CN110937510A - Offshore crane stability control method and system with double-pendulum characteristic - Google Patents

Offshore crane stability control method and system with double-pendulum characteristic Download PDF

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CN110937510A
CN110937510A CN201911258798.9A CN201911258798A CN110937510A CN 110937510 A CN110937510 A CN 110937510A CN 201911258798 A CN201911258798 A CN 201911258798A CN 110937510 A CN110937510 A CN 110937510A
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double
pendulum
offshore crane
dynamic model
swing angle
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CN110937510B (en
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马昕
李轾
李贻斌
宋锐
荣学文
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Shandong University
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Shandong University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B66—HOISTING; LIFTING; HAULING
    • B66C—CRANES; LOAD-ENGAGING ELEMENTS OR DEVICES FOR CRANES, CAPSTANS, WINCHES, OR TACKLES
    • B66C13/00—Other constructional features or details
    • B66C13/04—Auxiliary devices for controlling movements of suspended loads, or preventing cable slack
    • B66C13/06—Auxiliary devices for controlling movements of suspended loads, or preventing cable slack for minimising or preventing longitudinal or transverse swinging of loads
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B66—HOISTING; LIFTING; HAULING
    • B66C—CRANES; LOAD-ENGAGING ELEMENTS OR DEVICES FOR CRANES, CAPSTANS, WINCHES, OR TACKLES
    • B66C13/00—Other constructional features or details
    • B66C13/18—Control systems or devices
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B66—HOISTING; LIFTING; HAULING
    • B66C—CRANES; LOAD-ENGAGING ELEMENTS OR DEVICES FOR CRANES, CAPSTANS, WINCHES, OR TACKLES
    • B66C23/00—Cranes comprising essentially a beam, boom, or triangular structure acting as a cantilever and mounted for translatory of swinging movements in vertical or horizontal planes or a combination of such movements, e.g. jib-cranes, derricks, tower cranes
    • B66C23/88—Safety gear

Abstract

The invention discloses a method and a system for stably controlling an offshore crane with double-pendulum characteristics, wherein the method comprises the following steps: establishing a dynamic model of the double-pendulum offshore crane; introducing the elevation angle of the suspension arm, the length of a cable between the gravity center of the lifting hook and the top end of the suspension arm, the swing angle of the lifting hook and the swing angle state variable of the suspended object, and converting the dynamic model into a new dynamic model; defining the mechanical energy of the double-pendulum offshore crane, and obtaining a nonlinear controller with a bounded control signal according to the derivative of the mechanical energy and a new dynamic model; the controller is used for realizing stable control of the offshore crane with the double-pendulum characteristic. The invention fully considers the problems of disturbance caused by the rolling motion and the heave motion of the ship body and the saturation of the actuator, designs the nonlinear controller with bounded control signals, and the controller still has strong robustness when facing non-zero initial swing angle, external disturbance, sea wind interference and complex ship body motion.

Description

Offshore crane stability control method and system with double-pendulum characteristic
Technical Field
The invention relates to the technical field of offshore crane stability control, in particular to a method and a system for controlling stability of an offshore crane with double-pendulum characteristics.
Background
The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.
With the gradual trend of marine exploration and marine resource development to deep sea, the application of the offshore crane in the aspect of marine transportation is more and more extensive. An offshore crane is a special crane mounted on a ship, of the type that is normally operated in an offshore environment for placing cargo in a certain location. Similar to the land crane, the offshore crane may swing the hoisted object during the operation. However, offshore cranes have more complex dynamics than terrestrial cranes. But also offshore cranes are subject to disturbances introduced by the continuous hull motion. These disturbances may excite potential dynamics, which in turn may cause the crane system to oscillate, posing a significant threat to the safety of the entire plant and the operators. For the above reasons, it is of great significance to design a high performance offshore crane controller.
In recent years, scholars at home and abroad put forward a plurality of land crane control methods. These methods can be largely divided into two parts, namely open-loop control methods and closed-loop control methods. The open-loop method mainly comprises input shaping, adaptive input shaping, instruction smoothing and the like. The closed-loop control method mainly includes linear control, sliding mode control, adaptive control, optimal control, and various intelligent control methods such as fuzzy control, neural network control, and the like. Since the offshore crane is affected by the disturbance caused by the continuous hull motion during operation, the control method of the land crane cannot be directly applied to the offshore crane.
Despite considerable attention over the years, the design of high performance offshore crane controllers remains an urgent problem to be solved. The prior art analyzes dynamic models of various types of offshore cranes, such as: in the prior art, a model of an offshore crane is linearized, and a feedback controller is designed based on the linearized model to realize accurate hoisting of a hoisted object; however, such a controller based on a linearized model can achieve a better control effect only in a small range near the equilibrium point.
For the control problem of the land crane with the double-pendulum characteristic, the scholars at home and abroad carry out extensive research and obtain certain results. These efforts still cannot be directly applied to double pendulum offshore cranes. At present, the inventor knows that the prior art studies the stability control problem of the offshore crane with double pendulum characteristics, does not consider the heave motion of the vessel, and also does not consider the saturation problem of the actuator.
Disclosure of Invention
The invention aims to solve the defects of the prior art, provides a method and a system for stably controlling an offshore crane with double-pendulum characteristics, fully considers the problems of disturbance caused by rolling motion and heaving motion of a ship body and saturation of an actuator, designs a nonlinear controller with a bounded control signal, and has strong robustness when facing non-zero initial swing angle, external disturbance, sea wind interference and complex ship body motion.
In some embodiments, the following technical scheme is adopted:
a method for stabilizing and controlling an offshore crane with double pendulum characteristics comprises the following steps:
under the condition that disturbance caused by ship body rolling and heaving motion exists, a dynamic model of the double-pendulum offshore crane is established by taking a certain specific position where a lifting hook and a suspended object are stabilized under a geodetic coordinate system as a control target;
introducing the elevation angle of the suspension arm under a geodetic coordinate system, the length of a cable from the gravity center of the lifting hook to the top end of the suspension arm, the swing angle of the lifting hook and the swing angle state variable of the suspended object, and converting the dynamic model into a new dynamic model;
defining the mechanical energy of the double-pendulum offshore crane, and obtaining a nonlinear controller with a bounded control signal according to the derivative of the mechanical energy and a new dynamic model;
the controller is used for realizing stable control of the offshore crane with the double-pendulum characteristic.
In other embodiments, the following technical solutions are adopted:
an offshore crane stability control system with double pendulum feature comprising:
the device is used for setting a certain specific position of the lifting hook and the suspended object which are stabilized under a geodetic coordinate system as a control target and establishing a dynamic model of the double-pendulum offshore crane under the condition that disturbance caused by the rolling and heaving motions of the ship body exists;
the device is used for introducing the elevation angle of the suspension arm under a geodetic coordinate system, the length of a cable from the gravity center of the lifting hook to the top end of the suspension arm, the swing angle of the lifting hook and the swing angle state variable of the suspended object, and converting the dynamic model into a new dynamic model;
means for defining the mechanical energy of the double-pendulum offshore crane, obtaining a nonlinear controller with bounded control signals according to the derivative of the mechanical energy and the new dynamic model;
and the device is used for realizing stable control on the offshore crane with double-pendulum characteristics through the controller.
In other embodiments, the following technical solutions are adopted:
a marine crane stability controller specifically is:
Figure BDA0002311036400000031
Figure BDA0002311036400000032
wherein k isα1，kα2，kβ1，kβ2，γ1，γ2，kδ1，kδ2And kγAll are positive controller parameters, τ is the boom pitch control moment, F is the control force to adjust the length of the cable, mhcM represents the sum of the mass of the hook and the mass of the suspended objectjIndicating the mass of the boom, e1，e2，e3，e4Respectively, the elevation angle error of the suspension arm, the length error of the cable, the swing angle error of the lifting hook and the craneError of object swing angle;
Figure BDA0002311036400000033
respectively represent eiThe first derivative of (a).
In other embodiments, the following technical solutions are adopted:
a terminal device comprising a processor and a computer-readable storage medium, the processor being configured to implement instructions; the computer readable storage medium is used for storing a plurality of instructions which are suitable for being loaded by a processor and executing the offshore crane stability control method with the double-pendulum characteristic.
In other embodiments, the following technical solutions are adopted:
a computer readable storage medium having stored therein a plurality of instructions adapted to be loaded by a processor of a terminal device and to execute the above-mentioned marine crane stability control method with double pendulum feature.
Compared with the prior art, the invention has the beneficial effects that:
1) the invention establishes a dynamic model of the offshore crane with the double-pendulum characteristic by using a Lagrange method. The model fully considers the disturbance caused by the rolling and heaving motions of the ship body. In addition, the original model is converted into a new form by introducing some new state variables.
2) The invention provides a nonlinear controller with a bounded control signal to complete stable control on an offshore crane based on a converted new dynamic model under the condition that no linearization is carried out on the model, and the controller can gradually adjust a lifting hook and a suspended object to a desired position and can effectively inhibit swinging.
3) The closed loop stability of the system is strictly proved by utilizing the Lyapunov theory and the LaSael invariant set principle, and the effectiveness of the controller is proved through a plurality of simulation experiments.
Drawings
FIG. 1 is a schematic structural diagram of an offshore crane with a double pendulum feature according to a first embodiment of the present invention;
FIG. 2 is a comparison of experimental results for a controller of the present invention and a PID controller;
FIG. 3 is a simulation experiment result when the initial swing angle of the controller is not zero according to the present invention;
FIG. 4 is a simulation experiment result in the presence of external disturbances under the controller of the present invention;
FIG. 5 is a simulation experiment result of the presence of sea wind effects under the controller of the present invention;
FIG. 6 is the roll angle of the hull under rough sea conditions with the controller of the present invention;
FIG. 7 is the heave height of the hull under rough sea conditions with the controller of the present invention;
FIG. 8 shows the simulation experiment result of the complex hull motion under the controller of the present invention.
Detailed Description
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
The embodiments and features of the embodiments of the present invention may be combined with each other without conflict.
Example one
In one or more embodiments, disclosed is a method for stabilizing and controlling an offshore crane having a double pendulum characteristic, comprising the following processes:
(1) under the condition that disturbance caused by ship body rolling and heaving motion exists, a dynamic model of the double-pendulum offshore crane is established by taking a certain specific position where a lifting hook and a suspended object are stabilized under a geodetic coordinate system as a control target;
(2) introducing the elevation angle of the suspension arm under a geodetic coordinate system, the length of a cable from the gravity center of the lifting hook to the top end of the suspension arm, the swing angle of the lifting hook and the swing angle state variable of the suspended object, and converting the dynamic model into a new dynamic model;
(3) defining the mechanical energy of the double-pendulum offshore crane, and obtaining a nonlinear controller with a bounded control signal according to the derivative of the mechanical energy and a new dynamic model;
(4) the controller is used for realizing stable control of the offshore crane with the double-pendulum characteristic.
The process of the present invention is described in detail below.
The offshore crane with double pendulum feature is schematically shown in fig. 1. Wherein the coordinate system { xeOeyeAnd { x }sOsysAnd represents a geodetic coordinate system and a hull coordinate system respectively. Wherein xeAxis and yeThe axes being parallel and perpendicular to the ground, x, respectivelysAxis and ysThe axes are parallel and perpendicular to the deck, respectively. Using the lagrange method, the equations for the hook and the suspended load can be found as:
Figure BDA0002311036400000061
Figure BDA0002311036400000062
Figure BDA0002311036400000063
Figure BDA0002311036400000064
wherein m ishc＝mh+mcRepresents the mass m of the hookhMass m of the suspended mattercAnd (4) summing. m isjIndicating the mass of the boom. L isjBeing suspension armsThe radius of rotation. L is1The length of the cable between the centre of gravity of the hook to the top end of the boom is shown and is time varying. L is2Indicating the distance between the hook and the center of gravity of the hanging object. J denotes the moment of inertia of the boom. g is a gravitational acceleration constant. Theta1And theta2The swing angles of the lifting hook and the hoisted object are respectively under a ship body coordinate system. Phi represents the elevation angle of the boom under the hull coordinate system. ρ and h represent the roll angle and heave height of the hull, respectively. Tau is the pitching control moment of the suspension arm, and F is the control force for adjusting the length of the cable rope.
As can be seen from equations (1) to (4), the double pendulum offshore crane has very complex nonlinear dynamics. For convenience of controller design and stability analysis, the present embodiment transforms the prime-dynamics model as follows.
The following new state variables are first defined:
Figure BDA0002311036400000071
ξ thereiniAnd (i is 1,2,3 and 4) respectively representing the elevation angle of the boom, the length of a cable from the gravity center of the lifting hook to the top end of the boom, the swing angle of the lifting hook and the swing angle of a suspended object under a geodetic coordinate system.
By substituting the new state variables defined by equation (5) into equations (1) - (4), the dynamic model of a double pendulum offshore crane can be expressed as
Figure BDA0002311036400000072
Wherein vector ξ is [ ξ ]1,ξ2,ξ3,ξ4]T。
Figure BDA0002311036400000073
And
Figure BDA0002311036400000074
representing the second and first derivatives, U ═ τ, F,0, respectively, of vector ξ]TM (ξ) is an inertia matrix, which is specifically expressed as:
Figure BDA0002311036400000075
Figure BDA0002311036400000076
m12＝m21＝-mhcLjcos(ξ3-ξ1),m13＝m31＝mhcLjξ2sin(ξ3-ξ1),m14＝m41＝mcLjL2sin(ξ4-ξ1),m22＝mhc,m24＝m42＝mcL2sin(ξ3-ξ4),
Figure BDA0002311036400000077
m34＝m43＝mcLjξ2cos(ξ3-ξ4),
Figure BDA0002311036400000078
Figure BDA0002311036400000079
is a Coriolis and centrifugal force matrix, and is specifically expressed as:
Figure BDA00023110364000000710
Figure BDA00023110364000000711
Figure BDA00023110364000000712
Figure BDA00023110364000000713
Figure BDA00023110364000000714
Figure BDA00023110364000000715
for the disturbance vector, it is specifically expressed as:
Figure BDA0002311036400000081
wherein
Figure BDA0002311036400000082
The hull heave acceleration.
The kinetic model shown in formula (6) has the following characteristics:
properties 1 inertial matrix M (ξ) is a positive definite matrix, and inertial matrix M (ξ) is a matrix of Coriolis and centrifugal forces
Figure BDA0002311036400000088
There are the following relationships
Figure BDA0002311036400000083
Wherein
Figure BDA0002311036400000084
Is an arbitrary four-dimensional column vector.
For double pendulum offshore cranes, the control objective is to stabilize the hook and suspended load at a particular location in the geodetic coordinate system in the presence of disturbances caused by hull roll and heave motions. In the geodetic coordinate system, the desired position of the suspended object can be expressed as (x)cde,ycde) The desired position of the hook can then be expressed as (x)cde,ycde+L2). In the hull coordinate system, the position (x) of the suspended objectcds,ycds) Can be expressed as:
Figure BDA0002311036400000085
wherein phi isd，θ1d，θ2dAnd L1dRespectively the expected elevation angle of the suspension arm, the expected swing angle of the lifting hook,desired swing angle of the sling and desired length of the cable. According to the geometric relationship shown in FIG. 1, (x)cde,ycde) And (x)cds,ycds) The relationship of (1) is:
Figure BDA0002311036400000086
stability control requirements of offshore cranes:
θ1d＝θ2d＝ρ (13)
combined formulae (11) to (13) Phid，θ1d，θ2dAnd L1dCan be expressed as:
Figure BDA0002311036400000087
θ1d＝θ2d＝ρ (15)
Figure BDA0002311036400000091
the stability control of an offshore crane can be described as:
1) designing a bounded control input τ such that the boom pitch angle φ (t) converges to a desired pitch angle φdI.e., φ (t) → φd。
2) Designing a bounded control input F such that the cable length L1(t) convergence to the desired length L1dI.e. L1(t)→L1d。
3) The swing angle between the hook and the suspended object is suppressed to zero, namely theta1→ρ,θ2→ρ
Based on the transformed dynamics model (6), the new state variables ξ, according to the above analysisiThe expected value of (i ═ 1,2,3,4) can be expressed as:
Figure BDA0002311036400000092
then, the control target may be described as: the bounded control signals τ and F are designed such that
Figure BDA0002311036400000093
Prior to controller design, the present embodiment makes the following rationality assumptions:
suppose 1. swing angle ξ of hook and suspended object3，ξ4Satisfy the requirement of
Figure BDA0002311036400000094
And 2, the heave displacement of the ship body is smaller than the distance from the gravity center of the suspended object to the water surface.
Assumption 3. it is known from the prior art that the heave motion of a vessel can be decomposed into a set of sine waves of different frequencies and different amplitudes. In practical engineering, offshore cranes are usually operated under relatively mild sea conditions for safety reasons, and the heave motions of the vessel are relatively small due to the large volume and mass of the vessel. For the reasons, the acceleration reasonably considering the movement of the ship body can be made
Figure BDA0002311036400000096
Is bounded.
Assumption 4. since the heave motion of the vessel is small and periodic, the control process can be divided into several time segments and during each time segment both the speed and the acceleration of the heave motion approach zero, i.e. the velocity and the acceleration of the heave motion approach zero
Figure BDA0002311036400000095
The error signal is defined as follows:
Figure BDA0002311036400000101
wherein e isiAnd (i is 1,2,3 and 4) respectively representing a boom elevation angle error, a cable length error, a lifting hook swing angle error and a hanging object swing angle error.
Figure BDA0002311036400000102
Respectively represent eiThe first derivative of (a).
The mechanical energy defining a double pendulum offshore crane is as follows:
Figure BDA0002311036400000103
the derivation is carried out on both sides of the equal sign of the formula (20) to obtain
Figure BDA0002311036400000104
By utilizing properties 1 and formula (6),
Figure BDA0002311036400000109
expressed as:
Figure BDA0002311036400000105
according to equation (22), the control laws τ and F are designed as follows:
Figure BDA0002311036400000106
Figure BDA0002311036400000107
wherein k isαi，kβi，γi，kδi(i-1, 2) and kγAre all positive controller parameters.
Stability analysis was performed as follows.
Theorem 1. the control law designed in equations (23) - (24) of this embodiment enables the hook and the suspended load to be adjusted to the desired positions in the presence of disturbances caused by the ship's roll and heave motions, namely:
Figure BDA0002311036400000108
and (3) proving that: define scalar function V (t) as follows:
Figure BDA0002311036400000111
the derivation is performed on both sides of the equal sign of the formula (26) and the formulas (23) to (24) are substituted to obtain:
Figure BDA0002311036400000112
wherein
Figure BDA0002311036400000113
According to the assumption 3, it can be seen that in each control period N → 0. Then it is determined that,
Figure BDA0002311036400000114
can be expressed as:
Figure BDA0002311036400000115
from the above analysis, it can be seen that the scalar function V (t) is greater than zero, and therefore the function is a Lyapunov function, again because of the fact that
Figure BDA0002311036400000116
Less than zero, it is known that:
V(t)≤V(0)＜＜+∞ (29)
Figure BDA0002311036400000117
to further analyze the closed-loop asymptotic stability of the system, the present embodiment utilizes the Lassal invariant set principle. First, a set Ω is defined as follows:
Figure BDA0002311036400000118
definition set
Figure BDA0002311036400000119
Is the most in the set omegaA large invariant set. As can be seen from equation (28), in the set Ω:
Figure BDA00023110364000001110
wherein
Figure BDA00023110364000001111
Are some constant.
Substituting formulae (23) to (24) and (32) into formula (6) to obtain:
Figure BDA0002311036400000121
Figure BDA0002311036400000122
Figure BDA0002311036400000123
Figure BDA0002311036400000124
the equal sign of the formula (33) is integrated at both ends simultaneously to obtain
Figure BDA0002311036400000125
Wherein
Figure BDA0002311036400000126
Is a constant. As can be seen from the formula (30),
Figure BDA0002311036400000127
if λ1Not equal to 0, then kα1arctan(λ1)t+Δ1→ ∞, t → ∞. This is contradictory to equation (38). Then:
Figure BDA0002311036400000128
in this case, equation (37) can be written as:
Figure BDA0002311036400000129
further, the formula (34) is multiplied by λ4sin(ξ3-ξ4) Multiplying equation (35) by cos (ξ)3-ξ4) And the sum of the two is calculated, we can:
Figure BDA00023110364000001210
at this time, expression (41) is multiplied by mcL2Multiplying equation (36) by mhcλ4And subtracting the latter from the former to obtain:
Figure BDA00023110364000001211
by substituting formula (42) for formula (40), it is possible to obtain:
Figure BDA0002311036400000131
at this time, by integrating both sides of the equation (43) equal sign:
Figure BDA0002311036400000132
wherein the content of the first and second substances,
Figure BDA0002311036400000133
is a constant. Similarly, according to equation (30):
Figure BDA0002311036400000134
if Δ1Not equal to 0, then when t → ∞ Δ1t+Δ2→∞。This is contradictory to the conclusion in equation (45), and therefore:
Figure BDA0002311036400000135
wherein
Figure BDA0002311036400000136
Is a constant.
Equation (35) is added to equation (36) to obtain:
Figure BDA0002311036400000137
formula (46) may be substituted for formula (47):
Figure BDA0002311036400000138
from equations (46) and (48), it is possible to obtain:
Figure BDA0002311036400000139
in this case, the results of the combination of formula (39), formula (46), formula (48) and formula (49) are shown in the invariant set
Figure BDA0002311036400000141
In (1),
Figure BDA0002311036400000142
and, since the balance point is an invariant set
Figure BDA0002311036400000143
Then theorem 1 can be used according to the Lassal invariant set theorem, and the equilibrium point is asymptotically stable.
The effectiveness of the controller of the present embodiment is verified by a simulation experiment. The system parameters are selected as follows:
mh＝0.386Kg,mc＝0.232Kg,mj＝0.89Kg
Lj＝1m,L2＝0.1m,J＝0.184Kg·m2,g＝9.8m/s2
the initial and expected values of the state variables are set as follows:
ξ1(0)＝0deg,ξ2(0)＝0.1m
ξ1d＝30deg,ξ2d＝0.2m
the roll and heave motions of the hull are as follows:
Figure BDA0002311036400000144
Figure BDA0002311036400000145
in the simulation experiment, the controller parameters are
kα1＝0.2,kα2＝2.2,kβ1＝0.2,kβ2＝2.2
kδ1＝0.8,kδ2＝0.7,γ1＝0.3,γ2＝0.5
Kγ＝0.9
To further evaluate the effectiveness of the controller designed in this example, two sets of simulation experiments were designed. The first set of simulation experiments compared the control effect of the controller designed in this embodiment with the PID controller. The second set of experiments verified the robustness of the design controller of this embodiment under different circumstances.
A first group: performance comparison with PID controller
In this set of simulation experiments, the PID controller was constructed as follows
Figure BDA0002311036400000146
Figure BDA0002311036400000147
The parameters of the PID controller are adjusted by the PID toolkit in MATLAB: k is a radical ofτp＝9.4,kτi＝13.1,kτd＝1.1,kFp＝7.1,kFi＝14.1,kFd4.9. The simulation result is shown in fig. 2, and the dotted line indicates the control signal of the controller of the present embodiment, and the implementation indicates the control signal of the PID controller.
As can be seen from FIG. 2, the controller designed according to this embodiment can ensure boom elevation ξ1And cable length ξ2Converge to its desired value in around 5 seconds, moreover, the swing angle ξ of the hook3And swing angle ξ of the suspended object4Effective suppression is obtained. Moreover, it can be seen that the change of the control signal designed by the embodiment is relatively gentle. In contrast, although the PID controller has a small adjustment time during the control of the boom elevation, its overshoot is large. More importantly, the PID controller has limited capability of inhibiting the swinging of the lifting hook and the suspended object, and the swinging angle reaches about 10 degrees. In addition, the PID control signal varies relatively drastically. In general, the controller designed by the present embodiment has more excellent control performance than the PID controller.
Second group: robustness verification
To further verify the robustness of the actual controller herein, simulation experiments were designed in four different scenarios. The method comprises the following specific steps:
case 1 initial swing angle of hook and suspended object is not zero, initial swing angle of hook and suspended object is set to ξ3(0)＝10deg，ξ4(0) 20 deg. The simulation results are shown in fig. 3.
Case 2: the hook is disturbed by external disturbances. In this case, the external disturbance is simulated by a square wave signal. The hook was affected by an external disturbance at 10 seconds. Under the influence of the disturbance, the hook swings around 10 deg. The simulation results are shown in fig. 4.
Case 3: the lifting hook and the hanging object swing caused by sea wind. In this case, it is assumed that the hook and the hoists are affected by the continuous sea wind. During 0 to 15 seconds, the sea wind blows to the front. During this time, the swing angle of the hook and the sling reached 10deg at 7.5 seconds. During the period from 7.5 seconds to 15 seconds, the sea wind is gradually reduced, and the swing angle of the hoists and the lifting hooks under the influence of the sea wind is gradually reduced to zero. After 15 seconds the sea wind was blowing against the back. The sea wind strength gradually increases between 15 and 20 seconds. Under this influence the hook and sling swing angle reaches-8.7 deg. The simulation results are shown in fig. 5.
Case 4: complex hull roll and heave motions. When the offshore crane is operated under severe sea conditions, the rolling and heave motions of the hull are complicated. In this case, hull roll and heave motions are generated by the MATLAB marine system toolbox, specific values can be seen in fig. 6-7. The simulation results are shown in fig. 8.
In all four cases, the control parameters of the controller do not need to be readjusted. As can be seen from fig. 3, although the hook and the suspended object have a large initial swing angle, the controller can still suppress the swing angle to zero within 10 seconds. Furthermore, the elevation angle of the boom as well as the cable length can be converged to their desired value quickly and accurately. It can be seen from figure 4 that the swing angle of the hook and the suspended load reaches-13.8 deg. and-18.4 deg. under the influence of the disturbance. Thereafter, the swing angle of the hook and the suspended object is rapidly reduced to a very small value within 5 seconds under the control of the controller. The control result shows that the controller has strong robustness to disturbance. Further, the control effect under the influence of sea wind is shown in fig. 5. It can be seen that although the hook and the suspended object are disturbed by the continuous sea wind, the swing angle of the hook and the suspended object is well suppressed under the control of the controller, and other state variables can be quickly and accurately converged to a desired value. This shows that the controller is also robust to sustained sea wind disturbances. Finally, as can be seen from fig. 6-7, the roll and heave motions of the hull are complex, both amplitude and frequency being time varying. It can be seen from fig. 8 that despite the very violent hull movements the crane boom's elevation angle and cable length can be quickly and accurately converged to the desired values and the hook and suspended load's swing angles are suppressed to a small range (less than 2deg and 4deg, respectively).
In general, two sets of experiments not only prove the superior performance of the controller designed by the embodiment, but also verify that the controller still has strong robustness in the face of non-zero initial swing angle, external disturbance, sea wind interference and complex hull motion.
Example two
In one or more embodiments, an offshore crane stability control system with double pendulum feature is disclosed, comprising:
the device is used for setting a certain specific position of the lifting hook and the suspended object which are stabilized under a geodetic coordinate system as a control target and establishing a dynamic model of the double-pendulum offshore crane under the condition that disturbance caused by the rolling and heaving motions of the ship body exists;
a device for introducing the elevation angle of the suspension arm, the length of a cable from the gravity center of the lifting hook to the top end of the suspension arm, the swing angle of the lifting hook and the swing angle state variable of the suspended object, and converting the dynamic model into a new dynamic model;
means for defining the mechanical energy of the double-pendulum offshore crane, obtaining a nonlinear controller with bounded control signals according to the derivative of the mechanical energy and the new dynamic model;
and the device is used for realizing stable control on the offshore crane with double-pendulum characteristics through the controller.
The implementation manner or the working principle of each device described above refers to the method disclosed in the first embodiment, and details are not described here.
EXAMPLE III
In one or more embodiments, a terminal device is disclosed that includes a processor and a computer-readable storage medium, the processor to implement instructions; the computer readable storage medium is used for storing a plurality of instructions which are suitable for being loaded by a processor and executing the offshore crane stability control method with the double-pendulum characteristic.
In other embodiments, a computer-readable storage medium is disclosed, having stored therein a plurality of instructions adapted to be loaded by a processor of a terminal device and to execute the above-described marine crane stability control method with double pendulum feature.
Although the embodiments of the present invention have been described with reference to the accompanying drawings, it is not intended to limit the scope of the present invention, and it should be understood by those skilled in the art that various modifications and variations can be made without inventive efforts by those skilled in the art based on the technical solution of the present invention.

Claims (9)

1. A method for stably controlling an offshore crane with double-pendulum characteristics is characterized by comprising the following steps:
under the condition that disturbance caused by ship body rolling and heaving motion exists, a dynamic model of the double-pendulum offshore crane is established by taking a certain specific position where a lifting hook and a suspended object are stabilized under a geodetic coordinate system as a control target;
introducing the elevation angle of the suspension arm under a geodetic coordinate system, the length of a cable from the gravity center of the lifting hook to the top end of the suspension arm, the swing angle of the lifting hook and the swing angle state variable of the suspended object, and converting the dynamic model into a new dynamic model;
defining the mechanical energy of the double-pendulum offshore crane, and obtaining a nonlinear controller with a bounded control signal according to the derivative of the mechanical energy and a new dynamic model;
the controller is used for realizing stable control of the offshore crane with the double-pendulum characteristic.
2. The method for controlling the stability of the offshore crane with the double pendulum characteristic as claimed in claim 1, wherein a dynamic model of the double pendulum offshore crane is established by using a lagrangian method.
3. The method for controlling the stability of an offshore crane with double pendulum characteristics according to claim 1, characterized in that said dynamic model is transformed into a new dynamic model, in particular:
Figure FDA0002311036390000011
wherein, vector ξ is [ ξ ]1,ξ2,ξ3,ξ4]T，
Figure FDA0002311036390000012
And
Figure FDA0002311036390000013
representing the second and first derivatives, respectively, of vector ξ, ξi(i is 1,2,3 and 4) respectively represents the elevation angle of the suspension arm, the length of a cable between the gravity center of the lifting hook and the top end of the suspension arm under a geodetic coordinate system, the swing angle of the lifting hook and the swing angle of the suspended object, M (ξ) is an inertia matrix,
Figure FDA0002311036390000014
is a matrix of coriolis and centrifugal forces,
Figure FDA0002311036390000015
for the perturbation vector, U ═ τ, F,0]TThe input vector is controlled.
4. The method for controlling the stability of an offshore crane with double pendulum characteristics according to claim 1, characterized in that the mechanical energy of the double pendulum offshore crane is defined as:
Figure FDA0002311036390000016
wherein m ishcM represents the sum of the mass of the hook and the mass of the suspended objectcG is the gravitational acceleration constant, L2Indicating the distance between the hook and the center of gravity of the hanging object.
5. The method for controlling the stability of the offshore crane with the double pendulum characteristic as claimed in claim 1, wherein the nonlinear controller with the bounded control signal is obtained according to the derivative of the mechanical energy and the new dynamic model, and specifically comprises:
Figure FDA0002311036390000021
Figure FDA0002311036390000022
wherein k isα1，kα2，kβ1，kβ2，γ1，γ2，kδ1，kδ2And kγAll are positive controller parameters, τ is the boom pitch control moment, F is the control force to adjust the length of the cable, mhcM represents the sum of the mass of the hook and the mass of the suspended objectjIndicating the mass of the boom, e1，e2，e3，e4The method comprises the following steps of respectively determining an elevation angle error of a suspension arm, a length error of a cable, a swing angle error of a lifting hook and a swing angle error of a suspended object;
Figure FDA0002311036390000023
respectively represent eiThe first derivative of (a).
6. An offshore crane stability control system with double pendulum feature, comprising:
the device is used for setting a certain specific position of the lifting hook and the suspended object which are stabilized under a geodetic coordinate system as a control target and establishing a dynamic model of the double-pendulum offshore crane under the condition that disturbance caused by the rolling and heaving motions of the ship body exists;
a device for introducing the elevation angle of the suspension arm, the length of a cable from the gravity center of the lifting hook to the top end of the suspension arm, the swing angle of the lifting hook and the swing angle state variable of the suspended object, and converting the dynamic model into a new dynamic model;
means for defining the mechanical energy of the double-pendulum offshore crane, obtaining a nonlinear controller with bounded control signals according to the derivative of the mechanical energy and the new dynamic model;
and the device is used for realizing stable control on the offshore crane with double-pendulum characteristics through the controller.
7. The utility model provides an offshore crane stability control ware which characterized in that specifically does:
Figure FDA0002311036390000024
Figure FDA0002311036390000031
wherein k isα1，kα2，kβ1，kβ2，γ1，γ2，kδ1，kδ2And kγAll are positive controller parameters, τ is the boom pitch control moment, F is the control force to adjust the length of the cable, mhcM represents the sum of the mass of the hook and the mass of the suspended objectjIndicating the mass of the boom, e1，e2，e3，e4The method comprises the following steps of respectively determining an elevation angle error of a suspension arm, a length error of a cable, a swing angle error of a lifting hook and a swing angle error of a suspended object;
Figure FDA0002311036390000032
respectively represent eiThe first derivative of (a).
8. A terminal device comprising a processor and a computer-readable storage medium, the processor being configured to implement instructions; the computer readable storage medium is used for storing a plurality of instructions, wherein the instructions are suitable for being loaded by a processor and executing the offshore crane stability control method with double pendulum feature of any of claims 1-5.
9. A computer readable storage medium having stored therein a plurality of instructions, characterized in that said instructions are adapted to be loaded by a processor of a terminal device and to execute the method for controlling the stability of an offshore crane having double pendulum characteristics according to any of claims 1-5.
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