A method of anti-swing control of a tower crane and related apparatus

Abstract

The application discloses a tower crane sway control method and related device, the application is based on arbitrary Lagrange-Euler description and absolute node coordinate method constructs tower crane multi-flexible body system high-fidelity dynamic model, can consider tower body, boom metal structure deformation and hoisting, amplitude mechanism action dynamic coupling effect, compared with the traditional simplified model, more and actual physical system adapts, will not make the sway performance greatly drops, adopts S-shaped sine acceleration smoothing strategy, generates the smooth speed reference instruction of amplitude trolley, can solve the problem that the tower crane operation instruction easily causes transient impact, and through the convolution of the smooth speed reference instruction and the pulse sequence of the input shaper, generates the sway control instruction, realizes the efficient and accurate sway of the tower crane.

Description

Technical Field

[0001] This invention relates to a method and device for anti-sway control of a tower crane, belonging to the field of intelligent control technology for tower cranes. Background Technology

[0002] Tower cranes, as core lifting equipment in construction, logistics handling, and large equipment installation, undertake heavy tasks of vertical material lifting and horizontal transportation. Due to the typical high flexibility and underactuated characteristics of tower crane systems, when the trolley luffs or the boom rotates, the load suspended at the end of the flexible wire rope is prone to significant spatial swaying due to inertia and external gusts of wind. This swaying not only increases the lifting cycle and operational difficulty but can also lead to violent fluctuations in sling tension, inducing elastic vibrations in the tower body and boom, and in severe cases, even causing major safety accidents such as load instability or overturning of the entire machine. Therefore, achieving efficient and high-precision load anti-sway control is crucial to improving the operational efficiency and safety of tower cranes.

[0003] Current research on anti-sway control for tower cranes has formed a system encompassing open-loop shaping, closed-loop robust control, and intelligent adaptive control. Among these, input shaping control, as a classic open-loop algorithm, has strong practical value in engineering due to its simple structure, lack of need for additional feedback sensors, and independence from complex computing power. However, existing input shaping and its composite control strategies still face the following bottlenecks in practical engineering applications: 1. Most existing control algorithms are based on highly simplified dynamic models, typically simplifying the slings into massless rigid links or simple springs, and treating the load as a concentrated mass point. This simplified model exhibits significant model mismatch with the actual physical system, resulting in a substantial decrease in the controller's anti-sway performance; 2. Traditional input shapers often lack consideration for acceleration smoothness when processing speed switching commands. Directly applying control commands containing high-order harmonics can cause strong transient mechanical impacts on the flexible metal structure of the tower crane, accelerating component fatigue. Summary of the Invention

[0004] This invention provides a method and related device for controlling the swaying of a tower crane, which solves the problems disclosed in the background art.

[0005] According to one aspect of this application, a method for controlling the swaying of a tower crane is provided, comprising:

[0006] Based on the target speed of the luffing trolley, the time consumed during acceleration and deceleration, and the time consumed during constant speed, an S-shaped sinusoidal acceleration smoothing strategy is adopted to generate a smooth speed reference command for the luffing trolley.

[0007] The smooth speed reference command is convolved with the pulse sequence of the pre-built input shaper to generate the anti-sway control command. The input shaper is constructed based on the dynamic feature parameters of the tower crane multi-flexible body system. The dynamic feature parameters are extracted from the high-fidelity dynamic model of the tower crane multi-flexible body system. The high-fidelity dynamic model of the tower crane multi-flexible body system is constructed based on arbitrary Lagrange-Euler description and absolute node coordinate method.

[0008] The anti-sway control command is sent to the tower crane drive system to perform load anti-sway control under the condition of constant wire rope length.

[0009] Furthermore, the formula for generating the smooth speed reference command for the luffing trolley is as follows:

[0010] Acceleration phase 0≤t≤t1:

[0011] ;

[0012] In the formula, t1=T acc To accelerate to the end time, the time taken for both the acceleration and deceleration phases is T. acc V max Let v(t) be the target speed, v(t) be the smooth speed reference command of the variable amplitude trolley at time t, and ω be the speed reference value. d The damped natural frequency of the multi-flexible body system of the tower crane;

[0013] During the uniform velocity phase, t1≤t <t2:

[0014] v(t) = V max ;

[0015] In the formula, t2=T acc +T cruise At the start of deceleration, T cruise This refers to the time consumed during the constant speed phase;

[0016] During the deceleration phase, t2≤t <t3:

[0017] ;

[0018] In the formula, t3 = 2T acc +T cruise The moment when the movement stops. Relative time;

[0019] Stopping phase t≥t3:

[0020] v(t)=0.

[0021] Furthermore, the high-fidelity dynamic model of the tower crane multi-flexible body system is as follows:

[0022] ;

[0023] In the formula, M T Let M be the mass matrix of the tower crane. c For the unit mass matrix of the hoisting wire rope, e T and e c Let Q be the generalized coordinate vector of the tower crane and the wire rope, respectively. The two superscripts indicate the second derivative with respect to time. ela For the generalized elastic force vector of the multi-flexible body system of the tower crane, Q is the vector of the additional inertial force of the hoisting wire rope. ext Let λ be the generalized external force vector of the tower crane multi-body system, λ be the Lagrange multiplier vector, and C be the constraint equations of the tower crane multi-body system. e The Jacobian matrix is ​​obtained by differentiating C with respect to the generalized coordinates.

[0024] Furthermore, the input shaper is a ZV shaper, and the pulse sequence of the ZV shaper is:

[0025] ;

[0026] ;

[0027] ;

[0028] In the formula, I(s) is the transfer function of the shaper in the complex frequency domain, n is the number of pulses, and A i and t i Here, represents the gain coefficient and trigger time of the i-th pulse, respectively, and s is the complex frequency domain parameter. ,parameter , ω d The damped natural frequency of the multi-flexible body system of the tower crane. ω is the damping ratio of the multi-flexible body system of the tower crane. n Let be the undamped natural frequency of the multi-flexible-body system of the tower crane, t1=0 be the moment when the pulse excitation is applied, and A1 and A2 be the amplitudes of the pulse excitation at times t1 and t2, respectively. This is the amplitude ratio function of the residual oscillation of the multi-flexible body system of a tower crane.

[0029] Furthermore, the input shaper is a ZVD shaper, and the pulse sequence of the ZVD shaper is:

[0030] ;

[0031] ;

[0032] ;

[0033] In the formula, I(s) is the transfer function of the shaper in the complex frequency domain, n is the number of pulses, and A i and t i Here, represents the gain coefficient and trigger time of the i-th pulse, respectively, and s is the complex frequency domain parameter. ,parameter , ω d The damped natural frequency of the multi-flexible body system of the tower crane. ω is the damping ratio of the multi-flexible body system of the tower crane. n Let be the undamped natural frequency of the multi-flexible-body system of the tower crane, t1=0 be the moment when the pulse excitation is applied, and A1, A2, and A3 be the pulse excitation amplitudes at times t1, t2, and t3, respectively. This is the amplitude ratio function of the residual oscillation of the multi-flexible body system of a tower crane.

[0034] Furthermore, the input shaper is an EI shaper, and the pulse sequence of the EI shaper is:

[0035] ;

[0036] ;

[0037] ;

[0038] In the formula, I(s) is the transfer function of the shaper in the complex frequency domain, n is the number of pulses, and A i and t i These represent the gain coefficient and trigger time of the i-th pulse, respectively, where s is the complex frequency domain, and V... tol For the maximum allowable swing amplitude, the parameter , ω d Let L be the damped natural frequency of the multi-flexible-body system of the tower crane, L be the length of the pendulum model, and g be the acceleration due to gravity. ω is the damping ratio of the multi-flexible body system of the tower crane. n Let be the undamped natural frequency of the multi-flexible-body system of the tower crane, t1=0 be the moment when the pulse excitation is applied, and A1 and A2 be the amplitudes of the pulse excitation at times t1 and t2, respectively. Let ω1 and ω2 be the normalized frequency range boundaries corresponding to the intersection points of the EI shaper sensitivity curve and the allowable residual oscillation boundary, respectively.

[0039] According to another aspect of this application, a sway control device for a tower crane is provided, comprising:

[0040] The sliding speed reference command generation module generates a smooth speed reference command for the luffing trolley based on the target speed of the luffing trolley, the time consumed during acceleration and deceleration, and the time consumed during constant speed. It adopts an S-shaped sinusoidal acceleration smoothing strategy to generate a smooth speed reference command for the luffing trolley.

[0041] The anti-sway control command generation module convolves the smooth speed reference command with the pulse sequence of the pre-built input shaper to generate the anti-sway control command. The input shaper is constructed based on the dynamic feature parameters of the tower crane multi-flexible body system. The dynamic feature parameters are extracted from the high-fidelity dynamic model of the tower crane multi-flexible body system. The high-fidelity dynamic model of the tower crane multi-flexible body system is constructed based on arbitrary Lagrange-Euler description and absolute node coordinate method.

[0042] The sending module sends anti-sway control commands to the tower crane drive system to perform load anti-sway control under the condition of constant wire rope length.

[0043] According to another aspect of this application, a computer-readable storage medium is provided that stores one or more programs, the one or more programs including instructions that, when executed by a computing device, cause the computing device to perform a sway control method for a tower crane.

[0044] According to another aspect of this application, a computer device is provided, including one or more processors and one or more memories, one or more programs stored in the one or more memories and configured to be executed by the one or more processors, the one or more programs including instructions for performing a sway control method for a tower crane.

[0045] The beneficial effects achieved by this invention are as follows: This invention constructs a high-fidelity dynamic model of a tower crane multi-flexible body system based on arbitrary Lagrange-Euler description and absolute nodal coordinate method. It can consider the dynamic coupling effect between the deformation of the tower body and boom metal structure and the actions of the hoisting and luffing mechanisms. Compared with the traditional simplified model, it is more compatible with the actual physical system and will not significantly reduce the anti-sway performance. It adopts an S-shaped sinusoidal acceleration smoothing strategy to generate smooth speed reference commands for the luffing trolley, which can solve the problem that tower crane operation commands are prone to transient impacts. Furthermore, by convolving the smooth speed reference commands with the pulse sequence input to the shaper, anti-sway control commands are generated, realizing efficient and precise anti-sway of the tower crane. Attached Figure Description

[0046] Figure 1 A flowchart of the anti-sway control method for tower cranes;

[0047] Figure 2 This is a schematic diagram of a wire rope unit;

[0048] Figure 3A schematic diagram for calculating the position of the luffing trolley;

[0049] Figure 4 A schematic diagram of the tower crane structure and the constraints of the hoisting wire rope;

[0050] Figure 5 The speed curve of the variable amplitude trolley;

[0051] Figure 6 Comparison curves of the swing response;

[0052] Figure 7 This is a comparison curve of the displacement of the variable amplitude trolley;

[0053] Figure 8 A comparison diagram of tower structure configurations at the moment the luffing trolley reaches its destination.

[0054] Figure 9 This is a block diagram of the anti-sway control device for a tower crane. Detailed Implementation

[0055] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit this application or its application or use. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0056] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of this application.

[0057] At the same time, it should be understood that, for ease of description, the dimensions of the various parts shown in the accompanying drawings are not drawn according to actual scale.

[0058] Techniques, methods, and equipment known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and equipment should be considered part of the specification.

[0059] In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values.

[0060] It should be noted that similar symbols and letters in the accompanying drawings represent similar items; therefore, once an item is defined in one accompanying drawing, it does not need to be discussed further in subsequent accompanying drawings.

[0061] This application provides a method for anti-sway control of a tower crane based on a high-fidelity multibody model. This anti-sway control method can be executed by an anti-sway control device, which can be a terminal device or a controller. For ease of explanation, the following embodiments will be described as being executed by an anti-sway control device.

[0062] See Figure 1 , Figure 1 This is a flowchart of a sway control method for a tower crane according to an embodiment of this application. The sway control method can be executed by a sway control device and may include at least the following steps:

[0063] Step 1: Based on the target speed of the luffing trolley, the time consumed during acceleration and deceleration, and the time consumed during constant speed, an S-shaped sinusoidal acceleration smoothing strategy is adopted to generate a smooth speed reference command for the luffing trolley.

[0064] It should be noted that the target speed of the luffing trolley can be set to V. max The time consumed by both the acceleration and deceleration phases is T. acc The time taken during the uniform velocity phase is T. cruise .

[0065] The key timing nodes for instruction execution can be defined as follows:

[0066] t1=T acc To expedite the end time;

[0067] t2=T acc +T cruise This is the moment when deceleration begins;

[0068] t3=2T acc +T cruise The moment when the motion stops.

[0069] The equations of motion for each extreme point are as follows:

[0070] 1. Acceleration phase: 0 ≤ t ≤ t1. During this phase, the speed of the luffing trolley increases from 0 to V. max The corresponding smooth speed reference command and displacement can be expressed as:

[0071] ;

[0072] ;

[0073] In the formula, v(t) is the smooth speed reference command of the luffing trolley at time t, x(t) is the displacement of the luffing trolley at time t, and ω d The damped natural frequency of the multi-flexible body system of the tower crane. , ω nis the undamped natural inherent frequency of the tower crane multi-flexible-body system, is the damping ratio of the tower crane multi-flexible-body system, in the two ω d formulas, the former is the definition formula of a general second-order oscillatory system, and the latter is a special case of the former, that is, when the damping is 0, the two are numerically consistent.

[0074] 2. Constant speed phase t1≤t<t2, the luffing trolley accelerates to reach V max and keeps running at a constant speed, assuming that the displacement at the end of the acceleration section is , then the corresponding smooth speed reference command and displacement in this phase can be expressed as:

[0075] ;

[0076] .

[0077] 3. Deceleration phase t2≤t<t3, in this phase, the luffing trolley moves from V max decays smoothly to zero, in order to ensure the stability during parking, a relative time is introduced , the corresponding smooth speed reference command and displacement in this phase can be expressed as:

[0078] ;

[0079] .

[0080] 4. Stop phase t≥t3, in this phase, the luffing trolley decelerates to a stop, the speed is 0, and the displacement remains at the final target position, the corresponding smooth speed reference command and displacement in this phase can be expressed as:

[0081] ;

[0082] .

[0083] Here, an S-shaped sinusoidal acceleration smoothing strategy is adopted to generate the smooth speed reference command of the luffing trolley, which can solve the problem that the operation command of the tower crane is prone to cause transient impact, thereby reducing component fatigue.

[0084] Step 2: perform convolution processing on the smooth speed reference command and the pre-constructed pulse sequence of the input shaper to generate an anti-swing control command; wherein the input shaper is constructed according to the dynamic characteristic parameters of the tower crane multi-flexible-body system, the dynamic characteristic parameters are extracted from the high-fidelity dynamic model of the tower crane multi-flexible-body system, and the high-fidelity dynamic model of the tower crane multi-flexible-body system is constructed based on the Arbitrary Lagrange-Euler (ALE) description and the Absolute Nodal Coordinate Formulation (ANCF).

[0085] It should be noted that the node coordinates of the ALE-ANCF steel wire rope element are defined as follows:

[0086] ;

[0087] wherein, the superscript T denotes transposition, e is the coordinate vector of the steel wire rope element, see Figure 2 , the two nodes in the steel wire rope element (i.e., node 1 and node 2) are numbered with subscripts 1 and 2, r1 and r2 are respectively the spatial position vectors of node 1 and node 2, r 1,x and r 2,x are respectively the spatial gradient vectors of node 1 and node 2, s1 and s2 are respectively the material coordinates of node 1 and node 2.

[0088] The shape function of the ALE-ANCF steel wire rope element has the expression:

[0089] ;

[0090] wherein, I 3×3 and 0 3×1 are respectively a 3-row 3-column identity matrix and a 3-row 1-column zero vector, S F1 ~S F4 are shape function parameters, , is the dimensionless material coordinate, x is the coordinate of any material point (all points between 0<x<l, not nodes) on the element axis of the steel wire rope element in the undeformed state, all points between 0<x<l, not nodes, l is the element length defined by the material coordinates of the nodes, and l=s2-s1.

[0091] The global position r of any point of the ALE-ANCF steel wire rope element is:

[0092] .

[0093] The shape function matrix related to velocity is:

[0094] ;

[0095] wherein, s v is the shape function matrix related to velocity, and s is the material coordinate;

[0096] The expression of the element mass matrix can be as follows:

[0097] ;

[0098] wherein, ρ and A are respectively the density and cross-sectional area of the element material.

[0099] The dynamic equation of the hoisting steel wire rope can be as follows:

[0100] ;

[0101] In the formula, M c For the unit mass matrix of the hoisting wire rope, e c Let be the generalized coordinate vector of the wire rope, with two superscripts indicating the second derivative with respect to time. Let be the generalized elastic force vector of the wire rope. For the wire rope, a generalized external force vector is added. F is the vector of external force distributed per unit length on the wire rope element, or simply external force. Let be the additional inertial force vector of the hoisting wire rope, within the framework of any Lagrange-Euler description. r d It is a second-order vector related to velocity.

[0102] The metal structure model of the tower crane, i.e., the tower crane itself, is constructed using beam elements from the traditional finite element method, including the tower body and the jib. To accurately describe the luffing motion of the tower crane, a non-generalized coordinate system is introduced to define the real-time spatial position of the luffing trolley on the jib. See [link to relevant documentation]. Figure 3 The position vector r of the variable amplitude trolley P Defined by interpolation of the position coordinates of the crane boom beam element:

[0103] ;

[0104] In the formula, l beam r is the length of the crane boom beam unit. a and r b These are the coordinates of the two end nodes of the crane boom beam unit, which will change over time due to structural deformation.

[0105] Based on this, by applying kinematic constraints, the constraint equations corresponding to the coupling connection between the hoisting wire rope and the tower crane can be expressed as:

[0106] ;

[0107] In the formula, L(t) is a function of the distance the trolley travels on the boom versus time. The trolley and the beginning of the wire rope are physically aligned. C is the constraint equation of the tower crane's multi-flexible-body system. (See [link to relevant documentation]). Figure 4 The position vector of the end point of the hoisting wire rope is r. Q In the physically connected state, its position vector r relative to the luffing trolley P They completely overlap in three-dimensional space.

[0108] After establishing the constraint equations, the high-fidelity dynamic model of the tower crane multi-flexible body system can be:

[0109] ;

[0110] In the formula, M T Let e ​​be the mass matrix of the tower crane. T Let Q be the generalized coordinate vector of the tower crane. ela Let Q be the generalized elastic force vector of the multi-flexible-body system of the tower crane. ext Let C be the generalized external force vector of the tower crane's multi-flexible-body system, λ be the Lagrange multiplier vector, and C be the generalized external force vector of the multiplier system. e For the Jacobian matrix, through C( The derivative of the generalized coordinates is obtained.

[0111] It should be noted that the Newmark scheme can be used to solve the above dynamic equations. By iteratively solving the system dynamic equations, the displacement, velocity, and acceleration of the wire rope element nodes at each moment can be obtained, thus yielding the system's full-process response. Flexible multibody systems simultaneously exhibit large-scale rigid body motion and structural elastic vibration. Newmark is a second-order precision time-domain integration scheme; with proper parameter selection, high accuracy in displacement and velocity calculations within a time step can be achieved. Compared to first-order algorithms such as forward Euler, it exhibits less simulation distortion for vibration and oscillation under the same time step, and can more accurately capture the coupling effect of high-frequency elastic vibration of the wire rope and low-frequency oscillation of the pendulum.

[0112] It should be noted that the dynamic feature parameter is ω n and , You can choose the appropriate one; in some cases, you can assume an undamped situation.

[0113] The above establishes a high-fidelity dynamic model of a tower crane multi-flexible body system that can consider the dynamic coupling effect between the deformation of the tower body and boom metal structure and the actions of the hoisting and luffing mechanisms. The hoisting mechanism wire rope is discretized by cable elements based on arbitrary Euler-Lagrange description of absolute node coordinates. By establishing time-varying coupling constraint equations between the spatial position coordinates of the wire rope root node and the finite element node of the boom structure, the action of the luffing mechanism is described.

[0114] It should be noted that the input shaper can be assumed to be an input shaper containing n pulses, and its mathematical model can be expressed by a time delay system as follows:

[0115] ;

[0116] In the formula, I(s) is the transfer function of the shaper in the complex frequency domain, n is the number of pulses, and A i and t i and are the gain coefficient and trigger time of the i-th pulse, respectively, and s is the complex frequency domain.

[0117] When the input shaper is applied to the above model, according to the superposition principle of linear systems, its overall time-domain response is the algebraic sum of the individual discrete impulse responses. After the last impulse is executed, the amplitude ratio of the residual oscillation of the tower crane's multi-flexible-body system, i.e., the ratio of the residual oscillation amplitude after shaping to that before shaping, can be derived from trigonometric identities as a function of frequency and damping, i.e., the residual vibration ratio function. To completely eliminate the residual sway of the hook, this residual oscillation amplitude function must converge to zero.

[0118] The transfer function G(s) of a typical second-order oscillating system in the complex frequency domain can be defined as:

[0119] ;

[0120] In the formula, ω is the damping ratio of the multi-flexible body system of the tower crane. n The undamped natural frequency of the multi-flexible body system of the tower crane.

[0121] When a pulse excitation of amplitude A is applied to the above second-order system at a single time t1, the transient time-domain variation law of the tower crane multi-flexible body system is expressed as follows:

[0122] ;

[0123] In the formula, y(t) is the transient vibration output of the second-order vibration system of the tower crane multi-flexible body at time t under pulse excitation.

[0124] Since the extracted dominant mode exhibits linear system characteristics, based on the superposition principle of dynamic responses, when n pulse sequences are applied sequentially to a second-order system, the total system time-domain output is represented as the algebraic sum of the sub-responses:

[0125] .

[0126] To quantify the effect of oscillation suppression, a numerical evaluation of the residual state of the tower crane's multi-flexible-body system after the pulse sequence is completed is necessary. By introducing trigonometric identity transformations, expanding the sine term in the above equation, and separating the variables, the final residual oscillation envelope amplitude A under actual working conditions can be derived. amp :

[0127] ;

[0128] In the formula, the relevant substitution coefficients , t end This refers to the observation time used to evaluate residual oscillations after the last pulse excitation in the pulse sequence is applied (i.e., the analysis time after the entire pulse sequence has been executed).

[0129] From a physics perspective, to completely eliminate hook sway at the end of the command, the multi-flexible body system of the tower crane needs to be in t end There must be no residual oscillations afterward. This requires that the sine and cosine terms in the amplitude expression be simultaneously zero, from which the steady-state zero-amplitude equilibrium equations of the tower crane multi-flexible-body system can be derived:

[0130] ;

[0131] B i Substituting the values, we obtain the simplified system of equations:

[0132] .

[0133] To establish a unified evaluation index, the normalized oscillation amplitude is usually compared with the original step response amplitude without shaping, thereby deriving the residual vibration ratio function:

[0134] ;

[0135] In the formula, The residual vibration ratio function has coefficients. ,coefficient .

[0136] It should be noted that in some embodiments, the input shaper may be a ZV shaper. As the simplest feedforward compensation scheme, the ZV shaper consists of two discrete pulses. Its core design lies in the physical response excited by the second pulse to accurately counteract the sway of the tower crane multi-flexible body system caused by the first pulse.

[0137] The pulse sequence of the ZV shaper is the I(s) formula mentioned above, and its constraint equation is:

[0138] ;

[0139] The spatiotemporal distribution pattern of the two-pulse sequence of the ZV shaper is as follows:

[0140] ;

[0141] In the formula, the parameters ,parameter , ω d Let t1 = 0 and t2 = T / 2 be the damped natural frequency of the multi-flexible body system of the tower crane, and let A1 and A2 be the pulse excitation amplitudes at times t1 and t2, respectively.

[0142] It should be noted that in some embodiments, the input shaper can be a ZVD shaper, that is, based on the ZV shaper, an additional robust constraint condition is added to obtain the ZVD shaper, which contains 3 pulses, the pulse sequence of which is the I(s) formula mentioned above, and its constraint equation is:

[0143] ;

[0144] The spatiotemporal distribution pattern of the three-pulse sequence is as follows:

[0145] .

[0146] It should be noted that in some embodiments, the input shaper may be an EI shaper, and the pulse sequence of the EI shaper is the I(s) formula mentioned above.

[0147] ZVD shapers are strictly required to operate at the nominal natural frequency (i.e., ω) of the multi-flexible body system of tower cranes. n The residual swing at the center frequency must be absolutely zero, while the EI shaper employs a strategy of trading local minor overshoot for global wideband robustness, that is, actively relaxing the zero-position limit at the center frequency, allowing the tower crane multi-flexible body system to achieve a zero-position at ω. n There exists a controlled, small residual amplitude within the engineering allowable extreme range, typically set as the maximum permissible sway amplitude V of the tower crane's multi-flexible-body system. tol =5%.

[0148] To maintain overall stability while relaxing the central constraints, the EI shaper shifts the absolutely zero-oscillation operating point to both sides of the nominal frequency by adding a pair of conjugate zeros near the poles that need to be canceled. Specifically, it forces residual oscillations to zero at ω1, slightly lower than the model's nominal frequency, and ω2, slightly higher. Simultaneously, this shaper additionally constrains the operation at ω... n The residual oscillation at point 0 has a differential of zero, and its constraint equation can be:

[0149] ;

[0150] In the formula, A1, A2 and A3 are the pulse excitation amplitudes at times t1, t2 and t3, respectively, and t1=0, t2=T / 2 and t3=T are the times when the pulse excitation is applied.

[0151] The spatiotemporal distribution pattern of the three-pulse sequence is as follows:

[0152] ;

[0153] According to the classical pendulum theory, neglecting air resistance and the slight elastic elongation of the wire rope, the theoretical natural period and natural circular frequency of the small oscillation of the tower crane's multi-flexible-body system are calculated by the following two formulas:

[0154] ;

[0155] ;

[0156] In the formula, ω d Let L be the damped natural frequency of the multi-flexible body system of the tower crane, L be the length of the pendulum model, and g be the acceleration due to gravity.

[0157] Calculated based on system parameters and ω n By substituting the distribution law formula of the input shaper, its pulse sequence can be solved.

[0158] In the time domain, the smoothed velocity reference command is convolved with the pulse sequence to obtain the final anti-sway control command. The calculation formula is as follows:

[0159] ;

[0160] In the formula, v cmd (t) represents the de-swing control command at time t, v ref (t) represents the smooth speed reference command at time t.

[0161] The above method generates anti-sway control commands by convolving the smooth speed reference command with the pulse sequence of the input shaper, thereby achieving efficient and precise anti-sway control for tower cranes.

[0162] Step 3: Send the anti-sway control command to the tower crane drive system to perform load anti-sway control under the condition of constant wire rope length.

[0163] To verify the above method, see Figure 5 The target speed of the luffing trolley is set to 1 meter per second, and the acceleration and deceleration time is 3 seconds. Since the delay of the input shaper is a single cycle of the tower crane's multi-flexible body system, if the uniform motion time of the luffing trolley does not exceed the delay of the input shaper, it will start to decelerate before reaching the target speed. Therefore, the uniform motion time of the trolley is set to 18.5 seconds.

[0164] To systematically evaluate the differences in anti-sway effects of different input shapers, comparative simulations were conducted using the three input shapers mentioned above, based on the smoothing speed reference command. The horizontal displacement difference between the luffing trolley and the suspended load was used to represent the sway response of the tower crane's multi-flexible-body system. Figure 6 As shown, the tower crane multi-flexible body system, which only has speed smoothing processing without an input shaper, still exhibits severe steady-state swaying with an amplitude of approximately 2.5 meters after the luffing trolley reaches the target position. Furthermore, Figure 8The demonstration showed the tower crane configurations under different control strategies when the luffing trolley reached the endpoint. The peak transient displacement difference caused by the ZV shaper during acceleration and deceleration was approximately 1.2 meters, which reduced the maximum swing amplitude by about 52% compared to the unshaped command. The transient swing amplitudes of the ZVD shaper and the EI shaper almost overlapped, and the peak value was further compressed to 0.6 meters. This is because the latter two adopted a three-pulse sequence, which made the injection of kinetic energy into the multi-flexible body system of the tower crane more dispersed and smooth, greatly improving the trajectory wrapping and safety of the suspended load when it moved in the air.

[0165] After verifying and analyzing the anti-sway effects of various shapers Figure 7 The impact of different control strategies on the displacement trajectory of the luffing trolley was further compared. The figure shows the displacement-time history of the luffing trolley under ideal speed smoothing programming and in actual application of various input shapers. From the overall macro trend, regardless of pure smoothing programming or various shaping commands, the luffing trolley can smoothly and stably move from the initial position to the target position. In the stopping phase near the target position, all curves show good smooth transition characteristics, ensuring the accuracy of the luffing trolley's positioning.

[0166] The method described above achieves efficient and precise sway elimination in tower cranes. Based on an open-loop control architecture, this method requires no additional sensor feedback equipment and involves minimal computation, making it directly compatible with existing industrial PLC controllers. This approach achieves advanced sway elimination control without increasing hardware costs, demonstrating excellent prospects for engineering implementation.

[0167] See Figure 9 , Figure 9 This is a block diagram of an anti-sway control device for a tower crane according to an embodiment of this application. This device is a virtual device that can be loaded and executed by a computer device, which may include the aforementioned anti-sway control equipment. Figure 9 The device may include a sliding speed reference command generation module, a sway control command generation module, and a transmission module. When executing the above-mentioned sway control method, it can:

[0168] The sliding speed reference command generation module generates a smooth speed reference command for the luffing trolley based on the target speed of the luffing trolley, the time consumed during acceleration and deceleration, and the time consumed during constant speed. It adopts an S-shaped sine acceleration smoothing strategy to generate a smooth speed reference command for the luffing trolley.

[0169] The anti-sway control command generation module convolves the smooth speed reference command with the pulse sequence of the pre-built input shaper to generate the anti-sway control command. The input shaper is constructed based on the dynamic feature parameters of the tower crane multi-flexible body system. The dynamic feature parameters are extracted from the high-fidelity dynamic model of the tower crane multi-flexible body system. The high-fidelity dynamic model of the tower crane multi-flexible body system is constructed based on arbitrary Lagrange-Euler description and absolute node coordinate method.

[0170] The sending module sends anti-sway control commands to the tower crane drive system to perform load anti-sway control under the condition of constant wire rope length.

[0171] The aforementioned device achieves efficient and precise sway elimination for tower cranes. Furthermore, based on an open-loop control architecture, the device requires no additional sensor feedback equipment and involves minimal computation, making it directly compatible with existing industrial PLC controllers. Without increasing additional hardware costs, this device achieves advanced sway elimination control and has excellent prospects for engineering implementation.

[0172] This application also relates to a computer-readable storage medium that stores one or more programs, the one or more programs including instructions that, when executed by a computing device, cause the computing device to perform a sway control method for a tower crane.

[0173] This application also relates to a computer device including one or more processors and one or more memories, wherein one or more programs are stored in the one or more memories and configured to be executed by the one or more processors, and the one or more programs include instructions for performing a sway control method for a tower crane.

[0174] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0175] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0176] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0177] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0178] The above are merely embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of the claims of the present invention pending approval.

Claims

1. A method for controlling the swaying of a tower crane, characterized in that, include: Based on the target speed of the luffing trolley, the time consumed during acceleration and deceleration, and the time consumed during constant speed, an S-shaped sinusoidal acceleration smoothing strategy is adopted to generate a smooth speed reference command for the luffing trolley. The smooth speed reference command is convolved with the pulse sequence of the pre-built input shaper to generate the anti-sway control command. The input shaper is constructed based on the dynamic feature parameters of the tower crane multi-flexible body system. The dynamic feature parameters are extracted from the high-fidelity dynamic model of the tower crane multi-flexible body system. The high-fidelity dynamic model of the tower crane multi-flexible body system is constructed based on arbitrary Lagrange-Euler description and absolute node coordinate method. The anti-sway control command is sent to the tower crane drive system to perform load anti-sway control under the condition of constant wire rope length.

2. The method according to claim 1, characterized in that, The formula for generating the smooth speed reference command for the luffing trolley is: Acceleration phase 0≤t≤t1: ； In the formula, t1=T acc To accelerate to the end time, the time taken for both the acceleration and deceleration phases is T. acc V max Let v(t) be the target speed, v(t) be the smooth speed reference command of the variable amplitude trolley at time t, and ω be the speed reference value. d The damped natural frequency of the multi-flexible body system of the tower crane; During the uniform velocity phase, t1≤t <t2: v(t)=V max ; In the formula, t2=T acc +T cruise For the moment when deceleration begins, T cruise This refers to the time consumed during the constant speed phase; During the deceleration phase, t2≤t <t3: ； In the formula, t3 = 2T acc +T cruise The moment when the movement stops. Relative time; Stopping phase t≥t3: v(t)=0.

3. The method according to claim 1, characterized in that, The high-fidelity dynamic model of the multi-flexible body system of the tower crane is as follows: ； In the formula, M T Let M be the mass matrix of the tower crane. c For the unit mass matrix of the hoisting wire rope, e T and e c Let Q be the generalized coordinate vector of the tower crane and the wire rope, respectively. The two superscripts indicate the second derivative with respect to time. ela For the generalized elastic force vector of the multi-flexible body system of the tower crane, Q is the vector of the additional inertial force of the hoisting wire rope. ext Let λ be the generalized external force vector of the tower crane multi-body system, λ be the Lagrange multiplier vector, and C be the constraint equations of the tower crane multi-body system. e The Jacobian matrix is ​​obtained by differentiating C with respect to the generalized coordinates.

4. The method according to claim 1, characterized in that, The input shaper is a ZV shaper, and the pulse sequence of the ZV shaper is: ； ； ； In the formula, I(s) is the transfer function of the shaper in the complex frequency domain, n is the number of pulses, and A i and t i Here, represents the gain coefficient and trigger time of the i-th pulse, respectively, and s is the complex frequency domain parameter. ,parameter , ω d The damped natural frequency of the multi-flexible body system of the tower crane. ω is the damping ratio of the multi-flexible body system of the tower crane. n Let be the undamped natural frequency of the multi-flexible-body system of the tower crane, t1=0 be the moment when the pulse excitation is applied, and A1 and A2 be the amplitudes of the pulse excitation at times t1 and t2, respectively. This is the amplitude ratio function of the residual oscillation of the multi-flexible body system of a tower crane.

5. The method according to claim 1, characterized in that, The input shaper is a ZVD shaper, and the pulse sequence of the ZVD shaper is: ； ； ； In the formula, I(s) is the transfer function of the shaper in the complex frequency domain, n is the number of pulses, and A i and t i Here, represents the gain coefficient and trigger time of the i-th pulse, respectively, and s is the complex frequency domain parameter. ,parameter , ω d The damped natural frequency of the multi-flexible body system of the tower crane. ω is the damping ratio of the multi-flexible body system of the tower crane. n Let be the undamped natural frequency of the multi-flexible-body system of the tower crane, t1=0 be the moment when the pulse excitation is applied, and A1, A2, and A3 be the pulse excitation amplitudes at times t1, t2, and t3, respectively. This is the amplitude ratio function of the residual oscillation of the multi-flexible body system of a tower crane.

6. The method according to claim 1, characterized in that, The input shaper is an EI shaper, and the pulse sequence of the EI shaper is: ； ； ； In the formula, I(s) is the transfer function of the shaper in the complex frequency domain, n is the number of pulses, and A i and t i These represent the gain coefficient and trigger time of the i-th pulse, respectively, where s is the complex frequency domain, and V... tol For the maximum allowable swing amplitude, the parameter , ω d Let L be the damped natural frequency of the multi-flexible-body system of the tower crane, L be the length of the pendulum model, and g be the acceleration due to gravity. ω is the damping ratio of the multi-flexible body system of the tower crane. n Let be the undamped natural frequency of the multi-flexible-body system of the tower crane, t1=0 be the moment when the pulse excitation is applied, and A1 and A2 be the amplitudes of the pulse excitation at times t1 and t2, respectively. Let ω1 and ω2 be the normalized frequency range boundaries corresponding to the intersection points of the EI shaper sensitivity curve and the allowable residual oscillation boundary, respectively.

7. A sway control device for a tower crane, characterized in that, include: The sliding speed reference command generation module generates a smooth speed reference command for the luffing trolley based on the target speed of the luffing trolley, the time consumed during acceleration and deceleration, and the time consumed during constant speed. It adopts an S-shaped sinusoidal acceleration smoothing strategy to generate a smooth speed reference command for the luffing trolley. The anti-sway control command generation module convolves the smooth speed reference command with the pulse sequence of the pre-built input shaper to generate the anti-sway control command. The input shaper is constructed based on the dynamic feature parameters of the tower crane multi-flexible body system. The dynamic feature parameters are extracted from the high-fidelity dynamic model of the tower crane multi-flexible body system. The high-fidelity dynamic model of the tower crane multi-flexible body system is constructed based on arbitrary Lagrange-Euler description and absolute node coordinate method. The sending module sends anti-sway control commands to the tower crane drive system to perform load anti-sway control under the condition of constant wire rope length.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores one or more programs, the one or more programs including instructions that, when executed by a computing device, cause the computing device to perform the method of any one of claims 1 to 6.

9. A computer device, characterized in that, include: One or more processors and one or more memories, one or more programs stored in one or more memories and configured to be executed by one or more processors, the one or more programs including instructions for performing the method of any one of claims 1 to 6.

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