Integrated control method and system for double-pendulum bridge crane

Abstract

The invention relates to the technical field of anti-swing control of bridge cranes, in particular to a double-swing bridge crane integrated control method and system which comprises an equation calculation unit, a shaping design unit, a target setting unit, a convolution operation unit, an integral operation unit, an error calculation unit and a control calculation unit. By arranging a double-pendulum bridge crane system mathematical model with a double-pendulum effect and introducing an input shaper, the swing suppression and anti-interference performance of the system disclosed by the invention is improved based on the control of the control system on the double-pendulum bridge crane, and by arranging the multi-loop control system and the nonlinear PID integrated control system, the system has the advantages of high reliability and high reliability. Through the synergistic effect of input shaping and the controller, the vibration frequency characteristic and full-state real-time information of the double-pendulum bridge type crane system are fully considered, so that the double-pendulum bridge type crane system has good response speed and stability, the residual swing of the double-pendulum bridge type crane system is reduced, and the service life of the double-pendulum bridge type crane system is prolonged. And the engineering transportation efficiency of the double-pendulum bridge crane system is improved.

Description

Technical Field

[0001] This invention relates to the field of anti-sway control technology for bridge cranes, and in particular to an integrated control method and system for a double-sway bridge crane. Background Technology

[0002] Bridge cranes are key pieces of equipment in production and transportation, widely used in manufacturing, logistics warehousing, and port trade. The equipment mainly consists of a trolley, hook ropes, hoisting mechanism, drive motor, and crossbeam frame. In a single transport task, the motor drives the trolley, loaded with goods at its lower end, from the initial worktable to the designated working point. Once the trolley has reached its destination and the goods at its lower end are no longer swaying, the hoisting mechanism slowly places the goods onto the worktable. Furthermore, ensuring the stability and safety of transport is crucial when facing complex engineering environments (such as the effects of wind and waves during offshore operations). Therefore, achieving rapid positioning and effective suppression of goods swaying while improving the system's adaptability are key issues in crane transportation.

[0003] Among numerous crane anti-sway control methods, input shaping technology has been widely used due to its advantages such as simple structure and low cost. This technology shapes the input signal based on the inherent oscillation frequency of the crane system to reduce cargo swaying. Patent (CN201710007624.X) performs input shaping feedforward processing on the real-time measured hook sway angle and trolley displacement signals, and uses the processed signal to control the crane system, achieving precise trolley positioning and cargo sway suppression. Patent (CN202510394222.4) designs an input shaper based on the system transfer function to provide a preset acceleration control signal for the trolley. Results show that this method can effectively suppress cargo swaying. Addressing the performance degradation caused by input time delay and initial sway in engineering transportation, the articles (A robust input shaper for trajectory control of overhead cranes with non-zero initial states, 2021; On reference trajectory generation for overhead crane travel movements, 2022) propose input compensation and reparameterization methods, respectively. Results show that these methods can mitigate the impact of initial conditions on system performance to a certain extent. However, the lack of a feedback adjustment mechanism makes the control system face challenges when dealing with complex operating scenarios such as large changes in transportation conditions and external disturbances.

[0004] To address this issue and improve the dynamic performance and robustness of crane systems, recent research has focused on combining input shapers with various closed-loop control algorithms. The paper (Distributed delay adaptive output-based command shaping for different cable lengths of double-pendulum overhead cranes, 2024) proposes a composite control method combining an adaptive output algorithm with a distributed delay zero-vibration shaper. Results show that the developed system exhibits good dynamic performance and adaptability. Patent (CN202310097434.7) proposes a crane anti-sway control method integrating predictive control and an input shaper. This method ensures the system state is always within constraints while maintaining good dynamic performance. The paper (Control of an underactuated double-pendulum overhead crane using improved model reference command shaping: Design, simulation and experiment, 2021) combines a model reference command shaper with a PID controller, resulting in a system with good stability and ease of engineering deployment. Furthermore, the article (Combined input shaping and feedback control for double-pendulum systems, 2017) designed a composite control framework of double closed-loop PD feedback and input shaping.

[0005] The research on these composite control algorithms for bridge cranes has improved the dynamic performance and adaptability of the system to some extent. However, some problems still need to be solved and optimized: 1) The sway suppression performance of the system needs to be improved. The robustness of the current crane anti-sway control system to complex external disturbances and uncertainties needs to be improved. Cargo often has a certain amount of residual sway, which affects the efficiency of engineering transportation to some extent. 2) The design of the controller does not adequately address the double-pendulum effect. Most current research focuses on simplified single-pendulum models, but in engineering applications, the mass of the hook is not negligible, causing it to interact directly with the cargo and increasing the difficulty of positioning and anti-swing measures. 3) The application and deployment capabilities of the engineering need to be improved. The closed-loop mechanisms in the above studies rely heavily on prior set parameters. When the transportation environment is unknown, the parameters need to be readjusted to ensure optimal control performance. Therefore, their engineering application and deployment capabilities need to be improved. Summary of the Invention

[0006] This invention provides an integrated control method and system for a double pendulum bridge crane, which overcomes the shortcomings of the prior art and can effectively solve the problem of residual cargo sway affecting engineering transportation efficiency in existing double pendulum bridge crane control methods.

[0007] To solve the above problems, one of the technical solutions of this invention is achieved through the following method: an integrated control method for a double-swing bridge crane, comprising the following steps: The dynamic equations of the double pendulum bridge crane system are constructed, and the swing dynamic equations of the hook and the cargo are calculated. Based on the swing dynamics equation and using the input shaping principle, an input shaper is designed for use in a double swing bridge crane system. Set the target acceleration signal for the double pendulum bridge crane system, and output the target acceleration signal to the input shaper to obtain a new target acceleration trapezoidal input signal; The desired displacement trajectory is obtained by performing a convolution operation on the target acceleration trapezoidal input signal. The actual acceleration signal of the double pendulum bridge crane is collected and integrated to obtain the real-time displacement trajectory. The real-time displacement error signal is obtained by calculating the expected displacement trajectory and the real-time displacement trajectory. The control system calculates the control signal of the double pendulum bridge crane system based on the real-time displacement error signal and outputs it to the double pendulum bridge crane.

[0008] The above-mentioned dynamic equations for constructing a double-swing bridge crane system are used to calculate the swing dynamic equations for the hook and the load; including: Using the Euler-Lagrange method, the dynamic equation of the double pendulum bridge crane is derived, as shown in the following equation: , In the formula, The mass of the car; For the weight of the hook; For the quality of the goods; This refers to the length of the rope connecting the trolley and the hook. The length of the rope connecting the hook and the cargo; Represents gravitational acceleration; This represents the displacement of the trolley; This refers to the swing angle of the hook; The swing angle of the goods; This represents the driving force of the vehicle; within the safe transportation range, the following approximate relationship usually exists: , , ; The dynamic equations of the double-swing bridge crane are linearized as follows: , Furthermore, the swing dynamics equations for the hook and cargo are obtained from the above formulas, as shown below: .

[0009] The above-mentioned input shaper, based on the swing dynamics equation and employing the input shaping principle, is designed for use in a double-swing bridge crane system; including: Pulse Amplitude and pulse duration The calculation method is as follows: , In the formula, ; This is the system's inherent frequency; Let be the damping ratio of the system, and ; and The calculation method is as follows: , In the formula, Therefore, the input shaper of the double-swing bridge crane system is further obtained as follows: .

[0010] The above-mentioned target acceleration signal for the double-swing bridge crane system includes: Target acceleration The calculation method is as follows: .

[0011] The aforementioned control system calculates the control signal for the double-swing bridge crane system based on the real-time displacement error signal and outputs it to the double-swing bridge crane, including: The first PD controller calculates the preliminary acceleration signal of the double-swing bridge crane system based on the real-time displacement error signal. The calculation method is as follows: , In the formula, , pass The integral is obtained. This represents the displacement of the trolley; and These are the parameters for the first PD controller; Collect the real-time swing angle of the hook of the double pendulum bridge crane. The data is then output to the second PD controller, which is based on the real-time swing angle of the hook of the double-swing bridge crane. The acceleration adjustment signal was calculated. The calculation method is as follows: , In the formula, ; and For the parameters of the second PD controller; Collect the real-time swing angle of the cargo relative to the hook of the double-swing bridge crane. The data is then output to the third PD controller, which is based on the real-time swing angle of the cargo relative to the hook of the double-swing bridge crane. The acceleration adjustment signal was calculated. The calculation method is as follows: , In the formula, ; and For the parameters of the third PD controller; Based on the preliminary acceleration signal and acceleration adjustment signal and Calculate the control acceleration signal output by the first PD controller. The calculation method is as follows: ; Control acceleration signal The control signals for the double-swing bridge crane system are obtained by applying acceleration and speed limits. And output to the double swing bridge crane.

[0012] The aforementioned control system calculates the control signal for the double-swing bridge crane system based on the real-time displacement error signal and outputs it to the double-swing bridge crane, including: Collect the real-time swing angle of the hook of the double pendulum bridge crane. and the real-time swing angle of the cargo relative to the hook And output to a nonlinear PID controller; The nonlinear PID controller is based on the real-time displacement error signal and the real-time swing angle of the hook of the double pendulum crane. The real-time swing angle of the cargo relative to the hook of a double-swing bridge crane. The preliminary acceleration signal was calculated. The calculation method is as follows: , In the formula, ; This is the gain parameter used to adjust the displacement error; This is the gain parameter used to adjust the speed; This is the gain parameter used to adjust the swing of the hook; This is the gain parameter used to adjust the swing of the cargo; This is the integral gain parameter used to adjust the displacement error; This is a parameter used to scale the sensitivity to nonlinear terms; For the initial acceleration signal The control signals for the double-swing bridge crane system are obtained by applying acceleration and speed limits. And output to the double swing bridge crane.

[0013] The second technical solution of this invention is achieved through the following means: an integrated control system for a double-swing bridge crane, using an integrated control method for a double-swing bridge crane, comprising: The equation calculation unit constructs the dynamic equations of the double pendulum bridge crane system and calculates the swing dynamic equations of the hook and the cargo. The shaping design unit, based on the swing dynamics equation and using the input shaping principle, designs an input shaper for use in a double pendulum bridge crane system. The target setting unit sets the target acceleration signal for the double pendulum bridge crane system and outputs the target acceleration signal to the input shaper to obtain a new target acceleration trapezoidal input signal. The convolution operation unit performs convolution operations on the target acceleration trapezoidal input signal to obtain the desired displacement trajectory; The integral calculation unit collects the actual acceleration signal of the double pendulum bridge crane and performs integral calculation to obtain the real-time displacement trajectory. The error calculation unit calculates the real-time displacement error signal by comparing the expected displacement trajectory with the real-time displacement trajectory. The control calculation unit calculates the control signal of the double pendulum bridge crane system based on the real-time displacement error signal and outputs it to the double pendulum bridge crane.

[0014] The aforementioned control calculation unit includes a multi-loop control system, wherein the multi-loop control system includes: The first PD controller calculates the preliminary acceleration signal of the double pendulum bridge crane system based on the real-time displacement error signal. The calculation method is as follows: , In the formula, , pass The integral is obtained. This represents the displacement of the trolley; and These are the parameters for the first PD controller; The second PD controller collects the real-time swing angle of the hook of the double pendulum crane. The data is then output to the second PD controller, which is based on the real-time swing angle of the hook of the double-swing bridge crane. The acceleration adjustment signal was calculated. The calculation method is as follows: , In the formula, ; and For the parameters of the second PD controller; The third PD controller collects the real-time swing angle of the cargo relative to the hook of the double-swing bridge crane. The data is then output to the third PD controller, which is based on the real-time swing angle of the cargo relative to the hook of the double-swing bridge crane. The acceleration adjustment signal was calculated. The calculation method is as follows: , In the formula, ; and For the parameters of the third PD controller; Acceleration calculation module, based on preliminary acceleration signal and acceleration adjustment signal and Calculate the control acceleration signal output by the first PD controller. The calculation method is as follows: ; The acceleration and speed limiting module controls the acceleration signal. The control signals for the double-swing bridge crane system are obtained by applying acceleration and speed limits. And output to the double swing bridge crane.

[0015] The aforementioned control calculation unit includes a nonlinear PID integrated control system, wherein the nonlinear PID integrated control system includes: The data acquisition module collects the real-time swing angle of the hook of the double pendulum bridge crane. and the real-time swing angle of the cargo relative to the hook And output to a nonlinear PID controller; Nonlinear PID controllers are based on real-time displacement error signals and the real-time swing angle of the hook of a double pendulum crane. The real-time swing angle of the cargo relative to the hook of a double-swing bridge crane. The preliminary acceleration signal was calculated. The calculation method is as follows: , In the formula, ; This is the gain parameter used to adjust the displacement error; This is the gain parameter used to adjust the speed; This is the gain parameter used to adjust the swing of the hook; This is the gain parameter used to adjust the swing of the cargo; This is the integral gain parameter used to adjust the displacement error; This is a parameter used to scale the sensitivity to nonlinear terms; The acceleration and velocity limiting module processes the initial acceleration signal. The control signals for the double-swing bridge crane system are obtained by applying acceleration and speed limits. And output to the double swing bridge crane.

[0016] The convolution operation unit mentioned above includes a first integrator and a second integrator. The input shaper, the first integrator, the second integrator and the control calculation unit are connected in sequence. The first integrator is used to convert the target acceleration signal into a target velocity signal, and the second integrator is used to convert the target velocity signal into a target displacement signal, i.e. the desired displacement trajectory. The integration unit includes a third integrator and a fourth integrator. The double pendulum bridge crane, the third integrator, the fourth integrator, and the control calculation unit are connected in sequence. The third integrator is used to integrate the actual acceleration signal of the double pendulum bridge crane to obtain the actual speed signal. The fourth integrator is used to integrate the actual speed signal to obtain the actual displacement signal, i.e., the real-time displacement trajectory.

[0017] Compared with the prior art, the present invention has the following advantages: This invention improves the sway suppression and anti-interference performance of a double-swing bridge crane system by setting up a mathematical model of the double-swing effect and introducing an input shaper. Based on the control system's control of the double-swing bridge crane, it enhances the system's sway suppression and anti-interference performance. Furthermore, through the setting of a multi-loop control system and a nonlinear PID-like integrated control system, the synergistic effect of the input shaper and the controller fully considers the vibration frequency characteristics and real-time information of the double-swing bridge crane system. This results in the double-swing bridge crane system having good response speed and stability, reducing residual sway, improving the engineering transportation efficiency of the double-swing bridge crane system, and enhancing its application and deployment capabilities in engineering projects. Attached Figure Description

[0018] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0019] Figure 1 This is a flowchart of the method in Embodiment 1 of the present invention.

[0020] Figure 2 This is a dynamic model diagram of a bridge crane with a double pendulum effect in Embodiment 1 of the present invention.

[0021] Figure 3 This is a schematic diagram illustrating the working principle of the three-pulse input shaper in Embodiment 1 of the present invention.

[0022] Figure 4 This is a system structure block diagram of Embodiment 3 of the present invention.

[0023] Figure 5 This is a system structure diagram of the multi-loop control system in Embodiment 3 of the present invention.

[0024] Figure 6 This is a system structure block diagram of the nonlinear PID integrated control system in Embodiment 4 of the present invention.

[0025] Figure 7 This is a comparison diagram of the trolley displacement between the multi-loop PD control system and the nonlinear PID integrated control system in Embodiment 5 of the present invention.

[0026] Figure 8 This is a comparison diagram of the hook swing of the multi-loop PD control system and the nonlinear PID integrated control system in Embodiment 5 of the present invention.

[0027] Figure 9 This is a comparison diagram of the relative oscillation between the cargo and the hook in the multi-loop PD control system and the nonlinear PID integrated control system in Embodiment 5 of the present invention. Detailed Implementation

[0028] The present invention is not limited to the following embodiments, and the specific implementation can be determined according to the technical solution of the present invention and the actual situation.

[0029] Example 1: As Figure 1 As shown in the figure, an embodiment of the present invention discloses an integrated control method for a double-swing bridge crane, comprising the following steps: Step S101: Construct the dynamic equations of the double pendulum bridge crane system and calculate the swing dynamic equations of the hook and the cargo. Step S102: Based on the swing dynamics equation, and using the input shaping principle, design an input shaper for use in a double swing bridge crane system; Step S103: Set the target acceleration signal for the double pendulum bridge crane system and output the target acceleration signal to the input shaper to obtain a new target acceleration trapezoidal input signal; Step S104: Perform convolution operation on the target acceleration trapezoidal input signal to obtain the desired displacement trajectory; Step S105: Collect the actual acceleration signal of the double pendulum bridge crane and perform integration calculation to obtain the real-time displacement trajectory. Step S106: Calculate the real-time displacement error signal by comparing the desired displacement trajectory with the real-time displacement trajectory; In step S107, the control system calculates the control signal of the double pendulum bridge crane system based on the real-time displacement error signal and outputs it to the double pendulum bridge crane.

[0030] In step S101 above, such as Figure 2 As shown, the dynamic equations of the double-swing bridge crane system are constructed, and the swing dynamic equations of the hook and the load are calculated; including: Using the Euler-Lagrange method, the dynamic equation of the double pendulum bridge crane is derived, as shown in the following equation: , In the formula, The mass of the car; For the weight of the hook; For the quality of the goods; This refers to the length of the rope connecting the trolley and the hook. The length of the rope connecting the hook and the cargo; Represents gravitational acceleration; This represents the displacement of the trolley; This refers to the swing angle of the hook; The swing angle of the goods; This represents the driving force of the vehicle; within the safe transportation range, the following approximate relationship usually exists: , , ; The dynamic equations of the double-swing bridge crane are linearized as follows: , Furthermore, the swing dynamics equations for the hook and cargo are obtained from the above formulas, as shown below: .

[0031] As can be seen from the above swing dynamics equations, the double swing bridge crane system has underactuated characteristics. There are strong nonlinear coupling characteristics between the trolley motion, hook swing and cargo swing, as well as the control objectives of ensuring the rapid and accurate positioning of the trolley and minimizing the swing of the hook and cargo.

[0032] In the double pendulum bridge crane system, the cargo is suspended on the trolley by the hook, forming a two-stage swing structure. When the trolley moves, the hook and cargo inevitably swing like a pendulum. This phenomenon is particularly obvious when the trolley reaches the target position. Based on this, the present invention derives the dynamic equation of the double pendulum bridge crane by using the Euler-Lagrange method.

[0033] In step S102 above, such as Figure 3 As shown, based on the swing dynamics equations and employing the input shaping principle, an input shaper is designed for use in a double-swing bridge crane system; including: Pulse Amplitude and pulse duration The calculation method is as follows: , In the formula, ; This is the system's inherent frequency; Let be the damping ratio of the system, and ; and The calculation method is as follows: , In the formula, Therefore, the input shaper of the double-swing bridge crane system is further obtained as follows: .

[0034] The aforementioned input shaper employs a three-pulse input shaper, and its working principle is as follows: Figure 3 As shown, the input shaper obtains a new trapezoidal input signal by convolving a preset pulse sequence with the original input of the double pendulum bridge crane system. These pulse sequences take into account the oscillation frequency and damping of the double pendulum bridge crane system, which can effectively suppress or cancel the residual sway of the double pendulum bridge crane system, thus effectively reducing the sway of the double pendulum bridge crane system.

[0035] In step S103 above, setting the target acceleration signal for the double-swing bridge crane system includes: Target acceleration The calculation method is as follows: .

[0036] In step S104 above, the target acceleration trapezoidal input signal is convolved to obtain the desired displacement trajectory; wherein, the acceleration trapezoidal input signal is integrated by an integrator to obtain a velocity signal, and the velocity signal is further integrated to obtain a displacement signal, i.e., the desired displacement trajectory.

[0037] Step S105: Collect the actual acceleration signal of the double pendulum bridge crane and perform integration to obtain the real-time displacement trajectory; wherein, the actual acceleration signal is integrated by an integrator to obtain the actual velocity signal, and the velocity signal is further integrated to obtain the actual displacement signal, i.e., the real-time displacement trajectory.

[0038] Step S106: Calculate the real-time displacement error signal by comparing the expected displacement trajectory with the real-time displacement trajectory; wherein, the real-time displacement error signal can be obtained by subtracting the expected displacement trajectory from the real-time displacement trajectory.

[0039] In step S107 above, the control system calculates the control signal of the double-swing bridge crane system based on the real-time displacement error signal and outputs it to the double-swing bridge crane, including: The first PD controller calculates the preliminary acceleration signal of the double-swing bridge crane system based on the real-time displacement error signal. The calculation method is as follows: , In the formula, , pass The integral is obtained. This represents the displacement of the trolley; and These are the parameters of the first PD controller; where the parameters are obtained through preliminary simulation experiments. , This value will be applied to the engineering implementation and will help the double swing bridge crane system ensure good performance. Collect the real-time swing angle of the hook of the double pendulum bridge crane. The data is then output to the second PD controller, which is based on the real-time swing angle of the hook of the double-swing bridge crane. The acceleration adjustment signal was calculated. The calculation method is as follows: , In the formula, ; and These are the parameters of the second PD controller; among which, the parameters were obtained through preliminary simulation experiments. , This value will be applied to engineering implementation and will help ensure good performance of the double swing bridge crane system; Collect the real-time swing angle of the cargo relative to the hook of the double-swing bridge crane. The data is then output to the third PD controller, which is based on the real-time swing angle of the cargo relative to the hook of the double-swing bridge crane. The acceleration adjustment signal was calculated. The calculation method is as follows: , In the formula, ; and These are the parameters of the third PD controller; among them, the parameters were obtained through preliminary simulation experiments. , This value will be applied to engineering implementation and will help ensure good performance of the double swing bridge crane system; Based on the preliminary acceleration signal and acceleration adjustment signal and Calculate the control acceleration signal output by the first PD controller. The calculation method is as follows: ; Control acceleration signal The control signals for the double-swing bridge crane system are obtained by applying acceleration and speed limits. And output to the double swing bridge crane.

[0040] Example 2: This embodiment of the invention discloses that in step S107 above, the control system calculates the control signal of the double-swing bridge crane system based on the real-time displacement error signal and outputs it to the double-swing bridge crane, including: Collect the real-time swing angle of the hook of the double pendulum bridge crane. and the real-time swing angle of the cargo relative to the hook And output to a nonlinear PID controller; The nonlinear PID controller is based on the real-time displacement error signal and the real-time swing angle of the hook of the double pendulum crane. The real-time swing angle of the cargo relative to the hook of a double-swing bridge crane. The preliminary acceleration signal was calculated. The calculation method is as follows: , In the formula, ; This is the gain parameter used to adjust the displacement error; This is the gain parameter used to adjust the speed; This is the gain parameter used to adjust the swing of the hook; This is the gain parameter used to adjust the swing of the cargo; This is the integral gain parameter used to adjust the displacement error; These are parameters used to scale the sensitivity of the nonlinear term; where the parameters are obtained through preliminary simulation experiments. , , , , and This value will be applied to engineering implementation and will help ensure good performance of the double swing bridge crane system; For the initial acceleration signal The control signals for the double-swing bridge crane system are obtained by applying acceleration and speed limits. And output to the double swing bridge crane.

[0041] Example 3: As Figure 4 As shown, this embodiment of the invention discloses an integrated control system for a double-swing bridge crane, and an integrated control method for a double-swing bridge crane, including: The equation calculation unit constructs the dynamic equations of the double pendulum bridge crane system and calculates the swing dynamic equations of the hook and the cargo. The shaping design unit, based on the swing dynamics equation and using the input shaping principle, designs an input shaper for use in a double pendulum bridge crane system. The target setting unit sets the target acceleration signal for the double pendulum bridge crane system and outputs the target acceleration signal to the input shaper to obtain a new target acceleration trapezoidal input signal. The convolution operation unit performs convolution operations on the target acceleration trapezoidal input signal to obtain the desired displacement trajectory; The integral calculation unit collects the actual acceleration signal of the double pendulum bridge crane and performs integral calculation to obtain the real-time displacement trajectory. The error calculation unit calculates the real-time displacement error signal by comparing the expected displacement trajectory with the real-time displacement trajectory. The control calculation unit calculates the control signal of the double pendulum bridge crane system based on the real-time displacement error signal and outputs it to the double pendulum bridge crane.

[0042] like Figure 5 As shown, the aforementioned control calculation unit includes a multi-loop control system, wherein the multi-loop control system includes: The first PD controller calculates the preliminary acceleration signal of the double pendulum bridge crane system based on the real-time displacement error signal. The calculation method is as follows: , In the formula, , pass The integral is obtained. This represents the displacement of the trolley; and These are the parameters for the first PD controller; The second PD controller collects the real-time swing angle of the hook of the double pendulum crane. The data is then output to the second PD controller, which is based on the real-time swing angle of the hook of the double-swing bridge crane. The acceleration adjustment signal was calculated. The calculation method is as follows: , In the formula, ; and For the parameters of the second PD controller; The third PD controller collects the real-time swing angle of the cargo relative to the hook of the double-swing bridge crane. The data is then output to the third PD controller, which is based on the real-time swing angle of the cargo relative to the hook of the double-swing bridge crane. The acceleration adjustment signal was calculated. The calculation method is as follows: , In the formula, ; and For the parameters of the third PD controller; Acceleration calculation module, based on preliminary acceleration signal and acceleration adjustment signal and Calculate the control acceleration signal output by the first PD controller. The calculation method is as follows: ; The acceleration and speed limiting module controls the acceleration signal. The control signals for the double-swing bridge crane system are obtained by applying acceleration and speed limits. And output to the double swing bridge crane.

[0043] The acceleration and speed limiting modules simulate the limitations of the motor driver, specifically the speed and acceleration saturation phenomenon of an actual drive motor. Real-time acceleration of the trolley and real-time swing angle of the hook are also simulated in the double-swing bridge crane. and the real-time swing angle of the cargo relative to the hook All of them can be monitored and collected in real time through external sensors, and fed back to the integration unit, the second PD controller and the third PD controller, and the method steps of Embodiment 1 are repeatedly executed to realize the data loop loop until the running time reaches the set value.

[0044] The first PD controller, acceleration and speed limiting module, and integral calculation unit constitute the first feedback loop, which provides an initial acceleration signal. This feedback loop ensures that the trolley moves smoothly and accurately to the designed position.

[0045] The second PD controller, together with the acceleration and speed limiting module, forms a second feedback loop to suppress the swing of the hook and generate an acceleration adjustment signal.

[0046] The third PD controller, together with the acceleration and speed limiting module, forms a third feedback loop to suppress the swaying of the cargo and generate another acceleration adjustment signal.

[0047] Example 4: Figure 6 As shown, the control calculation unit includes a nonlinear PID integrated control system, wherein the nonlinear PID integrated control system includes: The data acquisition module collects the real-time swing angle of the hook of the double pendulum bridge crane. and the real-time swing angle of the cargo relative to the hook And output to a nonlinear PID controller; Nonlinear PID controllers are based on real-time displacement error signals and the real-time swing angle of the hook of a double pendulum crane. The real-time swing angle of the cargo relative to the hook of a double-swing bridge crane. The preliminary acceleration signal was calculated. The calculation method is as follows: , In the formula, ; This is the gain parameter used to adjust the displacement error; This is the gain parameter used to adjust the speed; This is the gain parameter used to adjust the swing of the hook; This is the gain parameter used to adjust the swing of the cargo; This is the integral gain parameter used to adjust the displacement error; This is a parameter used to scale the sensitivity to nonlinear terms; The acceleration and velocity limiting module processes the initial acceleration signal. The control signals for the double-swing bridge crane system are obtained by applying acceleration and speed limits. And output to the double swing bridge crane.

[0048] The nonlinear PID controller provides the initial acceleration signal for the entire control system, enabling coordinated control of the trolley position, hook swing, and cargo swing. External sensors measure the real-time acceleration of the double-swing bridge crane trolley and the real-time swing angle of the hook in real time. and the real-time swing angle of the cargo relative to the hook The real-time acceleration is fed back to the integral calculation unit to calculate the real-time swing angle of the hook. and the real-time swing angle of the cargo relative to the hook The feedback is sent to the nonlinear PID controller, and the method steps of Example 1 are repeated to realize the data loop cycle until the running time reaches the set value.

[0049] The convolution operation unit mentioned above includes a first integrator and a second integrator. The input shaper, the first integrator, the second integrator and the control calculation unit are connected in sequence. The first integrator is used to convert the target acceleration signal into a target velocity signal, and the second integrator is used to convert the target velocity signal into a target displacement signal, i.e. the desired displacement trajectory. The integration unit includes a third integrator and a fourth integrator. The double pendulum bridge crane, the third integrator, the fourth integrator, and the control calculation unit are connected in sequence. The third integrator is used to integrate the actual acceleration signal of the double pendulum bridge crane to obtain the actual speed signal. The fourth integrator is used to integrate the actual speed signal to obtain the actual displacement signal, i.e., the real-time displacement trajectory.

[0050] In summary, this invention improves the sway suppression and anti-interference performance of a double-swing bridge crane system by setting a mathematical model of the double-swing effect and introducing an input shaper. Based on the control system's control of the double-swing bridge crane, it enhances the system's sway suppression and anti-interference performance. Furthermore, through the setting of a multi-loop control system and a nonlinear PID-like integrated control system, the synergistic effect of input shaping and the controller fully considers the vibration frequency characteristics and real-time information of the double-swing bridge crane system. This results in the double-swing bridge crane system having good response speed and stability, reducing residual sway, improving the engineering transportation efficiency of the double-swing bridge crane system, and enhancing its application and deployment capabilities in engineering projects.

[0051] Example 5: The mechanical parameters of the bridge crane were selected as follows: , , , and Therefore, the parameters of the input shaper can be calculated according to step S102; this embodiment compares a multi-loop PD control system and a nonlinear PID-like integrated control system, and the results are as follows. Figure 7-9 As shown.

[0052] Depend on Figure 7 It can be seen that both types of control systems can ensure the rapid positioning of the vehicle. For example... Figure 8The nonlinear PID integrated control system designed for the hook sway exhibits superior suppression performance, achieving zero residual sway of the hook more quickly. Regarding the relative sway between the hook and the cargo, this nonlinear PID integrated control system reduces the maximum sway angle from 0.78 degrees to 0.16 degrees, while achieving zero residual sway within 12 seconds. Figure 9 As shown above, the analysis demonstrates that the designed nonlinear PID integrated control system, by effectively coordinating the regulation capability of the nonlinear PID controller and the oscillation suppression performance of input shaping, can achieve superior dynamic performance.

[0053] In summary, this invention utilizes both a multi-loop control system and a nonlinear PID integrated control system, both of which offer the advantage of achieving composite control. The nonlinear PID integrated control system, based on the multi-loop control system, features a simple structure, ease of engineering implementation, and better control performance (sway suppression and stability). Meanwhile, the multi-loop control system has the advantage of low input.

Claims

1. A double-pendulum bridge crane integrated control method, characterized by, The method comprises the following steps: The dynamic equation of the double-pendulum bridge crane system is constructed, and the swing dynamic equation of the hook and the cargo is calculated; Based on the swing dynamic equation, an input shaper applied to the double-pendulum bridge crane system is designed by using the input shaping principle; A target acceleration signal for the double-pendulum bridge crane system is set, and the target acceleration signal is output to the input shaper to obtain a new target acceleration trapezoidal input signal; The target acceleration trapezoidal input signal is subjected to convolution operation to obtain an expected displacement trajectory; The actual acceleration signal of the double-pendulum bridge crane is collected and subjected to integral operation to obtain a real-time displacement trajectory; The expected displacement trajectory and the real-time displacement trajectory are calculated to obtain a displacement real-time error signal; The control system calculates the control signal of the double-pendulum bridge crane system based on the displacement real-time error signal and outputs the control signal to the double-pendulum bridge crane.

2. The dual-bridge crane integrated control method according to claim 1, characterized in that, The dynamic equation of the double-pendulum bridge crane system is constructed, and the swing dynamic equation of the hook and the cargo is calculated; The dynamic equation of the double-pendulum bridge crane is derived by using the Euler-Lagrange method, and is shown in the following formula: ， wherein is the mass of the trolley; is the mass of the hook; is the mass of the cargo; is the length of the rope connecting the trolley and the hook; is the length of the rope connecting the hook and the cargo; denotes the gravitational acceleration; is the displacement of the trolley; is the swing angle of the hook; is the swing angle of the cargo; denotes the driving force of the trolley; in the safe transport range, the following approximate relationship usually exists: , , ; The dynamic equation of the double-pendulum bridge crane is linearized into the following formula: ， Further, the swing dynamic equation of the hook and the cargo is obtained from the above formula, and is shown in the following formula: 。 3. The dual-bridge crane integrated control method according to claim 1, characterized in that, The input shaper applied to the double-pendulum bridge crane system is designed by using the input shaping principle based on the swing dynamic equation. The target acceleration signal for the double-pendulum bridge crane system is set, and the target acceleration signal is output to the input shaper to obtain a new target acceleration trapezoidal input signal. pulse amplitude and pulse action time are calculated as follows: ， wherein ; is the natural frequency of the system; is the damping ratio of the system, and ; and are calculated as follows: ， wherein Thus, the input shaper for the double-gantry crane system is further obtained as follows: 。 4. The dual-bridge crane integrated control method according to claim 1, characterized in that, The control system calculates the control signal of the double-pendulum bridge crane system based on the displacement real-time error signal and outputs the control signal to the double-pendulum bridge crane, and comprises: Target acceleration is calculated as follows: 。 5. The dual-bridge crane integrated control method according to claim 4, characterized in that, The control system calculates the control signal of the double-pendulum bridge crane system based on the displacement real-time error signal and outputs the control signal to the double-pendulum bridge crane, and comprises: The first PD controller calculates the preliminary acceleration signal of the double-swing bridge crane system based on the real-time displacement error signal. The calculation method is as follows: ， In the formula, , By is calculated by integration, is the displacement of the trolley; and is the first PD controller parameter; Collecting real-time swing angle of double-pendulum bridge crane hook , and output to the second PD controller, the second PD controller calculates the acceleration adjustment signal based on the real-time swing angle of the double-pendulum bridge crane hook , and the calculation method is as follows:​ ， wherein ; and is a second PD controller parameter; Collect the real-time swing angle of the cargo relative to the hook of the double-swing bridge crane. The data is then output to the third PD controller, which is based on the real-time swing angle of the cargo relative to the hook of the double-swing bridge crane. The acceleration adjustment signal was calculated. The calculation method is as follows: ， wherein ; and is a third PD controller parameter; based on the preliminary acceleration signal and the acceleration adjustment signal and a control acceleration signal is calculated as a function of the first PD controller output ; Controlling acceleration signal Performing acceleration and speed limitation to obtain control signal of double-pendulum bridge crane system And output to double-pendulum bridge crane.

6. The dual-bridge crane integrated control method according to claim 4, characterized in that, The control system calculates the control signal of the double-pendulum bridge crane system based on the displacement real-time error signal and outputs the control signal to the double-pendulum bridge crane, and comprises: Collecting real-time swing angle of hook of double-swing bridge crane and real-time swing angle of goods relative to hook and output to nonlinear PID-like controller The nonlinear PID-like controller is based on real-time displacement error signal, real-time swing angle of the hook of the double-pendulum bridge crane and real-time swing angle of the hook of the double-pendulum bridge crane , and calculates a preliminary acceleration signal in the following manner: ， wherein ; is a gain parameter for adjusting displacement error; is a gain parameter for adjusting speed; is a gain parameter for adjusting hook swing; is a gain parameter for adjusting cargo swing; is an integral gain parameter for adjusting displacement error; is a parameter for scaling non-linear term sensitivity; to the preliminary acceleration signal performing acceleration and speed limiting to obtain control signals for a double-pendulum bridge crane system and outputting to the double-pendulum bridge crane.

7. A double-pendulum bridge crane integrated control system using the double-pendulum bridge crane integrated control method according to any one of claims 1 to 6, characterized by, The control system calculates the control signal of the double-pendulum bridge crane system based on the displacement real-time error signal and outputs the control signal to the double-pendulum bridge crane, and comprises: An equation calculation unit is configured to construct the dynamic equation of the double-pendulum bridge crane system, and to calculate the swing dynamic equation of the hook and the cargo; An input shaping design unit is configured to design the input shaper applied to the double-pendulum bridge crane system by using the input shaping principle based on the swing dynamic equation; A target setting unit is configured to set the target acceleration signal for the double-pendulum bridge crane system, and to output the target acceleration signal to the input shaper to obtain a new target acceleration trapezoidal input signal; A convolution operation unit is configured to subject the target acceleration trapezoidal input signal to convolution operation to obtain an expected displacement trajectory; An integral operation unit is configured to collect the actual acceleration signal of the double-pendulum bridge crane and to subject the actual acceleration signal to integral operation to obtain a real-time displacement trajectory; An error calculation unit is configured to calculate the displacement real-time error signal by calculating the expected displacement trajectory and the real-time displacement trajectory; A control calculation unit is configured to calculate the control signal of the double-pendulum bridge crane system based on the displacement real-time error signal, and to output the control signal to the double-pendulum bridge crane.

8. The twin-gantry crane integrated control system according to claim 7, characterized in that, The control calculation unit comprises a multi-loop control system, wherein the multi-loop control system comprises: a first PD controller, the first PD controller calculating a preliminary acceleration signal for the double-pendulum bridge crane system based on the displacement real-time error signal in the following way: ， wherein , By is calculated by integration of is the displacement of the trolley; and is a first PD controller parameter; The second PD controller collects the real-time swing angle of the hook of the double swing bridge crane , and outputs to the second PD controller, and the second PD controller calculates the acceleration adjustment signal based on the real-time swing angle of the hook of the double swing bridge crane , and the calculation method is as follows:​ ， wherein ; and is a second PD controller parameter; The third PD controller collects the real-time swing angle of the double-swing bridge crane goods relative to the hook , and outputs to the third PD controller, and the third PD controller calculates the acceleration adjustment signal based on the real-time swing angle of the double-swing bridge crane goods relative to the hook , and the calculation method is as follows:​ ， wherein ; and is a third PD controller parameter; an acceleration computation module, which computes a control acceleration signal based on the preliminary acceleration signal and an acceleration adjustment signal and , which computes a control acceleration signal output by the first PD controller in the following manner: ; an acceleration and speed limiting module to limit the acceleration signal to obtain a control signal for the double-pendulum bridge crane system and output to the double-pendulum bridge crane.

9. The twin-gantry crane integrated control system according to claim 7, wherein, The control calculation unit comprises a nonlinear PID integrated control system, wherein the nonlinear PID integrated control system comprises: The collection module collects the real-time swing angle of the double swing bridge crane hook and the real-time swing angle of the goods relative to the hook and outputs to the nonlinear PID controller The nonlinear PID-like controller is based on a displacement real-time error signal, a real-time swing angle of a double swing bridge crane hook and a real-time swing angle of a double swing bridge crane cargo relative to the hook , a preliminary acceleration signal is calculated in the following way: ， wherein ; is a gain parameter for adjusting displacement error; is a gain parameter for adjusting speed; is a gain parameter for adjusting hook swing; is a gain parameter for adjusting cargo swing; is an integral gain parameter for adjusting displacement error; is a parameter for scaling non-linear term sensitivity; an acceleration and speed limiting module to limit the preliminary acceleration signal to obtain a control signal of the double-pendulum bridge crane system and output to the double-pendulum bridge crane.

10. The dual gantry crane integrated control system of claim 7, wherein, The convolution operation unit comprises a first integrator and a second integrator, and an input shaper, the first integrator, the second integrator and a control calculation unit are sequentially connected, wherein the first integrator is used for converting the target acceleration signal into a target speed signal, and the second integrator is used for converting the target speed signal into a target displacement signal, i.e. an expected displacement trajectory; The integral operation unit comprises a third integrator and a fourth integrator, and the double-swing bridge crane, the third integrator, the fourth integrator and a control calculation unit are sequentially connected, wherein the third integrator is used for integrating the actual acceleration signal of the double-swing bridge crane to obtain an actual speed signal, and the fourth integrator is used for integrating the actual speed signal to obtain an actual displacement signal, i.e. a real-time displacement trajectory.

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