A gantry crane anti-sway control method and system based on the dynamic stability of a horizontally constrained simple pendulum system

Abstract

The present invention discloses a gantry crane anti-sway control method and system based on the dynamic stability of a horizontally constrained simple pendulum system. The method comprises the following steps: Step 1: Collecting the structural parameters and dynamic parameters of the crane; Step 2: Inputting the structural parameters and dynamic parameters into a preset Lagrangian model to obtain output data; Step 3: Performing mass normalization on the output data to obtain an undamped state-space equation and a control target; Step 4: Transforming the undamped state-space equation according to a variational method to obtain transformed data; Step 5: Calculating the optimal solution of the transformed data based on the construction of a transfer function and terminal displacement requirements, and controlling the crane according to the optimal solution. The present invention achieves optimal control of the crane by setting the transfer function and terminal displacement requirements, solves the problem of load swing during crane movement, and greatly improves the work efficiency of the crane operator.

Description

Technical Field

[0001] The present invention relates to the field of crane spreader system dynamics stability and control system thereof, and in particular to a gantry crane anti-sway control method and system based on the dynamics stability of a horizontally constrained simple pendulum system. Background Art

[0002] Cable cranes, as important industrial devices, are widely used in many fields, such as ports, construction sites, and logistics. However, cable crane systems are constrained by their inherent dynamic characteristics. Existing research generally assumes smooth and vibration-free motion in the control system. However, in practical applications, various uncertainties exist in the system. For example, the uncertainty of the vibration modal parameters of the flexible cable and the influence of load on position control have made the stability control of cable gantry crane spreader systems a research focus. Summary of the Invention

[0003] In order to at least partially solve the stability problem of the cable gantry crane spreader during use, the present invention provides a gantry crane anti-sway control method and system based on the dynamic stability of a horizontally constrained simple pendulum system. The present invention is based on a cable gantry crane spreader dynamics model based on vertical and horizontal motion. By constructing transfer functions and terminal displacement requirements to process data, the present invention achieves a rapid response to the cable gantry crane spreader control and reduces the vibration of the spreader.

[0004] In order to achieve the above object, the technical solution of the present invention is:

[0005] In a first aspect, the present invention provides a gantry crane anti-sway control method based on the dynamic stability of a horizontally constrained simple pendulum system, comprising the following steps:

[0006] Step 1: Collect the structural and dynamic parameters of the crane to facilitate crane control;

[0007] Step 2: Input the structural parameters and dynamic parameters into the preset Lagrangian model to obtain output data for subsequent processing;

[0008] Step 3: Perform mass normalization on the output data to obtain the undamped state space equation and control target, which can be used to represent the crane state in the undamped case.

[0009] Step 4: Transform the undamped state space equation according to the variational method to obtain the transformed data, which facilitates the subsequent optimal solution;

[0010] Step 5: Calculate the optimal solution for the converted data based on the constructed transfer function and the terminal displacement requirement, and control the crane according to the optimal solution to achieve a short time response for the crane control and high stability of the crane spreader.

[0011] Furthermore, in step 2, the preset Lagrangian model is expressed according to the following formula:

[0012]

[0013]

[0014]

[0015]

[0016] in, is the end load mass, is the mass of the crane translation mechanism, is the second-order derivative of the displacement distance of the crane translation mechanism, is the second-order derivative of the crane translation mechanism velocity, is the length of the sling, is the second-order derivative of the longitudinal swing angle of the crane, cos is the cosine function, sin is the sine function, is the longitudinal swing angle of the crane, c is the damping, is the speed of the crane translation mechanism at time t, , is the maximum speed of the crane translation mechanism, k is the stiffness coefficient, is the first derivative of the longitudinal swing angle of the crane, g is the acceleration of gravity, x is the displacement distance of the crane translation mechanism, is the first-order derivative of the displacement distance of the crane translation mechanism.

[0017] Furthermore, in step 3, the undamped state space equation and the control objective are expressed according to the following formula:

[0018]

[0019]

[0020] ;

[0021] ;

[0022] in, is the state vector, , , Z is the state matrix, , , is the state matrix at the fth moment, A is the system matrix, B is the control matrix, is the coefficient, J is the cost, is the fth moment, and v is the velocity.

[0023] Furthermore, in step 4, the converted data is expressed according to the following formula:

[0024]

[0025]

[0026]

[0027]

[0028] in, is the partial derivative of H, H is the output value of the Hamilton function, for The partial derivative, is a covariate variable, is the co-state equation, At time 0 data, v is the speed of the crane translation mechanism, is the maximum speed of the crane translation mechanism, t is the time, is the i-th moment.

[0029] Furthermore, in step five, the transfer function is expressed according to the following formula:

[0030]

[0031] in, is the output value of the transfer function, N is the time, s is the parameter, is the real part coefficient, is the imaginary coefficient;

[0032] The terminal displacement requirement is expressed as follows:

[0033]

[0034]

[0035]

[0036]

[0037]

[0038] in, is the N+1 moment, is the i-th moment, is the i+1th moment.

[0039] In a second aspect, the present invention provides a gantry crane anti-sway control system based on the dynamic stability of a horizontally constrained simple pendulum system, comprising:

[0040] The acquisition module is used to collect the structural and dynamic parameters of the crane to facilitate the control of the crane;

[0041] The Lagrangian module is used to input structural parameters and dynamic parameters into the preset Lagrangian model to obtain output data for subsequent processing;

[0042] A normalization module is used to perform mass normalization on the output data to obtain the undamped state space equation and the control target, so as to facilitate the representation of the crane state under the undamped condition based on the undamped state space equation and the control target;

[0043] The conversion module is used to convert the undamped state space equation according to the variational method to obtain the converted data, which is convenient for obtaining the optimal solution later;

[0044] The control module is used to calculate the optimal solution of the converted data based on the constructed transfer function and the terminal displacement requirement, and control the crane according to the optimal solution to achieve a short time response of the crane control and high stability of the crane spreader.

[0045] Furthermore, in the Lagrangian module, the preset Lagrangian model is expressed according to the following formula:

[0046]

[0047]

[0048]

[0049]

[0050] in, is the end load mass, is the mass of the crane translation mechanism, is the second-order derivative of the displacement distance of the crane translation mechanism, is the second-order derivative of the crane translation mechanism velocity, is the length of the sling, is the second-order derivative of the longitudinal swing angle of the crane, cos is the cosine function, sin is the sine function, is the longitudinal swing angle of the crane, c is the damping, is the speed of the crane translation mechanism at time t, , is the maximum speed of the crane translation mechanism, k is the stiffness coefficient, is the first derivative of the longitudinal swing angle of the crane, g is the acceleration of gravity, x is the displacement distance of the crane translation mechanism, is the first-order derivative of the displacement distance of the crane translation mechanism.

[0051] Furthermore, in the normalization module, the undamped state space equation and the control target are expressed according to the following formula:

[0052]

[0053]

[0054] ;

[0055] ;

[0056] in, is the state vector, , , Z is the state matrix, , , is the state matrix at the fth moment, A is the system matrix, B is the control matrix, is the coefficient, J is the cost, is the fth moment, and v is the velocity.

[0057] Furthermore, in the conversion module, the converted data is expressed according to the following formula:

[0058]

[0059]

[0060]

[0061]

[0062] in, is the partial derivative of H, H is the output value of the Hamilton function, for The partial derivative, is a covariate variable, is the co-state equation, At time 0 data, v is the speed of the crane translation mechanism, is the maximum speed of the crane translation mechanism, t is the time, is the i-th moment.

[0063] Furthermore, in the control module, the transfer function is expressed according to the following formula:

[0064]

[0065] in, is the output value of the transfer function, N is the time, s is the parameter, is the real part coefficient, is the imaginary coefficient;

[0066] The terminal displacement requirement is expressed as follows:

[0067]

[0068]

[0069]

[0070]

[0071]

[0072] in, is the N+1 moment, is the i-th moment, is the i+1th moment.

[0073] Beneficial effects of the present invention:

[0074] (1) By constructing a Lagrangian model and normalizing it, the state space equation and control target of the cable gantry crane spreader without considering damping are obtained.

[0075] (2) The present invention processes data by constructing a transfer function and terminal displacement requirements, thereby achieving the time optimal response of the cable gantry crane control under the condition of considering damping and reducing the vibration of the cable gantry crane spreader, so as to facilitate more effective control of the cable gantry crane spreader in practical applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 A flowchart of a gantry crane anti-sway control method based on the dynamic stability of a horizontally constrained simple pendulum system is provided in an embodiment of the present invention.

[0077] Figure 2 A schematic diagram of the physical scenario conditions of a gantry crane anti-sway control method based on the dynamic stability of a horizontally constrained simple pendulum system provided in an embodiment of the present invention.

[0078] Figure 3 A schematic diagram of a dynamic model of a gantry crane anti-sway control method based on the dynamic stability of a horizontally constrained simple pendulum system provided in an embodiment of the present invention.

[0079] Figure 4 An architectural diagram of a gantry crane anti-sway control system based on the dynamic stability of a horizontally constrained simple pendulum system provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0080] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly described below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0081] Example 1

[0082] like Figure 1 As shown, a gantry crane anti-sway control method based on the dynamic stability of a horizontally constrained simple pendulum system includes the following steps:

[0083] S101: Collect the structural parameters and dynamic parameters of the crane.

[0084] S102: Inputting structural parameters and dynamic parameters into a preset Lagrangian model to obtain output data.

[0085] S103: Performing mass normalization processing on the output data to obtain an undamped state space equation and a control target.

[0086] S104: transforming the undamped state space equation according to the variational method to obtain transformed data.

[0087] S105: Calculate the optimal solution of the converted data based on the constructed transfer function and the terminal displacement requirement, and control the crane according to the optimal solution.

[0088] Example 2

[0089] Based on the above embodiment, the embodiment of the present invention provides a specific process of a gantry crane anti-sway control method based on the dynamic stability of a horizontally constrained simple pendulum system. The specific process is as follows:

[0090] The present invention provides an anti-sway control method for a gantry crane with a vertical and horizontal motion cable system based on a dynamic model and with the goal of rapid response and vibration reduction.

[0091] S201: Collect the structural parameters and dynamic parameters of the crane.

[0092] Specifically, if Figure 2 As shown, the dynamic model of the crane is obtained based on the physical scene conditions of the crane, and the structural parameters and dynamic parameters of the crane are collected according to the dynamic model of the crane. The structural parameters and dynamic parameters of the crane include the end load mass, the mass of the crane translation mechanism, the rope length, the longitudinal swing angle of the crane, the damping, the maximum speed of the crane translation mechanism, the stiffness coefficient, the lateral force exerted on the crane translation mechanism, the rotational torque, the lateral swing angle of the crane, the longitudinal swing angle of the crane, the displacement distance of the crane translation mechanism, and the rotation angle of the crane.

[0093] S202: Inputting structural parameters and dynamic parameters into a preset Lagrangian model to obtain output data.

[0094] Specifically, if Figure 3 As shown in the figure, the dynamic model of the crane is obtained based on the physical scene conditions of the crane. According to the dynamic model of the crane, the Lagrangian model of the simple pendulum system of the crane subject to vertical excitation and horizontal constraint is constructed. The Lagrangian model is expressed according to the following formula:

[0095]

[0096]

[0097]

[0098]

[0099] Where T is the energy of the pendulum system, V is the potential energy, and D is the dissipated energy. is the partial derivative of T, is the partial derivative of V, is the partial derivative of D, is the longitudinal swing angle of the crane at time t, for The partial derivative, is the end load mass, is the mass of the crane translation mechanism, is the rope length, cos is the cosine function, sin is the sine function, is the speed of the crane translation mechanism at time t, g is the acceleration of gravity, c is the damping, and k is the stiffness coefficient.

[0100] Bringing the data into the Lagrange equation model, it can be expressed as follows:

[0101]

[0102]

[0103]

[0104]

[0105] in, is the end load mass, is the mass of the crane translation mechanism, is the second-order derivative of the displacement distance of the crane translation mechanism, is the second-order derivative of the crane translation mechanism velocity, is the length of the sling, is the second-order derivative of the longitudinal swing angle of the crane, cos is the cosine function, sin is the sine function, is the longitudinal swing angle of the crane, c is the damping, is the speed of the crane translation mechanism at time t, , is the maximum speed of the crane translation mechanism, k is the stiffness coefficient, is the first derivative of the longitudinal swing angle of the crane, g is the acceleration of gravity, x is the displacement distance of the crane translation mechanism, is the first-order derivative of the displacement distance of the crane translation mechanism.

[0106] S203: Performing mass normalization processing on the output data to obtain an undamped state space equation and a control target.

[0107] Specifically, we first assume that the crane is in an undamped state and perform mass normalization on the output results to obtain the undamped state space equation and control target. The undamped state space equation is expressed as follows:

[0108]

[0109] in, is the state vector, Z is the state matrix, A is the system matrix, B is the control matrix, and v is the velocity.

[0110] The control objective is expressed as follows:

[0111]

[0112]

[0113]

[0114] in, , , , , is the state matrix at the fth moment, is the coefficient, J is the cost, is the fth moment.

[0115] S204: Transforming the undamped state space equation according to the variational method to obtain transformed data.

[0116] Specifically, the transformed data is expressed according to the following formula:

[0117] in, is the partial derivative of H, H is the output value of the Hamilton function, for The partial derivative, is a covariate variable, is the co-state equation, At time 0 data, v is the speed of the crane translation mechanism, is the maximum speed of the crane translation mechanism, t is the time, is the i-th moment.

[0118] S205: Calculate the optimal solution of the converted data based on the constructed transfer function and the terminal displacement requirement, and control the crane according to the optimal solution.

[0119] Specifically, the transfer function is expressed as follows:

[0120]

[0121] in, is the output value of the transfer function, N is the time, s is the parameter, is the real part coefficient, is the imaginary coefficient;

[0122] The terminal displacement requirement is expressed as follows:

[0123]

[0124]

[0125]

[0126]

[0127]

[0128] in, is the N+1 moment, is the i-th moment, is the i+1th moment.

[0129] The optimal solution of the converted data is calculated based on the transfer function and terminal displacement requirements, and the crane is controlled to adjust the posture of the crane spreader, thereby reducing the vibration of the crane spreader and enhancing stability.

[0130] Example 3

[0131] Corresponding to the above method, such as Figure 4 As shown, a gantry crane anti-sway control system based on the dynamic stability of a horizontally constrained simple pendulum system includes:

[0132] The acquisition module is used to collect the structural parameters and dynamic parameters of the crane.

[0133] The Lagrangian module is used to input structural parameters and dynamic parameters into the preset Lagrangian model to obtain output data.

[0134] The normalization module is used to perform quality normalization on the output data to obtain the undamped state space equation and control target.

[0135] The conversion module is used to convert the undamped state space equation according to the variational method to obtain converted data.

[0136] The control module is used to calculate the optimal solution of the converted data based on the constructed transfer function and the terminal displacement requirement, and control the crane according to the optimal solution.

[0137] It should be noted that the embodiment of the present invention provides a gantry crane anti-sway control system based on the dynamic stability of a horizontally constrained simple pendulum system, which is intended to realize the above-mentioned gantry crane anti-sway control method based on the dynamic stability of a horizontally constrained simple pendulum system. Its specific functions can be referred to the above-mentioned method embodiments and will not be repeated here.

[0138] In summary, this invention constructs and normalizes a Lagrangian model to derive the state-space equations and control objectives for a cable gantry crane spreader without considering damping. By constructing a transfer function and terminal displacement requirements for data processing, this invention achieves optimal time response for cable gantry crane control while considering damping and reduces vibration of the cable gantry crane spreader, facilitating more efficient control of the cable gantry crane spreader in practical applications.

[0139] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A gantry crane anti-sway control method based on the dynamic stability of a horizontally constrained simple pendulum system, characterized in that: The following steps are involved: Step 1: Collect the structural and dynamic parameters of the crane; Step 2: Input the structural parameters and dynamic parameters into the preset Lagrangian model to obtain output data; Step 3: Perform mass normalization on the output data to obtain the undamped state space equation and control target; Step 4: Transform the undamped state space equation according to the variational method to obtain the transformed data; Step 5: Calculate the optimal solution of the converted data based on the constructed transfer function and terminal displacement requirements, and control the crane according to the optimal solution; In the step 2, the preset Lagrangian model is expressed according to the following formula: x＝lβ Among them, m p is the end load mass, m t is the mass of the crane translation mechanism, is the second-order derivative of the displacement distance of the crane translation mechanism, is the second-order derivative of the crane translation mechanism velocity, l is the length of the suspension rope, is the second-order derivative of the longitudinal swing angle of the crane, cos is the cosine function, sin is the sine function, β is the longitudinal swing angle of the crane, c is the damping, is the speed of the crane translation mechanism at time t, v m is the maximum speed of the crane translation mechanism, k is the stiffness coefficient, is the first derivative of the longitudinal swing angle of the crane, g is the acceleration of gravity, x is the displacement distance of the crane translation mechanism, is the first-order derivative of the displacement distance of the crane translation mechanism.

2. The gantry crane anti-sway control method based on the dynamic stability of the horizontally constrained simple pendulum system according to claim 1 is characterized in that: In step 3, the undamped state space equation and the control objective are expressed as follows: B＝{001} T in, is the state vector, 0≤v(t)≤v m , Z is the state matrix, Z(0)={000} T ,Z(t f )={z f 0z f } T , z f is the state matrix at the fth moment, A is the system matrix, B is the control matrix, ω n is the coefficient, J is the cost, t f is the fth moment, and v is the velocity.

3. The gantry crane anti-sway control method based on the dynamic stability of the horizontally constrained simple pendulum system according to claim 2 is characterized in that: In step 4, the converted data is expressed according to the following formula: v=v m H(-B T λ) Z(0)={000} T ;Z(t f )={t f 0t f } T H=0,t=0 in, is the partial derivative of H, H is the output value of the Hamilton function, is the partial derivative of λ, λ is the covariate variable, is the co-state equation, λ(0) is the data of λ at time 0, v is the speed of the crane translation mechanism, v m is the maximum speed of the crane translation mechanism, t is the time, T t is the tth moment.

4. The gantry crane anti-sway control method based on the dynamic stability of the horizontally constrained simple pendulum system according to claim 2 is characterized in that: In step 5, the transfer function is expressed according to the following formula: Among them, G c is the output value of the transfer function, i is the time, s is the parameter, σ k is the real part coefficient, ω d,k is the imaginary coefficient; The terminal displacement requirement is expressed as follows: minJ=T N+1 0≤(T i+1 -T i ),for i=0,1,2,…,N Among them, T N+1 is the N+1th moment, T i is the i-th moment, T i+1 is the i+1th moment.

5. A gantry crane anti-sway control system based on the dynamic stability of a horizontally constrained simple pendulum system, characterized in that: include: Acquisition module, used to collect the structural parameters and dynamic parameters of the crane; Lagrangian module, used to input structural parameters and dynamic parameters into the preset Lagrangian model to obtain output data; Normalization module, used to perform quality normalization on the output data to obtain the undamped state space equation and control target; A conversion module, used for converting the undamped state space equation according to the variational method to obtain converted data; A control module, for calculating an optimal solution for the transformed data based on a constructed transfer function and terminal displacement requirements, and controlling the crane according to the optimal solution; In the Lagrangian module, the preset Lagrangian model is expressed according to the following formula: x＝lβ Among them, m p is the end load mass, m t is the mass of the crane translation mechanism, is the second-order derivative of the displacement distance of the crane translation mechanism, is the second-order derivative of the crane translation mechanism velocity, l is the length of the suspension rope, is the second-order derivative of the longitudinal swing angle of the crane, cos is the cosine function, sin is the sine function, β is the longitudinal swing angle of the crane, c is the damping, is the speed of the crane translation mechanism at time t, v m is the maximum speed of the crane translation mechanism, k is the stiffness coefficient, is the first derivative of the longitudinal swing angle of the crane, g is the acceleration of gravity, x is the displacement distance of the crane translation mechanism, is the first-order derivative of the displacement distance of the crane translation mechanism.

6. The gantry crane anti-sway control system based on the dynamic stability of the horizontally constrained simple pendulum system according to claim 5, characterized in that: In the normalization module, the undamped state space equation and the control objective are expressed as follows: B＝{001} T in, is the state vector, 0≤v(t)≤v m , Z is the state matrix, Z(0)={000} T ,Z(t f )={z f 0z f } T , z f is the state matrix at the fth moment, A is the system matrix, B is the control matrix, ω n is the coefficient, J is the cost, t f is the fth moment, and v is the velocity.

7. The gantry crane anti-sway control system based on the dynamic stability of the horizontally constrained simple pendulum system according to claim 6, characterized in that: In the conversion module, the converted data is expressed according to the following formula: v=v m H(-B T λ) Z(0)={000} T ;Z(t f )={t f 0t f } T H=0,t=0 in, is the partial derivative of H, H is the output value of the Hamilton function, is the partial derivative of λ, λ is the covariate variable, is the co-state equation, λ(0) is the data of λ at time 0, v is the speed of the crane translation mechanism, v m is the maximum speed of the crane translation mechanism, t is the time, T t is the tth moment.

8. The gantry crane anti-sway control system based on the dynamic stability of the horizontally constrained simple pendulum system according to claim 6, characterized in that: In the control module, the transfer function is expressed according to the following formula: Among them, G c is the output value of the transfer function, i is the time, s is the parameter, σ k is the real part coefficient, ω d,k is the imaginary coefficient; The terminal displacement requirement is expressed as follows: minJ=T N+1 0≤(T i+1 -T i ),for i=0,1,2,…,N Among them, T N+1 is the N+1th moment, T i is the i-th moment, T i+1 is the i+1th moment.

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