Crane enhanced coupled positioning anti-swing control method and system with distributed mass load

Abstract

The present application relates to the technical field of motion control of underactuated crane system, and particularly relates to a crane enhanced coupling positioning and sway control method and system for a distributed mass load. Based on Lagrange dynamics equation, a nonlinear model of a six-degree-of-freedom bridge crane with distributed load is established, and the dynamic characteristics thereof are analyzed; based on the nonlinear model of the bridge crane, an energy function of the model is established, a new coupling signal is constructed based on displacement signals of the model, and is used to enhance dynamic coupling among the trolley, the hook and the load; a new state vector is constructed based on the constructed coupling signal, the new state vector is substituted into the energy function of the model, and a new quasi-energy function is obtained; and a nonlinear coupling controller with sway angle information is established according to the proposed new quasi-energy function; in the controller design, linearization processing of the dynamics equation of the crane system is not required, and finally efficient trajectory tracking positioning and load sway suppression are realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of motion control of underactuated crane system, in particular to a crane enhanced coupling positioning and swing elimination control method and system for distributed mass load. BACKGROUND

[0002] Crane system is a typical underactuated system, which has many advantages such as simple structure, low power consumption and wide application, and has been widely studied in recent years. Bridge crane is a crane for transporting goods in space. In actual working conditions, the bridge crane needs to reach the target position, and during the movement process, the swing of the effective load 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 properties of the load itself and the hook mass, the system often not only appears single-swing effect, but also shows secondary swing (hook and load swing) characteristics, which is closer to the actual crane model. The three-dimensional bridge crane model with double-swing effect has more state variables and more complex underactuated characteristics. In practice, the mass of the load transported by the crane is not concentrated, and there is obvious rotational inertia during the swing process, which cannot be analyzed as a simple mass point. Therefore, in actual application, the control effect of the existing control method directly applied to the three-dimensional bridge crane may be seriously reduced. In these cases, it is a very challenging problem to achieve accurate positioning of the trolley and the load while quickly suppressing the swing of the load. SUMMARY

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

[0004] Therefore, the problem to be solved by the present application is how to solve the problem that the mass of the load transported by the crane is not concentrated in practice, and there is obvious rotational inertia during the swing process, which cannot be analyzed as a mass point. Since the three-dimensional bridge crane system with double-swing 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] To solve the above technical problems, the present application provides the following technical solutions:

[0006] In a first aspect, the present application embodiment provides a crane enhanced coupling positioning and swing elimination control method for distributed mass load, which comprises: establishing a six-degree-of-freedom bridge crane nonlinear model with distributed mass load according to Lagrange dynamics equation 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 a displacement signal of the nonlinear model of the bridge crane, which is used to enhance the dynamic coupling among the trolley, the hook and the load, and a new state vector is constructed based on the constructed coupling signal, the new state vector is substituted into the energy function of the model, so that a new quasi-energy function is obtained;

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

[0009] Based on the nonlinear model of the bridge crane, target tracking trajectories in x and y directions are planned, which are used to verify the effect of the proposed nonlinear coupling controller in positioning and swing elimination.

[0010] As a preferred scheme of the crane enhanced coupling positioning and swing elimination control method of the distributed mass load, wherein: the six-degree-of-freedom nonlinear model of the bridge crane with the distributed mass load is established and the dynamic characteristics thereof are analyzed, wherein the six-degree-of-freedom nonlinear model of the bridge crane includes,

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

[0012]

[0013] q=[x y 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] wherein: M(q) is an inertia matrix of the bridge crane system, is a centripetal-Coriolis matrix, G(q) is a gravity vector, U is a control input vector, F s is a friction force vector, F rx and Fry Let θ1 and θ2 be the frictional forces between the trolley and the bridge, and θ3 and θ4 be the frictional forces between the bridge and the guide rail, respectively. Let x represent the displacement of the trolley in the x-direction, y represent the displacement of the trolley and the bridge in the y-direction, θ1 and θ2 be the deflection angles of the hook in the x and y directions, respectively, θ3 and θ4 be the deflection angles of the load in the x and y directions, and g be the acceleration due to gravity. x For the trolley mass, m y Let m1 be the total mass of the bridge trolley, m2 be the mass of the hook and the load respectively, and l1 be the length of the lifting rope between the trolley and the hook and the length of the lifting rope between the hook and the fixed end of the load respectively. h and l p These are the length of the lifting rope between the hook and the center of mass of the load, and the length of the load, respectively; I is the moment of inertia of the load.

[0018] Its dynamic characteristics include the trolley's positioning characteristics and its swing angle characteristics;

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

[0020]

[0021]

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

[0023] As a preferred embodiment of the crane enhanced coupling positioning anti-sway control method with distributed mass load described in this 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, The derivatives representing the six states of the crane system, For the kinetic energy component of the crane system, (m1+m2)l1g(1-cosθ1cosθ2)+m2gl h (1-cosθ3cosθ4) represents the total potential energy of the crane system.

[0026] As a preferred scheme of the enhanced coupling positioning anti-swing control method of the crane with distributed mass load, a new coupling signal is constructed based on the displacement signal of the nonlinear model of the bridge crane, which enhances the coupling nonlinear relationship between the states of the crane system.

[0027]

[0028] wherein k1, k2, k3, k4 are control gains to be determined, ε x and ε y are the new coupling signals constructed by adding the swing angle information to enhance the coupling nonlinear relationship between the states of the crane system.

[0029] As a preferred scheme of the enhanced coupling positioning anti-swing control method of the crane with distributed mass load, a new state vector is constructed based on the defined new coupling signal, and a quasi-energy function of the six-degree-of-freedom bridge crane mathematical model is obtained based on the new state vector.

[0030]

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

[0032] As a preferred scheme of the enhanced coupling positioning anti-swing control method of the crane with distributed mass load, an error variable is designed, and the following Lyapunov equation is designed based on the energy function of the six-degree-of-freedom bridge crane mathematical model.

[0033]

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

[0035] Further comprising derivation of the Lyapunov equation V:

[0036]

[0037] wherein is the first derivative of the quasi-energy function of the six-degree-of-freedom bridge crane system, the first derivative of the tracking displacement error of the trolley in the x direction, the first derivative of the tracking displacement error of the trolley in the y direction.

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

[0039]

[0040] wherein: k px , k dx , k py , k dy is the controller gain to be determined, and are the second derivatives of the reference trajectories 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, and is expressed as:

[0042]

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

[0044] In the second aspect, the embodiment of the present application provides a crane enhanced coupling positioning anti-swing control system of a distributed mass load, which comprises a construction module, a six-degree-of-freedom nonlinear model of a bridge crane with a distributed mass load is established and its dynamic characteristics are analyzed according to the Lagrange dynamics equation;

[0045] an iteration module, based on the nonlinear model of the bridge crane, an energy function of the nonlinear model of the bridge crane is established, a new coupling signal is constructed based on the displacement signal of the nonlinear model of the bridge crane, which is used to enhance the dynamic coupling among the trolley, the hook and the load, a new state vector is constructed based on the constructed coupling signal, the constructed new state vector is substituted into the energy function of the model, so that a new quasi-energy function is obtained;

[0046] a calculation module, a nonlinear coupling controller with swing angle information is established based on the proposed new quasi-energy function;

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

[0048] In a third aspect, an embodiment of the present application provides a computer device, comprising a memory and a processor, and the memory stores a computer program, wherein the computer program instructs the processor to implement the steps of the crane enhanced coupling positioning and swing elimination control method for distributed mass load as described in the first aspect of the present application.

[0049] In a fourth aspect, an embodiment of the present application provides a computer readable storage medium, which stores a computer program, wherein the computer program instructs a processor to implement the steps of the crane enhanced coupling positioning and swing elimination control method for distributed mass load as described in the first aspect of the present application.

[0050] The present application has the following beneficial effects: the present application enhances the coupling relationship between the states of the crane system by adding swing angle information in the displacement signal, thereby realizing accurate and rapid positioning of the trolley and swing angle suppression performance; meanwhile, the present application specifically models the distributed mass beam load and considers the moment of inertia, and is thus closer to the crane transport load in actual engineering; the present application does not need to linearize the dynamic equation of the crane system in the controller design, and can guarantee the control performance even if the state of the system is far away from the equilibrium point. BRIEF DESCRIPTION OF DRAWINGS

[0051] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following will briefly introduce the drawings needed to be used in the embodiment description. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative labor.

[0052] Figure 1 Flowchart of the crane enhanced coupling positioning and swing elimination control method for distributed mass load;

[0053] Figure 2 Computer device diagram of the crane enhanced coupling positioning and swing elimination control method for distributed mass load;

[0054] Figure 3 Principle diagram of the crane structure of the crane enhanced coupling positioning and swing elimination control method for distributed mass load;

[0055] Figure 4 Controller simulation result diagram of the crane enhanced coupling positioning and swing elimination control method for distributed mass load;

[0056] Figure 5Simulation result chart of comparative controller LQR method of enhanced coupling positioning anti-swing control method for crane with distributed mass load;

[0057] Figure 6 Simulation result chart of comparative controller Adaptive method of enhanced coupling positioning anti-swing control method for crane with distributed mass load. DETAILED DESCRIPTION

[0058] In order to make the above objectives, features and advantages of the present application more apparent, specific embodiments of the present application will be described in detail below with reference to the accompanying drawings.

[0059] In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present application. However, it will be apparent to one skilled in the art that the present application can be practiced without the specific details and that numerous implementation maybe made without departing from the scope of the present application. Therefore, the specific details set forth in the following description should not be taken as limiting the present application.

[0060] Secondly, the "one embodiment" or "embodiment" referred to herein means that the specific features, structures or characteristics can be included in at least one implementation of the present application. The "in one embodiment" appearing in different places in the specification does not mean the same embodiment, nor is it an embodiment that is independent of or alternatively excludes other embodiments.

[0061] Embodiment 1

[0062] Reference Figures 1-3 For the first embodiment of the present application, the embodiment provides an enhanced coupling positioning anti-swing control method for crane with distributed mass load, comprising,

[0063] Preferably, in practical applications, due to the influence of load properties, hook mass, etc., the bridge crane will exhibit a two-stage swing (hook, load swing) characteristic. Because the three-dimensional bridge crane system with double-swing effect has more state variables and more complex under-actuated characteristics, the traditional control method is directly applied to the double-swing three-dimensional bridge crane, and the positioning of the trolley and the load suppression effect are not good. On the other hand, the crane model has obvious nonlinear characteristics, and the traditional controller needs to linearize the model in the design process. Therefore, by exploring the coupling relationship between the trolley, the bridge movement, and the two-stage swing, two generalized velocity signals containing trolley movement and double-swing swing information are designed, and a new energy function is constructed based on the mechanical energy of the system and the generalized signal; 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 dynamics equation of the crane system in the controller design, and can ensure the control performance even if the state of the system is far from the equilibrium point. For the traditional controller, on the one hand, positioning can usually be achieved, but the swing suppression effect is not good and the overall convergence speed is slow; on the other hand, friction, unmodeled parts, etc. are unavoidable factors in motion; therefore, the embodiment mainly aims at the enhanced coupling positioning and swing suppression control method of the three-dimensional double-swing bridge crane with distributed mass load, and the specific process is as follows:

[0064] S100: According to the Lagrange dynamics equation, a nonlinear model of a six-degree-of-freedom bridge crane with distributed mass load is established and its dynamic characteristics are analyzed;

[0065] S101: The nonlinear model of the six-degree-of-freedom bridge crane with distributed mass load includes,

[0066] two driving forces and six state variables, 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 variables 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, y directions and the two deflection angles of the load in the x, y directions, and the nonlinear model is represented as follows:

[0067]

[0068] q = [x y 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] wherein 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, F s is the friction force vector, F rx and F ry are the friction forces between the trolley and the bridge and 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 direction and the y direction, respectively, θ3 and θ4 are the deflection angles of the load in the x direction and the y direction, respectively, g is the gravity acceleration, m x is the trolley mass, m y is the total mass of the bridge trolley, m1 and m2 are the masses of the hook and the load, respectively, l1 and l2 are the lengths of the ropes between the trolley-hook and the hook-load fixed end point, respectively, l h and l p are the lengths of the ropes between the hook-load center of mass and the load, respectively, I is the rotational inertia of the load;

[0073] The dynamic characteristics thereof include the trolley positioning characteristics and the swing angle swing characteristics;

[0074] Further, the mathematical model of the bridge crane with distributed mass load further comprises establishing a friction force feedforward compensation model to eliminate the friction force generated by the driving mechanism of the bridge crane, so as to reduce the positioning error caused by the friction force by compensating the disturbance to the system caused by the friction force in the forward channel of the system, and the friction force feedforward compensation model is expressed as follows:

[0075]

[0076] wherein f 11 , f 12 , f 21 , f 22 and ε are the parameters of the friction force feedforward compensation model, f 11 and f 12 correspond to the maximum static friction force, f 21 and f 22 are the viscous friction coefficients, and ε is the static friction coefficient.

[0077] Preferably, it is to 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 = 1 h m2C1C2C3C4 + 1 h m2C2C4S1S3

[0096] m 36 = -1 h m2C1C2S3S4 + 1 h m2C2C3S1S4

[0097] m 41 = -1m1S1S2 - 1m2S1S2

[0098] m 42 = -1m2C2 - 1m1C2

[0099] m 43 = 0

[0100] m 44 = 1 2 m1C1 2 S2 2 + 1 2 m2C1 2 S2 2 + 1 2 m1S1 2 S2 2 + 1 2 m2S1 2 S2 2 + 1 2 m1C2 2 + 1 2 m2C2 2

[0101] m 45 = 1 h m2C1C4S2S3 - 1 h m2C3C4S1S2

[0102] m 46 = 1 h m2C1C3S2S4 + 1 h m2S1S2S3S4 + 1 h m2C2C4

[0103] m 51 = 1 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] Further, according to the analysis of the characteristics of the bridge crane mathematical model, the characteristics specifically include the swing characteristics (double swing system) of the 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, a new coupling signal is constructed based on the displacement signal of the nonlinear model of the bridge crane, which is used 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, the constructed new state vector is substituted into the energy function of the model, so that a new quasi-energy function is obtained;

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

[0144]

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

[0146] S202: A new coupling signal is constructed based on the displacement signal of the nonlinear model of the bridge crane, which enhances the coupling nonlinear relationship between the states of the crane system:

[0147]

[0148] Wherein: k1, k2, k3, k4 are control gains to be determined, ε x and ε y are the constructed new coupling signals, in which the swing angle information is added to enhance the coupling nonlinear relationship between the states of the crane system.

[0149] S203: A new state vector is constructed based on the defined new coupling signal, and a quasi-energy function of the six-degree-of-freedom bridge crane mathematical model is obtained based on the new state vector:

[0150]

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

[0152] S204: following the dynamic rules of the bridge crane model, designing the error variable, and designing the following Lyapunov equation based on the energy function of the six-degree-of-freedom bridge crane mathematical model:

[0153]

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

[0155] where E1(t) is the quasi-energy function of the six-degree-of-freedom bridge crane system, k px and k py are controller gains. The Lyapunov equation is a quasi-energy equation designed based on the error variable, 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 target of swing elimination, the first derivative of the equation is proved to be semi-negative through derivation.

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

[0157]

[0158] where is the first derivative of the quasi-energy function of the six-degree-of-freedom bridge crane system, is the first derivative of the trolley x-direction tracking displacement error, is the first derivative of the trolley y-direction tracking displacement error.

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

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

[0161] The following reference trajectory is used for 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) dq(i)0 is the initial position of the trolley, t q(i)d t is the time required for the trolley to reach the target position, t f t is the time required for the trolley to reach the target position, t

[0164] In fact, as long as the trajectory meets the positioning start and end point constraint requirements, the selection of feasible reference trajectory is arbitrary. The following trajectories are usually available, such as step trajectory, S-shaped trajectory and input shaping trajectory. However, the step trajectory is a non-continuous trajectory, which will cause the initial output of the system actuator to be too large, affecting the control effect and being not conducive to the long-term operation of the actuator. For the input shaping trajectory, the change of the system rope length will cause the natural frequency of the vibration system to change accordingly. Then, the input shaping trajectory must be redesigned in time before use, which is very inconvenient. In the present application, we choose the trajectory shown above, which has the following advantages: 1) the curve is continuous with respect to time, so the required 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 class function, a nonlinear coupled controller with swing angle information is established, and the controller of the bridge crane system with distributed mass load is:

[0166]

[0167] wherein: k px , k dx , k py , k dy are the controller gains to be determined, and are the second derivatives of the reference trajectories of the trolley in the x and y directions, respectively.

[0168] Specifically, the gains (k px , k dx , k py and k dy ) similar to the PD part are all positive gains, the initial values of k px , k dx , k py and k dy are set to 10, 20, 10 and 30 respectively, and their values can be adjusted according to actual conditions; it should be noted that adjusting k px and k py can improve the positioning speed, but adjusting too large will usually cause overshoot and oscillation phenomenon; k1, k2, k3, k4 are also controller gains to be determined, and according to the trial and error method, after multiple adjustments, the initial values of k1, k2, k3, k4 are set to 0.5, 3, 0.5 and 1.5 respectively; finally, the related parameters f 11, f 12 , f 21 , f 22 After offline identification, the value of the static friction coefficient ε does not need to be changed, and the value of the static friction coefficient ε is selected as 0.01.

[0169] S400: planning a target tracking trajectory in the x and y directions based on the nonlinear model of the bridge crane, for verifying the effect of the proposed nonlinear coupling controller in positioning and swing elimination.

[0170] Further, the embodiment also provides a crane enhanced coupling positioning swing elimination control system for distributed mass load, comprising a modeling module, a six-degree-of-freedom nonlinear model of a bridge crane with distributed mass load is established according to Lagrange dynamics equation, and the dynamic characteristics thereof are analyzed;

[0171] An iteration module, based on the nonlinear model of the bridge crane, an energy function of the nonlinear model of the bridge crane is established, a new coupling signal is constructed based on the displacement signal of the nonlinear model of the bridge crane, for enhancing the dynamic coupling among the trolley, the hook and the load, a new state vector is constructed based on the constructed coupling signal, the constructed new state vector is substituted into the energy function of the model, so as to obtain a new quasi-energy function;

[0172] A calculation module, based on the proposed new quasi-energy function, a nonlinear coupling controller with swing angle information is established;

[0173] A verification module, based on the nonlinear model of the bridge crane, a target tracking trajectory in the x and y directions is planned, for verifying the effect of the proposed nonlinear coupling controller in positioning and swing elimination.

[0174] The embodiment also provides a computer device suitable for the case of the crane enhanced coupling positioning swing elimination control method for distributed mass load, comprising a memory and a processor; the memory is used for storing computer executable instructions, and the processor is used for executing the computer executable instructions, so as to realize the crane enhanced coupling positioning swing elimination control method for distributed mass load proposed in the above embodiment.

[0175] The computer device can be a terminal, and the computer device includes a processor, a memory, a communication interface, a display screen and an input device connected by a system bus. The processor of the computer device is configured 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 running the operating system and the computer program in the non-volatile storage medium. The communication interface of the computer device is configured to perform wired or wireless communication with an external terminal. The wireless communication can be achieved by WIFI, an operator network, NFC (near field communication) or other technologies. The display screen of the computer device can be a liquid crystal display screen or an electronic ink display screen. The input device of the computer device can be a touch layer overlaid on the display screen, or a key, trackball or touchpad arranged on the shell of the computer device, or an external keyboard, touchpad or mouse, etc.

[0176] The embodiment also provides a storage medium having a computer program stored thereon, and the computer program is executed by a processor to implement the crane enhanced coupling positioning and swing suppression control method for distributed mass load.

[0177] In summary, the embodiment mainly solves the enhanced coupling positioning and swing suppression control of a three-dimensional bridge crane with a distributed load, so as to realize accurate and rapid positioning of the trolley and swing angle suppression performance. First, a nonlinear model of a six-degree-of-freedom bridge crane with a distributed load is established based on the Lagrange dynamics equation, and the dynamic characteristics are analyzed. Then, an energy function of the model is established based on the nonlinear model of the bridge crane, and a new coupling signal is constructed based on the displacement signal of the model, which is used to enhance the dynamic coupling between the trolley, the hook and the load. A new state vector is constructed based on the constructed coupling signal, and the new state vector is substituted into the energy function of the model, so that a new quasi-energy function is obtained. Then, a nonlinear coupling controller with swing angle information is established according to the new quasi-energy function. Unlike the traditional method, the method does not need to linearize the dynamics equation of the crane system in the controller design, and finally realizes efficient trajectory tracking positioning and load swing suppression.

[0178] Embodiment 2

[0179] Reference Figure 4 - Figure 6 As a second embodiment of the present application, the embodiment provides a crane enhanced coupling positioning and swing suppression control method for distributed mass load. In order to verify the beneficial effects of the present application, economic benefit calculation and simulation experiments are used for scientific demonstration.

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

[0181] In order to better conduct the experiment, the controller LQR and Adaptive are selected for testing in the simulation environment in MATLAB / Simulink to verify the existence of friction of the device, and the controller using the control method is used for testing, wherein the control method used by the controller LQR is:

[0182]

[0183] For the LQR controller, the state vector And the Q matrix and the R matrix are set to Q = diag{50, 50, 50, 50, 50, 50, 2, 2, 2, 2, 2, 2}, R = [1, 1] T The final controller gain 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 is expressed as:

[0187]

[0188] For the Adaptive controller, the state vector The final controller gain 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 the method, the LQR controller and the Adaptive method are calculated by the above parameters, and the results are shown in Table 1.

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

[0190]

[0191] It can be seen from Figure 3 and 4 that in the presence of friction, the positioning time of the 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 the method is not large and does 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, the method can finally complete the convergence of the swing angle, while the Adaptive controller still has swing angle oscillation until the end of operation, so the swing suppression efficiency of the method is extremely high and the positioning is accurate. It can be seen from Figure 3 and Figures 4-5 that in the case of basically the same positioning time, the proposed controller can completely track the target trajectory and achieve positioning function, the LQR controller cannot achieve positioning, the Adaptive controller can achieve positioning but takes a long time, and the tracking and positioning process of the method is relatively smooth, the positioning is accurate, and there is no overshoot and steady-state error.

[0192] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present application and not to limit it. Although the present application has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the technical solutions of the present application can be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present application, and they should be covered in the scope of the claims of the present application.

Claims

1. A method of enhancing a coupled positioning anti-swing control of a crane loaded with a distributed mass, characterized by: Comprising, According to the Lagrange dynamics equation, a six-degree-of-freedom nonlinear model of a bridge 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, which is used 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, the constructed new state vector is substituted into the energy function of the model, so that a new quasi-energy function is obtained; Based on the proposed new quasi-energy function, a nonlinear coupling controller with swing angle information is established; Based on the nonlinear model of the bridge crane, target tracking trajectories in x and y directions are planned, which are used to verify the positioning and swing damping effects of the proposed nonlinear coupling controller; The six-degree-of-freedom nonlinear model of the bridge crane with distributed mass load includes, Two driving forces and six state variables, 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 variables 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, and the nonlinear model is represented as follows: ， ， ， ， ， wherein: is the moment of inertia matrix of the bridge crane system, is the centripetal-Coriolis matrix, is the gravity vector, is the control input vector, is the friction force vector, and are the friction forces between the trolley and the bridge and between the bridge and the guide rail, respectively, denotes the displacement of the trolley in direction, denotes the displacement of the trolley bridge in direction, and are the deflection angles of the hook in direction and direction, respectively, and are the deflection angles of the load in direction and direction, respectively, is the gravity acceleration, a 6x1 vector, is the trolley mass, is the total mass of the bridge trolley, and are the hook and load mass, respectively, and are the lengths of the hoisting rope between the trolley-hook and the hook-load fixed end point, respectively, and are the lengths of the hoisting rope between the hook-load center of mass and the load, respectively. The dynamic characteristics include trolley positioning characteristics and swing angle swing characteristics; The mathematical model of the bridge crane with distributed mass load also includes: ， ， wherein: , , , and are parameters of the friction feedforward compensation model, and correspond to the maximum static friction force, and are the viscous friction coefficients, t is the hyperbolic tangent function, and are the first derivatives of x with respect to time t, i.e. , y with respect to time t, i.e. , is the static friction coefficient; The new coupling signal is constructed based on the displacement signal of the nonlinear model of the bridge crane, which enhances the coupling nonlinear relationship between the states of the crane system: ， ， wherein: , , , is the control gain to be determined, and is the new coupling signal constructed, in which the swing angle information is added to enhance the coupling non-linear relationship between the crane system states. Based on the proposed new quasi-energy function, a nonlinear coupling controller with swing angle information is established, wherein the controller of the bridge crane system with distributed mass load is: ， ， ， ， wherein: , , , is the controller gain to be determined, and are the second derivatives of the reference trajectory of the trolley in the and directions, respectively; and are the friction between the trolley and the bridge and the friction between the bridge and the guide rail, respectively. Based on the nonlinear model of the bridge crane, target tracking trajectories in x and y directions are planned, wherein the target tracking trajectory is an S-shaped trajectory, represented as: ， wherein: is the target position of the trolley, is the start position of the trolley, is the time required for the trolley to reach the target position, is infinity.

2. The distributed mass load hoist enhanced coupling position sway control method of claim 1, wherein: Based on the nonlinear model of the bridge crane, an energy function of the nonlinear model of the bridge crane is established, and the energy function of the six-degree-of-freedom mathematical model of the bridge crane is: ， wherein, denotes the derivative of the six states of the crane system, is the kinetic energy part of the crane system, is the total potential energy part of the crane system.

3. The mass loaded crane enhanced coupled position sway control method of claim 2, wherein: Based on the defined new coupling signal, a new state vector is constructed, and based on the new state vector, a quasi-energy function of the six-degree-of-freedom mathematical model of the bridge crane is obtained: ， ， ， wherein, is the new state vector of the configuration, is the first derivative thereof, is the trolley error in the direction tracking displacement, is the trolley error in the direction tracking displacement.

4. The mass loaded crane enhanced coupled position sway control method of claim 3, wherein: An error variable is designed, and the following Lyapunov equation is designed based on the energy function of the six-degree-of-freedom mathematical model of the bridge crane: ， wherein is the potential function for the six degree of freedom bridge crane system, and is the controller gain; Also included is solving the Lyapunov equation Taking the derivative: ， wherein is a first derivative of the six degrees of freedom bridge crane system class function, is a first derivative of the six degrees of freedom bridge crane system class function, is a first derivative of the six degrees of freedom bridge crane system class function, is a first derivative of the six degrees of freedom bridge crane system class function, is a first derivative of the six degrees of freedom bridge crane system class function.

5. A distributed mass load hoist enhanced coupled positioning and sway control system based on the distributed mass load hoist enhanced coupled positioning and sway control method of any one of claims 1-4, characterized by: Further comprising, The construction module establishes a six-degree-of-freedom nonlinear model of a bridge crane with distributed mass load according to the Lagrange dynamics equation and analyzes its dynamic characteristics; The iteration 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, which is used 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, the constructed new state vector is substituted into the energy function of the model, so that a new quasi-energy function is obtained; A computing module, based on the new class function, establishes a nonlinear coupling controller with swing angle information; A verification module, based on the nonlinear model of the bridge crane, plans a target tracking trajectory in the x and y directions, and is used to verify the positioning and swing elimination effects of the proposed nonlinear coupling controller. 6.A computer device, comprising a memory and a processor, wherein the memory stores a computer program, and the computer device is characterized in that: The processor executes the computer program to implement the steps of the distributed mass load crane enhanced coupling positioning and swing elimination control method of any one of claims 1-4.

7. A computer readable storage medium having stored thereon a computer program, characterized in that: The computer program is executed by the processor to implement the steps of the distributed mass load crane enhanced coupling positioning and swing elimination control method of any one of claims 1-4.

Images