Method for stabilizing hoisting control of a bridge crane, bridge crane, controller thereof and use

Abstract

The application discloses a kind of bridge crane stable hoisting control method, bridge crane and its controller and application, bridge crane stable hoisting control method includes: S1, the dynamics model of bridge crane with slewing mechanism is constructed;S2, based on the dynamics model, energy analysis is carried out on bridge crane, coupling is selected with driven degree of freedom and underdriven degree of freedom, coupling error signal is obtained, and nonlinear state enhancement coupling controller is constructed according to coupling error signal.The bridge crane stable hoisting control method of the application, the dynamics model of bridge crane with slewing mechanism is established, and the state-enhanced coupling controller is designed based on system energy analysis, the transient performance and robustness of bridge crane system are improved by the controller, so that the swing and rotation phenomenon of bridge crane during transportation of long-size load is effectively inhibited, and the transportation safety is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of crane control, in particular to a bridge crane stable lifting control method, a bridge crane, a controller thereof and application. BACKGROUND

[0002] Due to the simple operation and strong carrying capacity of the crane, it is very common in construction sites, warehouses and ports. In view of the important value of the crane, scholars have carried out extensive and in-depth research, and through a series of methods, the control goal of reducing load swing has been successfully achieved. However, in the presence of interference and uncertainty, the applicability of these open-loop techniques may be affected. In order to solve this problem, researchers are constantly developing various types of closed-loop control algorithms for bridge cranes, and these methods can usually make the closed-loop system asymptotically stable and satisfactory robustness.

[0003] However, the above method cannot strictly guarantee the transient performance of the positioning control. Therefore, many researchers are currently studying the trajectory tracking control of the bridge crane. First, by further studying the dynamics equation of the system, the trajectory of the trolley is carefully designed to ensure that key performance indicators such as maximum load swing, time required for stabilization, and peak speed and acceleration of the trolley all meet the requirements accurately. Subsequently, a tracking controller is designed to guide the trolley to run along the predetermined path. In addition to model-based techniques, researchers are increasingly interested in applying intelligent control strategies to the operation of the bridge crane, which has great potential for the field.

[0004] Although there has been a lot of research on anti-swing control of the bridge crane, there are still some unsolved problems. For example, existing methods are not sufficient to solve the problem of rotation in addition to swing when transporting long-size loads. The method proposed by some scholars is mainly aimed at the rotation of goods for the arm crane equipped with a rotating hook. However, the rotating hook structure is not common in the bridge crane, and the rotation of the goods is more commonly controlled indirectly by using a rotating mechanism. There is little research on this specific rotating model. Therefore, the swing and rotation problems that occur when the bridge crane transports long-size loads have not been solved. SUMMARY

[0005] The technical problem to be solved by the present application is to provide a bridge crane stable lifting control method that prevents swing and rotation, a bridge crane, a controller thereof and application.

[0006] The technical scheme adopted by the present application to solve its technical problems is: a bridge crane stable lifting control method is provided, comprising the following steps:

[0007] S1, constructing a dynamic model of a bridge crane with a slewing mechanism; the bridge crane comprises a slewing mechanism, a trolley, a hoisting rope and a long-size load;

[0008] S2, performing energy analysis on the bridge crane based on the dynamic model, selecting a driving degree of freedom and an under-actuated degree of freedom to be coupled, obtaining a coupling error signal, and constructing a nonlinear state augmented coupling controller according to the coupling error signal.

[0009] In some embodiments, the dynamic model of the bridge crane satisfies the following formula:

[0010] M s q 2 +Cq 1 +G=u+f

[0011] wherein q is a state variable of the bridge crane, q 1 is a first-order derivative of q, q 2 is a second-order derivative of q, q= x is a horizontal displacement of a trolley of the bridge crane, is a rotation angle of a slewing mechanism of the bridge crane, l is a length of a hoisting rope of the bridge crane, θ1 is a swing angle of the long-size load, and θ2 is a slewing angle of the long-size load;

[0012] M s is an inertia matrix of the bridge crane:

[0013]

[0014] wherein:

[0015] m 11 =M+m,m 22 =J1+J2,

[0016] m 44 =mh 2 , m 14 =m 41 =mcosθ1h,

[0017] m 25 =m 52 =J2,

[0018]

[0019] M is the mass of the trolley, m is the mass of the long-size load, J1 is the rotational inertia of the slewing mechanism, J2 is the rotational inertia of the long-size load, R is the rotational radius of the long-size load, and h is the height of the long-size load in the vertical direction;

[0020] C is the Coriolis torque matrix of the bridge crane:

[0021] wherein:

[0022]

[0023] is the first derivative of θ1, is the first derivative of θ2, is the first derivative of l;

[0024] G is the gravity vector of the bridge crane:

[0025]

[0026] wherein g is the gravitational acceleration;

[0027] u is the control input variable of the bridge crane:

[0028]

[0029] wherein F x is the drive force of the trolley of the bridge crane, is the torque of the slewing gear of the bridge crane, F l is the traction force on the rope of the bridge crane;

[0030] f is the resistance encountered by the state variable of the bridge crane:

[0031]

[0032] wherein f x , f l , represents the resistance exerted on the five states of the bridge crane.

[0033] In some embodiments, step S2 comprises: adding the information of the underactuated degrees of freedom θ1and θ2to the matrices and state variables of the dynamic model of the bridge crane, obtaining a coupling error signal, and constructing a nonlinear state augmented coupling controller according to the coupling error signal.

[0034] In some embodiments, step S2 comprises:

[0035] dividing the matrices and state variables of the dynamic model of the bridge crane, as follows:

[0036] q2 = [l θ1 θ2] T ,

[0037] u2= [F l 0 0] T , q a2 = l,q u = [θ1θ2] T ,

[0038] u a2 = F l ,u a3 = [0 0] T ,G1= [0 0] T ,

[0039]

[0040] where M 11 ,C 11 ∈R 2*2 ,M 12 ,C 12 ∈R 2*3 ,M 21 ,C 21 ∈R 3*2 ,M 22 ,C 22 ∈R 3*3 ,R represents the real number set;

[0041] According to the above division, the following error variables are constructed:

[0042]

[0043] where q a1d ,q a2d ,q ud ,q 2d represent the expected values of q a1 ,q a2 ,q u ,q2 respectively, represent the first derivatives of e a1 ,e1,q1,e a2 ,q a2 ,e2,q2,e u ,q u ;

[0044] According to the above error variables, the following coupling error signals are designed:

[0045] e α = e a1 -ρ 2 Δ(q1,q2),

[0046] wherein represents the integral of the integrable part in the brackets; p(t) is used to adjust the ratio between q1 and q2;

[0047] According to the coupling error signal, the controller is constructed as follows:

[0048]

[0049] wherein,

[0050]

[0051] k i wherein i = 1, 2, 3, 4, 5, 6 are positive control gains; τ1, τ2 and k5, k6 > 0 are control parameters.

[0052] The application further provides a controller of the bridge crane, which is obtained by the above-mentioned bridge crane stable hoisting control method.

[0053] The application further provides a bridge crane comprising the above-mentioned controller.

[0054] In some embodiments, the bridge crane comprises a slewing mechanism, a trolley and a hoisting rope.

[0055] The application further provides an application of the bridge crane, which is used for hoisting of a nuclear power reactor.

[0056] The application further provides an application of the bridge crane, which is used for hoisting of spent fuel of a nuclear power plant.

[0057] The application has the beneficial effects that a five-degree-of-freedom dynamic model of the bridge crane with the slewing mechanism is established, a state-enhanced coupling controller is set based on energy analysis of the bridge crane system, the transient performance and robustness of the bridge crane system are improved through the controller, thereby effectively inhibiting the swing and slewing phenomenon of the bridge crane during transportation of long-size loads and improving transportation safety. BRIEF DESCRIPTION OF DRAWINGS

[0058] The application will be further described below in combination with the drawings and embodiments, wherein:

[0059] Figure 1 is a dynamic model diagram of a simplified structure of the bridge crane in the application;

[0060] Figure 2 is a top view of Figure 1

[0061] Figure 3 ​is a comparison chart of transient state test results of the bridge crane stable lifting control method of an embodiment of the present application and two control methods of prior art;

[0062] Figure 4 is a comparison chart of robustness test results of the bridge crane stable lifting control method of an embodiment of the present application and two control methods of prior art in an initial state;

[0063] Figure 5 is a comparison chart of robustness test results of the bridge crane stable lifting control method of an embodiment of the present application and two control methods of prior art after an additional disturbance is applied when the system reaches a stable state. DETAILED DESCRIPTION

[0064] In order to have a clearer understanding of the technical features, objectives and effects of the present application, the specific embodiments of the present application will be described in detail with reference to the drawings.

[0065] The bridge crane stable lifting control method of an embodiment of the present application comprises the following steps:

[0066] S1, constructing a dynamic model of a bridge crane with a slewing mechanism.

[0067] The bridge crane is a crane of prior art, and the dynamic model is constructed based on a bridge crane comprising a slewing mechanism, a trolley, a sling and a long-size load. A motor is installed on the slewing mechanism to provide one degree of freedom of rotation, thereby indirectly suppressing the slewing of the long-size load. The trolley can move in the horizontal direction, and the sling is connected between the trolley and the long-size load, and can lift or lower the long-size load in the vertical direction.

[0068] The dynamic model of the simplified structure of the bridge crane is shown in Figure 1 and Figure 2 The corresponding physical quantities of each structure are labeled in the figure, including the length of the sling l, the swing angle of the long-size load θ1, the slewing angle of the long-size load θ2, the horizontal displacement of the trolley x, the rotation radius of the long-size load R, the height of the long-size load in the vertical direction h, the rotation angle of the slewing mechanism , etc.

[0069] In an embodiment, the dynamic model of the bridge crane is established by using the Lagrange method, and the established dynamic model of the bridge crane satisfies the following formula:

[0070] M s q 2 +Cq 1 +G=u+f

[0071] wherein q is the state variable of the bridge crane, q 1is the first derivative of q, q 2 is the second derivative of q, q x is a horizontal displacement of a trolley of a bridge crane, is a rotation angle of a slewing mechanism of the bridge crane, l is a length of a rope of the bridge crane, θ1 is a swing angle of a long-size load, and θ2 is a slewing angle of the long-size load.

[0072] M s is an inertia matrix of the bridge crane:

[0073]

[0074] wherein:

[0075] m 11 = M + m, m 22 = J1 + J2,

[0076] m 44 = mh 2 , m 14 = m 41 = mcosθ1h,

[0077] m 25 = m 52 = J2,

[0078]

[0079] M is a mass of the trolley, m is a mass of the long-size load, J1 is a moment of inertia of the slewing mechanism, J2 is a moment of inertia of the long-size load, R is a radius of rotation of the long-size load, h is a height of the long-size load in a vertical direction, and the remaining variables are as described above.

[0080] C is a Coriolis matrix of the bridge crane:

[0081]

[0082] wherein, is a first derivative of θ1, is a first derivative of θ2, is a first derivative of l.

[0083] G is a gravity vector of the bridge crane:

[0084]

[0085] wherein g is a gravitational acceleration.

[0086] u is a control input variable of the bridge crane:

[0087]

[0088] wherein F x is a driving force of a trolley of the bridge crane, is a torque of a slewing mechanism of the bridge crane, F l is a traction force on a sling rope of the bridge crane.

[0089] f is a resistance encountered by a state quantity of the bridge crane system:

[0090]

[0091] wherein f x , f l , represents a resistance exerted on five states of the bridge crane.

[0092] S2, energy analysis is performed on the bridge crane based on a dynamics model, appropriate driving degrees of freedom and under-actuated degrees of freedom are selected for coupling, a coupling error signal is obtained, and a nonlinear state augmented coupling controller is constructed according to the coupling error signal, which can ensure the transient performance of the bridge crane system.

[0093] wherein, from the energy analysis on the bridge crane, it is concluded that the swing and rotation of the long-size load can be effectively eliminated by controlling the trolley and the slewing mechanism, while the lifting motion of the sling rope has little effect on the swing and rotation of the long-size load. Based on this, a state augmented coupling controller is constructed, the information of the under-actuated degrees of freedom is added to the appropriate driving degrees of freedom, thereby greatly improving the transient performance and robustness of the bridge crane.

[0094] For the appropriate driving degrees of freedom, the driving degrees of freedom most closely related to the under-actuated degrees of freedom.

[0095] In an embodiment, the coupling main body x and the information of the under-actuated degrees of freedom θ1 and θ2 is added to the coupling main body x and the coupling main body y, the coupling error signal is obtained, the controller is designed according to the coupling error signal, and the nonlinear state augmented coupling controller is obtained.

[0096] wherein it is worth noting that the form of the controller is similar to PD control, but has adjustable time-varying gain, thereby ensuring excellent transient performance of the bridge crane system, i.e., the swing and rotation of the long-size load can be rapidly eliminated while rapidly reaching the desired position and attitude.

[0097] Specifically, step S2 comprises:

[0098] ​The matrices and state variables of the dynamic model of the bridge crane are divided as follows:

[0099] q2 = [l θ1 θ2] T ,

[0100] u2 = [F l 0 0] T , q a2 = l,q u = [θ1 θ2] T ,

[0101] u a2 = F l ,u a3 = [0 0] T ,G1 = [0 0] T ,

[0102]

[0103] wherein M 11 ,C 11 ∈ R 2*2 ,M 12 ,C 12 ∈ R 2*3 ,M 21 ,C 21 ∈ R 3*2 ,M 22 ,C 22 ∈ R 3*3 ,R denotes the set of real numbers;

[0104] According to the above division, the following error variables are constructed:

[0105] e a1 = e1 = q a1 -q a1d ,e a2 = q a2 -q a2d ,

[0106] e u = e u = q u -q ud ,e2 = q2 - q 2d ,

[0107]

[0108] wherein q a1d ,q a2d ,q ud ,q2d represent q a1 , represent q a2 , represent q u , represent q represent e a1 , e a2 , e a2 , e u , e u , represent the first derivative of

[0109] According to the above error variable design, the following coupling error signal is obtained:

[0110] e α = e a1 - p 2 (q

[0111] wherein represents the integral of the integrable part in the parentheses; p(t) is used to adjust the ratio between q

[0112] According to the coupling error signal, the controller is constructed as follows:

[0113]

[0114] wherein,

[0115]

[0116] k i , i = 1, 2, 3, 4, 5, 6 are positive control gains; t

[0117] The controller obtained above is a nonlinear state enhanced coupling controller with time-varying adaptive coupling gain, which is used in the bridge crane to improve the transient performance and robustness of the bridge crane system and effectively suppress the swinging and turning phenomena of the bridge crane when transporting long-size loads.

[0118] Further, the stability of the bridge crane stable hoisting control method of the present application is analyzed and verified. Using the Lyapunov method, it is proved that the proposed control method is asymptotically stable.

[0119] First, the Lyapunov function is constructed as follows:

[0120]

[0121] wherein

[0122] Firstly, it needs to prove that V ≥ 0, obviously, l ≥ h, because Thus, mgl - mghcosθ1≥ 0.

[0123] In addition, since M and are positive definite matrices, and k1, k3, k5, k6, ∑ are positive numbers, it can be concluded that V ≥ 0.

[0124] Secondly, the derivative of V is calculated There are:

[0125]

[0126] Substitute the controller into the above formula to obtain the following expression:

[0127]

[0128] And the derivatives of ∏(t) and ρ(t) have the following properties:

[0129]

[0130] Substitute Simplify to

[0131] And obviously the direction of the resistance f is always opposite to the direction of the first derivative of the state quantity q 1 , so

[0132] Figures 3 to 5 The state quantity of the application in the simulation environment (the red line in the figure represents the proposed method) is compared with the MPC control method and the LQR control method.

[0133] Figure 3 For transient performance test results, Figure 3 In the control target is x = 5m, l = 5m, θ1= θ2= 0; and the initial state is x(0) = 0, l(0) = 15m, θ1= θ2= 0.

[0134] Figure 4 And Figure 5 For robustness test results, Figure 4 In the control target is the same as Figure 3 , but the initial state is changed to x(0) = 0, l(0) = 15m, θ1= θ2= 10°. Figure 5 In the control target and the initial state are the same as Figure 3 , but when the system is stable, a step disturbance with an amplitude of 10000N at 13.5s.

[0135] By Figures 3-5 As can be seen from the curve contrast, the control method can significantly improve the transient performance and robustness of the bridge crane.

[0136] In summary, the application first establishes a five-degree-of-freedom dynamic model of a bridge crane with a slewing mechanism, and then designs a state-enhanced coupling controller that couples the underactuated degrees of freedom and the driven degrees of freedom together, and designs a time-varying adaptive gain. The input and output errors of the system and the derivatives of the errors are used to compensate for the uncertainties of the dynamic model of the bridge crane by combining the designed adaptive neural network. The dynamic model of the bridge crane with a slewing mechanism in the application is very common in actual working conditions, so it has high application value. In addition, the nonlinear state-enhanced coupling controller constructed based on energy analysis adds appropriate non-driven state-related information to the controller to enhance the state coupling of the bridge crane system. In this way, the closed-loop system responds more timely and efficiently to the non-driven state, thereby ensuring the transient performance and robustness of the bridge crane system. The structure of the controller is relatively simple, which is convenient for practical application.

[0137] The stable hoisting control method of the bridge crane not only realizes stable hoisting, but also constructs a controller of the bridge crane, which improves the transient performance and robustness of the bridge crane system through the constructed controller, thereby effectively suppressing the swinging and slewing phenomenon of the bridge crane during transportation of long-size load. The long-size load is the hoisting target of the bridge crane, and its length is preferably equal to or greater than the diameter of the slewing mechanism.

[0138] The application is not only suitable for construction sites, warehouses, ports and other occasions, but also suitable for nuclear power fields, and further suitable for hoisting of nuclear power reactors including small reactors and hoisting of spent fuel in large reactors (pressurized water reactors, etc.).

[0139] The above description is only an embodiment of the application, and does not limit the patent scope of the application, and any equivalent structure or equivalent process transformation using the content of the specification and drawings, or direct or indirect application in other related technical fields, are also included in the patent protection scope of the application.

Claims

1. A method for stable hoisting control of a bridge crane, characterized in that, Includes the following steps: S1. Construct a dynamic model of a bridge crane with a slewing mechanism; the bridge crane includes a slewing mechanism, a trolley, a hoisting rope, and a long-dimensional load; S2. Based on the dynamic model, perform energy analysis on the bridge crane, select driven degrees of freedom and underdriven degrees of freedom for coupling, obtain coupling error signals, and construct a nonlinear state-enhanced coupling controller based on the coupling error signals. The dynamic model of the bridge crane satisfies the following equation: in, q For the state variables of the bridge crane, for q The first derivative, for q The second derivative, q = ( ), This refers to the horizontal displacement of the trolley of the bridge crane. This refers to the rotation angle of the slewing mechanism of the bridge crane. This refers to the length of the lifting rope of the bridge crane. For long-dimensional loads, the swing angle, For long-dimensional loads, the rotation angle is... M s The inertia matrix of the bridge crane: in: M For the quality of the trolley, m For the mass of long-dimensional loads, J 1 represents the moment of inertia of the rotary mechanism. J 2 represents the moment of inertia of a long-dimensional load. R For long-dimensional loads, the radius of rotation h The height of the long-dimensional load in the vertical direction; C Coriolis force matrix for bridge crane: ,in: for The first derivative, for The first derivative, for The first derivative; G Here is the gravity vector of the bridge crane: in g It is the acceleration due to gravity; u For the control input variables of the bridge crane: in, The driving force for the trolley of the bridge crane. This refers to the torque of the slewing mechanism of the bridge crane. The traction force on the lifting rope of the bridge crane; f The resistance encountered by the bridge crane in its state variables: in, Representing the five states of a bridge crane The resistance applied from above.

2. The method for stable hoisting control of a bridge crane according to claim 1, characterized in that, Step S2 includes: selecting the coupling subject and underactuated degrees of freedom and Information is added to it to obtain the coupling error signal, and a nonlinear state-enhanced coupling controller is constructed based on the coupling error signal.

3. The method for stable hoisting control of a bridge crane according to claim 2, characterized in that, Step S2 includes: The matrices and state variables of the dynamic model of the bridge crane are divided as follows: in Represents the set of real numbers; Based on the above division, the following error variables are constructed: in Represent Expected value represent The first derivative; Based on the above error variables, the following coupled error signal was obtained: in , This represents integrating the integrable part within the parentheses; Used for adjustment and The ratio between them; Based on the coupling error signal, the controller is constructed as follows: in, middle =1, 2, 3, 4, 5, 6 are positive control gains; and These are control parameters.

4. A controller for a bridge crane, characterized in that, The method for stable hoisting control of a bridge crane as described in any one of claims 1-3 is constructed.

5. A bridge crane, characterized in that, Includes the controller as described in claim 4.

6. The bridge crane according to claim 5, characterized in that, It also includes a slewing mechanism, a trolley, and a hoisting rope.

7. An application of the bridge crane as described in claim 5 or 6, characterized in that, Used for hoisting nuclear power reactors.

8. An application of the bridge crane as described in claim 5 or 6, characterized in that, Used for hoisting spent nuclear fuel.

Images