A method and system for S-curve and closed-loop motion control of stacker cranes

Abstract

This application relates to the field of equipment control technology, and in particular to an S-curve and closed-loop motion control method and system for stacker cranes. The proposed scheme involves acquiring parameters such as target position, velocity, acceleration, jerk, and structural rigidity level to generate a multi-segment velocity variation curve, and then combining this with a spectrum prediction model for resonance risk analysis and curve correction. A structural modal database and feedback compensation mechanism are introduced during the control process to achieve feedforward modulation based on modal avoidance and closed-loop control based on error compensation, thereby improving the stability and positioning accuracy of the stacker crane operation. This method is applicable to stacker crane structures with diverse rigidity levels.

Description

Technical Field

[0001] This application relates to the field of equipment control technology, and in particular to an S-curve and closed-loop motion control method and system for stacker cranes. Background Technology

[0002] In existing technologies, the motion control of stacker cranes mostly adopts a preset acceleration curve combined with a traditional PID controller for trajectory tracking. While this method can achieve basic walking and positioning functions under normal operating conditions, it still has significant shortcomings in complex practical applications. For example, during high-speed walking or long-stroke movement, problems such as structural vibration, end-effector rebound, and positioning overshoot often occur; these phenomena are even more prominent in flexible stacker cranes or ultra-high column structures, affecting equipment stability and response consistency.

[0003] Furthermore, most current control methods generate curves based solely on kinematic constraints, failing to effectively incorporate the rigidity characteristics of the stacker crane structure. This can lead to the curves themselves potentially inducing structural resonance, further exacerbating swaying and accuracy fluctuations during operation. Moreover, even with PID closed-loop feedback control for error correction, it's difficult to completely eliminate the impact of structural vibrations on end-position accuracy, especially near the target point, where brief inertial swaying and impact oscillations may still occur, making it difficult to meet the demands of high-precision stacking operations.

[0004] To address the above issues, this application presents a method and system for S-curve and closed-loop motion control of stacker cranes. Summary of the Invention

[0005] The technical problem this application aims to solve is to address the shortcomings of existing technologies by providing an S-curve and closed-loop motion control method and system for stacker cranes. By acquiring parameters such as target position, velocity, acceleration, jerk, and structural rigidity level, a multi-segment velocity variation curve is generated. This curve is then combined with a spectrum prediction model for resonance risk analysis and curve correction. A structural modal database and feedback compensation mechanism are introduced into the control process to achieve feedforward modulation based on modal avoidance and closed-loop control based on error compensation, improving the stability and positioning accuracy of the stacker crane. This method is applicable to stacker crane structures with diverse rigidity levels.

[0006] To achieve the above objectives, this application provides the following technical solution: an S-curve and closed-loop motion control method for a stacker crane, the stacker crane including a controller and a driver, the method comprising: acquiring user-defined parameters; generating a speed change curve and a position change curve based on the user-defined parameters, wherein the speed change curve is determined according to a preset speed change curve function, and the position change curve is obtained by integrating the speed change curve; discretizing the speed change curve and the position change curve to obtain the theoretical speed value and theoretical position value corresponding to each control cycle; obtaining the output rotational speed of the driver based on the theoretical speed value, and obtaining the actual position of the stacker crane based on the output rotational speed; comparing the actual position with the theoretical position value; generating a compensation speed value based on the comparison result and superimposing it on the theoretical speed value of the current control cycle to update the output rotational speed.

[0007] The velocity change curve includes at least one of four curve types: four-segment curve, five-segment curve, six-segment curve, and seven-segment curve. The four-segment curve includes an acceleration segment, a deceleration segment, an increase in deceleration segment, and a decrease in deceleration segment. The five-segment curve includes an acceleration segment, a deceleration segment, a constant velocity segment, an increase in deceleration segment, and a decrease in deceleration segment. The six-segment curve includes an acceleration segment, a constant acceleration segment, a deceleration segment, an increase in deceleration segment, a constant deceleration segment, and a decrease in deceleration segment. The seven-segment curve includes an acceleration segment, a constant acceleration segment, a deceleration segment, a constant velocity segment, an increase in deceleration segment, a constant deceleration segment, and a decrease in deceleration segment.

[0008] The user-defined parameters include target position, target maximum speed, maximum acceleration, and jerk. Generating a speed change curve based on the user-defined parameters includes: determining the corresponding curve type based on the target position, target maximum speed, maximum acceleration, and jerk; and calculating the speed change curve using a preset speed change curve function based on the curve type.

[0009] The acceleration and deceleration times of the driver are set to the minimum time unit supported by the driver. The actual position is compared with the theoretical position value, and a compensation speed value is generated and superimposed on the theoretical speed value of the current control cycle based on the comparison result. This includes: generating a compensation amount for correcting the speed command using a PID control algorithm based on the deviation between the actual and theoretical position values; superimposing the compensation amount on the theoretical speed value corresponding to the current control cycle to generate an updated speed command and sending it to the driver; wherein the parameters of the proportional, integral, and derivative terms in the PID control algorithm are adjusted according to the deviation.

[0010] The user-defined parameters also include the structural rigidity level of the stacker crane. The structural rigidity level is determined based on the structural dimensions, component materials, and historical vibration response of the stacker crane. According to the curve type, the velocity change curve is calculated by using a preset velocity change curve function, combined with a preset spectrum prediction mapping model and the structural rigidity level. The spectrum prediction mapping model is obtained by performing offline modal identification on the stacker crane. The offline modal identification includes extracting the natural modal frequencies, damping ratios, and mode shapes of the stacker crane in motion for the corresponding structural rigidity level, in order to generate a spectrum modal database.

[0011] The step of calculating the velocity change curve using a preset velocity change curve function, combined with a preset spectrum prediction mapping model and the structural rigidity level, includes: calculating an initial velocity change curve according to the curve type using the preset velocity change curve function; discretizing the initial velocity change curve in the time domain and using it as the input parameter of the spectrum prediction mapping model; performing a Fourier transform on the acceleration change rate of the input parameter using the spectrum prediction mapping model to obtain a spectrum excitation map, and obtaining the structural excitation frequency band based on the energy density distribution corresponding to each frequency point in the spectrum excitation map; matching the structural excitation frequency band with the structural modal information recorded in the spectrum modal database to obtain curve segments with a risk of excitation resonance, wherein the matching is based on resonance risk judgment rules to evaluate the inherent modal frequencies of the structural excitation frequency band and the structural modal information, the resonance risk judgment rules including: when the energy density of a frequency point in the structural excitation frequency band is greater than or equal to a preset modal threshold, and the corresponding frequency point belongs to the resonance sensitive frequency band range of a modal frequency, it is determined that the corresponding curve segment has a risk of exciting structural resonance; correcting the curve segment to obtain the velocity change curve.

[0012] The process of correcting the curve segment to obtain a velocity change curve includes: reconstructing the parameters of the curve segment using a perturbation optimization algorithm, wherein the parameters include the acceleration change rate corresponding to the curve segment, the duration of the curve segment, and the start and end velocity values ​​within the curve segment, wherein the perturbation optimization algorithm is configured as a nonlinear search algorithm based on a genetic mechanism, wherein the nonlinear search algorithm includes population initialization, fitness evaluation, crossover operation, mutation operation, and termination determination, wherein the fitness function in the fitness evaluation is the integral value of the spectral excitation energy corresponding to the structural excitation frequency band, and the termination determination is based on the convergence of the fitness function to a preset termination threshold; optimizing the initial velocity change curve according to the reconstructed parameters to obtain multiple candidate velocity change curves, inputting the candidate velocity change curves into the spectral prediction mapping model to obtain the spectral excitation spectrum corresponding to each candidate velocity change curve; selecting the candidate velocity change curve with the largest Euclidean distance from the intrinsic mode frequency and the smallest total spectral energy from the candidate velocity change curves as the correction result of the initial velocity change curve, and generating the velocity change curve.

[0013] The method of comparing the actual position with the theoretical position value and generating a compensation speed value based on the comparison result and superimposing it on the theoretical speed value of the current control cycle also includes: obtaining the structural rigidity level of the stacker crane; and calling the preset PID control parameter table under the corresponding structural rigidity level to set the coefficient values ​​of the proportional, integral and derivative terms based on the structural rigidity level.

[0014] An S-curve and closed-loop motion control system for a stacker crane, the system comprising: a trajectory generation module, used to generate velocity change curves and position change curves according to user-defined parameters, and to discretize the velocity change curves and position change curves to obtain theoretical velocity values ​​and theoretical position values ​​corresponding to each control cycle; a spectrum analysis module, used to perform frequency domain transformation on the generated initial velocity change curves based on a spectrum prediction mapping model, identify curve segments with the risk of exciting structural resonance, and perform resonance matching and judgment in conjunction with spectrum modal database information; a trajectory optimization module, used to perform parameter reconstruction based on a disturbance optimization algorithm on the curve segments with resonance risk, generate multiple candidate velocity change curves, and screen the candidate velocity change curves to obtain the final velocity change curve; and an adaptive control module, used to perform closed-loop PID control based on the theoretical velocity value and the feedback position deviation, generate a speed compensation amount in real time and superimpose it onto the theoretical velocity value, and output the updated speed command to the stacker crane driver.

[0015] Compared with existing technologies, the advantages of this application are as follows: By introducing structural rigidity levels, a spectrum prediction mapping model, and a resonance avoidance optimization mechanism, this application achieves adaptive generation of motion trajectory curves for stacker cranes with different structural characteristics, avoiding structural resonance caused by unreasonable trajectory parameter settings. Combined with a frequency band excitation evaluation and optimization correction algorithm based on modal recognition, the curves effectively avoid structural modal frequency excitation while ensuring time efficiency, thus improving the stability and positioning consistency of the motion process. Attached Figure Description

[0016] Other features, objects, and advantages of this application will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings.

[0017] Figure 1 This is a schematic diagram illustrating an exemplary application scenario of an embodiment of this application.

[0018] Figure 2 This is a schematic diagram of the controller module in an embodiment of this application.

[0019] Figure 3 This is a flowchart illustrating an S-curve and closed-loop motion control method for a stacker crane according to an embodiment of this application.

[0020] Figure 4 This is a schematic diagram of the seven-segment curve trajectory of an embodiment of this application.

[0021] Figure 5 This is a schematic flowchart illustrating a method for generating a speed change curve according to an embodiment of this application.

[0022] Figure 6 This is a flowchart illustrating another method for generating a speed change curve according to an embodiment of this application.

[0023] Explanation of reference numerals in the attached drawings: 100, ground track; 101, ceiling track; 102, base; 103, driver; 104, column; 105, controller; 1051, curve generation module; 1052, vibration identification module; 1053, adaptive feedback control module. Detailed Implementation

[0024] The technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments.

[0025] The term "embodiment" as used herein means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0026] This application applies to stacker crane systems with long stroke, low rigidity, and high-precision end-effector positioning requirements. Their motion control process is constrained by the structural flexibility response hysteresis and the inertial delay characteristics of traditional control models. During acceleration / deceleration transitions and end-effector positioning, issues such as position overshoot, structural rebound, and difficulty in stable convergence easily arise. Application scenarios include, but are not limited to: stacker cranes in automated storage and warehousing systems employing tall columns 104 and truss cantilever structures, operating on long-stroke vertical or horizontal tracks; stacker cranes with large variations in load / unload, where inertial coupling and flexible excitation lead to unstable motion; and industrial control stacker crane scenarios with limited speed response of the actuator 103 and long sampling periods in the control system.

[0027] It is understood that the core control strategy of this application is mainly aimed at the following stacker crane motion scenarios with typical control challenges, and meets at least one of the following conditions: the stacker crane structure has low rigidity or long cantilever structure, which has the risk of vibration and swaying during high acceleration or sudden stop motion; the end positioning section has the combined effect of inertial offset and structural elastic hysteresis, resulting in failure to brake and stabilize; S-curve control cannot achieve modeling and feedback of structural modal response, and there is a risk of excitation in the resonant frequency band; the control algorithm relies on a single closed-loop feedback model, which is difficult to respond to the structural trajectory coupling behavior under complex working conditions.

[0028] It should be noted that the adaptive S-curve generation and frequency domain structural response modeling method proposed in this application requires obtaining a pre-discrete model or rigid preset conditions of the stacker crane structure in advance, and using the vibration response characteristics in the control process as the driving input to dynamically complete the selection and correction of the curve shape.

[0029] It is worth noting that the spectrum prediction mapping mechanism and trajectory optimization algorithm proposed in this application do not depend on a specific type of stacking mechanism, driving scheme or path trajectory, and are also applicable to: industrial motion execution scenarios where the control system has a flexible resonance response; complex path control with dynamic updates and non-constant inertia models in motion path planning; and scenarios where the control output path has a need to avoid resonance-sensitive frequency bands and the execution path can be subject to continuous micro-perturbations.

[0030] See Figure 1 This figure is a schematic diagram of an exemplary application scenario provided by an embodiment of this application.

[0031] like Figure 1 As shown, this application is applied to a stacker crane, which includes a ground rail 100, a top rail 101, a base 102 that can move along the ground rail 100, a driver 103, a vertically arranged column 104, and a controller 105.

[0032] The ground rail 100 and the overhead rail 101 are respectively arranged below and above the working area of ​​the stacker crane, forming a guide channel for the horizontal movement of the stacker crane. The ground rail 100 supports the load weight of the base 102 and guides its running direction, while the overhead rail 101 is connected to the top of the column 104 to form a rigid closed-loop structure, which effectively suppresses lateral swaying and improves overall stability.

[0033] The base 102, mounted on the ground rail 100, serves as a support platform for the horizontal movement of the stacker crane and can move back and forth along the ground rail 100. The base 102 integrates a walking drive mechanism and a cable traction device to ensure a continuous supply of drive signals and power.

[0034] The column 104 extends vertically upward from the base 102 and connects through to the overhead rail 101, forming a cross-support structure. The column 104 provides a vertical guide rail for the stacker crane lifting device (not shown in the figure). It is usually made of lightweight, high-strength profiles, which ensures both bending stiffness and a certain degree of flexible response characteristics, and is a key object for dynamic behavior modeling.

[0035] The driver 103 is used to drive the base 102 to move in the horizontal direction.

[0036] In an embodiment not shown in the figure, the driver 103 may be configured inside the base 102. It may be configured to achieve high responsiveness and smooth acceleration and deceleration control by combining a servo motor with a gear rack, ball screw or other drive mechanism. Alternatively, the speed may be adjusted by a frequency converter.

[0037] The controller 105, typically an embedded PLC, industrial computing platform, or motion control card, has the following main responsibilities: acquiring the user-defined target position and motion parameters; generating a multi-segment S-curve velocity trajectory; performing resonance avoidance calculations based on the structural modal characteristics of the stacker crane; performing position error compensation and speed correction in real time; and outputting the final control command to the driver 103.

[0038] Understandably, the stacker crane control system can achieve full-process control and optimization of the entire machine's movement, especially solving the problems of swaying, resonance, and positioning errors caused by the inability to predict the elastic response of the structure under long-stroke, low-rigidity structural conditions, which are caused by traditional trajectory control methods. Figure 1 The structure shown is a typical application scenario in the implementation of this application. In actual applications, it can be expanded or adjusted according to the configuration of the stacker crane system, which will not be elaborated here.

[0039] See Figure 2 The figure is a schematic diagram of the controller 105 provided in the embodiment of this application.

[0040] Figure 2 The controller 105 is shown to include a curve generation module 1051, a vibration identification module 1052, and an adaptive feedback control module 1053. The curve generation module 1051 generates velocity and position change curves based on user-defined motion targets, and discretizes these curves to output theoretical velocity and position values ​​within a control cycle. The trajectory generation module supports various S-curve generation strategies and can dynamically select four to seven different velocity curve segments based on the stacker crane's structural rigidity level.

[0041] In an embodiment not shown in the figure, the curve generation module 1051 further includes a spectrum prediction submodule, which is used to input the generated curve into a preset frequency domain model for Fourier transform, predict potential excitation frequency bands, and perform resonance avoidance curve reconstruction operation.

[0042] The vibration identification module 1052 is used to determine whether the generated initial velocity curve poses a risk of structural resonance based on a preset structural modal database. The vibration identification module 1052 analyzes the spectral excitation map to match the frequency domain components of the curve's acceleration rate of change with the structural modal frequencies of the stacker crane. If a resonance-sensitive curve segment is identified, a perturbation optimization algorithm is used to optimize the parameters of the target curve segment, outputting an optimized velocity curve with resonance suppression, which replaces the original curve for subsequent control.

[0043] The adaptive feedback control module 1053 is used to execute a speed compensation control algorithm based on position deviation. The adaptive feedback control module 1053 compares the real-time feedback position of the stacker crane with the theoretical trajectory, calculates the deviation, and generates speed compensation commands through PID control logic. Simultaneously, the adaptive feedback control module 1053 supports input of structural rigidity level parameters and can automatically call a preset PID parameter table to match and dynamically adjust the coefficients of the proportional, integral, and derivative terms, improving the sensitivity and stability of the feedback control response. It is particularly suitable for the end-point micro-motion and rebound control requirements of the stacker crane.

[0044] The aforementioned modules work together to achieve a closed-loop control strategy covering the entire process from trajectory planning, structural mode recognition, resonance suppression to real-time error correction, effectively improving the dynamic response and end-point positioning accuracy of the stacker crane under long-stroke, low-rigidity structures. The controller 105 can be implemented using an industrial-grade embedded platform, possessing high real-time performance and system integration capabilities, and is compatible with various medium and large-sized stacker crane automation equipment.

[0045] Next, with reference to the accompanying drawings, we will describe an S-curve and closed-loop motion control method for a stacker crane provided in an embodiment of this application. Figure 3 The method shown is applied to stacker cranes.

[0046] S1: Get user-defined parameters.

[0047] In this embodiment, user-defined parameters include, but are not limited to: target position, target maximum velocity, maximum acceleration, jerk, and structural rigidity level. The structural rigidity level reflects the elastic response characteristics of the stacker crane's moving parts during acceleration and deceleration. It can be obtained based on the cross-sectional dimensions, construction materials, connection methods, and vibration response data from historical operation of the stacker crane components, using a combination of static analysis and modal experimental modeling. The introduction of the structural rigidity level enables the subsequent trajectory generation logic to coordinate with the specific mechanical structural characteristics, thereby effectively avoiding structural resonance or secondary swaying phenomena that may occur in high-inertia mechanisms at the end of the motion phase.

[0048] S2: Generate velocity change curves and position change curves based on the user-defined parameters.

[0049] In this embodiment, the velocity variation curve is determined according to the curve type corresponding to the structural rigidity level, and is modeled using a function. The number of curve segments can be four, five, six, or seven, covering various combinations such as acceleration rate of change segments, constant acceleration segments, uniform velocity segments, and deceleration segments. The position variation curve is obtained by integrating the velocity variation curve.

[0050] S3: Discretize the velocity change curve and position change curve to obtain the theoretical velocity value and theoretical position value corresponding to each control cycle.

[0051] In this embodiment, the curve is discretized with high density, with each discrete point corresponding to an executable control cycle. The discretization accuracy is set according to the end-control resolution of the stacker crane to ensure that the time resolution of the output control commands is sufficient to respond to the micro-vibration behavior of the structure. Through discretization, the continuous trajectory is mapped into a sequence of digital control commands that can be executed in real time.

[0052] S4: The output speed of the driver 103 is obtained based on the theoretical speed value, and the actual position of the stacker is obtained based on the output speed value. The actual position is compared with the theoretical position value, and a compensation speed value is generated based on the comparison result and superimposed on the theoretical speed value of the current control cycle to update the output speed.

[0053] In this embodiment, the actual position is obtained through encoder feedback from the driver 103 or an external displacement sensor. The control logic calculates the error term based on the real-time deviation, calls the adaptive PID control algorithm to generate a compensation speed value, and adds this compensation amount to the current theoretical speed command before outputting it to the driver 103 for execution. Regarding parameter settings, the corresponding preset PID parameter table is called according to the structural rigidity level, automatically matching the proportional, integral, and derivative coefficients to enhance the controller 105's response characteristics to flexible structures.

[0054] Understandably, this step is particularly important in the end positioning section of the stacker crane, as it can effectively buffer the rebound effect caused by residual inertia and improve the convergence speed and stability of the final positioning process.

[0055] Before delving into the specific technical details of the steps, this application's embodiments need to reiterate that the typical target of this application is not a general structure or a standard track motion mechanism, but rather a stacker crane type system with one or more of the following characteristics: structural height exceeding 5 meters, motion beams using thin-walled aluminum alloy or truss design, motion paths covering multiple areas and multi-layer racking systems, and the load end exhibiting significant nonlinear flexible response characteristics. The common feature of this type of structure is that although the motion control unit can complete path planning according to the theoretical trajectory, due to the limited overall rigidity of the mechanism and the elastic hysteresis effect at the connection points, it is extremely easy to induce low-to-medium frequency structural responses during acceleration and deceleration. Especially at the final stage, residual rebound, slow shaking, or micro-oscillations often occur, making it difficult to control the final positioning error within 1mm, affecting the stable operation of the stacker crane and the accuracy of cargo loading and unloading.

[0056] It should be noted that the aforementioned problems cannot be effectively solved solely by traditional PID error compensation or extending the deceleration phase. This is because in a flexible dominant structure, there is a nonlinear coupling between the excitation behavior and the trajectory curve. Even in an ideal state without external disturbances, the acceleration change of the trajectory itself is sufficient to create an excitation source and trigger resonance.

[0057] It is understood that the resonance effect described in this application does not originate from external collisions, structural manufacturing errors, or mechanical loosening caused by a single excitation. Rather, it arises from the continuous variation trend of higher-order derivatives (especially jerk) during trajectory planning, resulting in periodic and cumulative excitation inputs near specific structural modal frequencies. This leads to energy resonance coupling with the inherent elastic modes of the stacker crane. This resonance is characterized by high determinism, structural dependence, and difficulty in suppression through general feedback. This manifests as displacement amplification, response delay, or end-effector oscillations occurring within specific frequency ranges, even when the control system strictly follows the theoretical trajectory. Traditional closed-loop strategies based on position errors cannot predict these internally induced excitation modes, leading to response lag, compensation failure, and ultimately, system instability.

[0058] In this embodiment, by obtaining the structural stiffness level, the controlled object is no longer assumed to be a rigid body or an ideal flexible body. Instead, structural behavior is used as a constraint input, intervening in the trajectory design process in advance. The structural stiffness level can be determined through joint modeling of static structural analysis and vibration response during operation. It reflects the dynamic characteristic boundary of the target stacking mechanism and serves as the basis for subsequent settings of the number of curve segments, acceleration rate of change, and feedback gain. Based on this, instead of using the traditional 5-segment or 7-segment S-curve, a preset velocity change curve function can be used to construct a velocity change curve in the time domain that meets the avoidance requirements of a specific excitation frequency, while satisfying the maximum velocity and acceleration constraints, by adjusting the jerk rate of change and duration.

[0059] Furthermore, by utilizing the multiple resonance bandwidth information recorded in the structural modal database, spectral analysis is performed on the initial trajectory to identify potential excitation segments. This part not only determines whether there is deviation from the time-domain error analysis, but also determines whether there is resonance from the frequency-domain behavior, and uses this as an important boundary constraint for iterative trajectory optimization.

[0060] Furthermore, in the closed-loop control section, this application is not limited to traditional PID parameter adjustment. It also uses the structural rigidity level as a partition setting parameter, forming a set of PID control parameter tables with structural labels. During stacker crane operation, the matching control gain combination is automatically invoked based on the structural rigidity level, thereby achieving stable closed-loop control.

[0061] Next, the principle of the method in this application regarding the velocity change curve will be further elaborated.

[0062] Understandably, in typical stacker crane trajectory control, to achieve smooth start-up and shutdown and reduce structural vibration and control impact, the velocity change curve is usually described using a segmented S-shaped curve. The core idea is to continuously control the velocity change process through the first and second derivatives, so that the entire trajectory has better physical smoothness and dynamic adaptability, avoiding oscillations in the controller 105 output due to abrupt changes.

[0063] Specifically, the velocity change curve includes at least one of four curve types: four-segment curve, five-segment curve, six-segment curve, and seven-segment curve.

[0064] The four curve segments include an acceleration acceleration segment, an acceleration decrease segment, a deceleration increase segment, and a deceleration decrease segment.

[0065] It's easy to understand that the four-segment curve is the simplest form, mainly consisting of two acceleration processes and two deceleration processes. It achieves rapid speed increases and decreases by setting forward and reverse acceleration / deceleration segments, making it suitable for basic stacking operations with short strokes, light loads, and moderate precision requirements. However, the Jerk variation is concentrated during the acceleration and deceleration phases, which can easily cause impact peaks, potentially leading to mechanical fatigue or vibration during long-term operation.

[0066] The five curve segments include an acceleration acceleration segment, an acceleration decrease segment, a velocity constant segment, a deceleration increase segment, and a deceleration decrease segment.

[0067] It is easy to understand that the five-segment curve inserts a constant speed segment on top of the four segments, which can form a stable speed plateau in the middle segment. This design is suitable for situations where there is a need for long-distance horizontal movement in the working conditions. It can avoid the controller 105 being in a continuous speed regulation state and generating too much regulation load. It can also facilitate the early activation of the deceleration segment to achieve a smooth stop.

[0068] The six curve segments include an acceleration acceleration segment, a constant acceleration segment, a decreasing acceleration segment, an increasing deceleration segment, a constant deceleration segment, and a decreasing deceleration segment.

[0069] It's easy to understand that the six-segment curve further subdivides the acceleration and deceleration processes, adding segments with constant acceleration and constant deceleration. This means that in certain stages, the system operates with constant acceleration, making the Jerk variation more gradual and effectively avoiding structural shocks or wheel-rail resonance caused by continuous abrupt changes. This type is suitable for stacking mechanisms with a certain inertial delay in motion response, especially stacker cranes with large drive inertia.

[0070] The seven curve segments include an acceleration acceleration segment, a constant acceleration segment, a decreasing acceleration segment, a constant velocity segment, an increasing deceleration segment, a constant deceleration segment, and a decreasing deceleration segment.

[0071] It's easy to understand that the seven-segment curve is the most complete structure, encompassing seven stages. The seven-segment curve achieves multi-level controllable adjustment in three dimensions: speed, acceleration, and Jerk. It is best suited for stacker crane applications with long strokes, heavy loads, and high positioning requirements, significantly improving the predictability of end-point response and system stability.

[0072] Taking a seven-segment curve as an example, you can refer to... Figure 4 To understand, Figure 4 This is a schematic diagram of the seven-segment curve trajectory of an embodiment of this application.

[0073] Figure 4 This demonstrates the continuous changes in displacement, velocity, acceleration, and jerk during the walking motion of a stacker crane. It is suitable for scenarios requiring high levels of motion smoothness and structural response control, and is particularly well-suited for stacker crane mechanisms with significant structural flexibility or large inertia variations.

[0074] Figure 4 The velocity change curve is shown to consist of seven stages, namely: acceleration phase (…). ), the segment with constant acceleration ( ), acceleration decreasing segment ( ), uniform speed segment ( ), deceleration increase segment ( ), the segment with constant deceleration ( ), deceleration reduction segment ( ).

[0075] Furthermore, Figure 4 The curve corresponding to acceleration reflects the distribution of Jerk in the time domain. During acceleration and deceleration, Jerk maintains a constant non-zero value; while during the constant acceleration phase, Jerk is zero. In an embodiment not shown in the figure, Jerk also includes negative values, appearing during deceleration. By controlling the positive and negative values ​​of Jerk, the acceleration changes linearly when entering and exiting its maximum value, which helps to avoid transient shocks caused by sudden changes.

[0076] Next, we will further elaborate on the part of the method in this application regarding the generation of velocity change curves.

[0077] refer to Figure 5 , Figure 5 This is a schematic flowchart illustrating a method for generating a speed change curve according to an embodiment of this application.

[0078] In one example, generating a speed change curve includes: determining the corresponding curve type based on the target position, target maximum speed, maximum acceleration, and jerk; calculating the speed change curve using a preset speed change curve function based on the curve type; specifically, the goal of generating a speed change curve for the stacker crane's traveling section is to achieve a smooth start-up, operation, and stopping process while meeting motion constraints such as target position, maximum speed, maximum acceleration, and jerk, avoiding overshoot of the driver 103 or structural vibration caused by sudden acceleration changes, while improving the endpoint positioning accuracy.

[0079] In this embodiment, according to control theory, when the maximum value of Jerk is known, the acceleration change process over time can be obtained through integration, and then the velocity change relationship over time can be obtained through double integration. By modeling the motion process as a typical three-segment or multi-segment acceleration change curve, and controlling the acceleration slope of each segment according to the Jerk limit value, it can be ensured that the entire velocity change curve has continuous derivatives in the starting, changing, constant speed and deceleration stages, avoiding mechanical shock caused by sudden acceleration changes.

[0080] Furthermore, in determining the actual curve type, the time and displacement required for the theoretical maximum speed are first calculated and compared with the target displacement and maximum speed. If the travel is insufficient to support a complete uniform velocity segment, the curve is dynamically adjusted to a five- or six-segment structure (removing the uniform velocity segment or the segment with constant compression acceleration). If the travel is sufficient, a seven-segment curve model containing a complete acceleration variation segment, a uniform velocity segment, and a deceleration variation segment can be constructed. Within each segment, the duration between segments is calculated based on the target jerk, acceleration, and maximum speed to ensure the continuity of velocity and acceleration between segments and to achieve segmented closure of the entire velocity curve.

[0081] Furthermore, the velocity change curve function adopts a preset piecewise time-acceleration programming model, with the core being the control variable Jerk value, which generates acceleration, velocity, and displacement data through integration in the time domain.

[0082] Taking a typical seven-segment curve as an example, the first half is an acceleration process, first an acceleration increase segment (Jerk is positive), then an acceleration hold segment (Jerk is 0), and then an acceleration decrease segment (Jerk is negative); the middle segment is a uniform velocity segment (acceleration is 0), and the second half is a symmetrical deceleration process, including a deceleration increase segment (Jerk is negative), a deceleration hold segment (Jerk is 0), and a deceleration decrease segment (Jerk is positive). In each segment, the controller 105 performs real-time integration calculations according to the preset Jerk, deriving acceleration, velocity, and position sequentially, and performs continuity checks on the boundary conditions of each segment to ensure that the motion process is smooth and without abrupt changes.

[0083] It is understandable that the multi-segment curve generation logic of this application can flexibly match the curve structure according to different stroke lengths and target speeds, so that the motion process takes into account both speed and stability, and avoids structural vibration or drive saturation caused by improper parameter selection.

[0084] In yet another example, user-defined parameters also include the structural rigidity level of the stacker crane, which is determined based on the stacker crane's structural dimensions, component materials, and historical vibration response.

[0085] It is understood that the structural rigidity level of this application refers to a parameterized level label used to characterize the resistance of the stacker crane's overall structure to deformation under motion excitation during operation, and essentially reflects the elastic response characteristics of the stacker crane structure under unit load or excitation.

[0086] It is easy to understand that if the influence of structural rigidity level is not considered during the speed curve planning process, the generated trajectory curve will be seriously mismatched with the dynamic characteristics of the stacker crane structure itself, which is specifically reflected in the following three aspects.

[0087] Firstly, without considering the structural rigidity level, trajectory curves are often designed with motion performance in mind based on parameters such as target position, maximum velocity, maximum acceleration, and jerk, aiming for faster response and shorter running time. While this design may work in rigid structures, when applied to stacker cranes with flexible structures, its weak vibration resistance means frequent acceleration changes or large Jerk values ​​will directly excite the structure's modal response. This can lead to problems such as large end-effector micro-positioning affecting positioning accuracy; increased risk of dynamic resonance leading to structural stress concentration; and long-period swaying causing closed-loop control misjudgments and overcompensation.

[0088] Secondly, in flexible stacker cranes, the structure often has first or second-order modal frequencies. When the excitation frequency band of the trajectory curve happens to be near these modal frequencies, a resonance state with strong excitation and weak damping is likely to occur. If the structural rigidity level is not pre-judged, the generated curve may induce modal coupling in the acceleration and deceleration sections, producing low-frequency, high-amplitude resonance, or even forming a cumulative effect that is superimposed on the entire trajectory path.

[0089] Thirdly, traditional PID control structures are mainly designed to address closed-loop factors such as actuator lag and error feedback, and are unable to effectively correct the structural response caused by the excitation of the curve itself. If the Jerk variation of the trajectory itself is too large, even if the position error is sensed, the controller 105 will find it difficult to suppress the structural oscillations induced by it in real time, which will lead to the compensation causing even greater excitation and forming a negative cycle of amplified vibration.

[0090] In this embodiment, the structural rigidity level is used as an intermediate parameter to pre-emphasize the dynamic response capability of the stacker crane structure during the velocity curve generation process. Based on this, the following key planning parameters can be automatically adjusted: the number of segments in the S-curve; the maximum Jerk and maximum acceleration boundaries; and the time allocation for each segment.

[0091] In some optional implementations, the determination of the structural rigidity level comprehensively considers the following three key factors: The first key factor is structural dimensional parameters, including but not limited to the cross-sectional area of ​​the column (104), aspect ratio, component support span, and installation method. Large-size, high-section, short-cantilever structures typically have high inherent rigidity, making it easier to transmit driving loads and suppress low-frequency vibrations. The second key factor is component material information, such as carbon steel, aluminum alloy, or high-strength alloy steel. The elastic modulus, density, and damping characteristics of the material itself will directly affect the overall structural response performance under excitation conditions. The third key factor is historical vibration response data. By using operational monitoring data such as acceleration, position error, and vibration spectrum during the operation of the stacker crane under typical working conditions, combined with frequency domain analysis and modal recognition algorithms, parameters such as the measured natural frequency, principal mode shape, and damping ratio of the structure are extracted to supplement the dynamic evaluation of structural flexibility.

[0092] Those skilled in the art will understand that, for ease of classification, the structural stiffness level is divided into multiple discrete levels, such as three intervals: Level 1 (high stiffness), Level 2 (medium stiffness), and Level 3 (low stiffness). The controller 105 can automatically select the appropriate velocity variation curve type, acceleration boundary, and Jerk configuration parameters based on this level to achieve proactive adaptation of structural characteristics during the curve planning stage, thereby reducing the risk of vibration excitation.

[0093] Furthermore, the process of classifying the structural rigidity level can be completed through offline modal testing before the stacker crane leaves the factory, or it can be dynamically generated in the early stage of operation through online identification by active excitation and response acquisition. This application does not limit which specific method is adopted, nor does it limit the division range and method of rigidity level. Any parameterized level definition that can characterize the structure's anti-vibration capability can be regarded as an implementation form of the structural rigidity level in this application.

[0094] refer to Figure 6 , Figure 6 This is a flowchart illustrating another method for generating a speed change curve according to an embodiment of this application.

[0095] In another optional specific implementation, generating a velocity change curve according to the user-defined parameters includes: S2.1: determining the corresponding curve type based on the target position, target maximum velocity, maximum acceleration, and jerk; S2.2: calculating the velocity change curve based on the curve type using a preset velocity change curve function, combined with a preset spectrum prediction mapping model and the structural stiffness level. The spectrum prediction mapping model is obtained through offline modal identification of the stacker crane. The offline modal identification includes extracting the natural modal frequencies, damping ratios, and mode shapes of the structural stiffness level corresponding to the stacker crane in the motion state to generate a spectrum modal database. In this embodiment, the spectrum prediction mapping model is used to predict the structural response spectrum triggered by the velocity change curve. Essentially, it is a modeling mechanism that links motion excitation with structural dynamic modes, aiming to predict potentially excited resonant frequency bands during the trajectory planning stage, so that avoidance and optimization can be performed in subsequent curve construction, thereby achieving the purpose of actively suppressing structural vibration.

[0096] In some optional implementations, the spectrum prediction mapping model is constructed through the following offline modal identification process: First, after the stacker crane is manufactured or designed, an excitation experiment is conducted on the stacker crane using an external excitation source (such as an impact hammer, a sweep frequency signal, or an impulse response excitation, etc.), and its response data is recorded; In another optional implementation, finite element modeling technology can be used to simulate and analyze the dynamic characteristics of the stacker crane structure under different loads, actuator 103 operation, and installation states.

[0097] Furthermore, the excitation and response signals are processed in the frequency domain to extract the frequency response function of the structure, thereby obtaining the natural modal frequencies, damping ratios, and mode shape distribution parameters of the stacker crane under working conditions.

[0098] These parameters describe the structural amplification factor and reaction path of the stacker crane at various excitation frequencies, and are the core basis for determining resonance risk.

[0099] Furthermore, a database is established using the aforementioned natural modal frequencies, damping ratios, and mode shape distribution parameters, and the frequency domain excitation sensitive intervals corresponding to the stacker crane are marked.

[0100] Furthermore, based on the data recorded in the database, a spectrum mode database is constructed, and Fourier transform algorithm and perturbation optimization algorithm are configured to generate a spectrum prediction mapping model.

[0101] Understandably, by constructing a spectrum prediction mapping model, dynamic resonance risk detection and avoidance suggestions can be generated in the early stages of trajectory planning, without relying on later feedback control or additional sensor configuration. This is particularly suitable for high-speed, long-stroke, flexible structure-dominated stacker crane scenarios, effectively improving operational immunity and accurate positioning capabilities, and reducing the risk of structural fatigue damage.

[0102] In one example, the specific steps of S2.2 are as follows: S2.2.1: Calculate the initial velocity change curve according to the curve type using a preset velocity change curve function; specifically, how to calculate the velocity change curve according to the curve type and the preset velocity change curve function has been fully described in the foregoing, and will not be repeated here.

[0103] S2.2.2: The initial velocity change curve is discretized in the time domain and then used as the input parameter of the spectrum prediction mapping model. Specifically, the continuous velocity change curve is not convenient for digital signal processing operations such as fast Fourier transform. Therefore, it needs to be discretized at equal time intervals to obtain the velocity value and its first and second derivatives for each control cycle, thereby forming an input sequence with analytical accuracy.

[0104] In this embodiment, the time step of the discrete processing can be set to the consistent sampling time of the control cycle of the drive controller 105. The specific step can be adjusted according to the refresh frequency of the driver 103 to ensure the accuracy of the curve reconstruction in the time domain. To ensure the resolution and amplitude accuracy of the frequency domain results, the sequence length must meet the requirements of the Nyquist sampling theory. At the same time, to avoid spectral aliasing, the number of sampling points is generally set to a power of 2 to adapt to the computational efficiency requirements of the fast Fourier transform algorithm. After obtaining the discrete sequence, it is used as the input parameter of the spectral prediction mapping model for subsequent structural response prediction modeling.

[0105] S2.2.3: The acceleration rate of change of the input parameters is subjected to a Fourier transform using the spectrum prediction mapping model to obtain a spectrum excitation map. Based on the energy density distribution corresponding to each frequency point in the spectrum excitation map, the structural excitation frequency band is obtained. Specifically, the purpose of this step is to map the continuous change of the initial velocity curve in the time domain to the frequency domain, revealing the distribution of excitation intensity at different frequencies. Since stacker crane structures typically exhibit flexible dominance, their inherent modal frequencies are densely distributed, and multiple low-frequency resonance-sensitive regions exist. Therefore, it is necessary to conduct a refined analysis of the higher-order derivative characteristics of the motion curve, especially the frequency components of the acceleration rate of change, to determine whether there is a potential resonance excitation risk. This application uses a spectrum prediction mapping model to perform a discrete Fourier transform on the input discrete acceleration rate of change sequence to convert it to the frequency domain and form a spectrum excitation map for further structural response risk matching.

[0106] In this embodiment, the rate of change of acceleration is obtained from the initial velocity change curve through two-order time difference operation. At the same time, before the discrete sequence is processed, the input parameters are weighted by a window function to suppress the sidelobe leakage effect and ensure that the spectrum result after Fourier transform can accurately reflect the energy concentration trend of the higher-order dynamic characteristics in the curve.

[0107] Furthermore, the spectrum prediction mapping model does not simply perform Fourier transform calculations, but rather performs standardized calibration of the energy density calculation in the frequency domain based on the typical operating conditions of the stacker crane structure.

[0108] Understandably, each frequency point in the spectrum is associated with a corresponding normalized excitation energy value. This normalized excitation energy value is obtained by calculating the power spectral density after squaring the amplitude at that frequency point, and then weighted and integrated in conjunction with the duration of that frequency band in the velocity curve to reflect the strength of the excitation persistence in that frequency band during actual operation.

[0109] For example, in a certain velocity change curve, if the rate of change of acceleration changes continuously around a specific frequency and the amplitude of the frequency component is large, then the frequency point and its adjacent frequency band in its spectrum will show an energy peak; otherwise, the frequency band excitation intensity is weak and does not constitute the main cause of excitation resonance.

[0110] Furthermore, after the spectrum excitation map is generated, according to the structural response identification strategy preset in this application, all frequency intervals with energy density greater than the noise reference value in the spectrum excitation map are further extracted, and a certain range is extended to both sides with each local peak point as the center to form a structural excitation frequency band; the certain range mentioned in this application is adjusted according to the modal damping ratio recorded in the stacker crane structural identification data, and is usually set to 5%-10% of the target modal frequency to cover the potential resonance bandwidth.

[0111] Those skilled in the art will understand that the Jerk curve directly reflects the dynamic excitation behavior of the structural system in the control commands, especially for long-stroke stacker cranes with low stiffness and large inertia, whose structural response is extremely sensitive to changes in the Jerk signal. Traditional motion control systems typically only focus on the smoothness of the velocity curve or the constraints of acceleration, neglecting the strong coupling effect of the Jerk curve on the micro-vibration behavior of the structure. This leads to the risk of structural resonance caused by the excitation frequency induced by motion planning overlapping with the modal frequency when low-frequency modes exist in the structure itself. This application constructs a spectral excitation map through Fourier transform, which is essentially a means of predicting structural response risks in advance, effectively avoiding the response lag problem caused by relying solely on feedback adjustment.

[0112] S2.2.4: Match the structural excitation frequency band with the structural modal information recorded in the spectral modal database to obtain curve segments with a risk of triggering resonance. The matching is based on resonance risk judgment rules, which evaluate the inherent modal frequencies of the structural excitation frequency band and the structural modal information. The resonance risk judgment rules include: when the energy density of a frequency point in the structural excitation frequency band is greater than or equal to a preset modal threshold, and the corresponding frequency point belongs to the resonance-sensitive frequency band of a modal frequency, the corresponding curve segment is determined to have a risk of triggering structural resonance. Specifically, the purpose of this step is to identify whether there are potential motion segments in the current velocity change curve that could trigger structural resonance by matching the structural excitation frequency band extracted from the spectral excitation map with a pre-established structural modal spectral database. The identification process is not a simple frequency overlap search operation, but rather a resonance risk assessment logic built based on structural resonance theory and actual stacker crane operating conditions, used to accurately identify velocity curve segments that couple with the inherent modal frequencies of the structure, thereby causing abnormal structural vibration.

[0113] In this embodiment, the structural modal spectrum database is derived from the modal dataset constructed through offline modal identification in step S2.2 above. It records the modal frequency distribution, damping ratio information and corresponding vibration modes of the entire stacker crane or key parts, and is archived in layers according to the structural rigidity level.

[0114] Furthermore, in the actual matching operation, the controller 105 calls the structural excitation frequency band information in the spectrum excitation map and traverses all modal frequencies recorded in the database under the current structural stiffness level. For each modal frequency value, a resonance sensitive frequency band is set in its upper and lower frequency domains. The resonance sensitive frequency band is generally dynamically set according to the damping ratio, aiming to cover the frequency band energy distribution range formed by the expansion of structural damping during the actual structural response. Subsequently, each frequency point in the spectrum excitation map is cross-compared with the modal frequency band: if a frequency point falls within the resonance band range of the modal frequency, and the energy density value corresponding to the frequency point is greater than or equal to the preset modal excitation threshold, then it is determined that the frequency point has the potential risk of exciting the modal response; when multiple frequency points meet the above conditions at the same time, the excitation bandwidth they constitute is further evaluated. If the energy accumulation of continuous frequency points and the degree of mode matching are high, it can be inferred that the current velocity change curve contains a segment of curve that may cause resonance.

[0115] In some optional implementations, the matching process may also include the following three parameters as reference dimensions: the first parameter is the duration of the curve segment. If the duration of the curve segment corresponding to the excitation frequency band is significantly higher than the critical response period of the structural response (generally determined by modal damping), it indicates that the excitation is sufficient to induce structural response accumulation and increase the risk of resonance. The second parameter is the energy gradient of the curve segment. The energy change rate of the curve segment in the excitation frequency band is evaluated. If the energy increase or decrease trend matches the trend of the structural modal response, the matching weight is enhanced. The third parameter is multimodal superposition. For flexible structures with adjacent or overlapping modal frequencies, if the excitation frequency band spans multiple modal frequency bands, the corresponding curve segment should be marked with a higher risk level. When the above three parameters are met, the controller 105 marks the velocity curve segment as a curve segment with the risk of inducing structural resonance and records its start and end times, excitation frequency, energy value, and matching mode number, etc., as key parameters for subsequent correction.

[0116] S2.2.5: Correct the curve segment to obtain the velocity change curve; specifically, the purpose of this step is to reconstruct the velocity change curve of the identified curve segment that has the risk of triggering structural resonance, so that it can meet the original motion target constraint conditions while avoiding significant excitation in the sensitive band of structural modal frequency, thereby reducing the probability of triggering structural resonance.

[0117] In one example, the specific steps of S2.2.5 are as follows: S2.2.5.1: The parameters of the curve segment are reconstructed using a perturbation optimization algorithm. The parameters include the acceleration change rate corresponding to the curve segment, the duration of the curve segment, and the start and end velocity values ​​within the curve segment. The perturbation optimization algorithm is configured as a nonlinear search algorithm based on a genetic mechanism. The nonlinear search algorithm includes population initialization, fitness evaluation, crossover operation, mutation operation, and termination determination. The fitness function in the fitness evaluation is the integral value of the spectral excitation energy corresponding to the structural excitation frequency band. The termination determination is based on the convergence of the fitness function to a preset termination threshold. Specifically, when it is detected that one or more curve segments in the target velocity change curve have the risk of triggering structural modal resonance, in order to avoid such excitation behavior causing elastic oscillation or mechanical shaking of the entire or local structure of the stacker crane, multiple key control parameters of the corresponding curve segment need to be reconstructed.

[0118] It is understandable that, since the resonant response is highly sensitive to energy density in the frequency domain and the structure has different response characteristics to excitation in different frequency bands, it is difficult to effectively avoid modal excitation paths by simply adjusting a single parameter linearly.

[0119] In this embodiment, the perturbation optimization algorithm takes minimizing the excitation spectrum energy as the core optimization index, and pays special attention to the energy projection behavior of the optimization curve segment near the structural modal frequency.

[0120] In one implementation, the adjustable parameters first need to be modeled and constrained.

[0121] The parameters to be optimized in this application mainly include: the rate of change of acceleration within the curve segment, i.e., the rate of change of acceleration per unit time; the duration of the curve segment, i.e., the running period of the curve segment; and the start and end velocity values ​​within the curve segment, i.e., the velocity boundary conditions of the curve segment. These parameters are in a complex coupled relationship within the curve segment, which not only determines the macroscopic profile of the curve, but also directly affects the energy distribution pattern of its acceleration derivative signal in the frequency domain.

[0122] In another implementation, population initialization is performed first. Population initialization defines an initial solution set containing multiple individuals, each being a combination of specific parameter configurations. The initialization process can employ a distribution sampling strategy based on historical curve experience, combined with a multi-point perturbation mechanism to improve the coverage of the parameter space. No screening is performed at this stage; it only ensures that each set of parameters is valid within the constraint space.

[0123] In another implementation, a fitness evaluation operation is performed. The fitness function is the integral value of the spectral excitation energy corresponding to the structural excitation frequency band. This value can be obtained by deriving the acceleration curve from the velocity change curve constructed from the current individual parameters and inputting it into a preset spectral prediction mapping model for Fourier transform to obtain its spectrum. The total energy distribution within the modal frequency window in the spectrum is statistically analyzed and used as the fitness value of the individual. The higher the energy value, the higher the probability of the parameter set being excited by structural modal resonance, and the worse its fitness value; conversely, the lower the energy value, the better the fitness value. The fitness evaluation process is performed on all individuals in each generation of the population to ensure that the selection process is goal-oriented.

[0124] In another implementation, the algorithm proceeds to the stages corresponding to crossover and mutation operations. Crossover simulates the gene exchange mechanism in natural heredity, exchanging parameters between individuals with superior fitness to generate new candidate solutions and enhance the algorithm's global exploration capability. Mutation introduces random perturbations into individual parameters, breaking local optima traps with a low probability and improving the algorithm's ability to escape local optima. In this embodiment, the mutation method uses a Gaussian perturbation model, which involves superimposing a small offset value conforming to a Gaussian distribution onto a certain parameter value. The crossover and mutation ratios can be adjusted in real time based on population diversity; if the population tends to converge, the mutation probability is increased to introduce new candidate solutions.

[0125] In the final implementation, all generated new-generation individuals will re-enter the fitness evaluation process and compete for survival with high-fitness individuals from the previous generation. This process iterates repeatedly until a preset termination condition is met. In this application, the termination condition is that the convergence of the fitness function reaches a threshold, i.e., the fitness function of the best individual does not significantly improve over several consecutive generations, or the optimal value is less than the minimum allowable upper limit of the modal excitation energy.

[0126] It is easy to understand that perturbation optimization algorithms possess multi-peak search characteristics, which can avoid getting trapped in a single solution space, making them suitable for solving non-convex objective problems in spectrum avoidance problems. Their advantage lies in their ability to perform nonlinear, discontinuous, and even irregular solution space optimization without relying on model gradient information, making them particularly suitable for handling multivariable, strongly coupled, and high-dimensional velocity curve reconstruction problems. Through the aforementioned optimization process, one or more sets of parameter configurations with energy suppression effects in the modal excitation frequency band are ultimately obtained.

[0127] S2.2.5.2: Optimize the initial velocity change curve based on the reconstructed parameters to obtain multiple candidate velocity change curves. Input the candidate velocity change curves into the spectrum prediction mapping model to obtain the spectrum excitation map corresponding to each candidate velocity change curve. Specifically, after obtaining the curve segment control parameters solved by the genetic mechanism perturbation optimization algorithm, in order to further improve the energy distribution characteristics of the overall velocity trajectory outside the structural mode frequency band, it is necessary to perform structural optimization on the entire initial velocity change curve based on the combination of these parameters, and form multiple optional velocity change curve candidate sets.

[0128] In this embodiment, the curve optimization process uses the perturbation optimization result as the initial solution to perform parameter-driven function reconstruction on the corresponding curve segment. The reconstruction process follows the following control logic: First, using the input start and end velocity values ​​as boundary conditions, and combining the curve segment duration and acceleration change rate generated by the optimization algorithm, a seven-segment (or corresponding type) velocity model is fitted to the curve segment. Each segment velocity model is constructed based on a cubic or quintic spline function to meet the requirement of continuous connection between velocity, acceleration, and jerk between segments, avoiding non-smooth transitions in the time domain and ensuring the physical realizability of the trajectory.

[0129] Furthermore, after the curves are constructed, the derivative of each candidate velocity change curve is calculated to obtain its complete acceleration rate of change curve. Then, sampling discretization processing under a unified time reference is performed and input into the preset spectrum prediction mapping model in this application. Fourier transform operation is performed to obtain its spectrum excitation map.

[0130] To further ensure the minimization of excitation spectral energy in the region surrounding the modal frequency, the spectral excitation map corresponding to each candidate curve is compared and scored one by one with the previously constructed structural modal frequency bands. The scoring criteria mainly include two parts: first, the total energy value within the modal frequency band, i.e., the sum of the energy densities at frequency points within that band; second, the Euclidean distance from the center point of the modal frequency to the frequency where the excitation peak is located, used to measure whether the current excitation is far from the sensitive region. The above two indicators are weighted to construct a scoring function, resulting in the excitation risk score for the corresponding candidate curve.

[0131] It should be noted that in actual deployment, the number of curves, the range of parameter disturbances, and the sampling accuracy can be adapted and adjusted according to the operating characteristics of the equipment, the performance of the controller 105, and the structural response model to ensure sufficient solution space coverage without introducing system load.

[0132] S2.2.5.3: Select the candidate velocity change curve with the largest Euclidean distance from the natural mode frequency and the smallest total spectral energy from the candidate velocity change curves, and use it as the correction result of the initial velocity change curve to generate a velocity change curve; specifically, based on the excitation risk score obtained above, determine the corresponding candidate velocity change curve, use the candidate velocity change curve as the correction result of the initial velocity change curve, and generate a velocity change curve.

[0133] Next, we will further elaborate on the closed-loop control aspect of the method in this application.

[0134] Specifically, during the operation of a stacker crane, in order to ensure that its displacement trajectory remains consistent with the preset S-curve path, closed-loop control logic is needed to continuously adjust its motion state in real time. Closed-loop control can dynamically correct the output based on actual feedback during the movement, thereby effectively addressing tracking errors caused by structural elasticity, mechanical backlash, motor response delay, load disturbances, etc., and preventing overshoot, rebound, or jitter in rapid movement or end-positioning of the stacker crane.

[0135] In this embodiment, the closed-loop control logic is implemented collaboratively by the driver 103 and the controller 105. The controller 105 is responsible for trajectory planning and feedback error calculation, while the driver 103 is responsible for actual speed output and motor drive command execution. Specifically: the controller 105 first performs time discretization processing on the generated speed change curve and position change curve, converting them into theoretical speed and theoretical position values ​​within a discrete control cycle to ensure executability within the control cycle; based on the theoretical speed value of the current cycle, the controller 105 issues a target speed command to the driver 103, and the driver 103 controls the stacker crane motor to operate according to this speed command; the controller 105 synchronously reads the encoder position information fed back by the driver 103, calculates the actual displacement speed in combination with the time cycle, and compares it with the current theoretical position value; based on the deviation between the actual position and the theoretical position, the controller 105 calculates a set of speed increments (i.e., compensation speed values) for error compensation using a built-in PID control algorithm. This compensation amount is used to correct the speed command for the next cycle, thereby achieving closed-loop tracking.

[0136] In some optional implementations, the three control coefficients (proportional term P, integral term I, and derivative term D) of the PID control algorithm can be adaptively set according to the structural rigidity level of the stacker crane to enhance the stability and speed of the system response. For example, for structures with low rigidity, the P value can be appropriately reduced to avoid overshoot, the I term can be strengthened to prevent residual hysteresis, and the D term can be used to offset dynamic error fluctuations; while for structures with high rigidity, the P value can be increased to accelerate convergence, and the D term can be used for dynamic vibration absorption.

[0137] In one example, the acceleration and deceleration times of driver 103 are set to the smallest time unit supported by driver 103.

[0138] In another example, comparing the actual position with the theoretical position value and generating a compensation speed value based on the comparison result and adding it to the theoretical speed value of the current control cycle includes: generating a compensation amount for correcting the speed command using a PID control algorithm based on the deviation between the actual position and the theoretical position value; adding the compensation amount to the theoretical speed value corresponding to the current control cycle to generate an updated speed command and sending it to the driver 103, wherein the parameters of the proportional, integral, and derivative terms in the PID control algorithm are adjusted according to the deviation.

[0139] In one example, when the stacker crane reaches the end positioning interval close to the target position (the end positioning interval can be determined experimentally by those skilled in the art), the controller 105 switches to a micro-motion vibration suppression control mode. Specifically, this includes: within the end positioning interval, re-discretizing the target speed change curve, increasing the discretization frequency to generate a dense control point sequence, and outputting speed commands cycle by cycle based on this control point sequence; in the micro-motion vibration suppression control mode, the controller 105 constructs anti-rebound control logic, specifically including: setting a symmetrical speed reverse dead zone threshold, prohibiting the controller 105 from outputting control commands opposite to the main direction when a short-term reverse deviation occurs at the feedback position, to avoid secondary reverse swaying due to over-adjustment, where the feedback position refers to the position of the stacker crane when speed adjustment is required; superimposing a dynamic damping coefficient for high-frequency oscillation attenuation onto the speed command, the dynamic damping coefficient being adaptively adjusted according to the oscillation frequency and amplitude of the feedback speed, constructing an equivalent speed oscillation absorber; when the feedback position remains within the positioning window for two consecutive control cycles and the speed approaches zero, the controller 105 generates a positioning completion flag and controls the driver 103 to enter a braking state.

[0140] In one example, this application provides an S-curve and closed-loop motion control system for a stacker crane. The system includes: a trajectory generation module, used to generate speed change curves and position change curves according to user-defined parameters, and to discretize the speed change curves and position change curves to obtain theoretical speed values ​​and theoretical position values ​​corresponding to each control cycle; a spectrum analysis module, used to perform frequency domain transformation on the generated initial speed change curves based on a spectrum prediction mapping model, identify curve segments with the risk of exciting structural resonance, and perform resonance matching and judgment in conjunction with spectrum modal database information; a trajectory optimization module, used to perform parameter reconstruction based on a disturbance optimization algorithm on the curve segments with the risk of resonance, generate multiple candidate speed change curves, and screen the candidate speed change curves to obtain the speed change curve; and an adaptive control module, used to perform closed-loop PID control based on the theoretical speed value and the feedback position deviation, generate a speed compensation amount in real time and superimpose it onto the theoretical speed value, and output the updated speed command to the stacker crane driver 103.

[0141] Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of this application.

Claims

1. A method for S-curve and closed-loop motion control of a stacker crane, characterized in that, The stacker crane includes a controller and a drive, and the method includes: Get user-defined parameters; A velocity change curve and a position change curve are generated based on the user-defined parameters, wherein the velocity change curve is determined according to a preset velocity change curve function, and the position change curve is obtained by integrating the velocity change curve. Discretize the velocity change curve and the position change curve to obtain the theoretical velocity value and theoretical position value corresponding to each control cycle; The output speed of the driver is obtained based on the theoretical speed value, and the actual position of the stacker is obtained based on the output speed value. The actual position is compared with the theoretical position value, and a compensation speed value is generated based on the comparison result and superimposed on the theoretical speed value of the current control cycle to update the output speed. The user-defined parameters include target position, target maximum velocity, maximum acceleration, and jerk. A velocity change curve is generated based on the user-defined parameters, including: Based on the target position, target maximum velocity, maximum acceleration, and jerk, determine the corresponding curve type; Based on the curve type, the velocity change curve is calculated using a preset velocity change curve function; The user-defined parameters also include the structural rigidity level of the stacker crane, which is determined based on the stacker crane's structural dimensions, component materials, and historical vibration response. The method further includes: According to the curve type, the velocity change curve is calculated by using a preset velocity change curve function, combined with a preset spectrum prediction mapping model and the structural stiffness level. The spectrum prediction mapping model is obtained by performing offline modal identification on the stacker crane. The offline modal identification includes extracting the natural modal frequencies, damping ratios and mode shapes of the structural stiffness level corresponding to the stacker crane in motion to generate a spectrum modal database. The calculation of the velocity change curve using a preset velocity change curve function, combined with a preset spectrum prediction mapping model and the structural stiffness level, includes: Based on the curve type, the initial velocity change curve is calculated using a preset velocity change curve function; The initial velocity change curve is discretized in the time domain and then used as the input parameter of the spectrum prediction mapping model. The acceleration change rate of the input parameters is Fourier transformed by the spectrum prediction mapping model to obtain the spectrum excitation map, and the structure excitation frequency band is obtained according to the energy density distribution corresponding to each frequency point in the spectrum excitation map. The structure excitation frequency band is matched with the structure modal information recorded in the spectrum modal database to obtain the curve segment with the risk of excitation resonance. The matching is based on the resonance risk judgment rule, which evaluates the inherent modal frequencies of the structure excitation frequency band and the structure modal information. The resonance risk judgment rule includes: when the energy density of a frequency point in the structure excitation frequency band is greater than or equal to a preset modal threshold, and the corresponding frequency point belongs to the resonance sensitive frequency band of a modal frequency, it is determined that the corresponding curve segment has the risk of exciting structural resonance. The curve segment is corrected to obtain the velocity change curve.

2. The S-curve and closed-loop motion control method for a stacker crane according to claim 1, characterized in that, The velocity change curve includes at least one of four curve types: four-segment curve, five-segment curve, six-segment curve, and seven-segment curve. The four-segment curve includes an acceleration segment, a deceleration segment, an increase in deceleration segment, and a decrease in deceleration segment. The five-segment curve includes an acceleration segment, a deceleration segment, a constant velocity segment, an increase in deceleration segment, and a decrease in deceleration segment. The six-segment curve includes an acceleration segment, a constant acceleration segment, a deceleration segment, an increase in deceleration segment, a constant deceleration segment, and a decrease in deceleration segment. The seven-segment curve includes an acceleration segment, a constant acceleration segment, a deceleration segment, a constant velocity segment, an increase in deceleration segment, a constant deceleration segment, and a decrease in deceleration segment.

3. The S-curve and closed-loop motion control method for a stacker crane according to claim 1, characterized in that, The acceleration and deceleration times of the driver are set to the minimum time units supported by the driver.

4. The S-curve and closed-loop motion control method for a stacker crane according to claim 3, characterized in that, The actual position is compared with the theoretical position value, and a compensation velocity value is generated based on the comparison result and superimposed on the theoretical velocity value of the current control cycle, including: Based on the deviation between the actual position and the theoretical position value, a compensation amount for correcting the speed command is generated by a PID control algorithm. The compensation amount is then superimposed on the theoretical speed value corresponding to the current control cycle to generate an updated speed command, which is then sent to the driver. The parameters of the proportional, integral, and derivative terms in the PID control algorithm are adjusted according to the deviation.

5. The S-curve and closed-loop motion control method for a stacker crane according to claim 1, characterized in that, The curve segment is corrected to obtain the velocity change curve, including: The curve segment is reconstructed using a perturbation optimization algorithm. The parameters include the acceleration change rate corresponding to the curve segment, the duration of the curve segment, and the start and end velocity values ​​within the curve segment. The perturbation optimization algorithm is configured as a nonlinear search algorithm based on a genetic mechanism. The nonlinear search algorithm includes population initialization, fitness evaluation, crossover operation, mutation operation, and termination determination. The fitness function in the fitness evaluation is the integral value of the spectral excitation energy corresponding to the structural excitation frequency band. The termination determination is based on the fitness function converging to a preset termination threshold. The initial velocity change curve is optimized based on the reconstructed parameters to obtain multiple candidate velocity change curves. The candidate velocity change curves are then input into the spectrum prediction mapping model to obtain the spectrum excitation map corresponding to each candidate velocity change curve. From the candidate velocity change curves, select the candidate velocity change curve with the largest Euclidean distance from the natural mode frequency and the smallest total spectral energy in the corresponding spectral excitation spectrum, and use it as the correction result of the initial velocity change curve to generate the velocity change curve.

6. The S-curve and closed-loop motion control method for a stacker crane according to claim 4, characterized in that, The method further includes comparing the actual position with the theoretical position value, generating a compensation velocity value based on the comparison result, and adding it to the theoretical velocity value of the current control cycle. Obtain the structural rigidity rating of the stacker crane; Based on the structural rigidity level, the preset PID control parameter table for the corresponding structural rigidity level is called to set the coefficient values ​​of the proportional, integral, and derivative terms.

7. An S-curve and closed-loop motion control system for a stacker crane, used to implement the S-curve and closed-loop motion control method for a stacker crane as described in any one of claims 1-6, characterized in that, The system includes: The trajectory generation module is used to generate velocity change curves and position change curves according to user-defined parameters, and to discretize the velocity change curves and position change curves to obtain the theoretical velocity value and theoretical position value corresponding to each control cycle. The spectrum analysis module is used to perform frequency domain transformation on the generated initial velocity change curve based on the spectrum prediction mapping model, identify curve segments with the risk of exciting structural resonance, and perform resonance matching and judgment in combination with spectrum mode database information. The trajectory optimization module is used to perform parameter reconstruction based on the perturbation optimization algorithm on the curve segment with resonance risk, generate multiple candidate velocity change curves, and screen the candidate velocity change curves to obtain the velocity change curve. The adaptive control module is used to perform closed-loop PID control based on the deviation between the theoretical speed value and the feedback position, generate a speed compensation amount in real time and add it to the theoretical speed value, and output the updated speed command to the stacker crane driver.

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