A method and system for vibration suppression of a flexible stacker crane

Abstract

The application provides a flexible stacker crane vibration suppression method, which comprises the following steps: establishing a flexible stacker crane dynamics model; taking the trolley movement of the flexible stacker crane to a target position and the suppression of the mast vibration deflection when the trolley moves to the target position as control targets, and controlling the dynamics parameters in the established flexible stacker crane dynamics model by shaping instructions; wherein the shaping instructions comprise a segmented function shaping instruction and a disturbance suppression instruction, the segmented function shaping instruction is used for controlling the mast vibration caused by the trolley movement of the flexible stacker crane, and the disturbance suppression instruction is used for controlling the mast vibration caused by external disturbance.

Description

Technical Field

[0001] This invention belongs to the field of electromechanical control technology, and in particular relates to a vibration suppression method and system for a flexible stacking crane. 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] Stacker cranes are specialized lifting and transport equipment widely used in automated warehouses and workshops for handling and retrieving goods. To save costs, the mast of a stacker crane employs a lightweight structure. This reduction in weight leads to decreased mast rigidity, sometimes even resulting in a flexible structure. The horizontal inertial force generated by the acceleration and deceleration of the trolley can cause the flexible mast to bend and deform, generating vibration. This not only severely affects the positioning accuracy and operational efficiency of the stacker crane but may also cause the mast to collide with surrounding objects, damaging the crane and its load, leading to production safety accidents. Furthermore, the complex and variable operating environment of stacker cranes, coupled with external disturbances such as wind loads, can further exacerbate the vibration of the flexible mast. Therefore, designing mast vibration suppression and precise positioning control strategies to overcome the vibration problem of the mast during precise and rapid positioning and start-up / stop operations under high-speed, heavy-load, and externally disturbed conditions is of great significance for flexible stacker cranes.

[0004] In recent years, research institutions both domestically and internationally have proposed various control methods for different types of crane systems. Based on whether the control system includes feedback signals, these methods can be categorized into open-loop control and closed-loop control. Open-loop control methods include trajectory planning control and shaping control; closed-loop control methods include neural network control, adaptive control, iterative learning control, and backstepping control.

[0005] Despite significant advancements in crane motion control, several unresolved challenges remain. Existing technologies neglect the vibration and deformation of the crane's flexible structure, focusing solely on suppressing load sway. For stacker cranes, the variables of trolley movement, load sway, and flexible mast vibration exhibit strongly coupled nonlinear relationships. The vibration of the flexible mast further complicates the stability control of the stacker crane. Moreover, current technologies fail to consider the robustness of flexible stacker cranes to uncertain system parameters and external disturbances. Summary of the Invention

[0006] To overcome the shortcomings of the prior art, this invention provides a vibration suppression method and system for a flexible stacking crane. Based on fully considering the vibration response of the mast caused by parameter uncertainty and external disturbances, a piecewise function shaping command and an interference suppression command are designed to suppress the vibration of the flexible mast caused by trolley movement and external disturbances, respectively. This effectively solves the problem of mast vibration during trolley operation and improves the robustness of the stacking crane to system parameter uncertainty and external disturbances.

[0007] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solution: a vibration suppression method for a flexible stacking crane, comprising:

[0008] Establish a dynamic model for a flexible stacking crane;

[0009] The control objectives are to move the trolley of the flexible stacking crane to the target position and to suppress the vibration deflection of the mast when the trolley moves to the target position. The dynamic parameters in the established dynamic model of the flexible stacking crane are controlled by shaping commands.

[0010] The shaping instructions include piecewise function shaping instructions and disturbance suppression instructions. The piecewise function shaping instructions are used to control the mast vibration caused by the movement of the trolley of the flexible stacking crane, and the disturbance suppression instructions are used to control the mast vibration caused by external disturbances.

[0011] A second aspect of the present invention provides a vibration suppression system for a flexible stacker crane, comprising:

[0012] Dynamics Model Building Module: Establishes a dynamics model for the flexible stacking crane;

[0013] Control module: The control objectives are to move the trolley of the flexible stacking crane to the target position and to suppress the vibration and deflection of the mast when the trolley moves to the target position. The dynamic parameters in the established dynamic model of the flexible stacking crane are controlled by shaping commands.

[0014] The shaping instructions include piecewise function shaping instructions and disturbance suppression instructions. The piecewise function shaping instructions are used to control the mast vibration caused by the movement of the trolley of the flexible stacking crane, and the disturbance suppression instructions are used to control the mast vibration caused by external disturbances.

[0015] A third aspect of the present invention provides a computer device comprising: a processor, a memory, and a bus, wherein the memory stores machine-readable instructions executable by the processor, and when the computer device is running, the processor communicates with the memory via the bus, and when the machine-readable instructions are executed by the processor, perform the steps of a vibration suppression method for a flexible stacking crane as described in the first aspect above.

[0016] A fourth aspect of the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, performs the steps of a vibration suppression method for a flexible stacking crane as described in the first aspect above.

[0017] The above one or more technical solutions have the following beneficial effects:

[0018] In this invention, based on fully considering the mast vibration response caused by parameter uncertainty and external disturbances, piecewise function shaping instructions and disturbance suppression instructions are designed to suppress the vibration of the flexible mast caused by trolley movement and external disturbances, respectively. This effectively solves the mast vibration problem during trolley operation and improves the robustness of the stacker crane to system parameter uncertainty and external disturbances.

[0019] In this invention, a dynamic model of a stacker crane with a flexible mast handling load is established. The coupled vibration dynamics of the flexible structure include trolley transfer, flexible mast vibration, and load oscillation. The proposed robust command-based control method exhibits good vibration suppression capability for the flexible structure.

[0020] In this invention, a data-driven BP (Back Propagation) neural network parameter estimator is used to update and adjust vibration parameters in real time. Under specific working conditions, the data-driven estimator has more accurate vibration parameter prediction results than the traditional model-driven estimator.

[0021] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0022] 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.

[0023] Figure 1 This is a schematic diagram of the flexible stacking crane in Embodiment 1 of this disclosure;

[0024] Figure 2 This is a block diagram of the control system of the flexible stacker crane in Embodiment 1 of this disclosure;

[0025] Figure 3 This is a graph of first-order vibration frequency data in Embodiment 1 of this disclosure;

[0026] Figure 4 This is a graph of first-order damping ratio data in Embodiment 1 of this disclosure;

[0027] Figure 5This is a diagram of the BP neural network structure in Embodiment 1 of this disclosure;

[0028] Figure 6 This is a frequency-damping sensitivity characteristic diagram of ZV shaping control in Embodiment 1 of this disclosure;

[0029] Figure 7 This is a frequency-damping sensitivity characteristic diagram of EI shaping control in Embodiment 1 of this disclosure;

[0030] Figure 8 This is a frequency-damping sensitivity characteristic diagram of Smoother shaping control in Embodiment 1 of this disclosure;

[0031] Figure 9 This is a frequency-damping sensitivity characteristic diagram of the robust shaping instruction control (Proposed) in Embodiment 1 of this disclosure;

[0032] Figure 10 This is a frequency sensitivity diagram of the ZV shaping, EI shaping, Smoother shaping and robust shaping command control (Proposed) in Embodiment 1 of this disclosure when the damping ratio is 0.1;

[0033] Figure 11 This is a simulation result diagram of mast vibration under ZV shaping control in Embodiment 1 of this disclosure;

[0034] Figure 12 This is a simulation result diagram of mast vibration under EI shaping control in Embodiment 1 of this disclosure;

[0035] Figure 13 This is a simulation result diagram of mast vibration controlled by Smoother in Embodiment 1 of this disclosure;

[0036] Figure 14 This is a simulation result of mast vibration using the robust shaping command control (Proposed) in Embodiment 1 of this disclosure. Detailed Implementation

[0037] 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.

[0038] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations of the present invention.

[0039] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0040] Example 1

[0041] like Figures 1-14 As shown, this embodiment discloses a vibration suppression method for a flexible stacking crane, including:

[0042] Establish a dynamic model for a flexible stacking crane;

[0043] The control objectives are to move the trolley of the flexible stacking crane to the target position and to suppress the vibration deflection of the mast when the trolley moves to the target position. The dynamic parameters in the established dynamic model of the flexible stacking crane are controlled by shaping commands.

[0044] The shaping instructions include piecewise function shaping instructions and disturbance suppression instructions. The piecewise function shaping instructions are used to control the mast vibration caused by the movement of the trolley of the flexible stacking crane, and the disturbance suppression instructions are used to control the mast vibration caused by external disturbances.

[0045] In this embodiment, a schematic diagram of the flexible stacking crane is shown below. Figure 1 As shown, the system parameters of the flexible stacking crane are as follows: M represents the trolley mass, m1 represents the mast mass, m2 represents the load mass, l represents the mast length, w represents the bending deflection of the mast at a distance y from the drive origin, x represents the trolley displacement, E represents Young's modulus, I represents the moment of inertia of the mast interface, ρ represents the mast linear mass density, u represents the trolley control input, and g represents the gravitational acceleration.

[0046] Using the modal superposition method, the vibration deflection of the flexible mast can be expressed as:

[0047]

[0048] Where, φ k (y) represents the k-th order mode function, specifically as follows:

[0049] φ k (y)=cos(β k y)-cosh(β k y)+η k [sin(β k y)-sinh(β k y)] (2)

[0050]

[0051] Where β k Let represent the k-th order frequency coefficient. The frequency equation is expressed as:

[0052]

[0053] q k(t) is a function related to time t:

[0054]

[0055] in: They represent q respectively k (t) First and second derivatives with respect to time t Let ξ denote the second derivative of x(t) with respect to time t. k ,ω k Let λ represent the k-th order damping ratio and the natural frequency, respectively. k , Represents the coefficient. ω k ,λ k , The expression is as follows:

[0056]

[0057]

[0058]

[0059] By combining equations (1) and (5) and performing a Laplace transform, the mast vibration deflection transfer function at position y can be obtained:

[0060]

[0061] In this embodiment, due to the inherent flexible vibration characteristics of the stacker crane and its complex operating environment, the designed robust shaping command control method should meet the following control objectives:

[0062] (1) Positioning of the trolley: from the initial time t=0 to the end of the transportation time t=t d The trolley is controlled to move from its initial position to the target position, as shown in the following expression:

[0063] x(0) = x0, x(t) d )=x d ,x (i) (0)=0,x (i) (x d )=0,i=1,2. (10)

[0064] Where t d For the transportation time, x( 1 ) and x( 2 ) represent the velocity and acceleration of the trolley, x0 and x... d These represent the starting position and the target position of the trolley, respectively.

[0065] (2) Mast vibration deflection suppression: When the trolley is controlled and driven to the target position, the mast vibration deflection is effectively suppressed, as expressed by:

[0066]

[0067] like Figure 3 As shown, this embodiment uses a shaping command controller to control the flexible stacking crane. The shaping command controller includes piecewise function shaping commands and disturbance suppression commands, which can suppress mast vibration caused by trolley acceleration and deceleration and mast vibration caused by external disturbances, respectively.

[0068] Traditional model-driven parameter estimator formula (6) involves solving complex transcendental equations (4), which cannot be solved online in real time. Furthermore, the shaping command controller is designed with zero damping, neglecting the influence of damping ratio on vibration control.

[0069] This example demonstrates a data-driven BP neural network-based system parameter estimator that can effectively estimate the vibration frequency and damping ratio of a mast in real time online.

[0070] Under different mast lengths and load conditions, the mast bending deflection can be easily measured experimentally in the time domain. Then, the frequency and damping ratio of the mast vibration can be calculated using Fast Fourier Transform (FFT) and logarithmic decay methods, as shown below. Figure 3 and Figure 4 As shown.

[0071] The BP neural network used in this embodiment has three layers, such as... Figure 5 As shown, the input layer has two input neurons related to the load mass and mast length. The hidden layer has ten hidden neurons. The output layer has two output neurons related to the first-order vibration frequency and damping ratio. In other words, the BP neural network takes the load mass and mast length as input and outputs the first-order vibration frequency and damping ratio.

[0072] The activation function used in the BP neural network is the Sigmoid function, x i x represents the input to the hidden layer and the output of the hidden layer. j The calculation is as follows:

[0073]

[0074] Among them, W a It is the weight between the input layer and the hidden layer, b j It is the bias of the hidden layer.

[0075] The output layer is calculated as follows:

[0076]

[0077] Among them, W b It is the weight between the hidden layer and the output layer, c s It is the bias of the output layer.

[0078] This embodiment adopts Figure 3 and Figure 4 Data numbered (1)-(9) were used as the test dataset, and the following methods were employed. Figure 3 and Figure 4 The other data was used as the training dataset. The Levenberg-Marquardt (LM) algorithm was used to train the BP neural network, and the weights and biases in the BP neural network were calculated by minimizing the mean squared error (MSE). The expression for MSE is as follows:

[0079]

[0080] Among them, MSE ω and MSE ξ Let ω1(h) and ω1(h) represent the minimum mean square error of frequency and damping ratio, respectively. Let ξ1(h) and ξ2(h) represent the actual frequency value and the predicted frequency value of the h-th test sample, respectively. represents the actual damping ratio and the predicted damping ratio of the h-th test sample, respectively. n is the number of samples in the test set.

[0081] The weights and biases of the BP neural network are obtained using the LM algorithm, as shown below:

[0082]

[0083]

[0084]

[0085]

[0086] This embodiment uses frequency relative error and damping ratio to evaluate the performance of the established BP neural network:

[0087]

[0088] Where, ε ωp (h) and ε ξp (h) represents the relative errors of the frequency and damping ratio of the h-th sample, respectively.

[0089] Table 1 shows the predicted results for frequency ω1 and damping ratio ξ1. The frequency is estimated using model-driven estimation equation (6). ε ωc It is the actual frequency ω1 and the estimated frequency The relative error between them. ε ωp and ε ωc The maximum values ​​are denoted as 6.78% and 62.71%, respectively. Due to dynamic uncertainties such as friction, model-driven parameter estimators cannot accurately estimate frequencies under certain operating conditions. Prediction results show that the data-driven BP neural network parameter estimator is more accurate in parameter estimation than the traditional model-driven estimator. Furthermore, ε ξp The maximum value is 7.81%. Experimental results show that the predicted damping ratio does not differ significantly from the actual result. The proposed BP neural network parameter estimator is reliable for real-time prediction of vibration parameters.

[0090] Table 1. Prediction results of frequency ω1 and damping ratio ξ1

[0091]

[0092] In this embodiment, the mast vibration frequency and damping ratio are estimated in real time online using the aforementioned BP neural network. A piecewise function shaping instruction is designed using the estimated mast vibration frequency and damping ratio. This piecewise function shaping instruction suppresses the mast vibration caused by the trolley movement. The flexible crane system responds to the piecewise function shaping instruction u. s The harmonic response is:

[0093]

[0094] The amplitude of formula (17) is:

[0095]

[0096] in,

[0097] To suppress residual vibration, the frequency ω k And damping ratio ξ k The amplitude at that point is limited to zero.

[0098]

[0099]

[0100] To improve the robustness to parameter uncertainty, this embodiment introduces two new modification frequencies (1-p)ω. k and (1+p)ω k Furthermore, the amplitude at that point is also limited to zero. The residual vibration constraints at the modified frequency are shown below:

[0101]

[0102]

[0103]

[0104]

[0105] Where p∈(0,1) is the correction factor.

[0106] To suppress transient vibrations, the maximum transient amplitude of the mast during the trolley's movement should be less than the allowable vibration amplitude V. tol :

[0107]

[0108] Where, τ m τ is the duration of the piecewise function shaping instruction in the design. n It refers to any moment in the transient phase.

[0109] The trolley, under the control of piecewise function shaping instructions, should achieve the same speed value as under non-shaping instructions. Therefore, amplitude constraints should be introduced:

[0110]

[0111] Solving equations (19)-(26), we can obtain the time-optimal shaping instruction based on the piecewise function as follows:

[0112]

[0113] in,

[0114]

[0115]

[0116]

[0117] The piecewise function shaping instruction proposed in this embodiment is similar to a smoothing shaper, combining the characteristics of a notch filter and a low-pass filter. The notch filter targets the first-mode vibration, while the low-pass filter suppresses higher-mode vibrations. Therefore, the piecewise function shaping instruction is designed by estimating the first-order vibration frequency and damping ratio.

[0118] In this embodiment, the correction coefficient p is set to 0.25. For example, the estimated parameters ω1 = 0.75Hz and ξ1 = 0.0092 are substituted into equations (19)-(27), and the shaping command coefficient ε is adjusted. e (e = 1, 2, 3... 6) can be calculated as:

[0119] ε1=-8.2772, ε2=2.5457, ε3=-15.7680, ε4=2.4879, ε5=-8.7427, ε6=0.9422

[0120] To ensure control performance, if the first-order vibration frequency ω1 and damping ratio ξ1 change, the shaping command coefficient ε should be recalculated. e (e = 1, 2, 3... 6).

[0121] In this embodiment, the vibration of the mast and load caused by external interference is eliminated by disturbance suppression commands. The harmonic response of the flexible crane system to disturbance suppression commands and external interference is as follows:

[0122]

[0123] The amplitude of formula (31) is:

[0124]

[0125] in,

[0126]

[0127] To suppress mast vibration caused by external disturbances, the amplitude in formula (32) should be limited to 0:

[0128]

[0129]

[0130] To ensure that the speed and displacement of the trolley are not affected after the disturbance suppression command is applied, the following amplitude constraints should be met:

[0131]

[0132]

[0133] By solving equations (35)-(38), the disturbance suppression command is obtained:

[0134]

[0135] in, D m This indicates the maximum amplitude of the disturbance.

[0136] In this implementation, a composite robust shaping instruction is obtained by combining the piecewise function shaping instruction (27) and the disturbance suppression instruction (39):

[0137]

[0138] Where, ε e (e = 1, 2, 3... 6) are the integer shaping command coefficients, ξ k ,ω k Let represent the k-th order damping ratio and the natural frequency, respectively.

[0139] To verify the effectiveness of the robust shaping command control method proposed in this embodiment, the control effects of the proposed robust shaping command control method, ZV shaping method, EI shaping method and Smoother shaping method were compared through simulation in this example.

[0140] The system parameter settings for the flexible stacking crane proposed in this embodiment are as follows:

[0141] M=3kg, m1=0.0751kg, m2=0.2kg, l=0.4m, E=2.06×10 5 MPa,

[0142] I = 1.1947 × 10 -12 m 4 ρ=0.18775kg / m, g=9.81m / s 2 .

[0143] Figure 6 , Figure 7 , Figure 8 and Figure 9 These are frequency-damping sensitivity characteristic diagrams for ZV shaping control, EI shaping control, Smoother shaping control, and the robust shaping command control (Proposed) proposed in the embodiments of this disclosure.

[0144] Vibration percentage V is an important evaluation metric in shaping control methods. Normalized frequency is used to represent the ratio of the actual first-order mode frequency to the designed first-order mode frequency. Figure 6 This indicates that ZV shaping control is highly sensitive to frequency changes. For example... Figure 7 As shown, at a normalized frequency of 1, the vibration percentage of EI shaping is 5%. Figure 8 It can be seen that although Smoother shaping is not sensitive to frequency changes when the normalized frequency is greater than 1, the percentage of vibration increases rapidly when the normalized frequency is less than 1. Figure 9 As shown, due to the effect of the constraint equations, the vibration percentage of the robust shaping command control proposed in this embodiment of the present disclosure is at the normalized frequency ω1 / ω 1m =1 and The values ​​are all suppressed to 0, indicating that the proposed robust shaping instruction is not sensitive to frequency changes within a certain frequency range. Figure 10This diagram illustrates the frequency sensitivity characteristics of ZV shaping, EI shaping, Smoother shaping, and the robust shaping command control proposed in this disclosure embodiment at a damping ratio of 0.1. From... Figure 10 As can be seen, the robust shaping command control exhibits an insensitivity of 0.67 to 1.35 for a 5% damping ratio of 0.1. The insensitivity range of the robust shaping command control method increases with increasing damping ratio. Furthermore, the robust shaping command control is insensitive to changes in the damping ratio.

[0145] Figure 11 , Figure 12 , Figure 13 and Figure 14 The figures show the simulation results of mast vibration for ZV shaping control, EI shaping control, Smoother shaping control, and the robust shaping command control (Proposed) proposed in this disclosure. The residual vibrations for ZV shaping control, EI shaping control, Smoother shaping control, and robust shaping command control (Proposed) are 88.97 mm, 55.67 mm, 56.72 mm, 55.74 mm, and 0.20 mm, respectively. The experimental results show that none of the comparative control methods can suppress the vibration caused by disturbances, and only the robust shaping command control (Proposed) proposed in this disclosure can effectively eliminate mast vibration caused by trolley motion and external disturbances.

[0146] Example 2

[0147] The purpose of this embodiment is to provide a vibration suppression system for a flexible stacker crane, including:

[0148] Dynamics Model Building Module: Establishes a dynamics model for the flexible stacking crane;

[0149] Control module: The control objectives are to move the trolley of the flexible stacking crane to the target position and to suppress the vibration and deflection of the mast when the trolley moves to the target position. The dynamic parameters in the established dynamic model of the flexible stacking crane are controlled by shaping commands.

[0150] The shaping instructions include piecewise function shaping instructions and disturbance suppression instructions. The piecewise function shaping instructions are used to control the mast vibration caused by the movement of the trolley of the flexible stacking crane, and the disturbance suppression instructions are used to control the mast vibration caused by external disturbances.

[0151] Example 3

[0152] The purpose of this embodiment is to provide a computing device, including 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 above-described method.

[0153] Example 4

[0154] The purpose of this embodiment is to provide a computer-readable storage medium.

[0155] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, performs the steps of the above method.

[0156] The steps and methods involved in the apparatuses of Embodiments 2, 3, and 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.

[0157] Those skilled in the art will understand that the modules or steps of the present invention described above can be implemented using general-purpose computer devices. Optionally, they can be implemented using computer-executable program code, thereby allowing them to be stored in a storage device for execution by a computer device, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. The present invention is not limited to any particular combination of hardware and software.

[0158] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A vibration suppression method for a flexible stacking crane, characterized in that, include: Establish a dynamic model for a flexible stacking crane; The control objectives are to move the trolley of the flexible stacking crane to the target position and to suppress the vibration deflection of the mast when the trolley moves to the target position. The dynamic parameters in the established dynamic model of the flexible stacking crane are controlled by shaping commands. The shaping instructions include piecewise function shaping instructions and disturbance suppression instructions. The piecewise function shaping instructions are used to control the mast vibration caused by the movement of the trolley of the flexible stacking crane, and the disturbance suppression instructions are used to control the mast vibration caused by external disturbances. Based on the obtained first-order vibration frequency and damping ratio of the flexible stacking crane mast, a piecewise function shaping instruction is designed, specifically: Establish a harmonic response formula for a flexible crane to a piecewise function shaping command; The amplitude transfer function is obtained based on the established harmonic response formula; With vibration frequency Damping ratio The amplitude at that point is limited to zero, and the frequency is modified. and The amplitude at the point is limited to zero, and the maximum transient amplitude of the mast during the movement of the trolley should be less than the allowable vibration amplitude. The piecewise function shaping instruction is obtained by solving the constraint that the trolley reaches the same speed value as the non-shaping instruction under the control of the piecewise function shaping instruction; among which, It is a correction factor; The disturbance suppression command is established as follows: Establish the harmonic response of the flexible crane to disturbance suppression command and external interference; The amplitude transfer function is obtained based on the established harmonic response formula; The disturbance suppression command is obtained by solving the amplitude condition that the amplitude is limited to 0 and the speed and displacement of the trolley are not affected. The shaping instruction obtained through the piecewise function shaping instruction and the disturbance suppression instruction is specifically as follows: in, For integer command coefficients; Let represent the k-th order damping ratio and the natural frequency, respectively; ; Indicates the stacker crane's operating time; Indicates the initial moment of operation of the stacker crane; ; ; This indicates the maximum amplitude of the disturbance.

2. The vibration suppression method for a flexible stacking crane as described in claim 1, characterized in that, A dynamic model of a flexible stacking crane, incorporating the coupled motion of the trolley, mast vibration, and load oscillation, was established using the modal superposition method.

3. The vibration suppression method for a flexible stacking crane as described in claim 1, characterized in that, The vibration frequency and damping ratio of the mast are estimated online in real time using a BP neural network. The BP neural network has three layers, including an output layer, a hidden layer, and an output layer. The input of the BP neural network is the load mass of the flexible stacking crane and the length of the mast. The output of the BP neural network is the first-order vibration frequency and damping ratio of the mast of the flexible stacking crane.

4. The vibration suppression method for a flexible stacking crane as described in claim 1, characterized in that, Under disturbance suppression command control, the speed and displacement of the trolley are unaffected, and the amplitude condition satisfied is: in, This is a disturbance suppression command.

5. A vibration suppression system for a flexible stacking crane, employing a vibration suppression method for a flexible stacking crane as described in any one of claims 1 to 4, characterized in that, include: Dynamics Model Building Module: Establishes a dynamics model for the flexible stacking crane; Control module: The control objectives are to move the trolley of the flexible stacking crane to the target position and to suppress the vibration and deflection of the mast when the trolley moves to the target position. The dynamic parameters in the established dynamic model of the flexible stacking crane are controlled by shaping commands. The shaping instructions include piecewise function shaping instructions and disturbance suppression instructions. The piecewise function shaping instructions are used to control the mast vibration caused by the movement of the trolley of the flexible stacking crane, and the disturbance suppression instructions are used to control the mast vibration caused by external disturbances.

6. A computer device, characterized in that, include: The system includes a processor, a memory, and a bus. The memory stores machine-readable instructions executable by the processor. When the computer device is running, the processor communicates with the memory via the bus. When the machine-readable instructions are executed by the processor, they perform the steps of a vibration suppression method for a flexible stacking crane as described in any one of claims 1 to 4.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, performs the steps of a vibration suppression method for a flexible stacking crane as described in any one of claims 1 to 4.

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