A hybrid anti-swing control method for a portal crane

Abstract

The application discloses a mixed anti-swing control method suitable for a portal crane and belongs to the anti-swing control field of hoisting equipment. The method establishes an equivalent dynamic model of the crane based on the equivalent force / torque principle, linearizes and decouples at a vertical stable balance point of a hoisted load, and obtains two independent linear swing models of amplitude variation and rotation. A ZVD input shaping feedforward controller is designed according to model oscillation characteristic parameters to complete pre-processing of a driving signal, and a loop shaping feedback controller is synchronously designed. The two are combined to construct a feedforward-feedback mixed control system, and through the collaborative action, load anti-swing control is realized. The application has the advantages of smooth vibration suppression of open-loop control and robust disturbance resistance of closed-loop control, can effectively cope with initial swing angle, external wind disturbance and parameter perturbation scenes, has stable control performance and strong engineering practicability.

Description

Technical Field

[0001] This invention relates to the field of automatic control technology for gantry cranes, and more specifically to a hybrid anti-sway control method applicable to gantry cranes. Background Technology

[0002] Gantry cranes are large-scale material handling equipment widely used in ports, docks, and industrial and mining enterprises, undertaking core operational tasks such as bulk cargo loading and unloading, and heavy object transfer. As a typical underactuated multi-rigid-body coupled system, the crane is prone to continuous reciprocating oscillation of the load during luffing and slewing operations due to factors such as the impact of mechanism start-stop, motion coupling, and external wind disturbance. If the load sway cannot be effectively suppressed, it will not only reduce material handling efficiency and prolong the operation cycle, but may also cause safety accidents such as equipment collisions and heavy object falls. Therefore, effectively suppressing the load sway angle is a key engineering problem in the field of crane operation control.

[0003] Existing anti-sway control technologies for cranes are mainly divided into two major approaches: open-loop control and closed-loop control. Open-loop control, typically represented by input shaping technology, uses zero-vibration or zero-vibration derivative input shapers to cancel inherent system oscillations by convolving the input signal with a specific pulse sequence. This approach is simple to implement and sensor-free, effectively eliminating residual vibration under ideal conditions without initial sway. However, this method is highly sensitive to initial system conditions; when there is a non-zero initial sway angle or external disturbances, it cannot effectively suppress residual sway, and the control effect is insufficient to meet practical engineering requirements. Closed-loop control, on the other hand, adjusts the control output by real-time acquisition of sway angle feedback signals. Common schemes include PID control and linear quadratic optimal control, which can suppress initial sway angles and external disturbances. However, these methods often rely on accurate system dynamics models. Gantry cranes have complex structures and significant multi-body coupling characteristics, making the construction of high-precision dynamic models difficult, resulting in a high barrier to controller design. Furthermore, control performance is prone to degradation and lacks robustness when faced with parameter perturbations such as rope length changes and load mass fluctuations.

[0004] In summary, existing anti-sway control technologies for gantry cranes have significant technical shortcomings: pure open-loop control has weak anti-disturbance capability and poor adaptability to initial conditions; conventional closed-loop control is limited by modeling difficulty and lacks robustness; and a single control path cannot simultaneously meet the requirements of residual vibration elimination and disturbance suppression.

[0005] Therefore, establishing a simplified dynamic model for gantry cranes suitable for controller design and developing a hybrid anti-sway control method that combines residual vibration elimination capability under undisturbed conditions with robust anti-disturbance performance under complex conditions are technical problems that urgently need to be solved in this field. Summary of the Invention

[0006] To address the above technical problems, this invention provides a hybrid anti-sway control method suitable for gantry cranes, the method comprising the following steps: S1. Based on the principle of equivalent force / torque, establish an equivalent dynamic model of the gantry crane. The wire rope is equivalent to a rigid rod with uniform mass, and the load is equivalent to a point mass. The driving torque of the luffing mechanism and the driving torque of the slewing mechanism are used as the model inputs, and the spatial swing angle of the load is used as the generalized coordinate to establish the dynamic relationship between the driving input and the swing of the load. S2. Based on the equivalent dynamic model, linearization is performed near the equilibrium point corresponding to the vertically stable state of the suspended load to obtain the linear swing model in the amplitude direction and the linear swing model in the rotation direction for controller design. S3. Based on the linear oscillation model of the amplitude direction and rotation direction obtained in S2, determine the oscillation characteristic parameters of the two directions respectively. Design a ZVD input shaping feedforward controller according to the oscillation characteristic parameters, and use the ZVD input shaping feedforward controller to preprocess the drive input signal to suppress the load residual vibration generated under the condition of no initial oscillation. S4. Based on the linear oscillation model of the amplitude direction and the rotation direction, design... Loop forming feedback controller is used to suppress load sway caused by initial swing angle, model parameter changes and external disturbances; S5. Connect the ZVD input shaping feedforward controller designed in step S3 with the controller designed in step S4. By combining loop-forming feedback controllers, a hybrid feedforward and feedback control system is constructed. Through the synergistic effect of feedforward elimination of residual vibration and feedback robust stabilization, load anti-sway control of gantry cranes is achieved.

[0007] As a further improvement of the present invention, step S1 specifically includes the following steps: S11. Based on the principle of equivalent force / torque, the dynamic modeling boundary and constraint conditions of the gantry crane are defined, and the basic architecture of the multi-rigid-body underactuated coupling model is built. S12. The oscillating system composed of the wire rope and the suspended weight is simplified into a rigid body equivalent structure to obtain a simple pendulum form. S13. The driving force of the amplitude change and rotation motion is converted into an equivalent force / torque input. Combined with the generalized coordinates of the swing angle in the suspended weight space, the coupled dynamic mapping relationship between the driving input and the swing response is derived.

[0008] As a further improvement of the present invention, in step S2, the decoupled amplitude motion transfer function and rotational motion transfer function are respectively: in, For the weight of the load, For the quality of the wire rope, For the length of the rope, For the amplitude, This is the acceleration due to gravity.

[0009] As a further improvement of the present invention, step S3 specifically includes the following steps: S31. Solving the natural frequency of a system based on a linear transfer function With damping ratio The damped natural frequency of the system is obtained. And calculate the half-oscillation period. The calculation formula is: S32. Deriving Shaper Parameters Based on System Damping Ratio The calculation formula is: S33, Based on parameters With half-oscillation period Construct a ZVD input shaper, which consists of three sequentially delayed pulses with amplitudes of: The time delays corresponding to the three pulses are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 10, 19 ... , ; The transfer function form of the S34 and ZVD input shapers is as follows: .

[0010] As a further improvement of the present invention, step S4 specifically includes the following steps: S41, using the decoupled linear transfer function As the controlled object, a pre-compensator and a post-compensator are selected as weighting functions; the pre-compensator is: The rear compensator is: S42. Frequency shaping of the open-loop system is achieved by using a front compensator and a rear compensator to obtain the shaped system: The singular value curves of the formed system shall meet the preset frequency domain design specifications. S43, Solve The standard robust stabilization problem is addressed by a central controller. It consists of a front compensator, a central controller, and a rear compensator cascaded together. The loop-forming feedback controller has the following expression: .

[0011] As a further improvement of the present invention, step S5 specifically includes: ZVD input shaping feedforward controller and The loop-forming feedback controller is connected to form a hybrid feedforward and feedback control system. The feedforward controller acts on the forward path of the system to shape the reference input signal and eliminate residual vibration under the condition of no initial oscillation; the feedback controller acts on the closed-loop feedback path of the system to generate an adjustment amount based on the load oscillation angle feedback signal to suppress the oscillation caused by the initial oscillation angle, model parameter changes and external disturbances. The hybrid control system outputs the final control quantity to the luffing mechanism and the slewing mechanism to perform load anti-sway control.

[0012] As a further improvement to this invention, for the two decoupled dimensions of amplitude-shifting motion and rotational motion, the system's natural frequency and damping ratio for each corresponding dimension are calculated independently, and ZVD input shaping feedforward controllers for each corresponding dimension are designed. The loop forming feedback controller enables independent closed-loop control of the swing angle in the amplitude direction and the swing angle in the rotation direction.

[0013] As a further improvement of the present invention, the The loop forming feedback controller is designed to robustly stabilize model parameter perturbations caused by changes in rope length and load mass, as well as external disturbances caused by external wind disturbances. The controller is solved based on the coprime factor uncertainty model to ensure the stable operation of the closed-loop system under parameter perturbations and external disturbances.

[0014] Based on this, the present invention also provides a hybrid anti-sway control system suitable for gantry cranes, wherein the above-mentioned method of the system includes: The equivalent modeling module is used to establish a nonlinear dynamic model of the gantry crane based on the principle of equivalent force / torque, and to determine the coupled dynamic relationship between the drive input and the swing of the load. The model linearization and decoupling module is used to linearize the nonlinear dynamic model at the equilibrium point and decouple it to obtain the linear transfer function of the amplitude direction and the rotation direction. The feedforward controller design module is used to solve the oscillation characteristic parameters based on the linear transfer function, calculate the pulse amplitude and time delay of the ZVD input shaper, and design the ZVD input shaping feedforward controller. The feedback controller design module is used to select a weighted compensator to perform loop shaping on the open-loop system, and to obtain the solution after solving the central controller. Loop shaping feedback controller; The hybrid control execution module is used to combine the feedforward controller and the feedback controller to build a feedforward-feedback hybrid control system, and output the control quantity to drive the crane's luffing and slewing mechanisms to perform anti-sway control.

[0015] Based on this, the present invention also provides a computer-readable storage medium storing a computer program that, when executed, implements the above-described method.

[0016] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention employs ZVD input shaping feedforward and A hybrid control architecture combining loop shaping and feedback can eliminate residual vibration through feedforward shaping when there is no initial oscillation, and achieve rapid oscillation angle convergence through closed-loop adjustment when there is an initial oscillation angle or external wind disturbance. The control performance is superior to single control methods and conventional LQR control. Based on... The feedback controller with loop forming exhibits strong adaptability to perturbations of parameters such as rope length and load mass changes, as well as external wind disturbances. It has small swing angle fluctuations under disturbances, fast recovery and stability, and outstanding robustness. At the same time, the simplified modeling and decoupling based on the principle of equivalent force / torque reduces the model complexity while retaining the core dynamic characteristics, and has good practical value and application prospects. Attached Figure Description

[0017] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart of the method in an embodiment of the present invention; Figure 2 This is a simplified structural diagram of the gantry crane in an embodiment of the present invention; Figure 3 This is a graph showing the response curves of different input shapers under univariate amplitude motion in an embodiment of the present invention. Figure 4 As described in the embodiments of the present invention Loop forming design structure diagram; Figure 5 This is a block diagram illustrating the robust stabilization problem in an embodiment of the present invention; Figure 6 This is an overall structural diagram of the feedforward and feedback hybrid control system in an embodiment of the present invention; Figure 7 The swing angle in the amplitude direction is represented by different control methods in the embodiments of the present invention. The contrast response curves; Figure 8 The swing angle in the rotation direction is represented by different control methods in the embodiments of the present invention. The contrast response curves; Figure 9 This is a dynamic response diagram of the length of the long rope and the short rope in the rotation direction in an embodiment of the present invention; Figure 10 The diagram shows the response curves of the long rope and the short rope in the variable amplitude direction in this embodiment of the invention. Figure 11 This is a schematic diagram of the electrical principle in an embodiment of the present invention; Figure 12 The figure shows the response curve of the scaled-down experimental system at the initial angle in an embodiment of the present invention. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] It should be noted that, unless otherwise defined, the technical or scientific terms used in the embodiments of this disclosure should have the ordinary meaning understood by one of ordinary skill in the art to which this disclosure pertains. The terms "first," "second," and similar words used in the embodiments of this disclosure do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0021] First, some technical terms used in this invention will be explained: Input shaping: an open-loop vibration suppression method that cancels the inherent oscillations of the system by convolving the system input signal with a pulse sequence of specific amplitude and time delay, thereby eliminating residual load vibration at its source.

[0022] ZVD Input Shaper: Zero-vibration derivative input shaper, which optimizes the tolerance to system frequency fluctuations based on the basic zero-vibration shaper, and is suitable for oscillating systems with small parameter variations.

[0023] Loop Shaping: A robust controller design method that shapes the open-loop frequency response of the controlled object using a weighting function before solving the loop. The standard robust stabilization problem is solved by a control law that balances the system's dynamic response performance and robust stability.

[0024] Equivalent force / torque principle: An engineering method that simplifies the dynamic modeling process by equating the motion and forces of a complex multibody system with equivalent forces or equivalent torques corresponding to concentrated masses / moments of inertia.

[0025] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0026] Example 1 As the background technology shows, gantry cranes, as typical underactuated multi-rigid-body coupled systems, are prone to continuous swaying of the load during operation due to the start-stop of the mechanism, motion coupling, and external wind disturbances. Existing pure open-loop input shaping control is sensitive to initial conditions and has weak resistance to external disturbances, while conventional closed-loop control is highly dependent on accurate dynamic models. When faced with perturbations of parameters such as rope length and load mass changes, the control performance degrades significantly. A single control scheme cannot simultaneously meet the requirements of eliminating residual vibration in undisturbed working conditions and suppressing disturbances in complex working conditions.

[0027] Please see Figures 1-12 This invention provides a hybrid anti-sway control method suitable for gantry cranes, comprising the following steps: S1. Based on the principle of equivalent force / torque, establish an equivalent dynamic model of the gantry crane. The wire rope is equivalent to a rigid rod with uniform mass, and the load is equivalent to a point mass. The driving torque of the luffing mechanism and the driving torque of the slewing mechanism are used as the model inputs, and the spatial swing angle of the load is used as the generalized coordinate to establish the dynamic relationship between the driving input and the swing of the load. Please see Figure 1 , Figure 7 This embodiment provides a method based on input shaping and The hybrid anti-sway control method for gantry cranes with loop forming is implemented through the following steps: S1. Based on the principle of equivalent force / torque, establish an equivalent dynamic model of the gantry crane. The wire rope is equivalent to a rigid rod with uniform mass, and the load is equivalent to a point mass. The driving torque of the luffing mechanism and the driving torque of the slewing mechanism are used as the model inputs, and the spatial swing angle of the load is used as the generalized coordinate to establish the dynamic relationship between the driving input and the swing of the load. In this step, the equivalent dynamic model is constructed through three sub-steps: S11. Based on the principle of equivalent force / torque, the dynamic modeling boundary and constraint conditions of the gantry crane are defined, and the basic architecture of the multi-rigid-body underactuated coupling model is built.

[0028] Preferably, the modeling process focuses on the dynamic characteristics of the swing of the suspended load, and incorporates the luffing mechanism, slewing mechanism and the swing system of the suspended load into the modeling boundary, ignoring the dynamic coupling effects of the traveling mechanism and the hoisting mechanism; the constraint conditions are set as the small swing angle working condition of the crane in normal operation, and the suspended load is assumed to only swing in a regular plane, without any unsteady motion such as torsion or rolling.

[0029] Based on the aforementioned boundaries and constraints, a basic framework for a dual-input, dual-output, multi-rigid-body underactuated, strongly coupled nonlinear model is constructed. The driving forces in both the amplitude and rotation directions are used as system inputs, and the load swing angles in both directions are used as the controlled outputs. These modeling boundaries and constraints are defined because the entire system of a gantry crane contains multiple motion mechanisms. Including the dynamic characteristics of all mechanisms in the modeling scope would result in a high model order, significant difficulty in parameter identification, and poor engineering feasibility. Focusing on the core characteristics of the load swing and defining normal operating conditions allows for keeping the model complexity within an engineering-feasible range while ensuring control accuracy. This provides space for subsequent model simplification and controller design, and is a prerequisite for the entire modeling process.

[0030] S12. The oscillating system composed of the wire rope and the suspended weight is simplified into a rigid body equivalent structure to obtain a simple pendulum.

[0031] Preferably, the wire rope is equivalent to an inelastic rigid rod with a uniformly distributed mass along its length. The total length of the rod is the same as the actual working rope length, and the total mass is equal to the nominal mass of the wire rope. Its moment of inertia is calculated using the formula for a homogeneous rod rotating about its endpoint, and is equivalent to... The suspended weight is treated as an equivalent point mass concentrated at the end of a rigid rod, with the total mass being the same as the actual suspended weight. Its moment of inertia is calculated using the formula for a point mass rotating about an axis of rotation, and is equivalent to... .

[0032] In the equivalent process, the axial expansion and contraction deformation and lateral elastic vibration of the wire rope are ignored, and the influence of the geometric dimensions of the suspended weight and its rotational inertia on the oscillation process is also ignored.

[0033] The rigid body equivalent simplification treatment is adopted because the wire rope has a high elastic modulus, and the axial deformation under normal operating load is much smaller than the swing amplitude. The lateral vibration decays quickly and has minimal impact on the overall swing. The size of the suspended weight is a very small percentage of the rope length, and the rotation characteristics have almost no effect on the planar swing.

[0034] Through the above equivalence, the originally complex rope-weight coupled system can be simplified into a classic rigid pendulum model, which not only fully preserves the core oscillation characteristics of the system, but also greatly reduces the difficulty of deriving and solving the dynamic equations. This is the core application of the equivalent force / torque principle in this scenario, and also the basis for subsequent linearization processing.

[0035] S13. The driving force of the amplitude change and rotation motion is converted into an equivalent force / torque input. Combined with the generalized coordinates of the swing angle in the suspended weight space, the coupled dynamic mapping relationship between the driving input and the swing response is derived.

[0036] Preferably, the driving torque of the luffing mechanism and the driving torque of the slewing mechanism are selected as the driving inputs of the model, corresponding to the driving torques of the two degrees of freedom of motion; the swing angle of the suspended weight in the luffing plane is selected. Swing angle in the plane of rotation As the core generalized coordinate, the amplitude is also included. Rotation angle As system motion parameters.

[0037] Based on the angular momentum theorem of rigid body dynamics, dynamic equilibrium equations are written for the oscillating systems in the variable amplitude plane and the rotation plane, respectively. The effect of the driving torque is transformed into the equivalent torque acting on the oscillating system. Finally, a set of second-order nonlinear differential equations containing cross-coupling terms is derived, establishing a quantitative mapping relationship between the driving input torque and the angular acceleration and swing angle of the suspended load.

[0038] Overall, this step transforms the complex whole machine into a simplified dynamic model through the principle of equivalent force / torque. It accurately captures the core dynamic characteristics of the suspended load swinging and significantly reduces the modeling difficulty of complex multibody systems. It provides an engineering-practical model foundation for subsequent linear decoupling and controller design, and is the underlying support link of the entire hybrid anti-sway control method.

[0039] S2. Based on the equivalent dynamic model, linearization is performed near the equilibrium point corresponding to the vertically stable state of the suspended load to obtain the linear swing model in the amplitude direction and the linear swing model in the rotation direction for controller design. In this step, linearization and motion decoupling of the model are completed through three sub-steps, resulting in a standard linear oscillation model that can be directly used for controller design: S21. Select the vertically stable state of the suspended load as the linearization equilibrium point, and determine the working range and approximate premise of linearization.

[0040] Preferably, the stable working point where the suspended load is stationary and hanging vertically is selected as the linearization equilibrium point, corresponding to the steady-state position of the system motion parameters and the swing angle; the linearization is applicable to the small swing angle working condition of the crane during normal operation, and the swing angle amplitude is usually no more than 10 degrees, which satisfies the applicable conditions of small angle trigonometric function approximation.

[0041] The 10-degree range is the linear approximation reliable operating range of this model. A larger initial swing angle is set for simulation and physical experiments to verify the controller's fast convergence and anti-swing capability.

[0042] S22. Approximate the nonlinear dynamic model with a small-angle linearization to eliminate higher-order nonlinear terms.

[0043] Preferably, the nonlinear differential equations obtained in step S1 are subjected to Taylor expansion at the equilibrium point, retaining the first-order terms of the state and input variables and ignoring the second-order and higher-order infinitesimal terms; the trigonometric function terms in the equations are approximated by small angles to further simplify the expression of the dynamic equations.

[0044] S23. Ignoring the cross-coupling terms of amplitude and rotational motion, we decouple them to obtain two independent linear oscillation models and derive the corresponding transfer function forms.

[0045] Preferably, after linearization, the cross-coupling terms between amplitude-dependent motion and rotational motion are further ignored, and the original multi-input multi-output coupled model is split into two independent single-input single-output linear models in the amplitude-dependent direction and the rotational direction, both of which are in the form of second-order oscillatory elements.

[0046] By performing Laplace transforms on the two linear models respectively, the transfer functions for amplitude motion and rotational motion are derived. The amplitude motion transfer function is as follows: Rotational motion transfer function: in, For the weight of the load, For the quality of the wire rope, For the length of the rope, For the amplitude, This is the acceleration due to gravity.

[0047] As can be seen from the transfer function form, the model in both directions contains a pair of pure imaginary roots, corresponding to the inherent dynamic characteristics of the undamped free oscillation of the suspended weight.

[0048] Motion decoupling is performed because the coupling effect in the amplitude and rotation directions is relatively weak under normal operating conditions, and the error caused by ignoring the coupling term is within the acceptable range for engineering. The two independent second-order models after decoupling can be designed with controllers separately, eliminating the need to deal with the complex problem of multivariable coupled control, which greatly simplifies the design and debugging process of the controller, while ensuring the control accuracy in each direction.

[0049] Overall, this step transforms the originally complex nonlinear coupled model into a standard second-order linear oscillation model through equilibrium point linearization and motion decoupling. This provides a standardized model input for the subsequent design of input shaping feedforward controllers and robust feedback controllers, and is a key intermediate link connecting the underlying dynamic modeling and the upper-level controller design.

[0050] S3. Based on the linear oscillation model of the amplitude direction and rotation direction obtained in S2, determine the oscillation characteristic parameters of the two directions respectively. Design a ZVD input shaping feedforward controller according to the oscillation characteristic parameters, and use the ZVD input shaping feedforward controller to preprocess the drive input signal to suppress the load residual vibration generated under the condition of no initial oscillation. In this step, the design and feedforward preprocessing of the ZVD input shaping feedforward controller are completed through four sub-steps to achieve residual vibration suppression under conditions without initial oscillation: S31. Extract the system oscillation characteristic parameters based on the linear oscillation model, and determine the system's natural frequency and damping ratio.

[0051] Preferably, for the decoupled linear transfer functions in both the amplitude and rotation directions, the natural frequencies of the system are extracted from the characteristic polynomial of the denominator. With damping ratio ; Furthermore, based on the correspondence between damped and undamped oscillations, the damped natural frequency of the system is calculated. The calculation formula is: Accurate extraction of system oscillation characteristic parameters is crucial because the core design parameters of the input shaper depend entirely on the system's oscillation characteristics: the natural frequency determines the pulse delay interval, and the damping ratio determines the pulse amplitude ratio. The accuracy of parameter extraction directly determines whether the input shaper can accurately counteract the system's inherent oscillations, which is a core prerequisite for ensuring the final effect of feedforward control.

[0052] S32. Calculate the half-oscillation period and core parameters of the shaper. Determine the basic design parameters of the shaper.

[0053] Preferably, the half-oscillation period of the system is calculated based on the damped natural frequency. The calculation formula is: Based on the system damping ratio, the core parameters of the ZVD shaper are then derived. The calculation formula is: For a small-damped oscillating system A value close to 1 corresponds to the amplitudes of the three pulses becoming more equal. The optimal calculation yields the half-oscillation period. Shaping parameters under low damping conditions .

[0054] S33. Construct a ZVD input shaper with a three-pulse structure based on the core parameters to determine the amplitude and time delay of each pulse.

[0055] Preferably, based on parameters With half-oscillation period Construct a three-pulse ZVD input shaper, with the amplitudes of the three pulses being: The time delays corresponding to the three pulses are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 10, 19 ... ; The corresponding shaper transfer function is in the form of: Preferably, this embodiment uses a ZVD input shaper. In practical applications, it can be replaced with a zero-vibration (ZV) input shaper or an extremely insensitive (EI) input shaper depending on the robustness requirements. The ZV shaper has a two-pulse structure, which makes the implementation logic simpler. The EI shaper is more robust to parameter fluctuations and is suitable for application scenarios with larger system parameter fluctuations.

[0056] The three-pulse ZVD structure is adopted because, compared with the two-pulse ZV shaper, the ZVD shaper significantly improves the robustness to system frequency fluctuations while ensuring zero vibration. Even if there is a small deviation between the actual system frequency and the design value, it can still maintain a good vibration suppression effect. At the same time, the number of pulses is small and the total time delay is short, which has a smaller impact on the system response speed. It balances vibration suppression effect and response efficiency and is highly compatible with the operating characteristics of gantry cranes.

[0057] S34. Perform convolution operation between the driving input signal and the shaper pulse sequence to complete the feedforward shaping preprocessing of the driving signal.

[0058] Preferably, the original amplitude and slewing mechanism drive reference signals are convolved with the corresponding ZVD shaper pulse sequences to obtain shaped feedforward drive signals, which are then directly input to the mechanism drive unit.

[0059] Pulse convolution is used to achieve input shaping because the essence of this process is to reconstruct the signal, transforming the step or ramp input that would originally excite system oscillations into a segmented input that can cancel out the oscillation energy. This process only preprocesses the input side, without the need for sway angle feedback signals and additional sensing devices. It is simple to implement, the control process is smooth and shock-free, and it can eliminate the residual vibration of the load from the source under the condition of no initial sway.

[0060] Overall, this step designs a ZVD input shaper based on the system oscillation characteristics and achieves residual vibration suppression through open-loop feedforward. It fully leverages the advantages of open-loop control, such as sensorless dependence, simplicity of implementation, and smooth operation, and forms the core feedforward channel in the hybrid control architecture, responsible for smooth drive control under disturbance-free conditions.

[0061] S4. Based on the linear oscillation model of the amplitude direction and the rotation direction, design... Loop forming feedback controller is used to suppress load sway caused by initial swing angle, model parameter changes and external disturbances; This step is completed through three sub-steps. The design of the loop-forming feedback controller achieves robust stabilization under initial swing angle, parameter perturbations, and external disturbances. S41. Using the decoupled linear oscillation model as the controlled object, select the front compensator and the rear compensator as the weighting function.

[0062] Preferably, taking variable amplitude motion as an example, the linear transfer function obtained in S2 is... As the controlled object; select the front compensator. Rear compensator As weighting functions, they are applied to the system's input and output, respectively. Through the cooperation of these two compensators, the frequency domain characteristics of the open-loop system can be flexibly shaped, simultaneously meeting the multi-dimensional design requirements of dynamic performance and robust stability.

[0063] S42. The open-loop system is shaped in the frequency domain by a weighted compensator to obtain the shaped open-loop system, so that the frequency domain characteristics meet the preset design specifications.

[0064] Preferably, the front compensator, the controlled object, and the rear compensator are connected in a cascaded manner to obtain the formed open-loop system: By adjusting the parameters of the weighting function, the singular value curves of the shaped system can be made to meet the preset frequency domain design specifications, including low-frequency gain requirements, mid-frequency bandwidth requirements, and high-frequency attenuation requirements.

[0065] S43, Solve The standard robust stabilization problem yields a central controller, which, after cascading weighted functions, results in a complete feedback controller.

[0066] Preferably, for a shaped system model containing uncertainties related to coprime factors, a model is constructed. The standard robust stabilization problem is solved numerically to obtain the central controller. Finally, the front compensator, central controller, and rear compensator are cascaded in sequence to obtain a complete system. The loop shaping feedback controller has the following expression: Preferably, this embodiment preferentially adopts In practical applications, the loop shaping control scheme can also be replaced with one based on linear matrix inequalities, depending on the design requirements. The controller adapts to different uncertainty descriptions and performance requirements.

[0067] Overall, this step designs a feedback controller by combining frequency domain shaping and robust stabilization, which takes into account both the dynamic response performance and robust stability of the system. It can effectively cope with the initial swing angle, external disturbances and parameter perturbations, and forms the core feedback channel in the hybrid control architecture, responsible for the swing angle adjustment and stable control under complex operating conditions.

[0068] S5. Connect the ZVD input shaping feedforward controller designed in step S3 with the controller designed in step S4. By combining loop-forming feedback controllers, a hybrid feedforward and feedback control system is constructed. Through the synergistic effect of feedforward elimination of residual vibration and feedback robust stabilization, load anti-sway control of gantry cranes is achieved.

[0069] In this step, the construction and performance verification of the feedforward-feedback hybrid control system are completed through three sub-steps, achieving load anti-sway control under all operating conditions through the synergy of the two: S51. Connect the feedforward controller and the feedback controller according to the specified architecture to construct a feedforward-feedback hybrid control system.

[0070] Preferably, this embodiment adopts a parallel hybrid control architecture, where the ZVD input shaping feedforward controller acts on the system's forward path to perform shaping preprocessing on the reference drive signal; The loop forming feedback controller acts on the closed-loop feedback path of the system, generating a feedback adjustment quantity based on the real-time acquired load swing angle feedback signal; the two outputs are superimposed and used as the final control quantity input to the amplitude transformer and slewing mechanism.

[0071] In practical applications, a series hybrid architecture can also be adopted according to the system characteristics, with the feedforward shaper placed inside the feedback loop.

[0072] S52. Clarify the division of labor and coordination logic between feedforward and feedback channels to achieve anti-sway control covering all operating conditions.

[0073] Preferably, in the hybrid control architecture, the feedforward channel is responsible for the stable operating conditions without initial disturbances, shaping the drive signals during normal start-up, shutdown, and variable amplitude slewing processes to prevent load oscillations from being triggered at the source and ensure smooth operation without residual vibrations; the feedback channel is responsible for operating conditions with initial swing angles, external wind disturbances, or parameter changes, quickly converging the swing angle through closed-loop adjustment while maintaining system stability. The two work together to achieve load anti-sway control under all operating conditions.

[0074] S53. Build a simulation model to conduct multi-condition comparison verification and test the performance and robustness of the hybrid control scheme.

[0075] Preferably, a complete system model is built in a simulation environment, setting up two sets of control conditions: one with an initial swing angle and one without. These are compared with control conditions without shaping control, single ZVD input shaping control, and single... A horizontal comparison was conducted between the control and LQR optimal control schemes. One example involved setting the initial load swing angle to 5 degrees. Simulation results showed that a standalone ZVD controller could not eliminate the initial swing angle, while the hybrid controller of this invention could suppress the swing angle to zero within approximately 4 seconds, exhibiting low overshoot and faster convergence speed than a standalone controller. Controller and LQR controller.

[0076] Preferably, to verify robust performance, external wind disturbance loads are simulated during the 12th-14th second of the simulation, and the rope length is adjusted to the shortest and longest conditions respectively to carry out joint tests of parameter perturbation and external disturbance. The results show that, compared with the LQR controller, the hybrid controller of the present invention has a smaller swing angle fluctuation amplitude under the influence of model parameter changes and external disturbances, and recovers stability faster after disturbance.

[0077] Conducting multi-condition and multi-scheme comparative verification can intuitively demonstrate the performance advantages of the hybrid control scheme, while verifying the actual effect of robust design. By benchmarking against commonly used LQR control schemes in the industry, the technical advancement of this scheme can be clarified, while verifying the stability under parameter perturbation, ensuring that the scheme can adapt to real-world application scenarios where rope length and load change frequently in actual operations.

[0078] Overall, this step integrates the advantages of two control methods through a collaborative architecture of feedforward and feedback. Simulations verify the control performance and robustness of the solution, ultimately forming a complete hybrid anti-sway control scheme that can cover all operating conditions.

[0079] The technical solution of this invention combines ZVD feedforward control and feedback control. This method can achieve smooth control without residual vibration under conditions without initial oscillation, just like pure input shaping. At the same time, it can quickly and stably suppress the oscillation angle to zero when there is an initial oscillation angle or external wind disturbance, thus overcoming the defect of pure open-loop control that is sensitive to initial conditions.

[0080] The introduction of the loop forming feedback controller enhances the robustness of the entire control system to model uncertainties such as changes in crane rope length and load mass, as well as external disturbances such as wind disturbances. Simulation results show that, under parameter perturbations and external disturbances, the control performance of this method is significantly better than conventional control methods such as LQR.

[0081] Finally, the dynamic modeling and linearization method based on equivalent force / torque proposed in this invention accurately captures the core dynamic characteristics of gantry cranes, providing a simplified yet sufficiently accurate model basis for controller design, and has practical engineering value.

[0082] It should be noted that the method of this disclosure embodiment can be executed by a single device, such as a computer or server. The method of this embodiment can also be applied to a distributed scenario, where multiple devices cooperate to complete the task. In such a distributed scenario, one of these devices may execute only one or more steps of the method of this disclosure embodiment, and the multiple devices will interact with each other to complete the method described.

[0083] It should be noted that the above description describes some embodiments of this disclosure. Other embodiments are within the scope of the appended claims. In some cases, it should be understood that the sequence number of each step in the above embodiments does not imply the order of execution; the execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention. The actions or steps recorded in the claims can be performed in a different order than that in the above embodiments and can still achieve the desired result. In addition, the processes depicted in the drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0084] Example 2 Based on the same inventive concept, corresponding to any of the above embodiments, this disclosure also provides a hybrid anti-sway control system suitable for gantry cranes, including an equivalent modeling module, a model linearization decoupling module, a feedforward controller design module, a feedback controller design module, and a hybrid control execution module arranged in sequence; the five modules are connected sequentially along the control flow to jointly complete the entire process from model construction to anti-sway control output.

[0085] The equivalent modeling module is used to establish a nonlinear equivalent dynamic model of a gantry crane based on the principle of equivalent force / torque, determining the coupled dynamic relationship between the drive input and the swing of the load. The module has a built-in standardized multi-rigid-body modeling framework that can automatically simplify the rigid body of the wire rope and the load according to the structural parameters of different crane models, outputting a nonlinear dynamic model in a unified format, providing a reliable model foundation for subsequent processing.

[0086] The model linearization and decoupling module is used to linearize the nonlinear dynamic model at the equilibrium point, decoupling it to obtain linear transfer functions in the amplitude and rotation directions. The module incorporates an automatic equilibrium point selection algorithm and Taylor expansion linearization logic, which automatically eliminates higher-order infinitesimal terms and motion-cross-coupling terms, outputting two independent second-order oscillatory element models that directly adapt to the design input requirements of subsequent controllers.

[0087] The feedforward controller design module is used to solve for oscillation characteristic parameters based on a linear oscillation model and design a ZVD input shaping feedforward controller to perform shaping preprocessing on the drive input signal. The module has built-in oscillation parameter solving unit, shaper parameter calculation unit, and pulse convolution operation unit, which can automatically generate ZVD shapers for corresponding operating conditions. It also supports switching between multiple input shapers such as ZV and EI to adapt to the robustness requirements of different scenarios.

[0088] Feedback controller design module for designing based on linear oscillation model A loop-shaping feedback controller achieves robust stabilization under initial swing angle, parameter perturbations, and external disturbances. The module incorporates a weighted function configuration unit, a frequency domain shaping unit, and... The robust stabilizing solver unit can flexibly adjust the weighting parameters according to performance requirements, automatically solve the central controller and generate a complete feedback control law, and also supports the expansion and access of other robust control algorithms.

[0089] The hybrid control execution module combines a feedforward controller and a feedback controller to construct a feedforward-feedback hybrid control system. The output control signal drives the crane's luffing and slewing mechanisms to perform anti-sway control. The module supports switching between parallel and series hybrid architectures, and can acquire sway angle feedback signals in real time, superimposing them with feedforward shaping signals before outputting them to the drive mechanism. It also has a built-in data storage and performance monitoring unit that records the entire control process data for subsequent model optimization and performance iteration.

[0090] The system described above is used to implement the corresponding hybrid anti-sway control method for gantry cranes in any of the foregoing embodiments, and has the beneficial effects of the corresponding method embodiments, which will not be repeated here.

[0091] It should be noted that the hybrid anti-sway control system applicable to gantry cranes described above is embodied in the form of functional units. The term "module" here can be implemented in software and / or hardware, without specific limitations.

[0092] For example, a "module" can be a software program, a hardware circuit, or a combination of both that implements the above functions. The hardware circuit may include an application-specific integrated circuit (ASIC), electronic circuitry, a processor (e.g., a shared processor, a proprietary processor, or a group processor) and memory for executing one or more software or firmware programs, integrated logic circuitry, and / or other suitable components that support the described functions.

[0093] Example 3 Based on the same inventive concept, corresponding to the methods of any of the above embodiments, this disclosure also provides a non-transitory computer-readable storage medium storing computer instructions for causing the computer to execute the hybrid anti-sway control method for gantry cranes as described in any of the above embodiments.

[0094] The computer-readable medium of this embodiment includes permanent and non-permanent, removable and non-removable media, and information storage can be implemented by any method or technology. Information can be computer-readable instructions, data structures, program modules, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic magnetic disk storage or other magnetic storage devices, or any other non-transfer medium that can be used to store information accessible by a computing device.

[0095] The computer instructions stored in the storage medium of the above embodiments are used to cause the computer to execute the hybrid anti-sway control method for gantry cranes as described in any of the above embodiments, and have the beneficial effects of the corresponding method embodiments, which will not be repeated here.

[0096] Those skilled in the art should understand that the discussion of any of the above embodiments is merely exemplary and is not intended to imply that the scope of this disclosure (including the claims) is limited to these examples; within the framework of this disclosure, the technical features of the above embodiments or different embodiments can also be combined, the steps can be implemented in any order, and there are many other variations of different aspects of the embodiments of this disclosure as described above, which are not provided in detail for the sake of brevity.

[0097] Additionally, to simplify the description and discussion, and to avoid obscuring the embodiments of this disclosure, the provided drawings may or may not show well-known power / ground connections to integrated circuit (IC) chips and other components. Furthermore, the apparatus may be shown in block diagram form to avoid obscuring the embodiments of this disclosure, and this also takes into account the fact that the details of implementation of these block diagram apparatuses are highly dependent on the platform on which the embodiments of this disclosure will be implemented (i.e., these details should be fully understood by those skilled in the art). While specific details (e.g., circuitry) have been set forth to describe exemplary embodiments of this disclosure, it will be apparent to those skilled in the art that the embodiments of this disclosure may be implemented without these specific details or with variations thereof. Therefore, these descriptions should be considered illustrative rather than restrictive.

[0098] Although this disclosure has been described in conjunction with specific embodiments thereof, many substitutions, modifications, and variations of these embodiments will be apparent to those skilled in the art from the foregoing description. For example, other memory architectures (e.g., dynamic RAM (DRAM)) may be used with the embodiments discussed.

[0099] Therefore, the units of the various examples described in the embodiments of this application can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0100] This disclosure is intended to cover all such substitutions, modifications, and variations that fall within the broad scope of the appended claims. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this disclosure should be included within the scope of protection of this disclosure.

Claims

1. A hybrid anti-sway control method applicable to gantry cranes, characterized in that, The method includes the following steps: S1. Based on the principle of equivalent force / torque, establish an equivalent dynamic model of the gantry crane. The wire rope is equivalent to a rigid rod with uniform mass, and the load is equivalent to a point mass. The driving torque of the luffing mechanism and the driving torque of the slewing mechanism are used as the model inputs, and the spatial swing angle of the load is used as the generalized coordinate to establish the dynamic relationship between the driving input and the swing of the load. S2. Based on the equivalent dynamic model, linearization is performed near the equilibrium point corresponding to the vertically stable state of the suspended load to obtain the linear swing model in the amplitude direction and the linear swing model in the rotation direction for controller design. S3. Based on the linear oscillation models of the amplitude direction and rotation direction obtained in S2, the oscillation characteristic parameters of the two directions are determined respectively. Based on the oscillation characteristic parameters, a ZVD input shaping feedforward controller is designed, and the ZVD input shaping feedforward controller is used to preprocess the drive input signal to suppress the load residual vibration generated under the condition of no initial oscillation. S4. Based on the linear oscillation model of the amplitude direction and the rotation direction, design... Loop forming feedback controller is used to suppress load sway caused by initial swing angle, model parameter changes and external disturbances; S5. Connect the ZVD input shaping feedforward controller designed in step S3 with the controller designed in step S4. By combining loop-forming feedback controllers, a hybrid feedforward and feedback control system is constructed. Through the synergistic effect of feedforward elimination of residual vibration and feedback robust stabilization, load anti-sway control of gantry cranes is achieved.

2. The method according to claim 1, characterized in that, Step S1 specifically includes the following steps: S11. Based on the principle of equivalent force / torque, the dynamic modeling boundary and constraint conditions of the gantry crane are defined, and the basic architecture of the multi-rigid-body underactuated coupling model is built. S12. The oscillating system composed of the wire rope and the suspended weight is simplified into a rigid body equivalent structure to obtain a simple pendulum form. S13. The driving force of the amplitude change and rotation motion is converted into an equivalent force / torque input. Combined with the generalized coordinates of the swing angle in the suspended weight space, the coupled dynamic mapping relationship between the driving input and the swing response is derived.

3. The method according to claim 1, characterized in that, In step S2, the decoupled amplitude motion transfer function and rotational motion transfer function are respectively: in, For the weight of the load, For the quality of the wire rope, For the length of the rope, For the amplitude, This is the acceleration due to gravity.

4. The method according to claim 1, characterized in that, Step S3 specifically includes the following steps: S31. Solving the natural frequency of a system based on a linear transfer function With damping ratio The damped natural frequency of the system is obtained. And calculate the half-oscillation period. The calculation formula is: S32. Deriving Shaper Parameters Based on System Damping Ratio The calculation formula is: S33, Based on parameters With half-oscillation period Construct a ZVD input shaper, which consists of three sequentially delayed pulses with amplitudes as follows: The time delays corresponding to the three pulses are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 10, 19 ... , ; The transfer function form of the S34 and ZVD input shapers is as follows: 。 5. The method according to claim 1, characterized in that, Step S4 specifically includes the following steps: S41, using the decoupled linear transfer function As the controlled object, the pre-compensator and post-compensator are selected as weighting functions; the pre-compensator is: The rear compensator is: S42. Frequency shaping of the open-loop system is achieved by using a front compensator and a rear compensator to obtain the shaped system: The singular value curves of the formed system shall meet the preset frequency domain design specifications. S43, Solve The standard robust stabilization problem is addressed by a central controller. It consists of a front compensator, a central controller, and a rear compensator cascaded together. The loop-forming feedback controller has the following expression: 。 6. The method according to claim 1, characterized in that, Step S5 is as follows: ZVD input shaping feedforward controller and The loop-forming feedback controller is connected to form a hybrid feedforward and feedback control system. The feedforward controller acts on the forward path of the system to shape the reference input signal and eliminate residual vibrations under conditions without initial oscillation. The feedback controller acts on the closed-loop feedback path of the system, generates an adjustment amount based on the load swing angle feedback signal, and suppresses the swing caused by the initial swing angle, model parameter changes and external disturbances. The hybrid control system outputs the final control quantity to the luffing mechanism and the slewing mechanism to perform load anti-sway control.

7. The method according to claim 1, characterized in that, For the two decoupled dimensions of amplitude motion and rotational motion, the system's natural frequency and damping ratio for each dimension are calculated independently, and ZVD input shaping feedforward controllers for each dimension are designed accordingly. The loop forming feedback controller enables independent closed-loop control of the swing angle in the amplitude direction and the swing angle in the rotation direction.

8. The method according to claim 1, characterized in that, The loop forming feedback controller is designed to robustly stabilize model parameter perturbations caused by changes in rope length and load mass, as well as external disturbances caused by external wind disturbances. The controller is solved based on the coprime factor uncertainty model to ensure the stable operation of the closed-loop system under parameter perturbations and external disturbances.

9. A hybrid anti-sway control system suitable for gantry cranes, said system being used to implement the method according to any one of claims 1-8, characterized in that, The equivalent modeling module is used to establish a nonlinear dynamic model of the gantry crane based on the principle of equivalent force / torque, and to determine the coupled dynamic relationship between the drive input and the swing of the load. The model linearization and decoupling module is used to linearize the nonlinear dynamic model at the equilibrium point and decouple it to obtain the linear transfer function of the amplitude direction and the rotation direction. The feedforward controller design module is used to solve the oscillation characteristic parameters based on the linear transfer function, calculate the pulse amplitude and time delay of the ZVD input shaper, and design the ZVD input shaping feedforward controller. The feedback controller design module is used to select a weighted compensator to perform loop shaping on the open-loop system, and to obtain the solution after solving the central controller. Loop shaping feedback controller; The hybrid control execution module is used to combine the feedforward controller and the feedback controller to build a feedforward-feedback hybrid control system, and output the control quantity to drive the crane's luffing and slewing mechanisms to perform anti-sway control.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed, implements the method as described in any one of claims 1 to 8.

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