 2 These represent the maximum speed and acceleration of the actuator, respectively. ε = 1.5 is a parameter related to the initial acceleration.

[0229] The controller gain is selected as follows:

[0230] k px =50,k dx =25,k py =45,k dy =30,k pz =60,k dz =10,k wx =k wy =1.5,k λ =0.01, ξ=0.005.

[0231] The adaptive law updates the gain to Γ. x =diag{4.45,16.5},Γ y =diag{4.45,20.5},Γ z =11.

[0232] This embodiment will verify the effectiveness of the proposed adaptive anti-sway controller by comparing it with existing smoothers and energy-analysis-based (EAB) controllers. Neither of these existing technologies considers variations in the suspension rope length. For ease of comparison, the smoother shaper uses an average suspension rope length l1 = 0.3m to estimate the natural frequency of load swaying to design the trolley motion, bridge motion, and load lifting / lowering shaper; the EAB controller adds a traditional proportional-derivative (PD) controller to the existing trolley and bridge controllers to drive the load lifting / lowering motion.

[0233] The experimental results of the two existing technologies and the adaptive anti-sway control method designed in this embodiment are shown in Figures 3(a)-3(j). From the subplots x, y, and l1, it can be seen that both the EAB controller and the smoother have difficulty eliminating the actuator's positioning error. Due to the presence of the adaptive term and the overshoot limiting term, this embodiment achieves accurate, overshoot-free positioning performance. The subplot x shows that, under the same displacement, the transmission time of the controller in this embodiment (2; 76s) is shorter and more efficient than that of the EAB controller (3; 73s) and the smoother (4; 63s).

[0234] Furthermore, the maximum undriven sway angles of the EAB controller, the smoother, and this embodiment are 5.59°, 3.01°, and 2.82°, respectively. Using the EAB controller or smoother, significant residual sway is observed after 15 seconds. In contrast, the controller of this embodiment can eliminate undriven sway within 5 seconds. Compared to existing technologies, this embodiment demonstrates superior anti-sway suppression performance.

[0235] As can be seen from Figures 4-5(d), the controller of this embodiment can accurately estimate unknown friction parameters. Based on Figure 1, which illustrates the entire lifting process of the load in the three-dimensional workspace, it can be seen that the controller of this embodiment can accurately transport the load to the target location. In summary, compared with existing EAB controllers and smoothers, the controller of this embodiment has higher positioning accuracy and more effective anti-sway performance.

[0236] The above process establishes a closed-loop adaptive controller for a 7-DOF bridge crane system in three-dimensional space. The proposed controller considers more output degrees of freedom and more complex dynamic characteristics of the double-spherical pendulum and variable rope length. The asymptotic stability of the proposed controller is rigorously proven based on the original complex nonlinear dynamic model without any linearization operations.

[0237] The above process utilizes an adaptive term to estimate the uncertain frictional force of the actuator online, effectively eliminating positioning errors of the trolley, bridge, and suspension rope.

[0238] The above process utilizes an additional nonlinear overshoot limiting term to limit the overshoot of trolley displacement, bridge displacement, and rope length within a finite range during load transportation.

[0239] Example 2:

[0240] A system for implementing the above method includes:

[0241] The control target module is configured to: construct a dynamic model of the bridge crane system containing the frictional forces of the trolley, bridge, and lifting ropes based on the physical parameters of the trolley, bridge, hook, and load, and set the control target;

[0242] The anti-sway control module is configured to: obtain the energy function based on the dynamic model of the bridge crane system, and obtain the anti-sway controller based on the friction of the trolley, bridge frame and hoisting rope, the energy function and the control target;

[0243] The anti-sway actuator module is configured to: realize anti-sway control of the bridge crane based on the driving force of the trolley, bridge frame and hoisting rope output by the anti-sway controller.

[0244] Example 3:

[0245] This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps in the anti-sway control method for bridge cranes as described in Embodiment 1 above.

[0246] Example 4:

[0247] This embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps in the anti-sway control method for bridge cranes as described in Embodiment 1 above.

[0248] The steps or modules involved in Embodiments 2 to 4 above correspond to those in Embodiment 1. For specific implementation details, please refer to the relevant description section of Embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood as including any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and enabling the processor to perform any of the methods in this invention.

[0249] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for preventing swaying of a bridge crane, characterized in that, Includes the following steps: Based on the physical parameters of the trolley, bridge frame, hook, and load, a dynamic model of the bridge crane system containing the frictional forces of the trolley, bridge frame, and lifting rope is constructed, and a control objective is set. An energy function is obtained based on the dynamic model of the bridge crane system. An anti-sway controller is derived based on the frictional forces of the trolley, bridge frame, and lifting rope, the energy function, and the control objective. Anti-sway control of the bridge crane is achieved based on the driving force output by the anti-sway controller on the trolley, bridge frame, and lifting rope. The anti-sway controller is shown in the following equation: ； ； ;in, and These represent the driving forces of the trolley, bridge frame, and suspension rope, respectively. and These represent the positioning errors of the trolley, bridge frame, and suspension rope, respectively. These represent the displacements of the trolley and the cable tray, respectively. These represent the lengths of the hoisting rope and the rigging rope, respectively. and These represent the target displacements of the trolley and the bridge, respectively. Indicates the target length of the suspension rope. Indicates control gain. This is the maximum allowable overshoot of the actuator. All are measurable regression vectors. These represent the friction parameter vectors respectively. The estimated value.

2. The anti-sway control method for bridge cranes as described in claim 1, characterized in that, A dynamic model of the bridge crane system is constructed, including: determining the displacement of the trolley and bridge frame, the mass of the trolley, bridge frame, hook and load, the length of the lifting rope and rigging, and the position and swing angle of the hook and load in the three-dimensional coordinate system; establishing the dynamic equations of trolley displacement, bridge frame displacement, lifting rope length, hook swing angle and load swing angle based on the Lagrangian function, as well as the friction equations of the trolley, bridge frame and lifting rope, and converting them into matrix form.

3. The anti-sway control method for bridge cranes as described in claim 1, characterized in that, The control objectives include positioning and anti-swaying.

4. The anti-sway control method for bridge cranes as described in claim 3, characterized in that, The positioning specifically refers to: the trolley displacement and bridge frame displacement reaching the target value, and the suspension rope length changing to the target value.

5. The anti-sway control method for bridge cranes as described in claim 3, characterized in that, The anti-sway mechanism specifically refers to the elimination of hook sway angle and load sway angle.

6. The anti-sway control method for bridge cranes as described in claim 1, characterized in that, The energy function is obtained by differentiating the mechanical energy function derived from the dynamic model of the bridge crane system.

7. A bridge crane trajectory planning system, characterized in that, The anti-sway control method for a bridge crane according to any one of claims 1-6 includes: a control target module configured to: construct a dynamic model of the bridge crane system containing the frictional forces of the trolley, bridge frame, hook, and load based on the physical parameters of the trolley, bridge frame, hook, and load, and set a control target; an anti-sway control module configured to: obtain an energy function based on the dynamic model of the bridge crane system, and obtain an anti-sway controller based on the frictional forces of the trolley, bridge frame, and hook, the energy function, and the control target; and an anti-sway execution module configured to: realize anti-sway control of the bridge crane based on the driving force on the trolley, bridge frame, and hook output by the anti-sway controller.

8. A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the anti-sway control method for a bridge crane as described in any one of claims 1-6.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the anti-sway control method for a bridge crane as described in any one of claims 1-6.

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