CN108469736B - Marine crane anti-swing positioning control method and system based on state observation - Google Patents
Marine crane anti-swing positioning control method and system based on state observation Download PDFInfo
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Abstract
The invention discloses a marine crane anti-swing positioning control method and a marine crane anti-swing positioning control system based on state observation, which comprise the following steps: constructing an energy function and a state observer including a control target and rope length limitation based on a dynamic model of a marine crane system, and designing a nonlinear dynamic feedback control method for driving a suspender and a lifting rope to move according to the energy function; receiving set system parameters of the marine crane system; obtaining measurement values of a boom pitch angle, a lifting rope length and a load swing angle; obtaining input signals for controlling the movement of the suspender and the lifting rope according to the nonlinear dynamic feedback control method; and realizing accurate positioning of the load and quickly eliminating residual swing of the load according to the input signal. The invention can process the condition that the speed signal can not be directly measured, and simultaneously realize accurate positioning and quick pendulum elimination of the load.
Description
Technical Field
The invention belongs to the field of automatic control of ocean mechanical systems, and is suitable for accurate positioning and effective anti-swing control of nonlinear marine crane system loads which are interfered by sea waves and cannot directly and accurately measure speed signals.
Background
Currently, import and export trade of large goods mainly depends on sea transportation. Therefore, as a typical nonlinear control system, the marine crane has very important application value. Different from the traditional manual operation, the automatic control can effectively reduce the manpower loss and further improve the transportation efficiency. However, for the non-linear marine crane system, the complicated mechanical structure and the harsh working environment will present many challenges to the design and analysis of the automatic control strategy. Specifically, the main control task of a marine crane system is to stabilize the load at a given position and to quickly eliminate its residual swing by simultaneously adjusting the boom pitch angle and the hoist rope length, which means that the number of directly drivable control inputs is less than the number of system independent state variables. Thus, a marine crane can be considered as a typical under-actuated system, and the lack of controllable variables thereof increases the difficulty of designing the controller to some extent.
Today, many researchers are showing great interest in under-actuated systems. In particular, the results of the research on land crane systems are much more sophisticated than marine crane systems. Specifically, existing control methods for land crane systems can be broadly divided into two categories: open-loop control and closed-loop control. In practical application, the open-loop controller can reduce hardware loss and avoid the influence of inaccurate feedback information on control input, and the closed-loop control is more effective in resisting external unknown interference and has stronger robustness.
However, in most cases, it is difficult to apply the above control method directly to a marine crane due to the more complicated non-linear coupling characteristic of the system. Moreover, if the load is not effectively controlled, the pitching motion of the boom will cause the boom to generate a large swing angle and a residual swing. In addition, marine cranes are often used on large cargo vessels in the ocean and the external disturbances caused by sea waves must be considered and eliminated as much as possible. Thus, automatic control of a marine crane system is very challenging and receives a great deal of external attention. In order to eliminate the interference of sea waves, Mahl et al propose methods to compensate the movement of the hull, and thus effectively achieve load positioning. Similarly, based on a designed adaptive observer, Messineo et al propose a closed-loop control method to compensate for external disturbances. In addition, Liu et al, in addition to compensating for the wave disturbances, also uses fuzzy control to adjust the control gain. In addition, some sliding mode control-based strategies are proposed to complete accurate positioning of the boom/trolley and rapid load sway elimination. Raja Ismail and the like design a control method which can realize robust trajectory tracking and effectively resist external interference. On the basis of sliding mode control, the pendulum eliminating and positioning effects of the marine crane system are further improved by combining Ngo and the like with a fuzzy control method. Besides the existing closed-loop controller, the open-loop control strategy based on input shaping can solve the control problem of the marine crane under the condition of fully considering the interference of sea waves. Unlike traditional control methods, a series of intelligent algorithms enable on-line adjustment of control gain.
Although the existing control method can achieve basic goals of boom positioning, load sway elimination and the like to a certain extent, related research on a marine crane system is still in a starting stage. It can be found that the control performance in the transportation process needs to be further improved, and some unsolved hot problems still deserve to be studied deeply.
First, linearization is widely applied to the research of complex nonlinear systems (such as a marine crane system), and thus the difficulty of controller design and stability analysis can be reduced. However, in most cases, the linearized dynamic model will ignore the non-linear behavior of certain marine crane systems. For example, once the load swing angle is far away from the balance point under the influence of unknown disturbance, the simplified linear model cannot accurately reflect the system characteristics, and the control effect is greatly reduced. Secondly, in practical applications, the velocity signal is typically applied as feedback information in closed-loop control. However, considering that installing a speed sensor only increases hardware loss and the weight and volume of the whole system, most mechanical systems only keep a displacement/angle sensor in the hardware structure to obtain a feedback value of a state variable, and a speed signal cannot be directly measured and can only be calculated through a numerical differentiation operation. However, the above operation introduces extra noise to distort the original signal, which has a non-negligible effect on the control performance. In addition, the method of obtaining a velocity signal based on numerical differentiation is difficult to theoretically ensure the stability of the entire closed loop system.
In summary, in order to avoid the influence of the actual problems that the linear operation of the original model and the speed signal cannot be directly measured, a reasonable control method is urgently needed to be provided, so that the dynamic performance of the marine crane system is effectively improved.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a method and a system for positioning and controlling the swing elimination of a marine crane based on state observation. In addition, the method can carry out on-line reduction on the speed signal of the state variable, and ensure the stability of the whole closed-loop system consisting of the marine crane system, the observer and the controller. The method can process the condition that the speed signal cannot be directly measured, and simultaneously realizes accurate positioning of the suspender/lifting rope and quick load swing elimination.
In order to achieve the purpose, the invention adopts the following technical scheme:
a marine crane sway elimination positioning control method based on state observation comprises the following steps:
constructing an energy function and a state observer including a control target and rope length limitation based on a dynamic model of a marine crane system, and designing a nonlinear dynamic feedback control method for driving a suspender and a lifting rope to move according to the energy function;
setting system parameters of a marine crane system;
obtaining measurement values of a boom pitch angle, a lifting rope length and a load swing angle;
obtaining input signals for controlling the movement of the suspender and the lifting rope according to the nonlinear dynamic feedback control method;
and realizing accurate positioning of the load and quickly eliminating residual swing of the load according to the input signal.
Further, the control targets include: 1) under a geodetic coordinate system, adjusting the load to reach a specified position; 2) eliminating residual swing under a load geodetic coordinate system; 3) limiting the range of variation of the hoist rope throughout the control process.
Further, the system parameters of the marine crane system include: the load mass, the boom length, the product of the boom center of gravity distance to the axis of rotation and the boom mass, and the moment of inertia of the boom.
Further, the method further comprises: carrying out coordinate transformation on the original state variable of the system to obtain a transformed state quantity; and calculating a target value of the transformed system state quantity according to the specified position of the load in the geodetic coordinate system.
Further, the target value of the state quantity after the conversion is:
wherein arccos represents an inverse cosine function, (x)d,yd) Indicating the load in the geodetic coordinate system
Target position of lower, LbFor boom length, ζ1d,ζ2d,ζ3dRespectively, converted system state quantities ζ1,ζ2,ζ3The target value of (2).
Further, the nonlinear dynamic feedback control method for controlling the movement of the boom and the lifting rope comprises the following steps:
wherein u isb,ulRespectively driving the pitching motion of the suspender and the control input of the length of the lifting rope; k is a radical ofp1,kp2,kd1,kd2,
A positive control gain; positioning error e of hanger rod and hanging rope1＝ζ1-ζ1d,e2＝ζ2-ζ2d；
Respectively represent the converted system state quantities ζ1,ζ2On-line estimation of
A derivative with respect to time t; lmin,lmaxThe upper limit and the lower limit of the effective length of the lifting rope are respectively set; m, LbRespectively the load mass and the boom length, MdAnd g is the gravity acceleration, and represents the product of the distance from the gravity center of the suspender to the rotating shaft and the mass of the suspender.
Further, the method further comprises: and restoring the speed signal of the system state variable on line according to the system parameters of the marine crane system, the transformed system state variable and the system internal disturbance related to the ship rolling motion.
According to a second object of the present invention, the present invention further provides a marine crane sway-elimination positioning control device based on state observation, which comprises a memory, a processor and a computer program stored in the memory and capable of running on the processor, wherein the processor can implement the control method when executing the program.
According to a third object of the present invention, there is also provided a computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements the marine crane sway mitigation positioning control method.
According to a fourth object of the present invention, the present invention further provides a positioning system for eliminating the swing of a crane for a ship, comprising: angle sensor, displacement sensor and the pendulum-eliminating positioning control device.
The invention has the advantages of
1. In consideration of the influence of practical problems that sea wave interference and speed signals cannot be directly measured and the like, the invention provides a dynamic feedback control method based on state observation, which can realize accurate positioning of a load and quickly eliminate residual swing of the load by effectively controlling a suspender/lifting rope of a marine crane, and is more suitable for being applied to a practical system.
2. The observer designed by the invention can accurately restore the speed value of the state variable by utilizing the measurable output feedback signal (namely, angle and displacement), thereby avoiding the influence of numerical differentiation operation on a real signal. Although the separation principle is not applicable to a nonlinear marine crane system, the method can still strictly theoretically prove the stability of an integral closed-loop system consisting of the marine crane, the observer and the controller, and is expected to be further applied to an actual marine crane system, so that the method has very important practical significance.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the application and, together with the description, serve to explain the application and are not intended to limit the application.
FIG. 1 is a flow chart of a marine crane anti-swing positioning control method of the invention;
FIG. 2 shows the experimental results of the method of the present invention, in which the converted system state quantity, pitch control quantity and rope length control quantity correspond to ζ1、ζ2、ζ3、ubAnd ul；
FIG. 3 shows the results of a comparative experiment in which the system state quantity, the pitch control quantity and the rope length control quantity after the conversion correspond to ζ1、ζ2、ζ3、ubAnd ul。
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 in the present application may be combined with each other without conflict.
Example one
The embodiment discloses a marine crane sway elimination positioning control method based on state observation, as shown in fig. 1, including:
constructing an energy function and a state observer including a control target and rope length limitation based on a dynamic model of a marine crane system, and designing a nonlinear dynamic feedback control method for driving a suspender and a lifting rope to move according to the energy function;
setting system parameters such as the upper limit and the lower limit of the effective length of the lifting rope, the load mass, the length of the suspender, the distance from the gravity center of the suspender to the rotating shaft, the rotational inertia of the suspender and the like;
receiving measurements of a boom pitch angle phi (t), a hoist line length l (t), and a yaw angle of a load theta (t) based on an angle/displacement sensor mounted on a marine crane system;
and obtaining an input signal for controlling the movement of the suspender and the lifting rope according to the nonlinear dynamic feedback control method, realizing the accurate positioning of the load and quickly eliminating the residual swing of the load.
System nonlinear dynamics model and control target
The dynamic equation of the marine crane system established based on the Lagrange method is as follows:
wherein S isθ-φ,Cθ-φ,Sθ-γ,Cθ-γRespectively represent sin (theta-phi), cos (theta-phi), sin (theta-gamma), cos (theta-gamma); phi (t)),
Respectively, the pitch angle of the boom and its corresponding angular velocity and acceleration,/(t),
respectively, the length of the hoist rope and its corresponding speed and acceleration, theta (t),
respectively representing the load swing angle and its corresponding angular velocity and acceleration, gamma (t),
respectively representing the roll angle of the hull and its corresponding angular velocity and acceleration, ub(t),ul(t) control input signals acting on the boom and the lifting rope, respectively, t representing time, the variable being followed by (t) representing the variable as a function of time t; for simplicity, (t) after most variables is omitted; j, m, LbRespectively representing the moment of inertia, the load mass and the boom length, MdG represents the gravity acceleration, which is the product of the distance from the gravity center of the suspender to the rotating shaft and the mass of the suspender; f. ofd1(t),fd2(t),fd3(t) represents the system internal disturbances associated with hull roll motion, respectively, and may be expressed in the form:
where c represents the air resistance coefficient.
The positioning control of the load is usually in the geodetic coordinate system
Taking into account the influence of sea wave interference on the crane system for the ship, the load is loaded on the geodetic coordinate system
Target position of lower (x)d,yd) Can be expressed as
xd＝Lbcos(φd-γ)+lsin(θd-γ),
yd＝Lbsin(φd-γ)-lcos(θd-γ). (5)
Wherein phi isd,ld,θdTarget values of boom pitch angle, hoist rope length, and load swing angle are respectively expressed. Thus, when θ isdWhen the load is γ (t), complete cancellation of the load can be achieved. Thus, it is easy to obtain
Wherein arccos represents an inverse cosine function. Can see phid,ld,θdAre time-varying, thereby increasing the difficulty of effectively controlling the marine crane system. To solve the above problem, the following coordinate transformation can be implemented for subsequent controller/observer design:
therein, ζ1,ζ2,ζ3Is the transformed system state quantity. Thus, ζ can be easily understood from the formulas (6) and (7)1,ζ2,ζ3Target value of (ζ)1d,ζ2d,ζ3dIs a constant and can be expressed as follows:
to facilitate the correlation analysis hereinafter, equations (1) to (4) are transformed into the following matrix-vector form:
G(ζ)＝[(mLb+Md)gC1-mgC3mgζ2S3]T,
u＝[ubul0]T,
wherein,
and
respectively, converted system state quantities ζ1,ζ2,ζ3With respect to the first and second derivatives of time t,
the first and second derivatives of the transformed system state vector ζ with respect to time t,
S1-3,C1-3,C1,C3,S3respectively represent sin (ζ)1-ζ3),cos(ζ1-ζ3),cosζ1,cosζ3,sinζ3。
Based on the specific form of M (ζ), M (ζ) is known to be positive, and the following conclusions can be drawn:
λm‖η‖2≤ηTM(ζ)η≤λM‖η‖2, (10)
wherein η is any three-dimensional vector, the symbol "| · |", represents the 2-norm of the vector, λm,λMWhich represents a positive constant, the value of which,
the derivative of M (ζ) with respect to time is indicated. In addition, it can be seen that
The following properties are satisfied:
therein, ζ1,ζ2For arbitrary three-dimensional vectors, symbols
Infinite norm, l, representing a vectormaxIs the upper limit of the effective length of the lifting rope.
In summary, the control target of the marine crane system during the movement comprises the following four parts: 1) in the geodetic coordinate system
Next, the load is adjusted to a specified position (x)d,yd) Wherein x isd,ydRespectively, the load in the geodetic coordinate system
A target position of; 2)quick elimination of load geodetic coordinate system
Residual swing down; 3) effectively limiting the variation range of the lifting rope in the whole control process, i.e. ensuring
lmin＜l(t)＜lmax,
Where l (t) is the length of the hoist rope, t represents time, and the variable is followed by (t) as a function of time t; for simplicity, (t) after most variables is omitted; lmin,lmaxThe upper limit and the lower limit of the effective length of the lifting rope are respectively set; 4) and restoring the speed signal of the system state variable on line by using the state observer.
Thus, the control objective of the present invention can be expressed in the following mathematical form:
wherein,
each represents ζ1,ζ2,ζ3On-line estimation of
A derivative with respect to time t; lmin,lmaxRespectively the upper limit and the lower limit of the length limit range of the lifting rope.
(II) observer design
Next, a non-linear observer is constructed to restore the speed signal of the state variable on line. Based on the dynamic model of the marine crane system, the following observer can be designed:
wherein,
respectively representing the estimated value of ζ and its derivative with respect to time t,
representing an auxiliary vector, λmIs a positive constant, as defined in equation (10), Λo1＝diag{λo11,λo12,λo13},
Respectively, positive definite diagonal gain matrix, whose value range will be defined later. In addition, an error vector is estimated
Can be defined as
By taking the derivative of equation (14) with respect to time t and simultaneously multiplying M (ζ) on both sides of the obtained equation, in conjunction with equation (15), the following equation can be obtained:
wherein,
to represent
With respect to time tThe second derivative of the first order,
to represent
The first derivative with respect to time t. On the other hand, formula (9) can be rewritten as
Thus, combining formula (16) and formula (17) can be easily obtained
Wherein,
to represent
The second derivative with respect to time t. In view of the property represented by equation (13), the first two terms to the right of the equal sign of equation (18) can be transformed as follows:
and formula (19) is substituted for formula (18), and can be calculated
Equation (20) will be used to analyze the stability of the observer-based dynamic feedback control method later.
(III) controller design
To facilitate controller design, an error signal and a state observation signal are defined.
The following coordinate transformation is first introduced:
where φ (t) represents the pitch angle of the boom, l (t) represents the length of the hoist line, θ (t) represents the yaw angle of the load, γ (t) represents the roll angle of the hull due to the waves, ζ (t) represents the roll angle of the hull due to the waves1(t),ζ2(t),ζ3(t) are the state variables of the system after coordinate transformation, respectively, t represents time, and (t) after the variable represents that the variable is a function related to the time t; for simplicity, (t) after most variables is omitted;
representing the state vector of the system after coordinate transformation, wherein the symbol "T" represents matrix/vector transposition; by using the coordinate transformation and combining the control target, the target value of the transformed system state quantity can be obtained as
Wherein arccos stands for an inverse cosine function, xd,ydRespectively, the load in the geodetic coordinate system
Target position of lower, LbFor boom length, ζ1d,ζ2d,ζ3dRespectively is a state variable zeta of the system after coordinate transformation1,ζ2,ζ3The target value of (2).
Next, an error signal e of the system is defined1(t),e2(t) are each independently
e1＝ζ1-ζ1d,e2＝ζ2-ζ2d,
Therein, ζ1d,ζ2dTarget values of the pitch angle of the boom and the length of the rope are respectively obtained. The derivative of the error signal with respect to time t is then
Are respectively as
Wherein,
each represents ζ1(t),ζ2(t) derivative with respect to time t. In addition, a state variable ζ after coordinate transformation is defined1(t),ζ2(t),ζ3(t) an observed value of
The observation error is
An observed value representing the state vector ζ,
indicating the observed error of the state vector ζ.
Next, an energy function E of the marine crane system including the control target and the rope length limit is constructed as followsm(t)：
Wherein k isp1,kp2,
Indicating a positive control gain. In addition, E (t) represents the energy storage function of the crane system, Emp1(t),Emp2(t) represents a well-constructed energy function, such that Em(t) at the system equilibrium point
A minimum value is reached.
Next, for the energy function Em(t) deriving with respect to time t to obtain
The following were used:
considering that the speed signal cannot be directly obtained through state feedback, the following nonlinear dynamic feedback control method can be designed:
wherein k isd1,
Which indicates a positive control gain, is,
can be obtained by state observers (14), (15). To ensure the stability of the system, the value range of the gain can be selected as
Wherein,
therein, ζ1(0),ζ2(0) Are each ζ1(t),ζ2(t) initial value. Without loss of generality, the initial estimation value of the transformed state variable and the initial value of the derivative of the state variable with respect to the time t are selected as
(IV) stability analysis
The stability of the whole closed loop system consisting of the ship crane system, the observer and the controller is analyzed by utilizing the Lyapunov method and the Lassel invariance principle, and the effectiveness of the dynamic feedback controller (23) based on the state observers (14) and (15) is proved.
First, the following positive definite function is chosen in relation to the observed error signal:
and to V0Derived with respect to time t
Further calculation can be made by substituting the above formula (28) with the formula (20) by using the formula (10) and the formula (11)
Next, an energy function E is utilized for the entire closed-loop system (i.e., considering both the observer and the controller at the same time)m(t) and a positive definite function V0The following Lyapunov candidate function is constructed:
V(t)＝V0(t)+Em(t), (30)
then, the derivative of equation (30) is obtained with respect to time t, and equations (14), (15) and (23) are substituted
The following can be concluded using equation (29):
equation (31) may be further rewritten as follows:
wherein the intermediate vector psi1,ψ2,
Are respectively defined as
To ensure that the three matrices in equation (32) are positive, the following conditions need to be satisfied:
kd1,kd2>0,
namely, it is
kd1,kd2>0,
Further, by using the formula (21), the formula (27) and the formula (30), it is possible to obtain
Accordingly, it can be seen that a sufficient condition for making the three matrices in equation (32) positive is kd1,kd2>0,
Therefore, when the value of the control gain satisfies the formula (36), the formula (32) can be rewritten to
Wherein, β1,β2,β3,β4,β5,
Is a positive constant. Thus, it can be seen that the closed loop system equilibrium point is Lyapunov stable, i.e.
Note the initial value of the rope length ζ2(0) Is always in the effective range (l)min,lmax) Once inside, ζ2(t) is close to lminOr lmaxThen (ζ)2-lmin)2Or (ζ)2-lmax)2It will tend to 0, i.e., V (t) → ∞, clearly contradicting the conclusion in equation (38). Thus, the length of the lifting rope ζ2(t) will always be limited to the valid range (l)min,lmax) And (4) the following steps. In addition, by
It can be known that
V(t)≤V(0). (39)
Meanwhile, according to the formula (26), V (0) can be represented as
Wherein ω is defined in formula (25). From this, it is understood that when the control gain is selected based on the equation (24), the sufficient condition in the equation (36) can be satisfied.
Next, to prove the convergence of the state variables of the closed-loop system, a correlation analysis based on the invariant set is further required. Definition set
And collections
And is
Is composed of
Of the maximum invariant subset. Based on this, it is obvious that
In
Finally, formula (41) is substituted for u in formulae (9) and (23)bCan obtain
mgζ2sinζ3＝0. (43)
Because the length zeta of the lifting rope is controlled in the whole process2(t) can be limited to a valid range (l)min,lmax) In this way, can obtainThe following conclusions are drawn:
then, u in the formula (23) is usedlAnd equations (41) and (44), equation (9) can be further simplified to the following form:
in combination with the conclusions from formulae (16), (17) and formulae (41) to (46), it can be concluded that
Thus, set
The method only comprises the closed-loop system balance point, so that the system balance point can be proved to be asymptotically stable by utilizing the Lassel invariance principle, and the estimated value of the state variable can be converged to the true value of the state variable, thereby proving that the load positioning and swing eliminating control of the marine crane system can be processed when the speed signal cannot be directly measured.
Example two
An object of the present embodiment is to provide a computing device.
In order to achieve the purpose, the invention adopts the following technical scheme:
a marine crane sway-eliminating positioning control device based on state observation comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the processor executes the program to realize the following steps, and the control device comprises:
constructing an energy function and a state observer including a control target and rope length limitation based on a dynamic model of a marine crane system, and designing a nonlinear dynamic feedback control method for driving a suspender and a lifting rope to move according to the energy function;
setting system parameters of a marine crane system;
obtaining measurement values of a boom pitch angle, a lifting rope length and a load swing angle;
obtaining input signals for controlling the movement of the suspender and the lifting rope according to the nonlinear dynamic feedback control method;
and realizing accurate positioning of the load and quickly eliminating residual swing of the load according to the input signal.
EXAMPLE III
An object of the present embodiment is to provide a computer-readable storage medium.
In order to achieve the purpose, the invention adopts the following technical scheme:
a computer-readable storage medium, on which a computer program is stored which, when executed by a processor, performs the steps of:
constructing an energy function and a state observer including a control target and rope length limitation based on a dynamic model of a marine crane system, and designing a nonlinear dynamic feedback control method for driving a suspender and a lifting rope to move according to the energy function;
setting system parameters of a marine crane system;
obtaining measurement values of a boom pitch angle, a lifting rope length and a load swing angle;
obtaining input signals for controlling the movement of the suspender and the lifting rope according to the nonlinear dynamic feedback control method;
and realizing accurate positioning of the load and quickly eliminating residual swing of the load according to the input signal.
Example four
The embodiment aims to provide a marine crane sway-eliminating positioning system.
In order to achieve the purpose, the invention adopts the following technical scheme:
the embodiment provides a marine crane pendulum-eliminating positioning system, including: the device comprises an angle sensor, a displacement sensor and computing equipment, wherein the angle sensor is used for measuring a pitch angle of a suspender and a load swing angle, the displacement sensor is used for measuring the length of a lifting rope, and all the measured values are sent to the computing equipment.
The computing device includes a memory, a processor, and a computer program stored on the memory and executable on the processor.
The processor implements the following steps when executing the program:
constructing an energy function and a state observer including a control target and rope length limitation based on a dynamic model of a marine crane system, and designing a nonlinear dynamic feedback control method for driving a suspender and a lifting rope to move according to the energy function;
setting system parameters of a marine crane system;
obtaining measurement values of a boom pitch angle, a lifting rope length and a load swing angle;
obtaining input signals for controlling the movement of the suspender and the lifting rope according to the nonlinear dynamic feedback control method;
and realizing accurate positioning of the load and quickly eliminating residual swing of the load according to the input signal.
The steps and methods related to the apparatuses of the second, third and fourth embodiments correspond to those of the first embodiment, and specific embodiments can be found in the relevant description of the first embodiment. The term "computer-readable storage medium" should be taken to include a single medium or multiple media containing one or more sets of instructions; it should also be understood to include any medium that is capable of storing, encoding or carrying a set of instructions for execution by a processor and that cause the processor to perform any of the methods of the present invention.
Results of the experiment
In order to verify the effectiveness of the dynamic feedback controller designed by the invention, experiments can be carried out on the self-built hardware platform according to the steps. In the experiment, the values of system parameters such as load mass, suspender length and the like are as follows:
m＝0.34kg,Lb＝0.65m,g＝9.8m/s2,
Md＝0.29kg·m,J＝0.2457kg·m2.
converted system state quantity ζ1,ζ2,ζ3Is set to ζ1(0)＝0deg,ζ2(0)＝0.6m,φ3(0) 0deg, where deg represents angle and m represents meter. Loaded in the geodetic coordinate system
The lower target position is
ydThe system state quantity ζ after conversion can be obtained by taking the value of 0.125m as the value1,ζ2,ζ3Target value of (b) is ζ1d＝30deg,ζ2d＝0.2m,ζ3d0 deg. effective range of sling length (l)min,lmax) Is (0.05m,0.8 m). In addition, the roll motion of the hull is designed to be γ (t) ═ 6sin (0.4t +0.4) deg.
In the experiment, a nonlinear composite control method (Y.Fang, P.Wang, N.Sun, and Y.Zhang, Dynamics analysis and nonlinear control of an offset bore company, IEEE Transactions on Industrial Electronics, vol.61, No.1, pp.414-427, Jan.2014) proposed by Fang et al is taken as a comparison method to verify the effectiveness of the dynamic feedback control method based on state observation designed by the invention. Firstly, the control gains of the observers (14) and (15) and the controller (23) are as follows:
kp1＝24,kd1＝1.5,kp2＝150,kd2＝100,
λo11＝600,λo12＝500,λo13＝300,λo21＝500,λo22＝550,λo23＝300.
meanwhile, through parameter adjustment, the gain in the nonlinear composite control method proposed by Fang and the like can be selected as follows:
k1＝16.5,kL1＝32,k2＝3,kL2＝10,k3＝2.6,kα＝0.2,kβ＝0.25,kx＝0.9,σ＝0.01.
FIGS. 2 and 3 show phasesThe corresponding experimental results, wherein the transformed system state quantity, the boom pitch motion control quantity and the lifting rope length control quantity respectively correspond to phi1、φ2、φ3、FbAnd FlThe dotted lines in the 1 st and 2 nd subgraphs (from top to bottom) represent phi, respectively1,φ2Target position phi of1d,φ2d. By using the control method provided by the invention, the suspender and the lifting rope can reach the designated position within 2s, and the residual swing angle of the load can be completely converged to zero within 4 s. And, in the whole control process, the length of the lifting rope is always limited in an effective range. In addition, the anti-swing time of the invention is obviously shorter than that of the comparison method, and the comparison method can cause the positioning error and the overshoot of the suspender and the lifting rope, thereby greatly reducing the control performance of the marine crane system.
In conclusion, the method of the invention can obtain better control effect, effectively realize the positioning and the swing elimination of the load, and can be applied to an actual system.
Those skilled in the art will appreciate that the modules or steps of the present invention can be implemented using general purpose computing devices, that is, they can be implemented using program code that is executable by a computing device and that is stored in a memory device for execution by the computing device, that is, they can be separately fabricated into individual integrated circuit modules, or that multiple modules or steps thereof can be fabricated into a single integrated circuit module. The present invention is not limited to any specific combination of hardware and software.
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 (10)
1. A marine crane sway elimination positioning control method based on state observation is characterized by comprising the following steps:
constructing an energy function and a state observer including a control target and rope length limitation based on a dynamic model of a marine crane system, and designing a nonlinear dynamic feedback control method for driving a suspender and a lifting rope to move according to the energy function;
setting system parameters of a marine crane system;
obtaining measurement values of a boom pitch angle, a lifting rope length and a load swing angle;
obtaining input signals for controlling the movement of the suspender and the lifting rope according to the nonlinear dynamic feedback control method;
and realizing accurate positioning of the load and quickly eliminating residual swing of the load according to the input signal.
2. The marine crane sway-elimination positioning control method based on state observation according to claim 1, wherein the control targets comprise: 1) under a geodetic coordinate system, adjusting the load to reach a specified position; 2) eliminating residual swing under a load geodetic coordinate system; 3) limiting the range of variation of the hoist rope throughout the control process.
3. The marine crane sway mitigation positioning method based on state observations as claimed in claim 1, wherein the system parameters of the marine crane system comprise: the load mass, the boom length, the product of the boom center of gravity distance to the axis of rotation and the boom mass, and the moment of inertia of the boom.
4. The marine crane sway-elimination positioning control method based on state observation according to claim 1, further comprising: carrying out coordinate transformation on the original state variable of the system to obtain a transformed state quantity; and calculating a target value of the transformed system state quantity according to the specified position of the load in the geodetic coordinate system.
5. The marine crane sway-elimination positioning control method based on state observation according to claim 4, wherein the target values of the system state quantities are:
wherein arccos represents an inverse cosine function, (x)d,yd) Indicating the load in the geodetic coordinate system
Target position of lower, LbFor boom length, ζ1d,ζ2d,ζ3dRespectively, converted system state quantities ζ1,ζ2,ζ3The target value of (2).
6. The marine crane sway-elimination positioning control method based on state observation according to claim 5, wherein the nonlinear dynamic feedback control method for controlling the movement of the boom and the lifting rope is as follows:
wherein u isb,ulRespectively driving the pitching motion of the suspender and the control input of the length of the lifting rope; k is a radical ofp1,kp2,kd1,kd2,
A positive control gain; positioning error e of hanger rod and hanging rope1＝ζ1-ζ1d,e2＝ζ2-ζ2d；
Respectively represent the converted system state quantities ζ1,ζ2On-line estimation
A derivative with respect to time t; lmin,lmaxThe upper limit and the lower limit of the effective length of the lifting rope are respectively set; m, LbRespectively the load mass and the boom length, MdAnd g is the gravity acceleration, and represents the product of the distance from the gravity center of the suspender to the rotating shaft and the mass of the suspender.
7. The marine crane sway-elimination positioning control method based on state observation according to claim 1, further comprising: and restoring the speed signal of the system state variable on line according to the system parameters of the marine crane system, the transformed system state variable and the system internal disturbance related to the ship rolling motion.
8. A vessel crane sway-elimination positioning control device based on state observation, comprising a memory, a processor and a computer program stored on the memory and operable on the processor, wherein the processor, when executing the program, implements the vessel crane sway-elimination positioning control method according to any one of claims 1 to 7.
9. A computer-readable storage medium, on which a computer program is stored, which when executed by a processor implements a marine crane sway-elimination positioning control method as claimed in any one of claims 1 to 7.
10. A marine crane pendulum-removal positioning system, characterized by, includes: an angle sensor, a displacement sensor and a marine crane sway-elimination positioning control device based on state observation according to claim 8.
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| CN109740240B (en) * | 2018-12-28 | 2023-01-31 | 济南大学 | Design method and system of tower crane self-adaptive integral sliding mode controller capable of eliminating load swing |
| CN110937510B (en) * | 2019-12-10 | 2020-11-06 | 山东大学 | Offshore crane stability control method and system with double-pendulum characteristic |
| CN111176318B (en) * | 2020-02-10 | 2022-12-06 | 南开大学 | Positioning and swing eliminating method and system for flying and lifting system for eliminating steady-state error |
| CN112327623B (en) * | 2020-11-04 | 2022-03-08 | 中南大学 | Double-pendulum crane sliding mode control method based on load swing state observation |
| CN113031655B (en) * | 2021-03-23 | 2022-05-03 | 南开大学 | Flying and lifting system accompanied with load lifting and control method thereof |
| CN113387276B (en) * | 2021-07-08 | 2021-12-14 | 哈尔滨理工大学 | Ship crane control method for improving LQR |
| CN113651239A (en) * | 2021-07-15 | 2021-11-16 | 深圳市海浦蒙特科技有限公司 | Speed adjusting method, device and equipment of crane system |
| CN114408098B (en) * | 2021-12-23 | 2023-06-27 | 宜昌测试技术研究所 | Swing arm control method combining retraction point position and simulation angle |
Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE102014008094A1 (en) * | 2014-06-02 | 2015-12-03 | Liebherr-Werk Nenzing Gmbh | Method for controlling the alignment of a crane load and a jib crane |
| CN105293284A (en) * | 2015-11-18 | 2016-02-03 | 德马科起重机械有限公司 | Robust sliding mode observation method and robust sliding mode observer for lifting deflection angle of crane |
| CN105523476A (en) * | 2015-12-31 | 2016-04-27 | 北京起重运输机械设计研究院 | Anti-swing control method and system for bridge crane |
| CN105668422A (en) * | 2016-03-21 | 2016-06-15 | 南开大学 | Bridge crane emergency braking method for trolley stop and load swing eliminating |
| CN106365043A (en) * | 2016-09-12 | 2017-02-01 | 同济大学 | Bridge crane half-open-loop constant-speed anti-swing control method |
| CN106986271A (en) * | 2017-04-20 | 2017-07-28 | 南开大学 | Consider lasting interference and the marine hoist control method of parameter uncertainty |
| CN107024865A (en) * | 2017-05-02 | 2017-08-08 | 南开大学 | Drive lacking jib crane positions the pendulum nonlinear control method that disappears |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CL2012000933A1 (en) * | 2011-04-14 | 2014-07-25 | Harnischfeger Tech Inc | A method and a cable shovel for the generation of an ideal path, comprises: an oscillation engine, a hoisting engine, a feed motor, a bucket for digging and emptying materials and, positioning the shovel by means of the operation of the lifting motor, feed motor and oscillation engine and; a controller that includes an ideal path generator module. |
-
2018
- 2018-04-28 CN CN201810399899.7A patent/CN108469736B/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE102014008094A1 (en) * | 2014-06-02 | 2015-12-03 | Liebherr-Werk Nenzing Gmbh | Method for controlling the alignment of a crane load and a jib crane |
| CN105293284A (en) * | 2015-11-18 | 2016-02-03 | 德马科起重机械有限公司 | Robust sliding mode observation method and robust sliding mode observer for lifting deflection angle of crane |
| CN105523476A (en) * | 2015-12-31 | 2016-04-27 | 北京起重运输机械设计研究院 | Anti-swing control method and system for bridge crane |
| CN105668422A (en) * | 2016-03-21 | 2016-06-15 | 南开大学 | Bridge crane emergency braking method for trolley stop and load swing eliminating |
| CN106365043A (en) * | 2016-09-12 | 2017-02-01 | 同济大学 | Bridge crane half-open-loop constant-speed anti-swing control method |
| CN106986271A (en) * | 2017-04-20 | 2017-07-28 | 南开大学 | Consider lasting interference and the marine hoist control method of parameter uncertainty |
| CN107024865A (en) * | 2017-05-02 | 2017-08-08 | 南开大学 | Drive lacking jib crane positions the pendulum nonlinear control method that disappears |
Non-Patent Citations (4)
| Title |
|---|
| A novel sliding mode control method for underactuated overhead cranes;Mi Zhou 等;《2017 Chinese Automation Congress (CAC)》;20180101;第4548-4553页 * |
| Bounded tracking and anti-swing control of underactuated cranes for payload transportation and lowering;Ning Sun 等;《Proceedings of the 32nd Chinese Control Conference》;20131021;第653-661页 * |
| 欠驱动惯性轮摆***全局滑模控制;孙宁 等;《控制理论与应用》;20160531;第33卷(第5期);第653-660页 * |
| 欠驱动桥式吊车消摆跟踪控制;孙宁 等;《控制理论与应用》;20150331;第32卷(第3期);第326-333页 * |
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