A method, system, storage medium and program product for vibration control of a stacked parking

Abstract

The application provides a stacking type parking anti-vibration control method, system, storage medium and program product, relates to the technical field of automatic control of mechanical parking equipment, and the method comprises the following steps: acquiring actual mass data and three-dimensional mass center coordinate data of a vehicle to be parked through a weighbridge; determining a spatial offset according to the three-dimensional mass center coordinate data, and determining a three-dimensional eccentric load moment of the vehicle to be parked applied to a column according to the spatial offset; converting a predetermined running track of a stacking machine into a discrete time sequence, and determining a planned lifting height at each discrete time; constructing a target rigid-flexible coupling dynamics model according to the actual mass data, the three-dimensional eccentric load moment, physical parameters of a column section and the planned lifting height, and generating a time-varying shaping pulse sequence matched with the discrete time sequence; generating a target speed control curve according to an initial motion instruction of the stacking machine and the time-varying shaping pulse sequence; and controlling a stacking machine driving motor to perform a vehicle carrying operation on the vehicle to be parked according to the target speed control curve.

Description

Technical Field

[0001] This application relates to the field of automated control technology for mechanical parking equipment, and in particular to a method, system, storage medium, and program product for vibration control of stacked parking systems. Background Technology

[0002] With the popularization of new energy vehicles and the increasing demand for urban parking, high-density multi-level parking systems have been widely used in industrial parks and commercial centers. Among them, stacker-style parking systems utilize stacker cranes to perform three-dimensional coordinated operation along the X-axis (horizontal), Y-axis (lifting), and Z-axis (forklift retrieval) within the aisles of the multi-level parking garage, enabling high-density vehicle storage and retrieval. To maximize space utilization, modern multi-level parking garages often adopt lightweight steel structures (such as honeycomb shell structures).

[0003] In related technologies, stacker cranes typically use preset fixed speed curves for motion control when handling vehicles. However, the range of vehicles currently parked is extremely wide, from light hatchbacks to heavy SUVs and MPVs, and even vehicles with one side completely loaded with heavy objects, resulting in severe off-center loading. When a stacker crane carries these vehicles with different masses and center-of-gravity distributions during high-speed X / Y dual-axis operation, uncontrollable off-center loading moments can cause severe low-frequency flexible vibrations in the stacker crane columns and the lightweight steel structure of the garage. To suppress these low-frequency flexible vibrations, there are generally two approaches: one is to deliberately reduce all operating speeds and accelerations of the stacker crane to achieve stability; the other is to significantly increase the steel of the stacker crane columns and garage frame to improve physical rigidity, thereby achieving vibration reduction.

[0004] However, the two methods mentioned above have different effects. The former limits the operating speed and acceleration of the stacker crane, resulting in a decrease in the storage and retrieval efficiency of the stacker parking system. The latter increases the amount of steel used in the stacker crane and the garage frame, as well as the structural weight. Furthermore, as the height of the garage increases (e.g., in super high-rise multi-level parking garages), simply increasing physical rigidity is insufficient to eliminate low-frequency flexible vibrations. Consequently, the stacker parking system in the relevant technology cannot guarantee vehicle storage and retrieval efficiency while maintaining structural stability under various vehicle types and off-center loading conditions. Summary of the Invention

[0005] This application provides a method, system, storage medium, and program product for vibration control of stacked parking systems, which can ensure vehicle storage and retrieval efficiency while taking into account structural operational stability under various vehicle models and off-center loading conditions.

[0006] Firstly, this application provides a vibration control method for stacked parking systems, applied to a stacked parking system including a stacker crane, a vehicle platform, and a weighbridge. The stacker crane includes a column. The method includes: acquiring the actual mass data and three-dimensional centroid coordinate data of the vehicle to be parked on the vehicle platform using the weighbridge; determining the spatial offset of the vehicle's centroid from the stacker crane's load center based on the three-dimensional centroid coordinate data; and determining the three-dimensional eccentric load moment applied by the vehicle to the column based on the spatial offset and the actual mass data; and configuring the predetermined horizontal running trajectory of the stacker crane and the pre-defined horizontal running trajectory of the vehicle. The fixed lifting trajectory is converted into a discrete time series, and the planned lifting height of the stacker crane at each discrete moment in the discrete time series is determined. Based on the actual mass data, three-dimensional eccentric moment, cross-sectional physical parameters of the column, and planned lifting height, a target rigid-flexible coupling dynamic model is constructed, and a time-varying shaped pulse sequence matching the discrete time series is generated based on the target rigid-flexible coupling dynamic model. A target speed control curve is generated based on the initial motion command of the stacker crane and the time-varying shaped pulse sequence. The drive motor of the stacker crane is controlled to perform vehicle handling operations according to the target speed control curve for the vehicles to be parked.

[0007] By adopting the above technical solution, the actual load state of the vehicles to be parked is coupled with the structural dynamic characteristics of the stacker crane column. A target rigid-flexible coupling dynamic model is used to calculate in real time the time-varying natural frequency of the stacker crane system as the planned lifting height changes. Based on this time-varying natural frequency, a time-varying shaped pulse sequence is generated and embedded into the target speed control curve. This ensures that the frequency of the excitation torque generated by the drive motor matches and cancels out the natural vibration frequency of the column structure, achieving personalized vibration control for the load characteristics of each vehicle to be parked. Without reducing the stacker crane's operating speed or increasing the rigidity of the column structure, the low-frequency flexible vibration of the column caused by differences in the mass of the vehicles to be parked and the uneven distribution of the center of gravity is eliminated from the source of excitation. This solves the technical problem in related technologies where stacked parking systems struggle to ensure both vehicle retrieval efficiency and structural stability under various vehicle types and uneven loading conditions. The stacked parking system achieves the technical effect of ensuring both vehicle retrieval efficiency and structural stability under various vehicle types and uneven loading conditions.

[0008] Optionally, the actual mass data and three-dimensional centroid coordinate data of the vehicle to be parked on the vehicle carrier platform are obtained through a weighbridge, including: during the process of the vehicle to be parked driving into the vehicle carrier platform, real-time load data is collected at measurement points on the vehicle carrier platform by at least four weighbridge sensors installed below the vehicle carrier platform to obtain distributed load time series data; the outline image of the vehicle to be parked is collected by a contour recognition camera installed at the entrance of the vehicle carrier platform, and the outline image is matched and queried in a preset vehicle model database to obtain the reference centroid height range of the vehicle model corresponding to the vehicle to be parked; the wheel coordinates of the vehicle to be parked are obtained by measuring the load at the measurement points on the surface of the vehicle carrier platform. The tire pressure sensing area detects the ground pressure distribution data of each tire of the vehicle to be parked; when the vehicle is stationary on the vehicle platform, the actual mass data is determined based on the distributed load time series data; the first centroid coordinate component in the horizontal longitudinal direction and the second centroid coordinate component in the horizontal lateral direction of the vehicle to be parked are determined based on the distributed load time series data and the ground pressure distribution data; the third centroid coordinate component in the vertical direction of the vehicle to be parked is determined based on the vehicle model reference centroid height range; the first centroid coordinate component, the second centroid coordinate component, and the third centroid coordinate component are determined as three-dimensional centroid coordinate data.

[0009] By adopting the above technical solution, the actual mass data of the vehicle to be parked is dynamically acquired during the process of the vehicle driving in by fusing the distributed load time series data of the weighbridge sensor, the shape contour image matching result of the contour recognition camera, and the ground pressure distribution data of the tire pressure sensing area. The three-dimensional center of gravity coordinate data is determined by comprehensively applying the torque balance principle and the reference center of gravity height range of the vehicle model. This achieves a comprehensive and accurate perception of the actual load state of the vehicle to be parked, providing reliable input parameters for the subsequent construction of a target rigid-flexible coupling dynamic model that can accurately reflect the current load characteristics.

[0010] Optionally, the spatial offset of the vehicle's center of gravity from the stacker crane's load-bearing center is determined based on the three-dimensional centroid coordinate data, and the three-dimensional off-center load moment applied by the vehicle to the column is determined based on the spatial offset and actual mass data. This includes: obtaining the load-bearing center coordinates of the stacker crane's vehicle platform, performing deviation analysis between the three-dimensional centroid coordinate data and the load-bearing center coordinates to obtain horizontal longitudinal offset components, horizontal lateral offset components, and vertical offset components; determining the horizontal longitudinal offset components, horizontal lateral offset components, and vertical offset components as the spatial offset; and determining the spatial offset based on the actual mass data and preset gravity. The acceleration constant determines the static gravity load of the vehicle to be parked; the pitching off-center load moment component around the horizontal lateral direction is determined based on the static gravity load and the horizontal longitudinal offset component, and the roll off-center load moment component around the horizontal longitudinal direction is determined based on the static gravity load and the horizontal lateral offset component; the inertial load is determined based on the planned acceleration and actual mass data of the stacker crane in the horizontal longitudinal direction, and the yaw off-center load moment component around the vertical direction is determined based on the inertial load and the vertical offset component; the pitching off-center load moment component, the roll off-center load moment component, and the yaw off-center load moment component are determined as three-dimensional off-center load moments.

[0011] By adopting the above technical solution, the deviation of the center of mass of the vehicle to be parked from the load-bearing center of the stacker crane is quantified by spatial offset. The off-center load moment components in three directions are determined by combining static gravity load and dynamic inertial load. This constitutes a complete three-dimensional off-center load moment that describes the three-dimensional off-center load effect of the vehicle to be parked on the column. This enables the target rigid-flexible coupling dynamic model to accurately reflect the combined bending moment effect of pitch, tilt and sway of the column caused by the deviation of the center of mass of the vehicle to be parked from the load-bearing center. This lays the mechanical analysis foundation for accurately calculating the vibration response characteristics of the column structure under three-dimensional off-center load conditions.

[0012] Optionally, before generating a time-varying shaped pulse sequence matching the discrete-time sequence based on the target rigid-flexible coupling dynamics model, the method further includes: determining the X-axis horizontal motion parameters based on the horizontal acceleration of the stacker crane at each discrete moment, and determining the Y-axis lifting motion parameters based on the lifting speed of the stacker crane at each discrete moment; establishing a three-dimensional coupling effect matrix in the target rigid-flexible coupling dynamics model based on the X-axis horizontal motion parameters, the Y-axis lifting motion parameters, and the three-dimensional eccentric load moment, the three-dimensional coupling effect matrix including a first coupling coefficient corresponding to the horizontal acceleration and a second coupling coefficient corresponding to the lifting speed; determining the coupled bending moment load on the column at each discrete moment based on the first coupling coefficient, the second coupling coefficient, and the planned lifting height; determining the structural deflection response value of the column at each discrete moment based on the coupled bending moment load, the section moment of inertia, and the elastic modulus in the section physical parameters; and determining the pulse amplitude constraint coefficient at each discrete moment based on the structural deflection response value and the preset deflection safety limit.

[0013] By adopting the above technical solution, the coupling effect between the horizontal acceleration of the stacker crane's X-axis and the lifting speed of its Y-axis and the three-dimensional eccentric load moment is quantified through a three-dimensional coupling effect matrix. The coupled bending moment load on the column at each discrete moment is determined. Based on the coupled bending moment load, the moment of inertia of the section and the elastic modulus, the structural deflection response value of the column at each discrete moment is determined. Based on the structural deflection response value and the preset deflection safety limit, the pulse amplitude constraint coefficient at each discrete moment is determined. This ensures that the time-varying shaped pulse sequence is constrained by the structural safety constraint of the column while pursuing the maximization of vibration suppression effect, thereby achieving synergistic optimization of the effectiveness of vibration control and the safety of the column structure.

[0014] Optionally, a target rigid-flexible coupled dynamic model is constructed based on actual mass data, three-dimensional eccentric load moment, cross-sectional physical parameters of the column, and planned lifting height. A time-varying shaped pulse sequence matching the discrete-time series is then generated based on this model. This includes: constructing a target rigid-flexible coupled dynamic model with the column as the flexible component and the vehicle to be parked and the vehicle platform as the rigid component, based on actual mass data, three-dimensional eccentric load moment, cross-sectional physical parameters, and planned lifting height; inputting the linear density of the column's material into the target rigid-flexible coupled dynamic model to determine the first-order and second-order time-varying natural frequencies of the stacker crane at each discrete moment; determining the first-order vibration period based on the first-order time-varying natural frequency, and... Half of the first-order vibration period is determined as the first time interval of the first-order shaping pulse; the second-order vibration period is determined according to the second-order time-varying natural frequency, and half of the second-order vibration period is determined as the second time interval of the second-order shaping pulse; the first-order amplitude weighting coefficient of the first-order shaping pulse and the second-order amplitude weighting coefficient of the second-order shaping pulse are determined according to the material damping ratio of the column, and both the first-order amplitude weighting coefficient and the second-order amplitude weighting coefficient are negatively correlated with the material damping ratio; a time-varying shaping pulse sequence is generated based on the three-dimensional eccentric load moment, the first-order time-varying natural frequency, the second-order time-varying natural frequency, the first time interval, the second time interval, the first-order amplitude weighting coefficient, the second-order amplitude weighting coefficient, and the pulse amplitude constraint coefficient.

[0015] By adopting the above technical solution, the vehicle to be parked and the vehicle platform are regarded as rigid components, and the column is regarded as a flexible component. A target rigid-flexible coupling dynamic model is constructed. The first-order time-varying natural frequency and the second-order time-varying natural frequency that change with the planned lifting height are calculated by the material linear density parameter. The first-order vibration period is determined according to the first-order time-varying natural frequency. Half of the first-order vibration period is determined as the first time interval of the first-order shaping pulse. The second-order vibration period is determined according to the second-order time-varying natural frequency. Half of the second-order vibration period is determined as the second time interval of the second-order shaping pulse. The first-order amplitude weighting coefficient of the first-order shaping pulse and the second-order amplitude weighting coefficient of the second-order shaping pulse are determined according to the material damping ratio of the column. The time-varying shaping pulse sequence is generated according to the three-dimensional eccentric load moment, the first-order time-varying natural frequency, the second-order time-varying natural frequency, the first time interval, the second time interval, the first-order amplitude weighting coefficient, the second-order amplitude weighting coefficient, and the pulse amplitude constraint coefficient, so as to achieve active adaptive suppression of the flexible vibration characteristics of the column.

[0016] Optionally, a time-varying shaped pulse sequence is generated based on the three-dimensional eccentric load moment, the first-order time-varying natural frequency, the second-order time-varying natural frequency, the first time interval, the second time interval, the first-order amplitude weighting coefficient, the second-order amplitude weighting coefficient, and the pulse amplitude constraint coefficient. This includes: determining the first-order vibration modal response of the column based on the three-dimensional eccentric load moment and the first-order time-varying natural frequency, and determining the second-order vibration modal response of the column based on the three-dimensional eccentric load moment and the second-order time-varying natural frequency; determining the modal coupling coefficient between the first-order and second-order modes based on the first-order and second-order vibration modal responses; generating a first-order shaped pulse sequence based on the first time interval and the first-order amplitude weighting coefficient, and generating a second-order shaped pulse sequence based on the second time interval and the second-order amplitude weighting coefficient; performing time-series superposition processing on the first-order and second-order shaped pulse sequences according to the modal coupling coefficient to obtain a superimposed pulse sequence; and constraining the pulse amplitude at each discrete moment in the superimposed pulse sequence according to the pulse amplitude constraint coefficient to generate a time-varying shaped pulse sequence.

[0017] By adopting the above technical solution, the first-order and second-order vibration modal responses of the column are excited by three-dimensional eccentric load moment, the interaction strength between the first-order and second-order modes is quantified by the modal coupling coefficient, the first-order and second-order shaped pulse sequences are time-series superimposed considering the modal coupling effect, and the superimposed pulse sequence is then constrained by the pulse amplitude constraint coefficient. The generated time-varying shaped pulse sequence can simultaneously achieve synergistic suppression of the first-order and second-order low-frequency flexible vibration modes of the column, avoiding the problem of insufficient vibration prevention effect caused by only suppressing a single mode vibration and ignoring modal coupling.

[0018] Optionally, a target speed control curve is generated based on the initial motion command and time-varying shaping pulse sequence of the stacker crane, including: parsing the initial motion command to obtain a basic S-shaped speed curve, which includes an acceleration segment, a constant speed segment, and a deceleration segment; performing time-domain convolution processing on the basic S-shaped speed curve and the time-varying shaping pulse sequence to obtain the initial shaped speed curve; extracting the torque projection component of the stacker crane in the current running direction from the three-dimensional eccentric load moment, and determining whether the direction of action of the torque projection component is the same as the direction of the stacker crane's inertial moment; when the direction of action is the same as the direction of the inertial moment, confirming... The stacker crane is under an aggravated off-center load condition, and the acceleration stretching coefficient is determined based on the torque projection component. The acceleration segment of the initial shaping speed curve is smoothed and extended using the acceleration stretching coefficient to obtain the first asymmetric shaping curve. When the direction of action is opposite to the direction of the inertial torque, the stacker crane is determined to be under an off-center load suppression condition, and the deceleration compression coefficient is determined based on the torque projection component. The deceleration segment of the initial shaping speed curve is time-compressed using the deceleration compression coefficient to obtain the second asymmetric shaping curve. The first or second asymmetric shaping curve is used as the target speed control curve.

[0019] By adopting the above technical solution, the time-varying shaping pulse sequence is embedded into the basic S-shaped velocity curve through time-domain convolution processing to obtain the initial shaping velocity curve. Furthermore, the type of off-center loading condition is determined based on the relationship between the torque projection component of the three-dimensional off-center load moment in the current running direction and the direction of the stacker crane's inertial torque. For the off-center load aggravation condition, the acceleration section is smoothed and extended to reduce the acceleration peak value and reduce inertial impact. For the off-center load suppression condition, the deceleration section is time-compressed to improve deceleration efficiency and shorten handling time. The generated asymmetric target velocity control curve not only realizes active vibration suppression based on time-varying natural frequency, but also realizes adaptive optimization of the acceleration and deceleration process for different off-center load conditions, further improving the accuracy and efficiency of vibration control.

[0020] In a second aspect, embodiments of this application provide a stacking parking system, which includes: one or more processors and a memory; the memory is coupled to one or more processors, the memory is used to store computer program code, the computer program code includes computer instructions, and the one or more processors invoke the computer instructions to cause the stacking parking system to perform the method described in the first aspect and any possible implementation thereof.

[0021] Thirdly, embodiments of this application provide a computer-readable storage medium including program instructions that, when executed on a stacking parking system, cause the stacking parking system to perform the method described in the first aspect and any possible implementation thereof.

[0022] Fourthly, embodiments of this application provide a computer program product containing instructions that, when the computer program product is run on a stacking parking system, cause the stacking parking system to perform the method described in the first aspect and any possible implementation thereof.

[0023] By adopting the above technical solution, the actual load state of the vehicles to be parked is coupled with the structural dynamic characteristics of the stacker crane column. A target rigid-flexible coupling dynamic model is used to calculate in real time the time-varying natural frequency of the stacker crane system as the planned lifting height changes. Based on this time-varying natural frequency, a time-varying shaped pulse sequence is generated and embedded into the target speed control curve. This ensures that the frequency of the excitation torque generated by the drive motor matches and cancels out the natural vibration frequency of the column structure, achieving personalized vibration control for the load characteristics of each vehicle to be parked. Without reducing the stacker crane's operating speed or increasing the rigidity of the column structure, the low-frequency flexible vibration of the column caused by differences in the mass of the vehicles to be parked and the uneven distribution of the center of gravity is eliminated from the source of excitation. This solves the technical problem in related technologies where stacked parking systems struggle to ensure both vehicle retrieval efficiency and structural stability under various vehicle types and uneven loading conditions. The stacked parking system achieves the technical effect of ensuring both vehicle retrieval efficiency and structural stability under various vehicle types and uneven loading conditions. Attached Figure Description

[0024] Figure 1 This is a flowchart illustrating a stacked parking vibration control method in an embodiment of this application.

[0025] Figure 2 This is a schematic diagram of the physical device structure of a stacking parking system in the embodiments of this application. Detailed Implementation

[0026] The terminology used in the following embodiments of this application is for the purpose of describing particular embodiments only and is not intended to be limiting of this application. As used in the specification and appended claims of this application, the singular expressions “a,” “an,” “the,” “the,” “the,” and “this” are intended to include the plural expressions as well, unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used in this application refers to any or all possible combinations including one or more of the listed items.

[0027] Hereinafter, the terms "first" and "second" are used for descriptive purposes only and should not be construed as implying or suggesting relative importance or implicitly indicating the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature, and in the description of the embodiments of this application, unless otherwise stated, "multiple" means two or more.

[0028] This application provides a vibration control method for stacked parking systems, applied to a stacked parking system including a stacker crane, a vehicle platform, and a weighbridge. The stacker crane includes columns. (See reference...) Figure 1 , Figure 1 This is a flowchart illustrating a stacked parking vibration control method according to an embodiment of this application, including the following steps:

[0029] Step S101: Obtain the actual mass data and three-dimensional centroid coordinate data of the vehicle to be parked on the vehicle platform using the weighbridge;

[0030] Step S102: Determine the spatial offset of the center of mass of the vehicle to be parked from the load center of the stacker crane based on the three-dimensional centroid coordinate data, and determine the three-dimensional eccentric load moment applied to the column by the vehicle to be parked based on the spatial offset and the actual mass data.

[0031] Step S103: Convert the predetermined horizontal running trajectory and predetermined lifting running trajectory of the stacker crane into a discrete time series, and determine the planned lifting height of the stacker crane at each discrete moment in the discrete time series;

[0032] Step S104: Construct a target rigid-flexible coupling dynamic model based on actual mass data, three-dimensional eccentric load moment, column cross-sectional physical parameters and planned lifting height, and generate a time-varying shaped pulse sequence that matches the discrete time series based on the target rigid-flexible coupling dynamic model.

[0033] Step S105: Generate the target speed control curve based on the initial motion command of the stacker crane and the time-varying shaping pulse sequence;

[0034] Step S106: Control the stacker crane's drive motor to perform vehicle handling operations according to the target speed control curve for the parked vehicle.

[0035] The stacking parking system is a mechanical parking equipment system that utilizes a stacker crane in a three-dimensional parking garage to achieve automatic vehicle storage and retrieval through the coordinated movement of the X-axis horizontal motion, Y-axis lifting motion, and Z-axis forklift motion. The stacker crane is the core handling device of the stacking parking system. Its main structure includes columns, a vehicle platform, an X-axis horizontal traveling mechanism, a Y-axis lifting mechanism, and a Z-axis forklift mechanism. The columns are the main vertical support components of the stacker crane. They typically employ a frame structure made of high-strength steel or a lightweight honeycomb shell structure. During high-speed operation of the stacker crane, the columns exhibit the vibration characteristics of flexible components. The vehicle platform is a carrying platform for vehicles to enter and temporarily park. A weighbridge is integrated beneath the vehicle platform. The weighbridge includes at least four distributed weighbridge sensors, used to measure the mass and center of gravity distribution of the vehicles to be parked. The actual mass data of the vehicles to be parked refers to the total mass value of the vehicles actually measured by the weighbridge sensors. This actual mass data reflects the current true loading status of the vehicles. Three-dimensional centroid coordinate data refers to the spatial position coordinates of the centroid of the vehicle to be parked in the vehicle platform coordinate system. The three-dimensional centroid coordinate data consists of the first centroid coordinate component in the horizontal longitudinal direction, the second centroid coordinate component in the horizontal transverse direction, and the third centroid coordinate component in the vertical direction.

[0036] Spatial offset refers to the three-dimensional deviation vector of the three-dimensional centroid coordinates of the vehicle to be parked relative to the load-bearing center coordinates of the stacker crane. Spatial offset includes horizontal longitudinal offset components, horizontal lateral offset components, and vertical offset components. Three-dimensional off-center moment refers to the three-dimensional spatial moment exerted on the column by the deviation of the vehicle's centroid from the load-bearing center of the stacker crane. Three-dimensional off-center moment includes pitch off-center moment components around the horizontal lateral direction, tilt off-center moment components around the horizontal longitudinal direction, and yaw off-center moment components around the vertical direction. The planned horizontal running trajectory refers to the planned movement path of the stacker crane in the horizontal direction from its starting position to the target parking space. The planned lifting running trajectory refers to the planned movement path of the stacker crane in the lifting direction from its current height to the target height. The discrete time series is a series of discrete time points obtained by discretizing the planned horizontal running trajectory and the planned lifting running trajectory according to a fixed time step. The planned lifting height refers to the Y-axis lifting height value of the stacker crane at each discrete time point in the discrete time series. The physical parameters of the column's cross-section include its moment of inertia, elastic modulus, linear density, and damping ratio. The target rigid-flexible coupling dynamic model is a multibody dynamic model that incorporates the interaction between rigid and flexible components into a unified analytical framework. In this model, the rigid components are the vehicle to be parked and the vehicle platform, while the flexible component is the column. This model can describe the dynamic excitation of the column by the mass of the vehicle to be parked and the three-dimensional eccentric moment during the stacker crane's dual-axis (X-axis and Y-axis) operation, as well as the column's dynamic vibration response.

[0037] The time-varying shaping pulse sequence is a series of pulse signals calculated based on the target rigid-flexible coupling dynamic model. The time-varying shaping pulse sequence corresponds to each discrete moment in the discrete-time sequence. The amplitude of each pulse in the time-varying shaping pulse sequence is determined based on the three-dimensional off-center load torque, the time-varying natural frequency, and the amplitude weighting coefficient. The time interval is determined based on the vibration period corresponding to the time-varying natural frequency, thus achieving the suppression of column vibration. The initial motion command refers to the original motion control command issued by the stacker crane control system to the stacker crane drive motor. The initial motion command includes, but is not limited to, the starting position, target position, maximum running speed, and maximum acceleration. The target speed control curve is the speed control curve obtained by performing time-domain convolution processing between the basic S-shaped speed curve obtained from the initial motion command analysis and the time-varying shaping pulse sequence. The target speed control curve undergoes asymmetric correction based on the current off-center load condition and is used to guide the actual operation of the stacker crane drive motor.

[0038] In the above embodiment, assuming the vehicle to be parked is a heavy SUV, the heavy SUV drives into the vehicle platform located on the ground floor and needs to be moved to the target parking space on the 8th floor of the automated parking garage. When the heavy SUV is fully driven into the vehicle platform and is stationary, the four weighbridge sensors under the vehicle platform measure loads of 580kg, 620kg, 550kg, and 650kg respectively. Summing the loads measured by the four weighbridge sensors, the actual mass of the heavy SUV is determined to be 2400kg. Simultaneously, based on the distributed load time-series data of the four weighbridge sensors and the ground pressure distribution data detected by the tire pressure sensing area, the three-dimensional centroid coordinates of the heavy SUV in the vehicle platform coordinate system are calculated using the torque balance principle as (2100mm, -80mm, 850mm), where the first centroid coordinate component in the horizontal longitudinal direction is 2100mm, the second centroid coordinate component in the horizontal transverse direction is -80mm, and the third centroid coordinate component in the vertical direction is 850mm. The load center coordinates of the stacker crane's vehicle platform are preset to (2000mm, 0mm, 800mm). A deviation analysis is performed between the three-dimensional centroid coordinates of the heavy SUV and the load center coordinates of the stacker crane's vehicle platform, yielding a horizontal longitudinal offset component of 100mm, a horizontal lateral offset component of -80mm, and a vertical offset component of 50mm. Based on the actual mass of the heavy SUV (2400kg) and the preset gravitational acceleration constant of 9.8m / s², the static gravity load is determined to be 23520N. Based on the static gravity load of 23520N and the horizontal longitudinal offset component of 100mm, the pitching moment component in the horizontal lateral direction is determined to be 2352N·m; based on the static gravity load of 23520N and the horizontal lateral offset component of -80mm, the tilting moment component in the horizontal longitudinal direction is determined to be -1882N·m.

[0039] In the above embodiment, the predetermined horizontal trajectory length of the stacker crane from the ground level to the target parking space on the 8th floor is 45 meters, and the predetermined vertical trajectory height is 24 meters. The predetermined horizontal and vertical trajectories are discretized with a time step of 0.1 seconds to obtain a discrete time series including 150 discrete time points. The planned vertical height of the stacker crane at each discrete time point is determined to be 0 meters, 0.16 meters, 0.32 meters, ... up to 24 meters. Based on the actual mass data of the heavy SUV (2400 kg), the three-dimensional eccentric load moment (pitch component 2352 N·m, roll component -1882 N·m, yaw component 480 N·m), and the physical parameters of the column section (section moment of inertia 8.5 × 10⁻⁶),... －5 m 4 Elastic modulus 2.1×10 11Based on the parameters (Pa, material linear density 120 kg / m, material damping ratio 0.02), and the planned lifting height sequence, a target rigid-flexible coupled dynamic model was constructed, with the column as the flexible component and the heavy SUV and the vehicle platform as the rigid components. Calculations using the target rigid-flexible coupled dynamic model showed that when the stacker crane is at ground level (planned lifting height 0 meters), the first-order time-varying natural frequency is 1.8 Hz, and the second-order time-varying natural frequency is 5.2 Hz. When the stacker crane rises to a height of 12 meters, the first-order time-varying natural frequency decreases to 1.2 Hz, and the second-order time-varying natural frequency decreases to 3.8 Hz. When the stacker crane rises to its highest position of 24 meters, the first-order time-varying natural frequency further decreases to 0.9 Hz, and the second-order time-varying natural frequency decreases to 2.9 Hz.

[0040] In the above embodiment, a time-varying shaped pulse sequence matching the discrete time sequence is generated based on the first-order and second-order time-varying natural frequencies at each discrete moment. The first time interval of the first-order shaped pulse at the first discrete moment in the time-varying shaped pulse sequence is 0.28 seconds (half of the 1.8Hz vibration period), the first time interval of the first-order shaped pulse at the 50th discrete moment increases to 0.42 seconds (half of the 1.2Hz vibration period), and the first time interval of the first-order shaped pulse at the 150th discrete moment further increases to 0.56 seconds (half of the 0.9Hz vibration period). The initial motion command of the stacker crane (maximum horizontal running speed 2.5m / s, maximum lifting speed 0.8m / s, maximum acceleration 1.2m / s²) is parsed into a basic S-shaped velocity curve. Then, the basic S-shaped velocity curve is convolved with the time-varying shaped pulse sequence in the time domain to obtain the initial shaped velocity curve. Since the direction of the projection component of the three-dimensional off-center load moment of the heavy SUV in the current horizontal running direction is the same as the direction of the inertial moment during the acceleration of the stacker crane, it is determined that the stacker crane is in an aggravated off-center load condition. Based on the projection component of the moment, the acceleration segment stretching coefficient is determined to be 1.35. Using the acceleration segment stretching coefficient of 1.35, the acceleration segment of the initial shaping speed curve is smoothed and extended, extending the original 3.2-second acceleration segment to 4.3 seconds, resulting in the first asymmetric shaping curve as the target speed control curve. The stacking parking system controls the stacker crane's drive motor to perform vehicle handling operations on the heavy SUV according to the target speed control curve. The entire handling process is completed smoothly, and the vehicle to be parked is accurately moved to the target parking space on the 8th floor.

[0041] Through the above steps, the actual load state of the vehicles to be parked is coupled with the structural dynamic characteristics of the stacker crane column. A target rigid-flexible coupling dynamic model is used to calculate in real time the time-varying natural frequency of the stacker crane system as the planned lifting height changes. Based on this time-varying natural frequency, a time-varying shaped pulse sequence is generated and embedded into the target speed control curve. This ensures that the frequency of the excitation torque generated by the drive motor matches and cancels out the natural vibration frequency of the column structure, achieving personalized vibration control for the load characteristics of each vehicle to be parked. Without reducing the stacker crane's operating speed or increasing the rigidity of the column structure, the low-frequency flexible vibration of the column caused by differences in the mass of the vehicles to be parked and the uneven distribution of the center of gravity is eliminated at the source of excitation. This solves the technical problem in related technologies where stacked parking systems struggle to ensure both vehicle retrieval efficiency and structural stability under various vehicle types and uneven loading conditions. It achieves the technical effect of ensuring both vehicle retrieval efficiency and structural stability under various vehicle types and uneven loading conditions in stacked parking systems.

[0042] The entity performing the above steps can be a system, such as a stacking parking system, or equipment, or a controller or processor in the system or equipment, or a separate controller or processor, or other processing equipment or processing units with similar processing functions, but is not limited thereto.

[0043] In an optional embodiment, the actual mass data and three-dimensional centroid coordinate data of the vehicle to be parked on the vehicle carrier are obtained by using a weighbridge, including: during the process of the vehicle to be parked driving into the vehicle carrier, real-time load acquisition of the measurement points of the vehicle carrier by at least four weighbridge sensors set below the vehicle carrier to obtain distributed load time series data; acquiring the outline image of the vehicle to be parked by a contour recognition camera set at the entrance of the vehicle carrier, and matching and querying the outline image in a preset vehicle model database to obtain the reference centroid height range of the vehicle model corresponding to the vehicle to be parked; and acquiring the outline image of the vehicle to be parked by a contour recognition camera set at the entrance of the vehicle carrier, and matching and querying the outline image in a preset vehicle model database to obtain the reference centroid height range of the vehicle model corresponding to the vehicle to be parked; and acquiring the reference centroid height range of the vehicle to be parked by a weighbridge sensor set below the vehicle carrier. The tire pressure sensing area on the surface detects the ground pressure distribution data of each tire of the vehicle to be parked; when the vehicle to be parked is stationary on the vehicle platform, the actual mass data is determined based on the distributed load time series data; based on the distributed load time series data and the ground pressure distribution data, the first centroid coordinate component in the horizontal longitudinal direction and the second centroid coordinate component in the horizontal lateral direction of the vehicle to be parked are determined; based on the vehicle model reference centroid height range, the third centroid coordinate component in the vertical direction of the vehicle to be parked is determined; the first centroid coordinate component, the second centroid coordinate component, and the third centroid coordinate component are determined as three-dimensional centroid coordinate data.

[0044] The distributed load time-series data refers to the time-series data obtained by the weighbridge sensor continuously collecting the load at each measurement point at fixed time intervals (e.g., every 0.05 seconds) during the process of a vehicle entering the vehicle platform. This data records the dynamic changes in load distribution throughout the entire process, from the moment the vehicle enters until it comes to a complete stop. The contour recognition camera is a visual sensor installed at the entrance of the vehicle platform. It is used to collect the outline image of the vehicle, including its length, width, height, and other dimensional features. The preset vehicle model database is a pre-established database containing geometric parameters and center-of-gravity height reference ranges for various vehicle models. This database stores the standard center-of-gravity height ranges for various vehicle types, such as sedans, SUVs, and MPVs. For example, the reference center-of-gravity height range for sedans is 450mm to 550mm, for SUVs it is 650mm to 850mm, and for MPVs it is 700mm to 900mm. The tire pressure sensing area is a pressure sensor array area set on the surface of the vehicle platform. The tire pressure sensing area includes multiple pressure sensing units. Each pressure sensing unit is used to detect the ground pressure of the tires of the vehicle to be parked at that location. The ground pressure distribution data is the distribution data composed of the pressure values ​​measured by all pressure sensing units. The ground pressure distribution data can reflect the specific ground position and pressure magnitude of each tire of the vehicle to be parked.

[0045] In the above embodiment, a mid-size SUV is used as an example for detailed explanation. When the mid-size SUV drives into the vehicle platform, the four weighbridge sensors under the vehicle platform (located at the four corners of the vehicle platform, with coordinates of (0,0), (5000mm,0), (0,2500mm), and (5000mm,2500mm) respectively) begin to collect load data in real time. At time 0 during the entry of the mid-size SUV, the readings of the four weighbridge sensors were 0 kg, 0 kg, 0 kg, and 0 kg, respectively. At time 1, the front wheels began to drive onto the platform, and the readings of the four weighbridge sensors were 280 kg, 320 kg, 0 kg, and 0 kg, respectively. At time 3, the mid-size SUV was fully inside the platform, and the readings of the four weighbridge sensors were 420 kg, 480 kg, 380 kg, and 440 kg, respectively. At time 5, the mid-size SUV was stationary, and the readings of the four weighbridge sensors stabilized at 420 kg, 480 kg, 380 kg, and 440 kg. Based on the distributed load time sequence data when stationary, the readings of the four weighbridge sensors were summed to determine the actual mass of the mid-size SUV as 1720 kg. Simultaneously, a contour recognition camera positioned at the vehicle entrance captures an image of the mid-size SUV's exterior contour as it enters the vehicle. This image shows the SUV's length as 4750mm, width as 1880mm, and height as 1720mm. The image is then matched against a pre-defined vehicle model database. Based on these dimensions, the SUV is classified as a mid-size SUV, with a corresponding reference center of gravity height range of 680mm to 780mm.

[0046] In the above embodiment, the tire pressure sensing area set on the surface of the vehicle platform detects the ground pressure distribution data of the four tires of the mid-size SUV. The ground center position coordinates of the left front tire are (1200mm, 800mm), and the peak ground pressure is 4200N; the ground center position coordinates of the right front tire are (1200mm, 1700mm), and the peak ground pressure is 4800N; the ground center position coordinates of the left rear tire are (3800mm, 800mm), and the peak ground pressure is 3800N; the ground center position coordinates of the right rear tire are (3800mm, 1700mm), and the peak ground pressure is 4400N. The stacked parking system calculates the center of mass position of the mid-size SUV in the horizontal longitudinal direction based on the readings (420kg, 480kg, 380kg, 440kg) and coordinate positions of the four weighbridge sensors in the static state in the distributed load time sequence data, using the torque balance principle. Let the first center of mass coordinate component in the horizontal longitudinal direction be x. cAccording to the torque balance equation: (420 + 380) × 0 + (480 + 440) × 5000 = 1720 × x c Find x c =2674mm. Similarly, based on the moment balance equation, the second centroid coordinate component of this mid-size SUV in the horizontal lateral direction is calculated as y. c =1291mm. Further correction was made using ground pressure distribution data. Based on the grounding center coordinates of the four tires and the peak ground pressure, a more accurate centroid coordinate was calculated using the following weighted average formula: Horizontal longitudinal first centroid coordinate component x c =[(P1×x1)+(P2×x2)+(P3×x3)+(P4×x4)]÷(P1+P2+P3+P4), where y is the horizontal second centroid coordinate component. c = [(P1×y1)+(P2×y2)+(P3×y3)+(P4×y4)]÷(P1+P2+P3+P4), where P1 to P4 are the peak ground pressure values ​​of the four tires, and (x1,y1) to (x4,y4) are the ground contact center coordinates of the four tires. Substituting these values ​​into the numerical calculation yields the first centroid coordinate component x. c =[(4200×1200)+(4800×1200)+(3800×3800)+(4400×3800)]÷(4200+4800+3800+4400)=2580mm, second centroid coordinate component yc'=[(4200×800)+(4800×1700)+(3800×800)+(4400×1700)]÷(4200+4800+3800+4400)=1265mm. For the third centroid coordinate component in the vertical direction, the reference centroid height range for this mid-size SUV is obtained from the preset vehicle database as 680mm to 780mm. The median value of the reference centroid height range, 730mm, is taken as the third centroid coordinate component of this mid-size SUV in the vertical direction. The first centroid coordinate component 2580mm, the second centroid coordinate component 1265mm, and the third centroid coordinate component 730mm are determined as the three-dimensional centroid coordinate data (2580mm, 1265mm, 730mm) of this mid-size SUV.

[0047] In an optional embodiment, the spatial offset of the center of gravity of the vehicle to be parked from the load center of the stacker crane is determined based on the three-dimensional centroid coordinate data, and the three-dimensional off-center load moment applied by the vehicle to be parked to the column is determined based on the spatial offset and the actual mass data. This includes: obtaining the load center coordinates of the vehicle platform of the stacker crane, and performing a deviation analysis between the three-dimensional centroid coordinate data and the load center coordinates to obtain horizontal longitudinal offset components, horizontal lateral offset components, and vertical offset components; determining the horizontal longitudinal offset components, horizontal lateral offset components, and vertical offset components as the spatial offset; and determining the spatial offset based on the actual mass data and... The static gravity load of the vehicle to be parked is determined by a preset gravitational acceleration constant; the pitching off-center load moment component around the horizontal lateral direction is determined based on the static gravity load and the horizontal longitudinal offset component, and the roll off-center load moment component around the horizontal longitudinal direction is determined based on the static gravity load and the horizontal lateral offset component; the inertial load is determined based on the planned acceleration and actual mass data of the stacker crane in the horizontal longitudinal direction, and the yaw off-center load moment component around the vertical direction is determined based on the inertial load and the vertical offset component; the pitching off-center load moment component, the roll off-center load moment component, and the yaw off-center load moment component are determined as three-dimensional off-center load moments.

[0048] The load-bearing center coordinates of the stacker crane's vehicle-carrying platform refer to the spatial coordinates of the geometric center point of the platform used to carry the vehicle to be parked on the stacker crane within the coordinate system of the stacked parking system. The load-bearing center coordinates of the stacker crane's vehicle-carrying platform are typically located at the horizontal geometric center of the platform and the vertical height of the load-bearing surface. It should be noted that the stacker crane's vehicle-carrying platform is a different component from the ground-level vehicle-carrying platform. The ground-level platform is used for vehicle entry and mass center measurement, while the stacker crane's platform is used for the three-dimensional transport of vehicles within the automated parking system. The horizontal longitudinal offset component refers to the difference between the first centroid coordinate component of the three-dimensional centroid coordinate data of the vehicle to be parked and the horizontal longitudinal coordinate component of the load-bearing center coordinates of the stacker crane's vehicle-carrying platform. A positive value of the horizontal longitudinal offset component indicates that the centroid of the vehicle to be parked is biased towards the front of the stacker crane, while a negative value indicates biased towards the rear of the stacker crane. The horizontal offset component refers to the difference between the second centroid coordinate component of the three-dimensional centroid coordinate data of the vehicle to be parked and the horizontal offset component of the load-bearing center coordinate of the stacker crane's vehicle platform. A positive value of the horizontal offset component indicates that the centroid of the vehicle to be parked is biased to the right of the stacker crane, while a negative value indicates that it is biased to the left of the stacker crane. The vertical offset component refers to the difference between the third centroid coordinate component of the three-dimensional centroid coordinate data of the vehicle to be parked and the vertical offset component of the load-bearing center coordinate of the stacker crane's vehicle platform. A positive value of the vertical offset component indicates that the centroid of the vehicle to be parked is higher than the load-bearing surface of the vehicle platform, while a negative value indicates that it is lower than the load-bearing surface.

[0049] The static gravity load refers to the downward vertical gravitational force exerted by the vehicle's own mass when it is stationary. The formula for calculating the static gravity load is: Static Gravity Load = Actual Mass Data × Preset Gravitational Acceleration Constant, where the preset gravitational acceleration constant is taken as a standard value of 9.8 m / s² or 9.81 m / s². The pitching off-center load moment component refers to the moment exerted on the column by the vehicle's center of mass in the horizontal longitudinal direction, deviating from the load-bearing center of the stacker crane's platform. The formula for calculating the pitching off-center load moment component is: Pitching Off-Center Load Moment Component = Static Gravity Load × Horizontal Longitudinal Offset Component. The tilting off-center load moment component refers to the moment exerted on the column by the vehicle's center of mass in the horizontal lateral direction, deviating from the load-bearing center of the stacker crane's platform. The formula for calculating the tilting off-center load moment component is: Tilting Off-Center Load Moment Component = Static Gravity Load × Horizontal Longitudinal Offset Component. Inertial load refers to the horizontal force exerted by the vehicle to be parked due to inertia when the stacker crane accelerates or decelerates in the horizontal longitudinal direction. The formula for calculating inertial load is: Inertial load = Actual mass data × Planned acceleration, where the planned acceleration is the acceleration value of the stacker crane in the horizontal longitudinal direction. The yaw moment component refers to the torque exerted on the column about the vertical direction by the combined effect of the inertial load generated during the acceleration or deceleration of the stacker crane and the vertical offset of the center of mass of the vehicle to be parked. The formula for calculating the yaw moment component is: Yaw moment component = Inertial load × Vertical offset component.

[0050] In the above embodiment, based on the three-dimensional centroid coordinate data (2580mm, 1265mm, 730mm) and actual mass data of 1720kg of the mid-size SUV obtained in the previous embodiment, the process of determining the three-dimensional off-center load moment is further explained. The load center coordinates of the stacker crane's vehicle platform are obtained from the configuration parameters as (2500mm, 1250mm, 700mm), where the horizontal longitudinal coordinate component is 2500mm, the horizontal transverse coordinate component is 1250mm, and the vertical coordinate component is 700mm. A deviation analysis was performed on the three-dimensional centroid coordinates (2580mm, 1265mm, 730mm) of the mid-size SUV and the load-bearing center coordinates (2500mm, 1250mm, 700mm) of the stacker crane's vehicle platform. The calculated horizontal longitudinal offset component was 2580mm - 2500mm = 80mm, the horizontal lateral offset component was 1265mm - 1250mm = 15mm, and the vertical offset component was 730mm - 700mm = 30mm. The horizontal longitudinal offset component of 80mm, the horizontal lateral offset component of 15mm, and the vertical offset component of 30mm were determined as the spatial offset of the mid-size SUV's centroid from the load-bearing center of the stacker crane's vehicle platform.

[0051] In the above embodiment, based on the actual mass of the mid-size SUV (1720 kg) and the preset gravitational acceleration constant (9.8 m / s²), the static gravity load of the mid-size SUV is calculated to be 1720 kg × 9.8 m / s² = 16856 N. Based on the static gravity load of 16856 N and the horizontal longitudinal offset component of 80 mm (i.e., 0.08 m), the pitching off-center load moment component around the horizontal lateral direction is calculated to be 16856 N × 0.08 m = 1348 N·m. This pitching off-center load moment component is positive, indicating that the center of gravity of the mid-size SUV is biased towards the front of the stacker crane, and a moment will be generated when the stacker crane accelerates forward, causing the column to tilt forward. Based on the static gravity load of 16856N and the horizontal lateral offset component of 15mm (i.e. 0.015m), the lateral tilting moment component around the horizontal longitudinal direction is calculated to be 16856N×0.015m=253N·m. This lateral tilting moment component is positive, indicating that the center of gravity of the mid-size SUV is biased to the right of the stacker crane, which will generate a moment that causes the column to tilt to the right.

[0052] In the above embodiment, the planned acceleration of the stacker crane in the horizontal longitudinal direction is obtained from the initial motion command as 1.0 m / s². Based on the actual mass data of the mid-size SUV (1720 kg) and the planned acceleration of 1.0 m / s², the inertial load is calculated to be 1720 kg × 1.0 m / s² = 1720 N. Based on the inertial load of 1720 N and the vertical offset component of 30 mm (i.e., 0.03 m), the yaw moment component around the vertical direction is calculated to be 1720 N × 0.03 m = 52 N·m. This yaw moment component indicates that when the stacker crane accelerates, the center of gravity of the mid-size SUV being higher than the bearing surface of the vehicle platform will generate a torque that causes the column to twist around the vertical axis. The pitching off-center load moment component of 1348 N·m, the roll off-center load moment component of 253 N·m, and the yaw off-center load moment component of 52 N·m are determined as the three-dimensional off-center load moment applied to the pillar by the mid-size SUV. The three-dimensional off-center load moment can be expressed in vector form as (1348 N·m, 253 N·m, 52 N·m).

[0053] In an optional embodiment, before generating a time-varying shaped pulse sequence matching the discrete-time sequence based on the target rigid-flexible coupling dynamics model, the method further includes: determining the X-axis horizontal motion parameters based on the horizontal acceleration of the stacker crane at each discrete moment, and determining the Y-axis lifting motion parameters based on the lifting speed of the stacker crane at each discrete moment; establishing a three-dimensional coupling effect matrix in the target rigid-flexible coupling dynamics model based on the X-axis horizontal motion parameters, the Y-axis lifting motion parameters, and the three-dimensional eccentric load moment, the three-dimensional coupling effect matrix including a first coupling coefficient corresponding to the horizontal acceleration and a second coupling coefficient corresponding to the lifting speed; determining the coupled bending moment load on the column at each discrete moment based on the first coupling coefficient, the second coupling coefficient, and the planned lifting height; determining the structural deflection response value of the column at each discrete moment based on the coupled bending moment load, the section moment of inertia and the elastic modulus in the section physical parameters; and determining the pulse amplitude constraint coefficient at each discrete moment based on the structural deflection response value and the preset deflection safety limit.

[0054] The X-axis horizontal motion parameters describe the stacker crane's horizontal motion state, including its horizontal position, horizontal velocity, and horizontal acceleration at each discrete moment. The Y-axis lifting motion parameters describe the stacker crane's lifting motion state, including its lifting height, lifting speed, and lifting acceleration at each discrete moment. The three-dimensional coupling effect matrix is ​​established in the target rigid-flexible coupling dynamic model to quantify the interaction between the X-axis horizontal motion parameters, the Y-axis lifting motion parameters, and the three-dimensional eccentric moment. The rows of the three-dimensional coupling effect matrix correspond to the three components of the three-dimensional eccentric moment (pitch component, roll component, and yaw component), and the columns correspond to the motion parameters (horizontal acceleration, lifting speed, etc.). The matrix elements represent the coupling influence coefficients of each motion parameter on each eccentric moment component. The first coupling coefficient is the coupling influence coefficient of horizontal acceleration on the column vibration response in the three-dimensional coupling effect matrix. It quantifies the dynamic bending moment effect of changes in the stacker crane's horizontal acceleration on the column in various directions, and its magnitude reflects the excitation intensity of the horizontal acceleration on the column vibration. The second coupling coefficient is the coupling influence coefficient of lifting speed on the column vibration response in the three-dimensional coupling effect matrix. It quantifies the degree of influence of changes in the effective length of the column caused by changes in the stacker crane's lifting speed on the system's natural frequencies and vibration modes, and its magnitude reflects the degree to which the lifting motion alters the column's dynamic characteristics.

[0055] The coupled bending moment load refers to the comprehensive bending moment load actually borne by the column at each discrete moment during the dual-axis linkage process of horizontal movement on the X-axis and vertical movement on the Y-axis, due to the coupling effect of the three-dimensional eccentric load moment and the motion state. The coupled bending moment load simultaneously considers the combined effects of the static eccentric load moment, the inertial moment generated by the horizontal movement, and the changes in dynamic parameters caused by the vertical movement. The structural deflection response value refers to the elastic deformation displacement of the column under the action of the coupled bending moment load. The structural deflection response value is usually calculated as the horizontal displacement of the top of the column relative to the fixed bottom end of the column. The structural deflection response value is a key indicator for assessing the severity of column vibration and structural safety. The preset deflection safety limit is the maximum allowable deflection of the column pre-set according to the column material strength, structural stiffness, and parking accuracy requirements. The preset deflection safety limit is a safety threshold to ensure that the column does not undergo plastic deformation or fatigue failure, and that the vehicle positioning accuracy meets the requirements. The pulse amplitude constraint coefficient is a constraint coefficient used to limit the amplitude of the time-varying shaping pulse sequence, determined based on the comparison between the structural deflection response value and the preset deflection safety limit. The pulse amplitude constraint coefficient is used to prevent the amplitude of the time-varying shaping pulse sequence from being too large, which would cause the output torque of the drive motor to be too large and the column deflection to exceed the safety limit. The value range of the pulse amplitude constraint coefficient is usually between 0 and 1. When the structural deflection response value is close to the preset deflection safety limit, the pulse amplitude constraint coefficient takes a smaller value to limit the pulse amplitude. When the structural deflection response value is much smaller than the preset deflection safety limit, the pulse amplitude constraint coefficient takes a larger value to allow a larger pulse amplitude, thereby achieving a better vibration suppression effect.

[0056] In the above embodiments, based on the three-dimensional off-center load moments of the mid-size SUV obtained in the previous embodiments (pitch off-center load moment component 1348 N·m, roll off-center load moment component 253 N·m, yaw off-center load moment component 52 N·m), the process of establishing the three-dimensional coupling effect matrix and determining the pulse amplitude constraint coefficient is further explained. The predetermined horizontal running trajectory and predetermined vertical running trajectory of the stacker crane from the ground level to the target parking space on the 8th level are discretized according to a time step of 0.1 seconds to obtain a discrete time series containing 150 discrete time points. At the first discrete time step (t=0 seconds), the stacker crane is at the starting position on the ground level, with a planned lifting height of 0 meters, a horizontal acceleration of 0 m / s², and a lifting speed of 0 m / s. At the tenth discrete time step (t=1.0 seconds), the stacker crane is in the horizontal acceleration phase, with a planned lifting height of 0.16 meters, a horizontal acceleration of 1.0 m / s², and a lifting speed of 0.8 m / s. At the fiftyth discrete time step (t=5.0 seconds), the stacker crane has entered the uniform horizontal operation and uniform lifting phase, with the planned lifting height... The height is 4.8 meters, the horizontal acceleration is 0 m / s², and the lifting speed is 0.8 m / s. At the 140th discrete time (t=14.0 seconds), the stacker crane is in the horizontal deceleration and lifting deceleration stage, with a planned lifting height of 22.4 meters, a horizontal acceleration of -1.0 m / s², and a lifting speed of 0.4 m / s. At the 150th discrete time (t=15.0 seconds), the stacker crane reaches the target parking space on the 8th floor, with a planned lifting height of 24 meters, a horizontal acceleration of 0 m / s², and a lifting speed of 0 m / s.

[0057] In the above embodiment, the X-axis horizontal motion parameters are determined based on the horizontal acceleration of the stacker crane at each discrete moment, and the Y-axis lifting motion parameters are determined based on the lifting speed of the stacker crane at each discrete moment. At the 10th discrete moment, the X-axis horizontal motion parameters include a horizontal position of 0.5 meters, a horizontal speed of 1.0 m / s, and a horizontal acceleration of 1.0 m / s²; the Y-axis lifting motion parameters include a lifting height of 0.16 meters, a lifting speed of 0.8 m / s, and a lifting acceleration of 0 m / s². Based on the X-axis horizontal motion parameters, the Y-axis lifting motion parameters, and the three-dimensional eccentric load moment, a three-dimensional coupling effect matrix is ​​established in the target rigid-flexible coupling dynamic model. This three-dimensional coupling effect matrix is ​​a 3×2 matrix, with the first row corresponding to the pitching eccentric load moment component, the second row corresponding to the roll eccentric load moment component, and the third row corresponding to the yaw eccentric load moment component. The first column corresponds to the coupling effect of horizontal acceleration, and the second column corresponds to the coupling effect of lifting speed. At the 10th discrete moment, the specific values ​​of the three-dimensional coupling effect matrix are:

[0058] K couple =[k11 k12]=[0.85 0.12]

[0059] [k21 k22] [0.18 0.76]

[0060] [k31 k32] [0.62 0.09]

[0061] The first coupling coefficient k11 = 0.85 indicates that the horizontal acceleration of 1.0 m / s² has a coupling effect of 0.85 on the pitch eccentric load moment component. This coupling effect will increase the pitch eccentric load moment component from a static value of 1348 N·m to a dynamic value of 1348 × (1 + 0.85) = 2494 N·m. The second coupling coefficient k22 = 0.76 indicates that the rise / fall speed of 0.8 m / s has a coupling effect of 0.76 on the roll eccentric load moment component. This coupling effect will increase the roll eccentric load moment component from a static value of 253 N·m to a dynamic value of 253 × (1 + 0.76) = 445 N·m.

[0062] In the above embodiment, based on the first coupling coefficient of 0.85, the second coupling coefficient of 0.76, and the planned lifting height of 0.16 meters, the coupled bending moment load on the column at the 10th discrete moment is calculated. The coupled bending moment load on the column in the pitch direction is 2494 N·m, the coupled bending moment load on the column in the tilt direction is 445 N·m, and the coupled bending moment load on the column in the yaw direction is 52 × (1 + 0.62) = 84 N·m. The total coupled bending moment load on the column is the vector sum of the coupled bending moment loads in the above three directions, and the magnitude of the total coupled bending moment load is √(2494² + 445² + 84²) = 2534 N·m. Based on the coupled bending moment load of 2534 N·m and the section moment of inertia of the column's cross-section physical parameters of 8.5 × 10⁻⁶, the load is calculated. －5 m 4 And elastic modulus 2.1×10 11 Pa, using the cantilever beam end deflection calculation formula in mechanics of materials, determines the structural deflection response value of the column at the 10th discrete time step. When the stacker crane is at a height of 0.16 meters, the effective cantilever length of the column as a cantilever beam is approximately 0.16 meters. According to the cantilever beam end deflection formula δ=ML² / (2EI), where δ is the deflection at the free end of the cantilever beam, M is the bending moment load acting on the cantilever beam (2534 N·m), L is the effective length of the cantilever beam (0.16 meters), and E is the elastic modulus of the material (2.1 × 10⁻⁶). 11 Pa, I is the moment of inertia of the cross section, 8.5 × 10⁻⁶. －5 m 4 The structural deflection response at the 10th discrete time was calculated to be δ = 2534 × 0.16² / (2 × 2.1 × 10⁻⁶). 11 ×8.5×10 －5 = 0.0018 meters, or 1.8 millimeters.

[0063] In the above embodiment, the preset deflection safety limit is obtained from the configuration parameters as 10 mm. This preset deflection safety limit is set based on the yield strength of the column material and the vehicle positioning accuracy requirements. The stacked parking system calculates the pulse amplitude constraint coefficient for the 10th discrete moment based on the structural deflection response value of 1.8 mm and the preset deflection safety limit of 10 mm. Since the structural deflection response value of 1.8 mm is much smaller than the preset deflection safety limit of 10 mm, the deflection safety margin is large. Therefore, the stacked parking system sets the pulse amplitude constraint coefficient for the 10th discrete moment to 0.95, indicating that a larger pulse amplitude is allowed for the time-varying shaped pulse sequence at that moment to achieve better vibration suppression. Similarly, at the 140th discrete moment, the stacker crane rises to a height of 22.4 meters, and the effective cantilever length of the column increases to 22.4 meters. Assuming that the coupled bending moment load on the column at this moment is equivalent to that at the 10th discrete moment, approximately 2500 N·m, the structural deflection response value δ = (2500 × 22.4) is calculated using the cantilever beam end deflection formula δ = ML² / (2EI). 2 )÷(2×2.1×10 11 ×8.5×10 －5 The deflection response of the structure at this height is 0.0353 meters, or approximately 35.3 millimeters. Since this deflection response value of 35.3 millimeters far exceeds the preset safety deflection limit of 10 millimeters, the coupled bending moment load needs to be reduced by decreasing the operating speed and acceleration at this height during actual operation. After speed optimization, the actual coupled bending moment load at this moment is reduced to approximately 650 N·m, and the corresponding structural deflection response value is reduced to δ = (650 × 22.4) / (0.0353 m, approximately 35.3 mm). 2 )÷(2×2.1×10 11 ×8.5×10 －5 =0.0092 meters, or about 9.2 millimeters. The deflection response value of the structure is 9.2 millimeters, which is close to the preset deflection safety limit of 10 millimeters. Therefore, the pulse amplitude constraint coefficient of the 140th discrete moment is set to 0.35 to limit the pulse amplitude of the time-varying shaping pulse sequence at that moment and prevent the drive motor from outputting too much torque, causing the column deflection to exceed the safety limit.

[0064] In an optional embodiment, a target rigid-flexible coupled dynamic model is constructed based on actual mass data, three-dimensional eccentric load moment, cross-sectional physical parameters of the column, and planned lifting height. A time-varying shaped pulse sequence matching the discrete-time sequence is then generated based on the target rigid-flexible coupled dynamic model. This includes: constructing a target rigid-flexible coupled dynamic model with the column as a flexible component and the vehicle to be parked and the vehicle platform as rigid components based on actual mass data, three-dimensional eccentric load moment, cross-sectional physical parameters, and planned lifting height; inputting the linear density of the column's material into the target rigid-flexible coupled dynamic model to determine the first-order and second-order time-varying natural frequencies of the stacker crane at each discrete moment; and determining the first-order vibration frequency based on the first-order time-varying natural frequency. The period is determined, and half of the first-order vibration period is defined as the first time interval of the first-order shaping pulse. The second-order vibration period is determined based on the second-order time-varying natural frequency, and half of the second-order vibration period is defined as the second time interval of the second-order shaping pulse. The first-order amplitude weighting coefficient and the second-order amplitude weighting coefficient of the first-order shaping pulse are determined based on the material damping ratio of the column. Both the first-order amplitude weighting coefficient and the second-order amplitude weighting coefficient are negatively correlated with the material damping ratio. The time-varying shaping pulse sequence is generated based on the three-dimensional eccentric load moment, the first-order time-varying natural frequency, the second-order time-varying natural frequency, the first time interval, the second time interval, the first-order amplitude weighting coefficient, the second-order amplitude weighting coefficient, and the pulse amplitude constraint coefficient.

[0065] In the target rigid-flexible coupling dynamic model, rigid components refer to those whose deformation is assumed to be negligible in the dynamic analysis. The deformation of the vehicles to be parked and the vehicle platform during the stacker crane's handling process is much smaller than that of the column; therefore, the vehicles to be parked and the vehicle platform are considered rigid components. Flexible components in the target rigid-flexible coupling dynamic model refer to those whose elastic deformation must be considered in the dynamic analysis. As the main vertical support component of the stacker crane, the column will generate significant elastic vibration during high-speed operation; therefore, the column is considered a flexible component. Material linear density refers to the mass per unit length of the column. The unit of material linear density is kg / m. Material linear density equals the volume density of the column material multiplied by the cross-sectional area of ​​the column. Material linear density is a key parameter for calculating the distributed mass of the column as a cantilever beam structure. The first-order time-varying natural frequency refers to the natural frequency corresponding to the first-order vibration mode of the column as a flexible component in the target rigid-flexible coupling dynamic model. The first-order time-varying natural frequency changes with the planned lifting height of the stacker crane. When the lifting height of the stacker crane increases, the effective cantilever length of the column increases, leading to a decrease in the first-order time-varying natural frequency. The second-order time-varying natural frequency refers to the natural frequency corresponding to the second-order vibration mode of the column as a flexible component in the target rigid-flexible coupling dynamic model. The second-order time-varying natural frequency also changes with the planned lifting height of the stacker crane. The value of the second-order time-varying natural frequency is typically 2.5 to 3.5 times that of the first-order time-varying natural frequency. The first-order vibration period is the reciprocal of the first-order time-varying natural frequency, and its unit is seconds. The first-order vibration period represents the time required for the column's first-order vibration mode to complete one complete vibration cycle.

[0066] The second-order vibration period is the reciprocal of the second-order time-varying natural frequency, and its unit is seconds. The second-order vibration period represents the time required for the column's second-order vibration mode to complete one complete vibration cycle. The first time interval is the time interval between two consecutive pulses in the first-order shaping pulse. This first time interval is set to half the first-order vibration period, ensuring that the vibration responses of the two consecutive pulses to the column are out of phase, thus achieving vibration cancellation. The second time interval is also the time interval between two consecutive pulses in the second-order shaping pulse, set to half the second-order vibration period. This ensures that the vibration responses of the two consecutive pulses to the column's second-order vibration mode are out of phase, thus achieving second-order vibration cancellation. The material damping ratio is a dimensionless parameter characterizing the energy dissipation capacity of the column material. The material damping ratio typically ranges from 0.01 to 0.05; a higher material damping ratio indicates a stronger natural vibration attenuation capability of the column material. The first-order amplitude weighting coefficient is used to determine the amplitude of the first-order shaped pulse. It is negatively correlated with the material damping ratio. When the material damping ratio is large, the column has a strong natural attenuation capability for first-order vibrations; therefore, a smaller first-order amplitude weighting coefficient can be set to reduce the amplitude of the first-order shaped pulse. When the material damping ratio is small, a larger first-order amplitude weighting coefficient needs to be set to increase the amplitude of the first-order shaped pulse, thereby achieving effective vibration suppression. The second-order amplitude weighting coefficient is used to determine the amplitude of the second-order shaped pulse. It is also negatively correlated with the material damping ratio. The mechanism of the second-order amplitude weighting coefficient is the same as that of the first-order coefficient, but it applies to the second-order vibration mode.

[0067] In the above embodiments, based on the three-dimensional coupling effect matrix established in the previous embodiments and the determined pulse amplitude constraint coefficients, the process of constructing a target rigid-flexible coupling dynamic model and generating a time-varying shaped pulse sequence is further explained. Based on the actual mass data of a mid-size SUV (1720 kg), three-dimensional eccentric load moments (pitch load moment component 1348 N·m, roll load moment component 253 N·m, yaw load moment component 52 N·m), and the physical parameters of the column section (section moment of inertia 8.5 × 10⁻⁶),... －5 m 4 Elastic modulus 2.1×10 11Based on the given parameters (Pa, material linear density 120 kg / m³, material damping ratio 0.02), and the planned lifting height sequence, a target rigid-flexible coupling dynamic model is constructed, with the column as the flexible component and the mid-sized SUV and the vehicle platform as the rigid components. In this model, the column is modeled as a cantilever beam structure with one end fixed to the ground and the other end bearing a concentrated mass. The concentrated mass includes the actual mass of the mid-sized SUV (1720 kg), the mass of the vehicle platform (500 kg), and the mass of the stacker crane platform (800 kg), totaling 3020 kg. The distributed mass of the cantilever beam is determined by the material linear density of 120 kg / m³, and the elastic properties of the cantilever beam are determined by the moment of inertia of the cross section (8.5 × 10⁻⁶). －5 m 4 And elastic modulus 2.1×10 11 Pa is determined, and the energy dissipation characteristics of the cantilever beam are determined by the material damping ratio of 0.02. The three-dimensional eccentric moment is applied as an external excitation to the center of mass of the concentrated mass. In the target rigid-flexible coupling dynamic model, the three-dimensional eccentric moment is manifested as an external moment that causes the cantilever beam to produce bending and torsional vibrations.

[0068] In the above embodiment, the linear density of the column material, 120 kg / m, is input into the target rigid-flexible coupling dynamic model. Combined with the planned lifting height at each discrete moment in the planned lifting height sequence, the first and second time-varying natural frequencies of the stacker crane at each discrete moment are determined by solving the cantilever beam vibration equation. At the first discrete moment (t=0 seconds), the stacker crane is located on the ground level, and the planned lifting height is 0 meters. At this time, the effective cantilever length of the column is the shortest, and the concentrated mass of 3020 kg is located near the base of the column. According to the cantilever beam natural frequency formula f=λ... 2 / (2πL 2The formula is calculated as λ × √(EI / m), where λ is the modal constant (first-order mode λ1 = 1.875, second-order mode λ2 = 4.694), L is the effective cantilever length, E is the elastic modulus, I is the moment of inertia of the section, and m is the equivalent mass. The calculated first-order time-varying natural frequency is f1 = 2.1 Hz, and the second-order time-varying natural frequency is f2 = 6.3 Hz. At the 10th discrete time (t = 1.0 sec), the stacker crane has risen to the planned lifting height of 0.16 meters, and the effective cantilever length of the column is 0.16 meters. The calculated first-order time-varying natural frequency is f1 = 2.0 Hz, and the second-order time-varying natural frequency is f2 = 6.0 Hz, which is slightly lower than the natural frequency at the first discrete time. At the 50th discrete time step (t=5.0 seconds), the stacker crane has risen to the planned lifting height of 4.8 meters, and the effective cantilever length of the column is 4.8 meters. The calculated first-order time-varying natural frequency f1=1.3Hz and the second-order time-varying natural frequency f2=3.9Hz, showing a significant decrease in natural frequencies. At the 140th discrete time step (t=14.0 seconds), the stacker crane has risen to the planned lifting height of 22.4 meters, and the effective cantilever length of the column is 22.4 meters. The calculated first-order time-varying natural frequency f1=0.6Hz and the second-order time-varying natural frequency f2=1.8Hz, showing a minimum natural frequency. At the 150th discrete time step (t=15.0 seconds), the stacker crane reaches the 8th layer target parking space, with a planned lifting height of 24 meters. The effective cantilever length of the column reaches its maximum value of 24 meters, and the calculated first-order time-varying natural frequency f1=0.5Hz and the second-order time-varying natural frequency f2=1.5Hz.

[0069] In the above embodiments, the first-order vibration period is determined based on the first-order time-varying natural frequency at each discrete moment. At the first discrete moment, the first-order time-varying natural frequency f1 = 2.1 Hz, and the first-order vibration period T1 = 1 / f1 = 0.48 seconds. Half of the first-order vibration period of 0.48 seconds, 0.24 seconds, is determined as the first time interval of the first-order shaping pulse. At the 50th discrete moment, the first-order time-varying natural frequency f1 = 1.3 Hz, the first-order vibration period T1 = 0.77 seconds, and the first time interval is 0.39 seconds. At the 150th discrete moment, the first-order time-varying natural frequency f1 = 0.5 Hz, the first-order vibration period T1 = 2.0 seconds, and the first time interval is 1.0 second. The second-order vibration period is determined based on the second-order time-varying natural frequency at each discrete moment. At the first discrete moment, the second-order time-varying natural frequency f2 = 6.3 Hz, and the second-order vibration period T2 = 0.16 seconds. Half of this second-order vibration period, 0.08 seconds, is determined as the second time interval of the second-order shaping pulse. At the 50th discrete moment, the second-order time-varying natural frequency f2 = 3.9 Hz, and the second-order vibration period T2 = 0.26 seconds, with a second time interval of 0.13 seconds. At the 150th discrete moment, the second-order time-varying natural frequency f2 = 1.5 Hz, and the second-order vibration period T2 = 0.67 seconds, with a second time interval of 0.34 seconds. Based on the column's material damping ratio of 0.02, the first-order amplitude weighting coefficient of the first-order shaping pulse and the second-order amplitude weighting coefficient of the second-order shaping pulse are determined respectively. According to the formula for calculating the amplitude weighting coefficient of the damping system in the input shaping control theory, the relationship between the first-order amplitude weighting coefficient α1 and the material damping ratio ζ is α1 = 1 / (1 + ζ). Substituting the material damping ratio 0.02, the first-order amplitude weighting coefficient α1 = 1 / (1 + 0.02) = 0.98 is calculated. The relationship between the second-order amplitude weighting coefficient α2 and the material damping ratio ζ is α2 = 0.9 / (1 + ζ), where the coefficient 0.9 is a reduction factor set considering that the vibration energy of the second-order mode is usually lower than that of the first-order mode. Substituting the material damping ratio 0.02, the second-order amplitude weighting coefficient α2 = 0.9 / (1 + 0.02) = 0.88 is calculated. Since the material damping ratio 0.02 is relatively small, it indicates that the column material has a weak natural attenuation ability for vibration. Therefore, both the first-order and second-order amplitude weighting coefficients are taken with large values ​​to ensure that the time-varying shaped pulse sequence has sufficient amplitude to achieve effective vibration suppression.

[0070] In the above embodiment, a time-varying shaped pulse sequence matching the discrete time sequence is generated based on the three-dimensional eccentric load moments (pitch eccentric load moment component 1348 N·m, roll eccentric load moment component 253 N·m, yaw eccentric load moment component 52 N·m), the first and second time-varying natural frequencies at each discrete moment, the first and second time intervals, the first-order amplitude weighting coefficient 0.98 and the second-order amplitude weighting coefficient 0.88, and the pulse amplitude constraint coefficient at each discrete moment. At the 10th discrete moment (t=1.0 sec), the basic amplitude of the first-order shaped pulse is calculated as A1=1348 / (2π×2.0) based on the pitch eccentric load moment component 1348 N·m and the first-order time-varying natural frequency 2.0 Hz. 2 =8.5 N·m. After correction by a first-order amplitude weighting coefficient of 0.98, the amplitude of the first-order shaped pulse is 8.5 × 0.98 = 8.3 N·m. After constraint by a pulse amplitude constraint coefficient of 0.95, the final amplitude of the first-order shaped pulse is 8.3 × 0.95 = 7.9 N·m. The basic amplitude of the second-order shaped pulse is calculated based on the tilting moment component of 253 N·m and the second-order time-varying natural frequency of 6.0 Hz as A2 = 253 ÷ (2π × 6.0). 2 =0.6 N·m. After correction by a second-order amplitude weighting coefficient of 0.88, the amplitude of the second-order shaped pulse is 0.6 × 0.88 = 0.5 N·m. After constraint by a pulse amplitude constraint coefficient of 0.95, the final amplitude of the second-order shaped pulse is 0.5 × 0.95 = 0.5 N·m. At the 140th discrete time (t = 14.0 seconds), since the first-order time-varying natural frequency decreases to 0.6 Hz, the fundamental amplitude of the first-order shaped pulse increases to A1 = 1348 ÷ (2π × 0.6). 2 =95 N·m, but since the pulse amplitude constraint coefficient at this moment is 0.35 (because the structural deflection response value is close to the safety limit), the final first-order shaping pulse amplitude is constrained to 95 × 0.98 × 0.35 = 32.6 N·m, avoiding excessive pulse amplitude that would cause the column deflection to exceed the safety limit. Through the above calculation process, a time-varying shaping pulse sequence including 150 discrete time points was generated. The pulse amplitude and time interval of each discrete time in this time-varying shaping pulse sequence were adaptively adjusted according to the time-varying natural frequency, three-dimensional eccentric load moment and structural safety constraints corresponding to the current planned lifting height.

[0071] In an optional embodiment, generating a time-varying shaped pulse sequence based on the three-dimensional off-center load moment, the first-order time-varying natural frequency, the second-order time-varying natural frequency, the first time interval, the second time interval, the first-order amplitude weighting coefficient, the second-order amplitude weighting coefficient, and the pulse amplitude constraint coefficient includes: determining the first-order vibration modal response of the column based on the three-dimensional off-center load moment and the first-order time-varying natural frequency, and determining the second-order vibration modal response of the column based on the three-dimensional off-center load moment and the second-order time-varying natural frequency; determining the modal coupling coefficient between the first-order and second-order modes based on the first-order and second-order vibration modal responses; generating a first-order shaped pulse sequence based on the first time interval and the first-order amplitude weighting coefficient, and generating a second-order shaped pulse sequence based on the second time interval and the second-order amplitude weighting coefficient; performing time-series superposition processing on the first-order shaped pulse sequence and the second-order shaped pulse sequence according to the modal coupling coefficient to obtain a superimposed pulse sequence; and constraining the pulse amplitude at each discrete moment in the superimposed pulse sequence according to the pulse amplitude constraint coefficient to generate a time-varying shaped pulse sequence.

[0072] The first-order vibration modal response refers to the vibration response characteristics of the column under three-dimensional eccentric torque excitation. It describes the vibration amplitude, phase, and attenuation characteristics of the column near its first natural frequency. The first-order vibration mode typically exhibits the basic bending vibration pattern of the entire column. The second-order vibration modal response refers to the vibration response characteristics of the column under three-dimensional eccentric torque excitation. It describes the vibration amplitude, phase, and attenuation characteristics of the column near its second natural frequency. The second-order vibration mode typically exhibits a complex vibration pattern with a vibration node in the middle of the column and vibrations in the upper and lower sections. The modal coupling coefficient is a coefficient that quantifies the interaction strength between the first-order and second-order vibration modal responses. It reflects the energy exchange and phase correlation between the first-order and second-order vibration modes under three-dimensional eccentric torque excitation. When different components (pitch, roll, yaw) of the three-dimensional eccentric torque simultaneously excite the first and second-order vibration modes, a coupling effect occurs between the two modes through the geometric and material nonlinearities of the structure. The modal coupling coefficient is used to quantify the strength of this coupling effect. The first-order shaped pulse sequence is a shaped pulse sequence for the first-order vibration mode generated based on the first time interval and the first-order amplitude weighting coefficient. The time interval between the two pulses in each pulse pair in the first-order shaped pulse sequence is equal to the first time interval, and the pulse amplitude is determined according to the first-order amplitude weighting coefficient. The first-order shaped pulse sequence is used to suppress the first-order vibration mode of the column.

[0073] The second-order shaped pulse sequence is a shaped pulse sequence for the second-order vibration mode generated based on the second time interval and the second-order amplitude weighting coefficient. The time interval between the two pulses in each pulse pair in the second-order shaped pulse sequence is equal to the second time interval, and the pulse amplitude is determined according to the second-order amplitude weighting coefficient. The second-order shaped pulse sequence is used to suppress the second-order vibration mode of the column. The time-series superposition processing refers to superimposing the first-order and second-order shaped pulse sequences in the time domain according to each discrete moment in the discrete time series. The time-series superposition processing needs to consider the weighting relationship of the modal coupling coefficient on the two pulse sequences. The superimposed pulse sequence obtained after the time-series superposition processing integrates the vibration suppression effects of the first-order and second-order shaped pulse sequences, and can simultaneously suppress the first-order and second-order vibration modes of the column. The superimposed pulse sequence is a composite pulse sequence obtained by time-series superposition of a first-order shaped pulse sequence and a second-order shaped pulse sequence. The pulse amplitude at each discrete moment in the superimposed pulse sequence is the sum of the amplitude of the first-order shaped pulse and the second-order shaped pulse amplitude weighted by modal coupling coefficients. Constraint processing refers to limiting the pulse amplitude at each discrete moment in the superimposed pulse sequence according to pulse amplitude constraint coefficients. Constraint processing ensures that the pulse amplitude does not exceed the maximum allowable value for structural safety. The time-varying shaped pulse sequence generated after constraint processing can effectively suppress vibration and ensure the safety of the column structure.

[0074] In the above embodiments, based on the target rigid-flexible coupling dynamic model constructed in the previous embodiments and the determined time-varying natural frequency, the detailed process of generating a time-varying shaped pulse sequence according to the modal coupling coefficient is further explained. Based on the three-dimensional eccentric load moments of the medium-sized SUV (pitch load moment component 1348 N·m, roll load moment component 253 N·m, yaw load moment component 52 N·m) and the first-order time-varying natural frequency of 2.0 Hz at the 10th discrete moment, the first-order vibration modal response of the column is calculated in the target rigid-flexible coupling dynamic model. The pitch load moment component 1348 N·m mainly excites the first-order bending vibration of the column in the horizontal longitudinal direction. The bending vibration equation of the cantilever beam in the target rigid-flexible coupling dynamic model is used as the basis for this calculation. The first-order vibration modal response was obtained with an amplitude of 12.5 mm and a phase angle of 0°, where E is the elastic modulus, I is the moment of inertia of the section, y is the deflection, x is the coordinate along the length of the column, ρ is the material density, A is the cross-sectional area, t is time, and M(t) is the time-varying external bending moment load. The lateral tilting moment component of 253 N·m mainly excites the first-order bending vibration of the column in the horizontal transverse direction. Using the same cantilever beam bending vibration equation, the first-order vibration modal response in this direction was obtained with an amplitude of 2.8 mm and a phase angle of 5°. The yaw moment component of 52 N·m excites the torsional vibration of the column. Based on the cantilever beam torsional vibration equation in the target rigid-flexible coupling dynamic model... Solving for the first-order vibration mode response in the torsional direction, we obtain a rotation amplitude of 0.15° and a phase angle of -8°, where G is the shear modulus, J is the torsional section modulus, and θ is the torsional angle. Let T(t) be the polar moment of inertia, and T(t) be the time-varying external torque load. Based on the three-dimensional eccentric load moment of a mid-size SUV and the second-order time-varying natural frequency of 6.0 Hz at the 10th discrete moment, the second-order vibration modal response of the column is calculated in the target rigid-flexible coupling dynamic model. The pitch eccentric load moment component of 1348 N·m excites the column's second-order bending vibration in the horizontal longitudinal direction. Solving according to the cantilever beam bending vibration equation, the amplitude of the second-order vibration modal response is obtained as 3.2 mm, and the phase angle is -15°. The roll eccentric load moment component of 253 N·m excites the column's second-order bending vibration in the horizontal transverse direction. Solving according to the cantilever beam bending vibration equation, the amplitude of the second-order vibration modal response in this direction is obtained as 0.9 mm, and the phase angle is -12°. The eccentric load moment component of 52 N·m excites the second-order torsional vibration of the column. According to the torsional vibration equation of the cantilever beam, the rotation amplitude of the second-order vibration mode response in the torsional direction is 0.05° and the phase angle is 20°.

[0075] In the above embodiment, the modal coupling coefficient between the first-order and second-order vibration modal responses is determined based on the first-order and second-order vibration modal responses. In the horizontal longitudinal direction, the phase difference between the amplitude of the first-order vibration modal response (12.5 mm) and the amplitude of the second-order vibration modal response (3.2 mm) is 15°. This phase difference indicates energy exchange between the two modes. According to the modal coupling theory of structural vibration, when the frequency ratio of two vibration modes is close to an integer ratio and a phase difference exists, energy coupling will occur between the two modes through the nonlinear effects of the structure. The modal coupling coefficient can be determined by multiplying the amplitude ratio of the two modal responses by the cosine of the phase difference. The modal coupling coefficient β is calculated. pitch =(3.2÷12.5)×cos(15°)=0.247. In the horizontal transverse direction, the phase difference between the first-order vibration modal response amplitude of 2.8mm and the second-order vibration modal response amplitude of 0.9mm is 17°, and the modal coupling coefficient β... roll=(0.9÷2.8)×cos(17°)=0.307. In the torsional direction, the phase difference between the first-order vibration modal response rotation angle amplitude of 0.15° and the second-order vibration modal response rotation angle amplitude of 0.05° is 28°, and the modal coupling coefficient β... yaw =(0.05÷0.15)×cos(28°)=0.294. The weighted average of the modal coupling coefficients in the three directions yields the comprehensive modal coupling coefficient β=[(0.247×1348)+(0.307×253)+(0.294×52)]÷(1348+253+52)=0.261. A first-order shaped pulse sequence is generated based on the first time interval and the first-order amplitude weighting coefficient. At the 10th discrete moment, the first time interval is 0.38 seconds (corresponding to half of the 0.5-second oscillation period of the first-order time-varying natural frequency of 2.0Hz), and the first-order amplitude weighting coefficient is 0.98. The stacking parking system generates a first-order shaping pulse with an amplitude of 7.9 N·m at time t = 1.0 seconds, and a second first-order shaping pulse with an amplitude of -7.9 × 0.98 = -7.7 N·m at time t = 1.0 + 0.38 = 1.38 seconds. The opposite phase of this pulse pair suppresses the first-order vibration mode. Similarly, corresponding first-order shaping pulse pairs are generated at each discrete moment in the discrete time series, forming a complete first-order shaping pulse sequence.

[0076] In the above embodiment, a second-order shaped pulse sequence is generated based on the second time interval and the second-order amplitude weighting coefficient. At the 10th discrete time, the second time interval is 0.13 seconds (corresponding to half of the 0.26-second vibration period of the second-order time-varying natural frequency of 6.0 Hz), and the second-order amplitude weighting coefficient is 0.88. The stacking parking system sets the first second-order shaped pulse at time t=1.0 seconds, with an amplitude of 0.5 N·m, and sets the second second-order shaped pulse at time t=1.0 + 0.13 = 1.13 seconds, with an amplitude of -0.5 × 0.88 = -0.44 N·m. The phases of the first and second second-order shaped pulses are opposite, which can suppress the second-order vibration mode. Similarly, corresponding second-order shaped pulse pairs are generated at each discrete time of the discrete time sequence to form a complete second-order shaped pulse sequence. Based on the modal coupling coefficient β=0.261, the first-order and second-order shaped pulse sequences are time-series superimposed according to discrete time sequences. At the 10th discrete time (t=1.0 s), the amplitude of the first-order shaped pulse is 7.9 N·m, and the amplitude of the second-order shaped pulse is 0.5 N·m. Weighted superposition according to the modal coupling coefficient yields a superimposed pulse sequence amplitude of 7.9 + (0.261 × 0.5) = 8.03 N·m at that time. At time t=1.13 s, only the second-order shaped pulse (amplitude -0.44 N·m) exists, and the superimposed pulse sequence amplitude at that time is 0.261 × (-0.44) = -0.11 N·m. At time t=1.38 s, only the first-order shaped pulse (amplitude -7.7 N·m) exists, and the superimposed pulse sequence amplitude at that time is -7.7 N·m. Through this time-series superposition processing, the pulse amplitude at each discrete moment in the superimposed pulse sequence comprehensively considers the suppression requirements of the first-order shaped pulse on the first-order vibration mode and the suppression requirements of the second-order shaped pulse on the second-order vibration mode. The mutual influence between the two modes is quantified through the mode coupling coefficient, so that the superimposed pulse sequence can simultaneously achieve the coordinated suppression of the first-order and second-order vibration modes of the column when the drive motor is executed.

[0077] In the above embodiment, the pulse amplitude of 8.03 N·m in the superimposed pulse sequence at the 10th discrete time step is constrained by a constraint coefficient of 0.95. Since this pulse amplitude of 8.03 N·m is less than the constraint limit of 8.03 ÷ 0.95 = 8.45 N·m, the pulse amplitude remains unchanged. At the 140th discrete time step, the pulse amplitude of the superimposed pulse sequence is 35.2 N·m. The pulse amplitude constraint coefficient at this time step is 0.35, and the constraint limit is 35.2 ÷ 0.35 = 100.6 N·m. Since the pulse amplitude of 35.2 N·m is less than the constraint limit, the pulse amplitude also remains unchanged. However, if the amplitude of the superimposed pulse sequence at a certain discrete moment exceeds the constraint limit, the pulse amplitude is reduced to the constraint limit. For example, if the superimposed pulse amplitude at a certain moment is 120 N·m, the pulse amplitude constraint coefficient is 0.35, and the constraint limit is 100.6 N·m, then the pulse amplitude is reduced to 100.6 N·m. Through the above constraint processing, a time-varying shaped pulse sequence is generated, which includes pulse amplitude data at 150 discrete time points. Each pulse amplitude has undergone first-order and second-order modal coupling superposition and structural safety constraint processing, which can achieve coordinated suppression of first-order and second-order low-frequency flexible vibrations while ensuring the safety of the column structure.

[0078] In an optional embodiment, generating a target speed control curve based on the initial motion command and time-varying shaping pulse sequence of the stacker crane includes: parsing the initial motion command to obtain a basic S-shaped speed curve, which includes an acceleration segment, a constant speed segment, and a deceleration segment; performing time-domain convolution processing on the basic S-shaped speed curve and the time-varying shaping pulse sequence to obtain an initial shaped speed curve; extracting the torque projection component of the stacker crane in the current running direction from the three-dimensional eccentric load moment, and determining whether the direction of action of the torque projection component is the same as the direction of the stacker crane's inertial moment; when the direction of action is the same as the direction of the inertial moment... Simultaneously, it is determined that the stacker crane is under an aggravated off-center load condition, and the acceleration section stretching coefficient is determined based on the torque projection component. The acceleration section of the initial shaping speed curve is smoothed and extended using the acceleration section stretching coefficient to obtain the first asymmetric shaping curve. When the direction of action is opposite to the direction of the inertial torque, it is determined that the stacker crane is under an off-center load suppression condition, and the deceleration section compression coefficient is determined based on the torque projection component. The deceleration section compression coefficient is used to perform time compression processing on the deceleration section of the initial shaping speed curve to obtain the second asymmetric shaping curve. The first asymmetric shaping curve or the second asymmetric shaping curve is used as the target speed control curve.

[0079] The initial motion command is the raw motion control command generated by the stacking parking system based on the vehicle handling task. It includes motion parameters such as starting position coordinates, target position coordinates, maximum running speed, and maximum acceleration. However, the initial motion command does not consider the impact of the actual mass and off-center load characteristics of the vehicles to be parked on vibration. The basic S-shaped velocity curve is a standard S-shaped velocity curve obtained after analyzing the initial motion command. It consists of three stages: acceleration, constant speed, and deceleration. The acceleration stage uses an S-shaped acceleration curve to smoothly increase the speed; the constant speed stage maintains a constant speed; and the deceleration stage uses an S-shaped deceleration curve to smoothly reduce the speed to zero. The basic S-shaped velocity curve has better smoothness than the traditional trapezoidal velocity curve, but it still does not optimize vibration suppression. Temporal convolution processing is the process of convolving the basic S-shaped velocity curve with a time-varying shaped pulse sequence in the time domain. Temporal convolution processing embeds the vibration suppression effect of the time-varying shaped pulse sequence into the basic S-shaped velocity curve. The mathematical expression for temporal convolution processing is v. shaped (t)=∫v basic (τ)×u pulse (t-τ)dτ, where v basic Based on the S-shaped velocity curve, u pulse For time-varying shaped pulse sequences, v shaped This is the initial shaping speed curve after convolution processing.

[0080] The initial shaping velocity curve is obtained by time-domain convolution of the basic S-shaped velocity curve and the time-varying shaping pulse sequence. While the initial shaping velocity curve already includes suppression of column vibration, it remains a symmetrical velocity curve and has not undergone asymmetric optimization based on the specific off-center loading condition. The torque projection component refers to the projection component of the three-dimensional off-center loading moment in the current operating direction of the stacker crane. When the stacker crane runs along the horizontal longitudinal direction, the torque projection component is mainly the projection of the pitch off-center loading moment component in that direction. When the stacker crane runs along the horizontal transverse direction, the torque projection component is mainly the projection of the tilt off-center loading moment component in that direction. The inertial moment direction refers to the direction of the moment generated by the inertial force produced during the acceleration or deceleration of the stacker crane acting on the center of mass of the vehicle to be parked. The inertial moment direction is related to the acceleration direction of the stacker crane and the offset direction of the center of mass of the vehicle to be parked relative to the load center. The aggravated off-center load condition refers to a condition in which the direction of the projected component of the moment is the same as the direction of the stacker crane's moment of inertia. Under the aggravated off-center load condition, the superposition of the off-center load moment and the moment of inertia causes the column to bear a larger bending moment load, increasing the risk of vibration.

[0081] Among them, the off-center load suppression condition refers to the condition where the direction of the moment projection component is opposite to the direction of the stacker crane's inertial moment. Under the off-center load suppression condition, the off-center load moment and the inertial moment partially cancel each other out, resulting in a smaller bending moment load on the column and a reduced vibration risk. The acceleration segment stretching coefficient is a coefficient used to extend the acceleration segment time under the off-center load aggravation condition, determined based on the magnitude of the moment projection component. The acceleration segment stretching coefficient is greater than 1; the larger the coefficient, the greater the extension of the acceleration segment and the greater the reduction in peak acceleration. The smoothing extension process involves stretching the acceleration segment of the initial shaping velocity curve on the time axis using the acceleration segment stretching coefficient. This process increases the duration of the acceleration segment while keeping the total acceleration change constant, thereby reducing the peak acceleration and inertial impact during acceleration. The velocity curve after smoothing extension has a smaller slope and a smoother curve in the acceleration segment. The first asymmetric shaping curve is an asymmetric velocity curve obtained after smoothing and extending the acceleration segment of the initial shaping velocity curve. The acceleration segment time of the first asymmetric shaping curve is longer than the deceleration segment time, making it suitable for the off-center load aggravation condition.

[0082] The deceleration compression coefficient, determined based on the magnitude of the torque projection component under eccentric load suppression conditions, is used to shorten the deceleration period. A deceleration compression coefficient less than 1 indicates a greater degree of shortening and improved deceleration efficiency. Time compression processing involves compressing the deceleration section of the initial shaping speed curve using the deceleration compression coefficient. This reduces the duration of the deceleration section while maintaining a constant total deceleration change, thereby improving deceleration efficiency and shortening the total handling time. The speed curve after time compression exhibits a steeper slope and more pronounced curve in the deceleration section, while still maintaining its S-shaped smoothness. The second asymmetric shaping curve is obtained by time compression of the deceleration section of the initial shaping speed curve. The deceleration time of the second asymmetric shaping curve is shorter than the acceleration time, making it suitable for eccentric load suppression conditions.

[0083] In the above embodiments, based on the time-varying shaped pulse sequence generated in the preceding embodiments, the detailed process of generating the target speed control curve according to the off-center load condition type is further explained. The initial motion command of the stacker crane is analyzed, which includes: starting position at the ground floor entrance (horizontal coordinate 0 meters, lifting height 0 meters), target position at parking space number 12 on the 8th floor (horizontal coordinate 45 meters, lifting height 24 meters), maximum horizontal running speed 2.5 m / s, maximum lifting speed 0.8 m / s, maximum horizontal acceleration 1.2 m / s², and maximum lifting acceleration 0.5 m / s². Based on the above initial motion command, the stacker parking system generates a basic S-shaped speed curve. The horizontal motion portion of this basic S-shaped velocity curve includes: an acceleration phase from t=0 seconds to t=3.5 seconds, where the velocity smoothly increases from 0 m / s to 2.5 m / s, using an S-shaped acceleration curve, with acceleration smoothly increasing from 0 m / s² to a maximum value of 1.2 m / s² and then smoothly decreasing back to 0 m / s²; a constant velocity phase from t=3.5 seconds to t=17.5 seconds, where the velocity remains constant at 2.5 m / s; and a deceleration phase from t=17.5 seconds to t=21.0 seconds, where the velocity smoothly decreases from 2.5 m / s to 0 m / s, using an S-shaped deceleration curve, with deceleration smoothly increasing from 0 m / s² to a maximum value of -1.2 m / s² and then smoothly decreasing back to 0 m / s². The rising and falling motion portions of this basic S-shaped velocity curve occur synchronously. The time distribution of the acceleration, constant velocity, and deceleration phases is the same as the horizontal motion portion, except that the maximum velocity is 0.8 m / s and the maximum acceleration is 0.5 m / s².

[0084] In the above embodiment, the basic S-shaped velocity curve and the time-varying shaped pulse sequence are subjected to temporal convolution. In the temporal convolution, the pulse amplitude at each discrete moment in the time-varying shaped pulse sequence is used as a weighting coefficient to adjust the velocity value of the basic S-shaped velocity curve near that moment. Specifically, at the 10th discrete moment (t=1.0 second), the pulse amplitude of the time-varying shaped pulse sequence is 8.03 N·m. This pulse amplitude is converted into a velocity adjustment Δv = 8.03 ÷ (1720 × 1.0) = 0.0047 m / s. The velocity value of the basic S-shaped velocity curve at t=1.0 second is 0.35 m / s, and the velocity value after convolution is 0.35 + 0.0047 = 0.3547 m / s. Similarly, the velocity value at each discrete moment in the discrete time sequence is convolved and adjusted to obtain the initial shaped velocity curve. Compared to the basic S-shaped velocity curve, the initial shaping velocity curve shows a slight increase in velocity at the positive pulse position of the time-varying shaping pulse sequence and a slight decrease in velocity at the negative pulse position. This fine-tuning of velocity allows the excitation torque frequency generated by the drive motor to match and cancel out the natural vibration frequency of the column structure. The torque projection component of the stacker crane in the current horizontal longitudinal direction is extracted from the three-dimensional off-center load moments of the mid-size SUV (pitch off-center load moment component 1348 N·m, roll off-center load moment component 253 N·m, yaw off-center load moment component 52 N·m). Since the stacker crane mainly operates in the horizontal longitudinal direction, the torque projection component is primarily the pitch off-center load moment component of 1348 N·m. This pitch off-center load moment component is positive, indicating that the center of mass of the mid-size SUV is biased towards the front of the stacker crane. When the stacker crane accelerates forward, the inertial force acting on the forward-biased center of mass generates an inertial moment that tilts the column forward. The direction of this inertial moment is the same as the direction of the pitch off-center load moment component.

[0085] In the above embodiment, the direction of the projected moment component 1348 N·m (forward tilt) is determined to be the same as the direction of the inertial moment (forward tilt) during the forward acceleration of the stacker crane. Therefore, it is determined that the stacker crane is in an aggravated off-center load condition. Under the aggravated off-center load condition, the superposition of the off-center load moment and the inertial moment will cause the column to bear a larger bending moment load during the acceleration phase, significantly increasing the vibration risk. In order to reduce the vibration risk during the acceleration phase, the tensile coefficient of the acceleration section is determined based on the projected moment component 1348 N·m. The formula for calculating the tensile coefficient of the acceleration section is: k stretch =1+(M projection ÷M reference )×0.2, where M projection The projected component of the torque is 1348 N·m, M reference The reference torque is 1000 N·m, which is determined based on the allowable bending moment of the column, and the allowable bending moment of the column is equal to the yield strength σ of the column material. sThe product of the section modulus W and the section modulus, i.e., Mreference = σ s ×W. For the column in this embodiment, assume the material yield strength σ s =235MPa (yield strength of Q235 steel), section bending modulus W=I / c, where I is the moment of inertia of the section 8.5×10 －5 m 4 Let c be the distance from the centroid of the cross section to the edge. Assuming c = 0.1 m, then W = (8.5 × 10⁻⁶ m). －5 ) ÷ 0.1 = 8.5 × 10 －4 m³, the calculated reference torque Mreference = 235 × 10 6 Pa×8.5×10 －4 m³ = 199750 N·m. For safety, a conservative reference torque value of 1000 N·m is adopted as the benchmark for judging the degree of off-center loading. Substituting the torque projection component of 1348 N·m, the acceleration section tensile coefficient k is calculated. stretch =1+(1348÷1000)×0.2=1.27. The acceleration segment of the initial shaped velocity curve is smoothed and extended using an acceleration segment stretching coefficient of 1.27. The acceleration segment time of the initial shaped velocity curve is 3.5 seconds, and the acceleration segment time after stretching by 1.27 is 3.5×1.27=4.45 seconds. In the smoothing extension process, the S-shaped curve shape of the acceleration segment remains unchanged, but the time axis is stretched. The slope of the velocity increase decreases from the original 2.5÷3.5=0.71m / s² to 2.5÷4.45=0.56m / s², and the peak value of the maximum acceleration decreases from 1.2m / s² to approximately 0.95m / s². The constant velocity segment and the deceleration segment remain unchanged. The constant velocity segment starts from t=4.45 seconds to t=18.45 seconds, and the deceleration segment starts from t=18.45 seconds to t=21.95 seconds. Through smoothing and lengthening, the stacked parking system obtains a first asymmetric shaping curve. The acceleration period of this first asymmetric shaping curve is 4.45 seconds, which is longer than the deceleration period of 3.5 seconds. The reduced peak acceleration during the acceleration period reduces the inertial impact during acceleration and effectively reduces the column bending moment load and vibration risk under the condition of aggravated eccentric loading.

[0086] In the above embodiment, the first asymmetric shaping curve is used as the target speed control curve, and the stacker crane's drive motor is controlled to perform vehicle handling operations according to this target speed control curve. During actual handling, the stacker crane smoothly accelerates to 2.5 m / s in 4.45 seconds during the acceleration phase, an increase of 0.95 seconds compared to the 3.5 seconds acceleration time of the basic S-shaped speed curve. However, due to the reduced peak acceleration, the maximum deflection of the column during the acceleration phase decreases from 15.2 mm when using the basic S-shaped speed curve to 9.8 mm, significantly reducing the vibration amplitude. Throughout the entire handling process (total time 21.95 seconds), the peak horizontal displacement amplitude at the top of the column remains within ±9.8 mm, achieving a vibration suppression effect of 69% compared to the ±32 mm amplitude when using a fixed speed curve control. To further illustrate the handling of off-center load suppression conditions, consider another scenario: the vehicle to be parked is a sedan with its trunk fully loaded with goods. The sedan's center of gravity is offset to the rear, with three-dimensional center of gravity coordinates of (1800mm, 1250mm, 600mm). The load-bearing center coordinates of the stacker crane's platform are (2000mm, 1250mm, 700mm). The calculated horizontal longitudinal offset component is 1800 - 2000 = -200mm (a negative value indicates the center of gravity is offset to the rear). Based on the sedan's actual mass of 1500kg and static gravity load of 14700N, the calculated pitch off-center load moment component is 14700 × (-0.2) = -2940N·m. A negative value indicates that this moment causes the column to tilt backward. When the stacker crane accelerates forward, the inertial force acting on the rearward-off center of gravity will generate an inertial moment that causes the column to tilt forward. The direction of this inertial moment is opposite to the direction of the pitch off-center load moment component.

[0087] In the above embodiment, the direction of the projected torque component -2940 N·m (tilting backward) is determined to be opposite to the direction of the inertial moment during the forward acceleration of the stacker crane (tilting forward). Therefore, the stacker crane is determined to be in an off-center load suppression condition. Under the off-center load suppression condition, the off-center load moment and the inertial moment partially cancel each other out, resulting in a smaller bending moment load on the column, reducing the vibration risk, and allowing for a more aggressive deceleration strategy to shorten the handling time. The stacker parking system determines the deceleration compression coefficient based on the projected torque component -2940 N·m. The formula for calculating the deceleration compression coefficient is: k compress =1-(|M projection |÷M reference )×0.15, where |M projection |The absolute value of the projected torque component is 2940 N·m. The compression coefficient k of the deceleration section is calculated. compress=1-(2940÷1000)×0.15=0.56. The deceleration section of the initial shaping velocity curve is compressed using a deceleration compression coefficient of 0.56. The deceleration time of the initial shaping velocity curve is 3.5 seconds, and after compression with a coefficient of 0.56, the deceleration time is 3.5×0.56=1.96 seconds. In the time compression process, the S-shaped curve of the deceleration section remains unchanged, but the time axis is compressed. The slope of the velocity reduction increases from the original 2.5÷3.5=0.71m / s² to 2.5÷1.96=1.28m / s², and the peak value of the maximum deceleration increases from -1.2m / s² to approximately -1.53m / s². Due to the eccentric load suppression condition, the inertial moment generated by the increased peak deceleration partially cancels out the eccentric load moment, and the total bending moment load borne by the column remains within the safe range. The acceleration and constant speed phases remain unchanged, while the deceleration phase begins at t=17.5 seconds and ends at t=19.46 seconds. Through time compression processing, a second asymmetric shaping curve is obtained. The deceleration phase of this second asymmetric shaping curve, at 1.96 seconds, is shorter than the acceleration phase at 3.5 seconds. The improved deceleration efficiency shortens the total handling time, reducing it from 21.0 seconds to 19.46 seconds, thus improving storage and retrieval efficiency while maintaining vibration suppression.

[0088] It should be noted that the examples of all the specific values ​​mentioned above are merely exemplary embodiments, and the specific values ​​are not limited to the examples mentioned above.

[0089] Through the embodiments of this application, a target rigid-flexible coupled dynamic model including the load characteristics of the vehicle to be parked is constructed based on the actual mass data and three-dimensional centroid coordinate data of the vehicle to be parked. The time-varying natural frequency that changes with the planned lifting height of the stacker crane is calculated in real time. Based on the time-varying natural frequency, time-varying shaped pulse sequences for the first-order vibration mode and the second-order vibration mode are generated. The speed control curve is asymmetrically optimized according to the specific off-center load condition, so that the frequency of the excitation torque generated by the drive motor matches and cancels out the natural vibration frequency of the column structure. This realizes personalized anti-vibration control for the load characteristics of each vehicle to be parked. Without reducing the operating speed of the stacker crane or increasing the rigidity of the column structure, the low-frequency flexible vibration of the column caused by the mass difference and centroid distribution off-center load of the vehicles to be parked is effectively suppressed, ensuring the vehicle storage and retrieval efficiency and structural stability of the stacking parking system under multiple vehicle types and off-center load conditions.

[0090] The stacking parking system in the embodiments of this invention is described below from the perspective of hardware processing. (See attached document.) Figure 2 , Figure 2 This is a schematic diagram of the physical device structure of a stacking parking system in the embodiments of this application.

[0091] It should be noted that, Figure 2The structure of the stacked parking system shown is merely an example and should not impose any limitations on the functionality and scope of use of the embodiments of the present invention.

[0092] like Figure 2 As shown, the stacking parking system includes a Central Processing Unit (CPU) 201, which can perform various appropriate actions and processes based on programs stored in Read-Only Memory (ROM) 202 or programs loaded from storage section 208 into Random Access Memory (RAM) 203, such as executing the methods described in the above embodiments. The RAM 203 also stores various programs and data required for platform operation. The CPU 201, ROM 202, and RAM 203 are interconnected via bus 204. An I / O interface 205 is also connected to bus 204. The following components are connected to the I / O interface 205: an input section 206 including audio input devices, push-button switches, etc.; an output section 207 including a Liquid Crystal Display (LCD) and audio output devices, indicator lights, etc.; a storage section 208 including a hard disk, etc.; and a communication section 209 including a network interface card such as a LAN (Local Area Network) card, modem, etc. The communication section 209 performs communication processing via a network such as the Internet. The drive 210 is also connected to the I / O interface 205 as needed. Removable media 211, such as disks, optical disks, magneto-optical disks, semiconductor memories, etc., are installed on the drive 210 as needed so that computer programs read from them can be installed into the storage section 208 as needed.

[0093] In particular, according to embodiments of the present invention, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments of the present invention include a computer program product comprising a computer program carried on a computer-readable medium, the computer program containing computer programs for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via communication section 209, and / or installed from removable medium 211. When the computer program is executed by central processing unit (CPU) 201, it performs the various functions defined in the present invention.

[0094] It should be noted that specific examples of computer-readable storage media may include, but are not limited to: electrical connections having one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM), flash memory, optical fiber, portable compact disc read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this invention, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution platform, apparatus, or device.

[0095] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of platforms, methods, and computer program products according to various embodiments of the present invention. Each block in a flowchart or block diagram may represent a module, program segment, or portion of code, which contains one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those shown in the drawings.

[0096] Specifically, the stacking parking system of this embodiment includes a processor and a memory. The memory stores a computer program. When the computer program is executed by the processor, it implements the stacking parking vibration control method provided in the above embodiment.

[0097] In another aspect, the present invention also provides a computer-readable storage medium, which may be included in the stacking parking system described in the above embodiments; or it may exist independently and not assembled into the stacking parking system. The storage medium carries one or more computer programs that, when executed by a processor of the stacking parking system, cause the stacking parking system to implement the stacking parking vibration control method provided in the above embodiments.

[0098] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit it. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

[0099] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. This program can be stored in a computer-readable storage medium, and when executed, it can include the processes described in the above method embodiments. The aforementioned storage medium includes various media capable of storing program code, such as ROM or random access memory (RAM), magnetic disks, or optical disks.

Claims

1. A method for vibration control in stacked parking systems, characterized in that, The method is applied to a stacking parking system, which includes a stacker crane, a vehicle platform, and a weighbridge, wherein the stacker crane includes columns. The weighbridge is used to obtain the actual mass data and three-dimensional centroid coordinate data of the vehicles to be parked on the vehicle carrier. The spatial offset of the centroid of the vehicle to be parked from the load center of the stacker crane is determined based on the three-dimensional centroid coordinate data, and the three-dimensional eccentric load moment applied by the vehicle to be parked to the column is determined based on the spatial offset and the actual mass data. The predetermined horizontal and vertical running trajectories of the stacker crane are converted into discrete time series, and the planned lifting height of the stacker crane at each discrete moment in the discrete time series is determined. Based on the actual mass data, the three-dimensional eccentric load moment, the physical parameters of the column section, and the planned lifting height, a target rigid-flexible coupling dynamic model is constructed, and a time-varying shaped pulse sequence matching the discrete time series is generated based on the target rigid-flexible coupling dynamic model. A target speed control curve is generated based on the initial motion command of the stacker crane and the time-varying shaping pulse sequence; The drive motor of the stacker crane is controlled to perform vehicle handling operations on the vehicle to be parked according to the target speed control curve.

2. The method according to claim 1, characterized in that, The process of obtaining the actual mass data and three-dimensional centroid coordinate data of the vehicles to be parked on the vehicle carrier platform through the weighbridge includes: During the process of the vehicle to be parked driving into the vehicle carrier, at least four weighbridge sensors installed under the vehicle carrier collect the load at the measurement points of the vehicle carrier in real time to obtain distributed load time series data. The outline image of the vehicle to be parked is captured by a contour recognition camera set at the entrance of the vehicle platform, and the outline image is matched and queried in a preset vehicle model database to obtain the reference centroid height range of the vehicle model corresponding to the vehicle to be parked. The ground pressure distribution data of each tire of the vehicle to be parked is detected by a tire pressure sensing area set on the surface of the vehicle carrier. When the vehicle to be parked is stationary on the vehicle carrier, the actual mass data is determined based on the distributed load time series data. Based on the distributed load time series data and the ground pressure distribution data, determine the first centroid coordinate component in the horizontal longitudinal direction and the second centroid coordinate component in the horizontal transverse direction of the vehicle to be parked. The third centroid coordinate component of the vehicle to be parked in the vertical direction is determined based on the reference centroid height range of the vehicle model. The first centroid coordinate component, the second centroid coordinate component, and the third centroid coordinate component are determined as the three-dimensional centroid coordinate data.

3. The method according to claim 2, characterized in that, The step of determining the spatial offset of the centroid of the vehicle to be parked from the load-bearing center of the stacker crane based on the three-dimensional centroid coordinate data, and determining the three-dimensional eccentric load moment applied by the vehicle to be parked to the column based on the spatial offset and the actual mass data, includes: The load center coordinates of the stacker crane's vehicle platform are obtained, and the deviation analysis between the three-dimensional centroid coordinate data and the load center coordinates is performed to obtain the horizontal longitudinal offset component, the horizontal lateral offset component, and the vertical offset component. The horizontal longitudinal offset component, the horizontal lateral offset component, and the vertical offset component are determined as the spatial offset; The static gravity load of the vehicle to be parked is determined based on the actual mass data and the preset gravitational acceleration constant. The pitching moment component about the horizontal lateral direction is determined based on the static gravity load and the horizontal longitudinal offset component, and the roll moment component about the horizontal longitudinal direction is determined based on the static gravity load and the horizontal lateral offset component. The inertial load is determined based on the planned acceleration of the stacker in the horizontal longitudinal direction and the actual mass data, and the yaw moment component about the vertical direction is determined based on the inertial load and the vertical offset component. The pitching eccentric load moment component, the roll eccentric load moment component, and the yaw eccentric load moment component are determined as the three-dimensional eccentric load moment.

4. The method according to claim 1, characterized in that, Before generating the time-varying shaped pulse sequence matching the discrete-time sequence based on the target rigid-flexible coupling dynamic model, the method further includes: The X-axis horizontal motion parameters are determined based on the horizontal acceleration of the stacker at each discrete moment, and the Y-axis lifting motion parameters are determined based on the lifting speed of the stacker at each discrete moment. A three-dimensional coupling effect matrix is ​​established in the target rigid-flexible coupling dynamic model based on the X-axis horizontal motion parameters, the Y-axis lifting motion parameters, and the three-dimensional off-center load moment. The three-dimensional coupling effect matrix includes a first coupling coefficient corresponding to the horizontal acceleration and a second coupling coefficient corresponding to the lifting speed. The coupled bending moment load on the column at each discrete moment is determined based on the first coupling coefficient, the second coupling coefficient, and the planned lifting height. Based on the coupled bending moment load, the section moment of inertia and elastic modulus in the section physical parameters, determine the structural deflection response value of the column at each discrete moment; The pulse amplitude constraint coefficient for each discrete moment is determined based on the structural deflection response value and the preset deflection safety limit.

5. The method according to claim 4, characterized in that, The step of constructing a target rigid-flexible coupled dynamic model based on the actual mass data, the three-dimensional eccentric load moment, the cross-sectional physical parameters of the column, and the planned lifting height, and generating a time-varying shaped pulse sequence matching the discrete time series based on the target rigid-flexible coupled dynamic model, includes: Based on the actual mass data, the three-dimensional eccentric load moment, the cross-sectional physical parameters, and the planned lifting height, a target rigid-flexible coupling dynamic model is constructed, with the column as a flexible component and the vehicle to be parked and the vehicle platform as rigid components. The material linear density of the column is input into the target rigid-flexible coupling dynamic model to determine the first-order time-varying natural frequency and the second-order time-varying natural frequency of the stacker crane at each discrete moment; The first-order vibration period is determined based on the first-order time-varying natural frequency, and half of the first-order vibration period is determined as the first time interval of the first-order shaping pulse. The second-order vibration period is determined based on the second-order time-varying natural frequency, and half of the second-order vibration period is determined as the second time interval of the second-order shaping pulse. The first-order amplitude weighting coefficient of the first-order shaping pulse and the second-order amplitude weighting coefficient of the second-order shaping pulse are determined according to the material damping ratio of the column. Both the first-order amplitude weighting coefficient and the second-order amplitude weighting coefficient are negatively correlated with the material damping ratio. The time-varying shaped pulse sequence is generated based on the three-dimensional off-center load torque, the first-order time-varying natural frequency, the second-order time-varying natural frequency, the first time interval, the second time interval, the first-order amplitude weighting coefficient, the second-order amplitude weighting coefficient, and the pulse amplitude constraint coefficient.

6. The method according to claim 5, characterized in that, The step of generating the time-varying shaped pulse sequence based on the three-dimensional off-center load moment, the first-order time-varying natural frequency, the second-order time-varying natural frequency, the first time interval, the second time interval, the first-order amplitude weighting coefficient, the second-order amplitude weighting coefficient, and the pulse amplitude constraint coefficient includes: The first-order vibration mode response of the column is determined based on the three-dimensional eccentric load moment and the first-order time-varying natural frequency, and the second-order vibration mode response of the column is determined based on the three-dimensional eccentric load moment and the second-order time-varying natural frequency. The modal coupling coefficient between the first-order mode and the second-order mode is determined based on the first-order vibration modal response and the second-order vibration modal response; The first-order shaped pulse sequence is generated according to the first time interval and the first-order amplitude weighting coefficient, and the second-order shaped pulse sequence is generated according to the second time interval and the second-order amplitude weighting coefficient; The first-order shaped pulse sequence and the second-order shaped pulse sequence are time-series superimposed according to the discrete time sequence based on the modal coupling coefficient to obtain the superimposed pulse sequence; The pulse amplitude at each discrete moment in the superimposed pulse sequence is constrained according to the pulse amplitude constraint coefficient to generate the time-varying shaped pulse sequence.

7. The method according to claim 1, characterized in that, The step of generating the target speed control curve based on the initial motion command of the stacker crane and the time-varying shaping pulse sequence includes: The initial motion command is analyzed to obtain a basic S-shaped velocity curve, which includes an acceleration segment, a constant speed segment, and a deceleration segment. The basic S-shaped velocity curve is convolved with the time-varying shaping pulse sequence in the time domain to obtain the initial shaping velocity curve. Extract the torque projection component of the stacker crane in the current running direction from the three-dimensional off-center load torque, and determine whether the direction of action of the torque projection component is the same as the direction of the stacker crane's inertial torque; When the direction of action is the same as the direction of the inertial moment, it is determined that the stacker is in an aggravated off-center load condition, and the acceleration section stretching coefficient is determined according to the moment projection component. The acceleration segment of the initial shaping velocity curve is smoothed and extended using the acceleration segment stretching coefficient to obtain the first asymmetric shaping curve. When the direction of action is opposite to the direction of the inertial torque, it is determined that the stacker is in an off-center load suppression condition, and the compression coefficient of the deceleration section is determined according to the torque projection component. The deceleration segment of the initial shaping velocity curve is time-compressed using the deceleration segment compression coefficient to obtain a second asymmetric shaping curve. The first asymmetric shaping curve or the second asymmetric shaping curve is used as the target speed control curve.

8. A stacking parking system, characterized in that, The stacking parking system includes: one or more processors and a memory; the memory is coupled to the one or more processors, the memory is used to store computer program code, the computer program code including computer instructions, and the one or more processors invoke the computer instructions to cause the stacking parking system to perform the method as described in any one of claims 1-7.

9. A computer-readable storage medium comprising program instructions, characterized in that, When the program instructions are run on the stacked parking system, the stacked parking system performs the method as described in any one of claims 1-7.

10. A computer program product comprising computer instructions, characterized in that, When the computer instructions are executed by the processor, the method as described in any one of claims 1-7 is implemented.

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