Enhanced coupling positioning anti-swing control method and system for crane with distributed mass load

Abstract

The invention relates to the technical field of under-actuated crane system motion control, in particular to an enhanced coupling positioning anti-swing control method and system for a crane with distributed mass loads. Based on a Lagrange kinetic equation, establishing a six-degree-of-freedom bridge crane nonlinear model with distributed loads, and analyzing the kinetic characteristics of the six-degree-of-freedom bridge crane nonlinear model; establishing an energy function of the model based on the bridge crane nonlinear model, constructing a new coupling signal based on a displacement signal of the model to enhance dynamic coupling among a trolley, a lifting hook and a load, and constructing a new state vector based on the constructed coupling signal to enhance dynamic coupling among the trolley, the lifting hook and the load. Substituting the constructed new state vector into an energy function of the model so as to obtain a new class energy function; establishing a nonlinear coupling controller with swing angle information according to the proposed new energy-like function; according to the method, linear processing does not need to be carried out on a kinetic equation of a crane system in controller design, and finally efficient trajectory tracking and positioning and load swing suppression are achieved.

Description

Technical Field

[0001] The invention relates to the technical field of motion control of an underactuated crane system, and in particular to a method and system for enhanced coupling positioning and anti-sway control of a crane with a distributed mass load. Background Art

[0002] As a typical under-actuated system, the crane system has many advantages such as simple structure, low power consumption, and wide application occasions. It has been widely studied in recent years. A bridge crane is a crane that transports goods in space. In actual working conditions, the bridge crane needs to reach the target position, and during the movement, the swing of the payload needs to be kept within an acceptable range to avoid accidents. However, in actual application scenarios, due to the influence of factors such as the load's own properties and the hook mass, the system often not only has a single pendulum effect, but also exhibits a secondary swing (hook, load swing) characteristic, which is closer to the actual crane model. The three-dimensional bridge crane model with double pendulum effect has more state quantities in the crane system and more complex under-actuated characteristics. In practice, the mass of the load transported by the crane is not concentrated, and the load has a relatively obvious moment of inertia during the swing process, and it cannot be regarded as a simple mass point for analysis. Therefore, in practical applications, the control effect of the existing control method directly applied to the three-dimensional bridge crane may be seriously reduced. In these cases, it has become a very challenging problem to achieve accurate positioning of the trolley and the load while quickly suppressing the swing of the load. Summary of the invention

[0003] In view of the problems existing in the prior art, the present invention is proposed.

[0004] Therefore, the problem to be solved by the present invention is how to solve the problem that the mass of the load transported by the crane is not concentrated in practice, and the load has a relatively obvious moment of inertia during the swing process, and cannot be analyzed as a mass point. Since the three-dimensional bridge crane system with double pendulum effect has more state variables, the coupling between the state variables is more nonlinear, making the swing suppression control of the hook and the load more challenging.

[0005] In order to solve the above technical problems, the present invention provides the following technical solutions:

[0006] In a first aspect, an embodiment of the present invention provides a method for enhanced coupled positioning and anti-sway control of a crane with a distributed mass load, which includes, according to the Lagrangian dynamic equation, establishing a nonlinear model of a six-degree-of-freedom bridge crane with a distributed mass load and analyzing its dynamic characteristics;

[0007] Based on the nonlinear model of the bridge crane, an energy function of the nonlinear model of the bridge crane is established, and a new coupling signal is constructed based on the displacement signal of the nonlinear model of the bridge crane to enhance the dynamic coupling between the trolley, the hook and the load, and a new state vector is constructed based on the constructed coupling signal, and the constructed new state vector is substituted into the energy function of the model to obtain a new class energy function;

[0008] Based on the proposed new energy-like function, a nonlinear coupling controller with swing angle information is established;

[0009] The target tracking trajectory in the x and y directions is planned based on the nonlinear model of the bridge crane to verify the positioning and sway elimination effect of the proposed nonlinear coupling controller.

[0010] As a preferred solution of the crane enhanced coupling positioning and anti-sway control method with distributed mass load of the present invention, wherein: the nonlinear model of the six-degree-of-freedom bridge crane with distributed mass load is established and its dynamic characteristics are analyzed, wherein the nonlinear model of the six-degree-of-freedom bridge crane includes:

[0011] Two driving forces and six state quantities, wherein the two driving forces are the driving force of the trolley in the x direction and the driving force of the trolley bridge in the y direction, and the six state quantities are the displacement of the trolley in the x direction, the displacement of the trolley bridge in the y direction, the two deflection angles of the hook in the x and y directions, and the two deflection angles of the load in the x and y directions. The nonlinear model is expressed as follows:

[0012]

[0013] q=[xy θ1 θ2 θ3 θ4] T

[0014] G(q)=[g1 g2 g3 g4 g5 g6] T

[0015] U=[F x F y 0 0 0 0] T

[0016] F s =[F rx F ry 0 0 0 0] T

[0017] Where: M(q) is the inertia matrix of the bridge crane system, is the centripetal-Coriolis matrix, G(q) is the gravity vector, U is the control input vector, and F s is the friction force vector, F rx and Fry are the friction between the trolley and the bridge and the friction between the bridge and the guide rail, respectively; x represents the displacement of the trolley in the x direction; y represents the displacement of the trolley bridge in the y direction; θ1 and θ2 are the deflection angles of the hook in the x and y directions, respectively; θ3 and θ4 are the deflection angles of the load in the x and y directions, respectively; g is the acceleration due to gravity; m x is the mass of the trolley, m y is the total mass of the bridge trolley, m1 and m2 are the masses of the hook and load respectively, l1 and l2 are the length of the rope between the trolley and the hook and the length of the rope between the fixed end points of the hook and the load respectively, l h and l p are the length of the lifting rope between the hook and the mass center of the load and the length of the load, respectively, and I is the moment of inertia of the load;

[0018] Its dynamic characteristics include the positioning characteristics of the trolley and the swing angle characteristics;

[0019] The mathematical model of the bridge crane with distributed mass load also includes:

[0020]

[0021]

[0022] Where: f 11 、f 12 、f 21 、f 22 and ε are the parameters of the friction feedforward compensation model, f 11 and f 12 The value of corresponds to the maximum static friction, f 21 and f 22 is the viscous friction coefficient and ε is the static friction coefficient.

[0023] As a preferred solution of the distributed mass load crane enhanced coupling positioning and anti-sway control method of the present invention, wherein: based on the nonlinear model of the bridge crane, the energy function of the nonlinear model of the bridge crane is established, and the energy function of the mathematical model of the six-degree-of-freedom bridge crane is:

[0024]

[0025] in, Derivatives representing the six states of the crane system, is the kinetic energy of the crane system, (m1+m2)l1g(1-cosθ1cosθ2)+m2gl h (1-cosθ3cosθ4) is the total potential energy of the crane system.

[0026] As a preferred solution of the crane enhanced coupling positioning and anti-sway control method for distributed mass load of the present invention, wherein: the displacement signal based on the nonlinear model of the bridge crane constructs a new coupling signal, which constructs a coupling signal that strengthens the coupling nonlinear relationship between the crane system states:

[0027]

[0028] Among them: k1, k2, k3, k4 are the control gains to be determined, ε x and ε y In order to construct a new coupling signal, the swing angle information is added to it to enhance the coupling nonlinear relationship between the crane system states.

[0029] As a preferred solution of the distributed mass load crane enhanced coupling positioning and anti-sway control method of the present invention, a new state vector is constructed based on the defined new coupling signal, and the class energy function of the mathematical model of the six-degree-of-freedom bridge crane is obtained based on the new state vector:

[0030]

[0031] where λ e is the new state vector constructed, Its first-order derivative, e x =ε x -x d is the tracking displacement error of the trolley in the x direction, e y =ε y -y d is the tracking displacement error of the trolley in the y direction.

[0032] As a preferred solution of the distributed mass load crane enhanced coupling positioning and anti-sway control method of the present invention, wherein: the error variable is designed, and the following Lyapunov equation is designed based on the energy function of the mathematical model of the six-degree-of-freedom bridge crane:

[0033]

[0034] Where E1(t) is the energy function of the six-degree-of-freedom bridge crane system, k px and k py is the controller gain;

[0035] It also includes the derivation of the Lyapunov equation V:

[0036]

[0037] in is the first-order derivative of the energy-like function of the six-degree-of-freedom bridge crane system, is the first-order derivative of the x-axis tracking displacement error of the trolley, It is the first-order derivative of the trolley’s y-axis tracking displacement error.

[0038] As a preferred solution of the distributed mass load crane enhanced coupling positioning and anti-sway control method of the present invention, wherein: based on the proposed new energy-like function, a nonlinear coupling controller with swing angle information is established, wherein the controller of the distributed mass load bridge crane system is:

[0039]

[0040] Where: k px , k dx , k py , k dy is the controller gain to be determined, and are the second-order derivatives of the reference trajectory of the trolley in the x and y directions, respectively;

[0041] The target tracking trajectory in the x and y directions is planned based on the nonlinear model of the bridge crane, wherein the target tracking trajectory is an S-shaped trajectory, which is expressed as:

[0042]

[0043] Where: q(i) d is the target position of the trolley, q(i)0 is the starting position of the trolley, is the time required for the trolley to reach the target position, t f Is infinite.

[0044] In a second aspect, an embodiment of the present invention provides a crane enhanced coupling positioning and sway elimination control system with a distributed mass load, which includes a construction module, and according to the Lagrangian dynamic equation, a nonlinear model of a six-degree-of-freedom bridge crane with a distributed mass load is established and its dynamic characteristics are analyzed;

[0045] An iterative module, based on the nonlinear model of the bridge crane, establishes an energy function of the nonlinear model of the bridge crane, and constructs a new coupling signal based on the displacement signal of the nonlinear model of the bridge crane to enhance the dynamic coupling between the trolley, the hook and the load, and constructs a new state vector based on the constructed coupling signal, and substitutes the constructed new state vector into the energy function of the model to obtain a new class energy function;

[0046] The calculation module establishes a nonlinear coupling controller with swing angle information based on the proposed new energy-like function;

[0047] The verification module plans the target tracking trajectory in the x and y directions based on the nonlinear model of the bridge crane, and is used to verify the positioning and sway elimination effect of the proposed nonlinear coupling controller.

[0048] In a third aspect, an embodiment of the present invention provides a computer device, comprising a memory and a processor, wherein the memory stores a computer program, wherein: when the computer program instructions are executed by the processor, the steps of the enhanced coupling positioning and anti-sway control method for a crane with a distributed mass load as described in the first aspect of the present invention are implemented.

[0049] In a fourth aspect, an embodiment of the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein: when the computer program instructions are executed by a processor, the steps of the enhanced coupling positioning and anti-sway control method for a crane with a distributed mass load as described in the first aspect of the present invention are implemented.

[0050] The beneficial effects of the present invention are as follows: the present invention enhances the coupling relationship between the states of the crane system by adding the swing angle information to the displacement signal, thereby realizing accurate and rapid positioning of the trolley and the swing angle suppression performance; at the same time, the present invention specifically models the distributed mass beam load and takes into account the moment of inertia, thus being closer to the crane transportation load in actual engineering; the present invention does not need to linearize the dynamic equations of the crane system in the controller design, and can ensure control performance even if the state of the system is far away from the equilibrium point. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0052] Figure 1 A flow chart of the enhanced coupled positioning and anti-sway control method for a crane with distributed mass load;

[0053] Figure 2 Computer equipment diagram for enhanced coupled positioning and anti-sway control method for cranes with distributed mass loads;

[0054] Figure 3 The crane structure principle diagram of the crane with distributed mass load and enhanced coupled positioning and anti-sway control method;

[0055] Figure 4 This is a diagram showing the controller simulation results for the enhanced coupled positioning and anti-sway control method for a crane with distributed mass load;

[0056] Figure 5The simulation result diagram of the LQR method for the comparison controller of the enhanced coupled positioning and anti-sway control method for the crane with distributed mass load;

[0057] Figure 6 The simulation results of the adaptive method are shown for the comparison of the enhanced coupled positioning and anti-sway control method for cranes with distributed mass loads. DETAILED DESCRIPTION

[0058] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below in conjunction with the accompanying drawings.

[0059] In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein, and those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0060] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The term "in one embodiment" that appears in different places in this specification does not necessarily refer to the same embodiment, nor is it a separate or selective embodiment that is mutually exclusive with other embodiments.

[0061] Example 1

[0062] Reference Figure 1 to Figure 3 , which is the first embodiment of the present invention, provides a method for controlling the crane's enhanced coupling positioning and anti-swaying with a distributed mass load, comprising:

[0063] Preferably, in practical applications, the bridge crane system will exhibit secondary swing (hook, load swing) characteristics due to the load's own properties, hook mass, etc. Since the three-dimensional bridge crane system with double pendulum effect has more state quantities and more complex under-driven characteristics, the traditional control method is directly applied to the double pendulum three-dimensional bridge crane, and the trolley positioning and load suppression effects are not good. On the other hand, the crane model has obvious nonlinear characteristics, and the traditional controller needs to linearize the model during the design process. Therefore, this paper explores the coupling relationship between the trolley, bridge motion, and secondary swing, designs two generalized velocity signals containing trolley motion and double pendulum swing information, and constructs a new energy function based on the system mechanical energy and generalized signals; when modeling the crane, the distributed mass beam load is specifically modeled and the moment of inertia is considered; this method does not need to linearize the dynamic equations of the crane system in the controller design, and the control performance can be guaranteed even if the state of the system is far away from the equilibrium point. For traditional controllers, on the one hand, usually only positioning can be achieved, but the swing suppression effect is poor and the overall convergence speed is slow; on the other hand, friction, unmodeled parts, etc. are inevitable influencing factors in motion; therefore, this embodiment mainly focuses on the enhanced coupling positioning and swing suppression control method of a three-dimensional double-swing bridge crane with distributed mass load, and its specific process is as follows:

[0064] S100: Based on the Lagrangian dynamic equation, a nonlinear model of a six-degree-of-freedom overhead crane with distributed mass load is established and its dynamic characteristics are analyzed;

[0065] S101: The nonlinear model of a six-degree-of-freedom bridge crane with a distributed mass load is established and its dynamic characteristics are analyzed, wherein the nonlinear model of the six-degree-of-freedom bridge crane includes:

[0066] Two driving forces and six state quantities, wherein the two driving forces are the driving force of the trolley in the x direction and the driving force of the trolley bridge in the y direction, and the six state quantities are the displacement of the trolley in the x direction, the displacement of the trolley bridge in the y direction, the two deflection angles of the hook in the x and y directions, and the two deflection angles of the load in the x and y directions. The nonlinear model is expressed as follows:

[0067]

[0068] q=[xy θ1 θ2 θ3 θ4] T

[0069] G(q)=[g1 g2 g3 g4 g5 g6] T

[0070] U=[F x F y 0 0 0 0]T

[0071] F s =[F rx F ry 0 0 0 0] T

[0072] Where: M(q) is the inertia matrix of the bridge crane system, is the centripetal-Coriolis matrix, G(q) is the gravity vector, U is the control input vector, and F s is the friction force vector, F rx and F ry are the friction between the trolley and the bridge and the friction between the bridge and the guide rail, respectively; x represents the displacement of the trolley in the x direction; y represents the displacement of the trolley bridge in the y direction; θ1 and θ2 are the deflection angles of the hook in the x and y directions, respectively; θ3 and θ4 are the deflection angles of the load in the x and y directions, respectively; g is the acceleration due to gravity; m x is the mass of the trolley, m y is the total mass of the bridge trolley, m1 and m2 are the masses of the hook and load respectively, l1 and l2 are the length of the rope between the trolley and the hook and the length of the rope between the fixed end points of the hook and the load respectively, l h and l p are the length of the lifting rope between the hook and the mass center of the load and the length of the load, respectively, and I is the moment of inertia of the load;

[0073] Its dynamic characteristics include the positioning characteristics of the trolley and the swing angle characteristics;

[0074] Furthermore, the mathematical model of the bridge crane with distributed mass load also includes establishing a friction feedforward compensation model to eliminate the friction generated by the bridge crane drive mechanism, and reducing the positioning error caused by the friction by compensating the disturbance caused by the friction to the system in the forward channel of the system. The friction feedforward compensation model is expressed as follows:

[0075]

[0076] Where: f 11 、f 12 、f 21 、f 22 and ε are the parameters of the friction feedforward compensation model, f 11 and f 12 The value of corresponds to the maximum static friction, f 21 and f 22 is the viscous friction coefficient and ε is the static friction coefficient.

[0077] Preferably, it should be noted that the inertia matrix of the bridge crane system is as follows:

[0078]

[0079] m 11 =m1+m2+m x

[0080] m 12 =0

[0081] m 13 =l1m1C1C2+l1m2C1C2

[0082] m 14 =-l1m1S1S2-l1m2S1S2

[0083] m 15 =l h m2C3C4

[0084] m 16 =-l h m2S3S4

[0085] m 21 =0

[0086] m 22 =m1+m2+m y

[0087] m 23 =0

[0088] m 24 =-l1m1C2-l1m2C2

[0089] m 25 =0

[0090] m 26 =-l h m2C4

[0091] m 31 =l1m1C1C2+l1m2C1C2

[0092] m 32 =0

[0093] m 33 =l1 2 m1C1 2 C2 2 +l1 2 m2C1 2 C2 2 +l1 2 m1C2 2 S1 2 +l1 2 m2C2 2 S1 2

[0094] m 34 =0

[0095] m 35 =l1l h m2C1C2C3C4+l1l h m2C2C4S1S3

[0096] m 36 =-l1l h m2C1C2S3S4+l1l h m2C2C3S1S4

[0097] m 41 =-l1m1S1S2-l1m2S1S2

[0098] m 42 =-l1m2C2-l1m1C2

[0099] m 43 =0

[0100] m 44 =l1 2 m1C1 2 S2 2 +l1 2 m2C1 2 S2 2 +l1 2 m1S1 2 S2 2 +l1 2 m2S1 2 S2 2 +l1 2 m1C2 2 +l1 2 m2C2 2

[0101] m 45 =l1l h m2C1C4S2S3-l1l h m2C3C4S1S2

[0102] m 46 =l1l h m2C1C3S2S4+l1l h m2S1S2S3S4+l1l h m2C2C4

[0103] m 51 =l h m2C3C4

[0104] m 52 =0

[0105] m 53 =l1l h m2C1C2C3C4+l1l h m2C2C4S1S3

[0106] m 54 =l1l h m2C1C4S2S3-l1l h m2C3C4S1S2

[0107] m 55 = l h 2 m2C3 2 C4 2 +l h 2 m2C4 2 S3 2 +Im2

[0108] m 56 =0

[0109] m 61 =-l h m2S3S4

[0110] m 62 =-l h m2C4

[0111] m 63 =-l1l h m2C1C2S3S4+l1l h m2C2C3S1S4

[0112] m 64 =l1l h m2C1C3S2S4+l1l h m2S1S2S3S4+l1l h m2C2C4

[0113] m 65 =0

[0114] m 66 = l h 2 m2C3 2 S4 2 +l h 2 m2S3 2 S4 2 +l h 2 m2C4 2

[0115] Centripetal-Coriolis Matrix As follows:

[0116]

[0117] c 11 = 0

[0118] c 12 = 0

[0119]

[0120] c 21 = 0

[0121] c 22 = 0

[0122] c 23 = 0

[0123]

[0124] c 25 = 0

[0125]

[0126] c 31 = 0

[0127] c 32 = 0

[0128] c 33

[0129] c 34

[0130]

[0131]

[0132] c 41 = 0

[0133] c 42 = 0

[0134]

[0135] c 51 = 0

[0136] c 52 = 0

[0137]

[0138] c 61 = 0

[0139] c 62 = 0

[0140]

[0141] Furthermore, the characteristics are analyzed based on the mathematical model of the bridge crane, and the characteristics specifically include its swing characteristics (double pendulum system) load, etc.

[0142] S200: Based on the nonlinear model of the bridge crane, an energy function of the nonlinear model of the bridge crane is established, and a new coupling signal is constructed based on the displacement signal of the nonlinear model of the bridge crane to enhance the dynamic coupling between the trolley, the hook and the load, and a new state vector is constructed based on the constructed coupling signal, and the constructed new state vector is substituted into the energy function of the model to obtain a new class energy function;

[0143] S201: Based on the nonlinear model of the bridge crane, an energy function of the nonlinear model of the bridge crane is established, and an energy function of the mathematical model of the six-degree-of-freedom bridge crane is established:

[0144]

[0145] in, Derivatives representing the six states of the crane system, is the kinetic energy of the crane system, (m1+m2)l1g(1-cosθ1cosθ2)+m2gl h (1-cosθ3cosθ4) is the total potential energy of the crane system.

[0146] S202: The displacement signal based on the nonlinear model of the bridge crane is used to construct a new coupling signal, wherein the coupling signal is constructed to strengthen the coupling nonlinear relationship between the crane system states:

[0147]

[0148] Among them: k1, k2, k3, k4 are the control gains to be determined, ε x and ε y In order to construct a new coupling signal, the swing angle information is added to it to enhance the coupling nonlinear relationship between the crane system states.

[0149] S203: construct a new state vector based on the defined new coupling signal, and obtain the class energy function of the mathematical model of the six-degree-of-freedom bridge crane based on the new state vector:

[0150]

[0151] where λ e is the new state vector constructed, Its first-order derivative, e x=ε x -x d is the tracking displacement error of the trolley in the x direction, e y =ε y -y d is the tracking displacement error of the trolley in the y direction.

[0152] S204: Following the dynamics rules of the bridge crane model, the error variables are designed, and the following Lyapunov equation is designed based on the energy function of the six-degree-of-freedom bridge crane mathematical model:

[0153]

[0154] Where E1(t) is the energy function of the six-degree-of-freedom bridge crane system, k px and k py is the controller gain;

[0155] Where E1(t) is the energy function of the six-degree-of-freedom bridge crane system, k px and k py is the controller gain. The Lyapunov equation is a quasi-energy equation designed based on error variables. In order to ensure the stability of the system, the equation is designed as a positive definite equation. Combined with the positioning requirements of the control system and the control goal of eliminating swing, the first-order derivative of the equation is proved to be semi-negative definite through derivation.

[0156] It also includes the derivation of the Lyapunov equation V:

[0157]

[0158] in is the first-order derivative of the energy-like function of the six-degree-of-freedom bridge crane system, is the first-order derivative of the x-axis tracking displacement error of the trolley, It is the first-order derivative of the trolley’s y-axis tracking displacement error.

[0159] S300: Based on the proposed new energy-like function, a nonlinear coupling controller with swing angle information is established;

[0160] S301: Planning a target tracking trajectory of a displacement signal based on the crane model to verify the effect of the controller in suppressing the swing angle.

[0161] The following reference trajectory is used to perform tracking control of the bridge crane system to verify the positioning function, where the reference trajectory is an S-shaped trajectory:

[0162]

[0163] Where: q(i) dis the target position of the trolley, q(i)0 is the starting position of the trolley, t q(i)d is the time required for the trolley to reach the target position, t f Is infinite.

[0164] In fact, as long as the trajectory meets the positioning start and end point constraints, the selection of a feasible reference trajectory is arbitrary. The following trajectories are generally available, such as step-type trajectories, S-shaped trajectories, and input shaping trajectories. However, the step-type trajectory is a discontinuous trajectory, which will cause the initial output of the system actuator to be too large, affecting the control effect and being detrimental to the long-term operation of the actuator. For the input shaping trajectory, changes in the system rope length will cause the natural frequency of the vibration system to change accordingly. Then, the input shaping trajectory must be redesigned at any time before use, which is very inconvenient. In the present invention, we select the trajectory shown above, which has the following advantages: 1) The curve is continuous with respect to time, so the desired system state can be uninterrupted; 2) The trajectory contains a sinusoidal function part with a smoothing effect; 3) The arrival time can be manually adjusted according to actual needs.

[0165] S401: Based on the proposed new energy-like function, a nonlinear coupling controller with swing angle information is established, wherein the controller of the bridge crane system with distributed mass load is:

[0166]

[0167] Where: k px , k dx , k py , k dy is the controller gain to be determined, and are the second-order derivatives of the reference trajectory of the trolley in the x and y directions, respectively.

[0168] Specifically, the gain of the PD section (k px , k dx , k py and k dy ) are all positive gains, k px , k dx , k py and k dy The initial values ​​of k are set to 10, 20, 10 and 30 respectively, and their values ​​can be adjusted according to actual conditions. It should be noted that the adjustment of k px and k py It can improve the positioning speed, but excessive adjustment usually causes overshoot and oscillation. k1, k2, k3, and k4 are also controller gains to be determined. According to the trial and error method, after multiple adjustments, the initial values ​​of k1, k2, k3, and k4 are set to 0.5, 3, 0.5, and 1.5 respectively. Finally, the relevant parameters of the feedforward friction model, f 11、f 12 、f 21 、f 22 After offline identification, there is no need to change the value selection, and the value of ε static friction coefficient is selected as 0.01.

[0169] S400: Planning target tracking trajectories in the x and y directions based on the nonlinear model of the bridge crane to verify the positioning and sway elimination effect of the proposed nonlinear coupling controller.

[0170] Furthermore, the present embodiment also provides a crane enhanced coupling positioning and anti-sway control system with a distributed mass load, including: a construction module, which establishes a nonlinear model of a six-degree-of-freedom bridge crane with a distributed mass load and analyzes its dynamic characteristics according to the Lagrangian dynamic equation;

[0171] An iterative module, based on the nonlinear model of the bridge crane, establishes an energy function of the nonlinear model of the bridge crane, and constructs a new coupling signal based on the displacement signal of the nonlinear model of the bridge crane to enhance the dynamic coupling between the trolley, the hook and the load, and constructs a new state vector based on the constructed coupling signal, and substitutes the constructed new state vector into the energy function of the model to obtain a new class energy function;

[0172] The calculation module establishes a nonlinear coupling controller with swing angle information based on the proposed new energy-like function;

[0173] The verification module plans the target tracking trajectory in the x and y directions based on the nonlinear model of the bridge crane, and is used to verify the positioning and sway elimination effect of the proposed nonlinear coupling controller.

[0174] This embodiment also provides a computer device, which is suitable for the case of an enhanced coupling positioning and anti-sway control method for a crane with a distributed mass load, and includes a memory and a processor; the memory is used to store computer executable instructions, and the processor is used to execute the computer executable instructions to implement the enhanced coupling positioning and anti-sway control method for a crane with a distributed mass load as proposed in the above embodiment.

[0175] The computer device may be a terminal, and the computer device includes a processor, a memory, a communication interface, a display screen and an input device connected via a system bus. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The communication interface of the computer device is used to communicate with an external terminal in a wired or wireless manner, and the wireless manner can be achieved through WIFI, an operator network, NFC (near field communication) or other technologies. The display screen of the computer device may be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer device may be a touch layer covering the display screen, or a key, trackball or touchpad provided on the housing of the computer device, or an external keyboard, touchpad or mouse, etc.

[0176] This embodiment also provides a storage medium on which a computer program is stored. When the program is executed by a processor, the enhanced coupling positioning and anti-sway control method for a crane with a distributed mass load as proposed in the above embodiment is implemented.

[0177] In summary, this embodiment mainly solves the problem of enhanced coupling positioning and anti-swing control of three-dimensional bridge cranes with distributed loads, thereby achieving accurate and rapid positioning and swing angle suppression performance of the trolley. First, based on the Lagrangian dynamic equation, a nonlinear model of a six-degree-of-freedom bridge crane with distributed loads is established, and its dynamic characteristics are analyzed; then, based on the nonlinear model of the bridge crane, an energy function of the model is established, and a new coupling signal is constructed based on the displacement signal of the model to enhance the dynamic coupling between the trolley, the hook, and the load, and a new state vector is constructed based on the constructed coupling signal, and the constructed new state vector is substituted into the energy function of the model to obtain a new class energy function; then, according to the proposed new class energy function, a nonlinear coupling controller with swing angle information is established; unlike traditional methods, this method does not require linearization of the dynamic equations of the crane system in controller design, and ultimately achieves efficient trajectory tracking positioning and load swing suppression.

[0178] Example 2

[0179] Reference Figure 4 - Figure 6 , which is the second embodiment of the present invention, provides a method for enhancing coupled positioning and anti-sway control of a crane with a distributed mass load. In order to verify the beneficial effects of the present invention, scientific demonstration is carried out through economic benefit calculation and simulation experiments.

[0180] In this embodiment, the traditional controllers LQR and Adaptive are selected for testing, and the test results are compared by means of scientific demonstration to verify the real effect of this method.

[0181] In order to better conduct the experiment, the friction of the device is verified in the simulation environment of MATLAB / Simulink. The controllers LQR and Adaptive are selected to conduct experiments with the controller using this control method. The control method used by the controller LQR is:

[0182]

[0183] For the LQR controller, the state vector And the Q matrix and R matrix are set to Q = diag{50,50,50,50,50,50,2,2,2,2,2,2}, R = [1,1] T Finally, the controller gain is k p1 =50, k p2 =50, k d1 =18, k d2 =22, k1=-26, k2=9.6, k3=1.5, k4=-0.7, k5=28, k6=-12, k7=1.4, k8=-0.7.

[0184] The control method used by the controller Adaptive is:

[0185]

[0186] The adaptive law and It is expressed as:

[0187]

[0188] For the Adaptive controller, the state vector Finally, the controller gain is k px =5, k py =10, k dx =5, k dy =15, k 11 =400, k 12 =800, k 13 =800, k 14 =400, k 21 =300, k 22 =500, k 23 =400, k 24 =800, The amplitudes of this method, the LQR controller and the Adaptive method are calculated using the above parameters, and the results are shown in Table 1 below:

[0189] Table 1: Comparison results of maximum amplitude experiments.

[0190]

[0191] Also refer to Figure 3 and 4 It can be seen from Figure 5 that in the presence of friction, the positioning time of this method is still shorter than that of the LQR controller and the Adaptive controller, and the LQR controller has obvious overshoot in the x and y directions. The amplitude of the hook and the load caused by the controller of this method is not large and will not exceed 1.25 [deg], while the amplitude of the hook and the load caused by the LQR controller all exceeds 1.5 [deg], and it takes more than 10 [s] to completely eliminate the swing; compared with the Adaptive controller, this method can eventually complete the convergence of the swing angle, while the Adaptive controller still has swing angle oscillation until the end of the operation. Therefore, the swing suppression efficiency of this method is extremely high and the positioning is accurate. Also refer to Figure 3 and Figures 4-5 It can be seen that when the positioning time is basically the same, the proposed controller can completely track the target trajectory and realize the positioning function, the LQR controller cannot realize positioning, the Adaptive controller can realize positioning but the time is longer, and the tracking and positioning process of this method is relatively smooth, the positioning is accurate, there is no overshoot and no steady-state error.

[0192] 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 preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A method for enhancing coupling positioning and eliminating sway control of a crane with distributed mass load, characterized in that: include, According to the Lagrangian dynamic equation, a nonlinear model of a six-degree-of-freedom overhead crane with distributed mass load is established and its dynamic characteristics are analyzed. Based on the nonlinear model of the bridge crane, an energy function of the nonlinear model of the bridge crane is established, and a new coupling signal is constructed based on the displacement signal of the nonlinear model of the bridge crane to enhance the dynamic coupling between the trolley, the hook and the load, and a new state vector is constructed based on the constructed coupling signal, and the constructed new state vector is substituted into the energy function of the model to obtain a new class energy function; Based on the proposed new energy-like function, a nonlinear coupling controller with swing angle information is established; The target tracking trajectory in the x and y directions is planned based on the nonlinear model of the bridge crane to verify the positioning and sway elimination effect of the proposed nonlinear coupling controller.

2. The method for enhancing coupling positioning and eliminating sway control of a crane with a distributed mass load as claimed in claim 1, characterized in that: The nonlinear model of a six-degree-of-freedom bridge crane with a distributed mass load is established and its dynamic characteristics are analyzed, wherein the nonlinear model of the six-degree-of-freedom bridge crane includes: Two driving forces and six state quantities, wherein the two driving forces are the driving force of the trolley in the x direction and the driving force of the trolley bridge in the y direction, and the six state quantities are the displacement of the trolley in the x direction, the displacement of the trolley bridge in the y direction, the two deflection angles of the hook in the x and y directions, and the two deflection angles of the load in the x and y directions. The nonlinear model is expressed as follows: q=[x yθ1θ2θ3θ4] T G(q)=[g1 g2 g3 g4 g5 g6] T U=[F x F y 0 0 0 0] T F s =[F rx F ry 0 0 0 0] T Where: M(q) is the inertia matrix of the bridge crane system, is the centripetal-Coriolis matrix, G(q) is the gravity vector, U is the control input vector, and F s is the friction force vector, F rx and F ry are the friction between the trolley and the bridge and the friction between the bridge and the guide rail, respectively; x represents the displacement of the trolley in the x direction; y represents the displacement of the trolley bridge in the y direction; θ1 and θ2 are the deflection angles of the hook in the x and y directions, respectively; θ3 and θ4 are the deflection angles of the load in the x and y directions, respectively; g is the acceleration due to gravity; m x is the mass of the trolley, m y is the total mass of the bridge trolley, m1 and m2 are the masses of the hook and load respectively, l1 and l2 are the length of the rope between the trolley and the hook and the length of the rope between the fixed end points of the hook and the load respectively, l h and l p are the length of the lifting rope between the hook and the mass center of the load and the length of the load, respectively, and I is the moment of inertia of the load; Its dynamic characteristics include the positioning characteristics of the trolley and the swing angle characteristics; The mathematical model of the bridge crane with distributed mass load also includes: Where: f 11 、f 12 、f 21 、f 22 and ε are the parameters of the friction feedforward compensation model, f 11 and f 12 The value of corresponds to the maximum static friction, f 21 and f 22 is the viscous friction coefficient and ε is the static friction coefficient.

3. The method for enhancing coupling positioning and eliminating sway control of a crane with distributed mass load as claimed in claim 2, characterized in that: Based on the nonlinear model of the bridge crane, an energy function of the nonlinear model of the bridge crane and an energy function of the mathematical model of the six-degree-of-freedom bridge crane are established: in, represents the derivatives of the six states of the crane system, is the kinetic energy of the crane system, (m1+m2)l1g(1-cosθ1cosθ2)+m2gl h (1-cosθ3cosθ4) is the total potential energy of the crane system.

4. The method for enhancing coupling positioning and eliminating sway control of a crane with a distributed mass load as claimed in claim 3, characterized in that: The displacement signal based on the nonlinear model of the bridge crane constructs a new coupling signal, which constructs a coupling signal that strengthens the coupling nonlinear relationship between the crane system states: Among them: k1, k2, k3, k4 are the control gains to be determined, ε x and ε y In order to construct a new coupling signal, the swing angle information is added to it to enhance the coupling nonlinear relationship between the crane system states.

5. The method for enhancing coupling positioning and eliminating sway control of a crane with distributed mass load according to claim 4, characterized in that: Based on the defined new coupling signal, a new state vector is constructed, and based on the new state vector, the class energy function of the mathematical model of the six-degree-of-freedom bridge crane is obtained: where λ e is the new state vector constructed, Its first-order derivative, e x =ε x -x d is the tracking displacement error of the trolley in the x direction, e y =ε y -y d is the tracking displacement error of the trolley in the y direction.

6. The method for enhancing coupling positioning and eliminating sway control of a crane with a distributed mass load as claimed in claim 5, characterized in that: The error variables are designed, and the following Lyapunov equation is designed based on the energy function of the mathematical model of the six-degree-of-freedom bridge crane: Where E1(t) is the energy function of the six-degree-of-freedom bridge crane system, k px and k py is the controller gain; It also includes the derivation of the Lyapunov equation V: in is the first-order derivative of the energy-like function of the six-degree-of-freedom bridge crane system, is the first-order derivative of the x-axis tracking displacement error of the trolley, It is the first-order derivative of the trolley’s y-axis tracking displacement error.

7. The method for enhancing coupling positioning and eliminating sway control of a crane with distributed mass load according to claim 6, characterized in that: Based on the proposed new energy-like function, a nonlinear coupling controller with swing angle information is established, wherein the controller of the bridge crane system with distributed mass load is: Where: k px , k dx , k py , k dy is the controller gain to be determined, and are the second-order derivatives of the reference trajectory of the trolley in the x and y directions, respectively; The target tracking trajectory in the x and y directions is planned based on the nonlinear model of the bridge crane, wherein the target tracking trajectory is an S-shaped trajectory, which is expressed as: Where: q(i) d is the target position of the trolley, q(i)0 is the starting position of the trolley, t q(i)d is the time required for the trolley to reach the target position, t f Is infinite.

8. A crane enhanced coupling positioning and sway elimination control system for a distributed mass load, based on the crane enhanced coupling positioning and sway elimination control method for a distributed mass load according to any one of claims 1 to 7, characterized in that: Also includes, The construction module establishes a nonlinear model of a six-degree-of-freedom overhead crane with distributed mass load and analyzes its dynamic characteristics according to the Lagrangian dynamic equation; An iterative module, based on the nonlinear model of the bridge crane, establishes an energy function of the nonlinear model of the bridge crane, and constructs a new coupling signal based on the displacement signal of the nonlinear model of the bridge crane to enhance the dynamic coupling between the trolley, the hook and the load, and constructs a new state vector based on the constructed coupling signal, and substitutes the constructed new state vector into the energy function of the model to obtain a new class energy function; The calculation module establishes a nonlinear coupling controller with swing angle information based on the proposed new energy-like function; The verification module plans the target tracking trajectory in the x and y directions based on the nonlinear model of the bridge crane, and is used to verify the positioning and sway elimination effect of the proposed nonlinear coupling controller.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the enhanced coupling positioning and anti-sway control method for a crane with a distributed mass load as described in any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the enhanced coupling positioning and anti-sway control method for a crane with a distributed mass load as claimed in any one of claims 1 to 7 are implemented.

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