CN110407094B - Bridge crane positioning anti-swing control method based on dynamic smooth track - Google Patents

Bridge crane positioning anti-swing control method based on dynamic smooth track Download PDF

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CN110407094B
CN110407094B CN201910555584.1A CN201910555584A CN110407094B CN 110407094 B CN110407094 B CN 110407094B CN 201910555584 A CN201910555584 A CN 201910555584A CN 110407094 B CN110407094 B CN 110407094B
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acceleration
load
trolley
track
bridge crane
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CN110407094A (en
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范波
张炜炜
付主木
许惠
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Henan University of Science and Technology
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Henan University of Science and Technology
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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

Abstract

The invention discloses a bridge crane positioning anti-swing control method based on a dynamic smooth track, which is based on a two-dimensional bridge crane dynamic model, adopts a phase plane analysis method aiming at the defect of three-section acceleration, takes the three-section acceleration as a basis and introduces an acceleration smooth transition link to obtain an analytical expression convenient to apply and design a control system, reduces the direct impact of acceleration change on a trolley, considers the requirements of accurate positioning and load anti-swing of the trolley and simultaneously improves the response speed of the system; compared with the existing track control method, the method can enable the trolley to accurately reach the designated position and prevent the load from swinging, effectively reduces the impact of acceleration change on the trolley, achieves a better control effect, solves the problems of residual swinging of the load, low load positioning precision and violent load swinging when the trolley pulls a lifting rope in the transportation process of the bridge crane to cause the inertial swinging of the load and positioning, and realizes efficient positioning anti-swinging control when the load of the bridge crane is lifted.

Description

Bridge crane positioning anti-swing control method based on dynamic smooth track
Technical Field
The invention relates to the technical field of bridge crane control, in particular to a bridge crane positioning anti-swing control method based on a dynamic smooth track.
Background
At present, the bridge crane is widely applied to various fields of national economic construction as a transport machine and plays an extremely important role. In order to create higher value, the working efficiency of the bridge crane must be continuously improved, and the safe operation index, the trolley positioning and the load anti-swing performance determine the conveying efficiency of the bridge crane to a great extent.
Aiming at the positioning and anti-swing of the bridge crane, scholars at home and abroad carry out extensive research, wherein more classically, an open-loop and closed-loop control method is designed on the basis of a two-dimensional bridge crane dynamic model. The closed-loop control needs to monitor the running state of the bridge crane in real time by means of various distance, speed, angle and gravity sensors, but the method causes the design of a bridge crane control system to be complex, the stability to be poor and the cost to be multiplied; the open-loop control mode is simple and easy to implement, has good control effect in actual engineering, and has reliability and universality.
First, the open-loop control method is most representative of input shaping and trajectory planning. In the prior art, a time-lag filter is designed by analyzing natural oscillation frequency and damping ratio, and effective control is carried out on swinging. And then through continuous research, a pendulum eliminating method of PD combined input shaping control is designed, and the pendulum eliminating method has a remarkable inhibiting effect on the pendulum. However, the method linearizes the swing angle of the bridge crane model near the balance point, and if the swing exceeds the linearization value, the swing angle change is difficult to judge;
in addition, in the prior art, a S-shaped track is constructed, and a self-adaptive tracking controller is designed to perform tracking control on the S-shaped track, so that positioning and anti-swing are realized; but the S-shaped track only has positioning performance and cannot eliminate load swing, and the inhibition performance of the load swing is completely realized by a tracking controller;
thirdly, in the prior art, iterative learning is adopted to plan the running track of the bridge crane, and a better control effect is obtained on a bridge crane experimental platform controlled by a servo motor; however, when the method is applied, iterative optimization is required, and indexes such as the maximum speed, the maximum acceleration, the load swing angle and the like of the trolley cannot be guaranteed;
fourthly, in the prior art, a trajectory planning method based on a phase plane is provided; however, the jerk is not smooth at the switching point due to the method, so that the actuator is easy to be impacted greatly, and the phenomenon of skidding occurs.
Disclosure of Invention
In view of the above, in order to solve the above-mentioned deficiencies of the prior art, an object of the present invention is to provide a method for controlling positioning and anti-swing of a bridge crane based on a dynamic smooth trajectory, which combines the flexibility of applying a robot technology and the high efficiency of an automation technology, and applies the method to a bridge crane system, so as to solve the problems of inertial swing of a load and residual swing of the load during positioning caused by a trolley pulling a lifting rope during transportation of the bridge crane, solve the problems of low load positioning accuracy and severe load swing, and realize efficient positioning and anti-swing control during load lifting of the bridge crane.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a bridge crane positioning anti-swing control method based on a dynamic smooth track comprises the following steps:
s1: obtaining the displacement and swing angle information of the load and the control quantity of the rope length coupled to the displacement of the trolley;
s2: analyzing the relation between the displacement swing angle and the acceleration of the trolley in a two-dimensional coordinate system based on a two-dimensional bridge crane dynamic model, and establishing an acceleration control signal based on the displacement swing angle by combining a phase plane analysis method;
s21: establishing a two-dimensional bridge crane dynamic model: according to a two-dimensional bridge crane simplified model, under a generalized coordinate, a Lagrange dynamical equation is utilized to establish a two-dimensional bridge crane dynamical model with a fixed rope length:
Figure GDA0002694953560000031
Figure GDA0002694953560000032
s22: and (3) obtaining a phase plane curve equation when the trolley runs at the constant acceleration a by combining a phase plane analysis method:
Figure GDA0002694953560000033
wherein θ (0) is 0 and
Figure GDA0002694953560000034
indicating the swing angle and the initial angular velocity in the initial state,
Figure GDA0002694953560000035
representing the natural oscillation frequency;
s23: establishing phase equilibriumSurface curve: based on step S22, at the abscissa of θ (t),
Figure GDA0002694953560000036
in a coordinate system of ordinate, expressed as [ -a/g, 0 [ - ]]Is used as the center of a circle,
Figure GDA0002694953560000037
a circle with a radius, namely a phase plane curve;
s24: according to the phase plane curve, the motion condition of the bridge crane is analyzed, and when a is not equal to 0, the load has a fixed angular speed omeganPerforming simple pendulum motion; when a is 0, the load and the trolley keep relatively static;
s3: establishing a motion control system, establishing a symmetrical acceleration motion track, namely a three-section acceleration track, by utilizing the swinging rule of the load in the running process, and setting various performance indexes to ensure that the trolley accurately reaches a specified position and eliminate load swinging;
s31: the expression of the three-section type acceleration track is as follows:
Figure GDA0002694953560000041
s32: introducing an acceleration smooth transition curve: based on step S31, in case of a determination of the transport distance, i.e. the specified position displacement uxWhen x (t), the transport displacement in the acceleration stage is the same as that in the deceleration stage, the acceleration trajectory curve is centrosymmetric, and the whole transport process meets the following performance indexes:
(1) safe swing angle index: maximum pivot angle u during operationθ≥|θ(t)|；
(2) Maximum acceleration index: maximum acceleration during operation
Figure GDA0002694953560000042
(3) Maximum speed index: maximum speed of operation
Figure GDA0002694953560000043
(4) The steady state index is as follows: the swing angle theta (t) during uniform motion and stop motion is 0;
s4: by adjusting the displacement time functions of the load in an acceleration stage, a uniform motion stage and a deceleration stage, a dynamic smooth positioning anti-swing track of the load is constructed on the premise of not influencing positioning; obtaining a track equation under each performance index according to the three-section type acceleration track expression; if the impact on the trolley under the smooth track is more relieved than the three-section acceleration track, the track planning is finished.
Further, in step S21, f (t) represents a resultant force acting on the trolley, M and M represent the mass of the trolley and the load, respectively, x (t) represents a displacement of the trolley in the horizontal direction, θ (t) represents an included angle of the load in the vertical direction, i.e., a swing angle,
Figure GDA0002694953560000044
and
Figure GDA0002694953560000045
respectively, the angular velocity and the angular acceleration of the load swing, l the length of the hoist rope, and g the acceleration of gravity.
Further, in step S31, within a given carrying distance, each performance index is limited, and a that satisfies the requirement is calculated from the phase planemax、taAnd tcAnd obtaining an accurate expression of the three-section acceleration trajectory, so that the bridge crane can reach the specified conveying position within the safe operation range at the fastest speed to eliminate swing.
Further, the performance indexes are as follows: and limiting the maximum acceleration, the maximum speed, the rope length and the maximum swing angle.
Further, the accurate expression of the three-stage acceleration trajectory is as follows:
Figure GDA0002694953560000051
wherein, ω is pi/t1To avoid load-reciprocating pendulumMoving, then t1∈(0,π/2ωn)。
The invention has the beneficial effects that:
on the basis of a two-dimensional bridge crane dynamic model, aiming at the defects of three-section acceleration, a phase plane analysis method is adopted, the three-section acceleration is taken as the basis, and an acceleration smooth transition link is introduced to obtain an analytical expression which is convenient to apply, so that a control system is designed according to an equation, the direct impact of acceleration change on a trolley is reduced, the requirements of accurate positioning and load anti-swing of the trolley are met, and the response speed of the system is improved; compared with the existing track control method, the method can enable the trolley to accurately reach the designated position and prevent the load from swinging, effectively reduces the impact of acceleration change on the trolley, achieves a better control effect, solves the problems of inertial swinging of the load and residual swinging of the load during positioning caused by the fact that the trolley pulls a lifting rope in the transportation process of the bridge crane, solves the problems of low load positioning precision and violent load swinging, and realizes efficient positioning anti-swinging control during load lifting of the bridge crane.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a schematic diagram of a bridge crane dynamics model of the present invention;
FIG. 2 is a schematic diagram of a phase plane curve;
FIG. 3 is a schematic diagram of a three-segment acceleration trajectory;
FIG. 4 is a schematic diagram of a smooth varying acceleration trajectory;
FIG. 5 is a phase plane curve schematic of a smooth acceleration trajectory;
FIG. 6 is a graph showing the results of a displacement experiment;
FIG. 7 is a schematic diagram of the variation trend of the displacement experiment;
FIG. 8 is a diagram illustrating the results of two trajectory displacement experiments;
fig. 9 is a schematic diagram of the results of two trajectory swing angle experiments.
Detailed Description
The following specific examples are given to further clarify, complete and detailed the technical solution of the present invention. The present embodiment is a preferred embodiment based on the technical solution of the present invention, but the scope of the present invention is not limited to the following embodiments.
A bridge crane positioning anti-swing control method based on a dynamic smooth track comprises the following steps:
s1: obtaining the displacement and swing angle information of the load and the control quantity of the rope length coupled to the displacement of the trolley;
s2: analyzing the relation between the displacement swing angle and the acceleration of the trolley in a two-dimensional coordinate system based on a two-dimensional bridge crane dynamic model, and establishing an acceleration control signal based on the displacement swing angle by combining a phase plane analysis method;
s21: establishing a two-dimensional bridge crane dynamic model: according to a two-dimensional bridge crane simplified model, under a generalized coordinate, a Lagrange dynamical equation is utilized to establish a two-dimensional bridge crane dynamical model with a fixed rope length:
Figure GDA0002694953560000071
Figure GDA0002694953560000072
s22: and (3) obtaining a phase plane curve equation when the trolley runs at the constant acceleration a by combining a phase plane analysis method:
Figure GDA0002694953560000073
wherein θ (0) is 0 and
Figure GDA0002694953560000074
indicating the swing angle and the initial angular velocity in the initial state,
Figure GDA0002694953560000075
representing the natural oscillation frequency;
s23: establishing a phase plane curve: based on step S22, at the abscissa of θ (t),
Figure GDA0002694953560000076
in a coordinate system of ordinate, expressed as [ -a/g, 0 [ - ]]Is used as the center of a circle,
Figure GDA0002694953560000077
a circle with a radius, namely a phase plane curve;
s24: according to the phase plane curve, the motion condition of the bridge crane is analyzed, and when a is not equal to 0, the load has a fixed angular speed omeganPerforming simple pendulum motion; when a is 0, the load and the trolley keep relatively static;
s3: establishing a motion control system, establishing a symmetrical acceleration motion track, namely a three-section acceleration track, by utilizing the swinging rule of the load in the running process, and setting various performance indexes to ensure that the trolley accurately reaches a specified position and eliminate load swinging;
s31: the expression of the three-section type acceleration track is as follows:
Figure GDA0002694953560000081
s32: introducing an acceleration smooth transition curve: based on step S31, in case of a determination of the transport distance, i.e. the specified position displacement uxWhen x (t), the transport displacement in the acceleration stage is the same as that in the deceleration stage, the acceleration trajectory curve is centrosymmetric, and the whole transport process meets the following performance indexes:
(1) safe swing angle index: maximum pivot angle u during operationθ≥|θ(t)|；
(2) Maximum acceleration index: maximum acceleration during operation
Figure GDA0002694953560000082
(3) Maximum speed index: maximum speed of operation
Figure GDA0002694953560000083
(4) The steady state index is as follows: the swing angle theta (t) during uniform motion and stop motion is 0;
s4: by adjusting the displacement time functions of the load in an acceleration stage, a uniform motion stage and a deceleration stage, a dynamic smooth positioning anti-swing track of the load is constructed on the premise of not influencing positioning; obtaining a track equation under each performance index according to the three-section type acceleration track expression; if the impact on the trolley under the smooth track is more relieved than the three-section acceleration track, the track planning is finished.
Further, in step S21, f (t) represents a resultant force acting on the trolley, M and M represent the mass of the trolley and the load, respectively, x (t) represents a displacement of the trolley in the horizontal direction, θ (t) represents an included angle of the load in the vertical direction, i.e., a swing angle,
Figure GDA0002694953560000084
and
Figure GDA0002694953560000085
respectively, the angular velocity and the angular acceleration of the load swing, l the length of the hoist rope, and g the acceleration of gravity.
Further, in step S31, within a given carrying distance, each performance index is limited, and a that satisfies the requirement is calculated from the phase planemax、taAnd tcAnd obtaining an accurate expression of the three-section acceleration trajectory, so that the bridge crane can reach the specified conveying position within the safe operation range at the fastest speed to eliminate swing.
Further, the performance indexes are as follows: and limiting the maximum acceleration, the maximum speed, the rope length and the maximum swing angle.
Further, the accurate expression of the three-stage acceleration trajectory is as follows:
Figure GDA0002694953560000091
wherein, ω is pi/t1To avoid the load from oscillating back and forth, t1∈(0,π/2ωn)。
Examples
The invention is further explained in detail by the following embodiments with reference to the attached drawings;
step 1: the dynamic model analysis of the bridge crane, the load transported by the bridge crane mainly depends on the actions of a cart, a trolley and a lifting rope, so that a five-degree-of-freedom three-dimensional mathematical model of the bridge crane is established. The two-degree-of-freedom pivot angle in the model is determined by the adding (subtracting) speed and the rope length of the cart and the trolley, and the motions of the cart and the trolley are in a decoupling state, so that only the motion in one direction needs to be researched, and the control rules in the other direction are the same. Establishing a simplified two-dimensional bridge crane dynamic model in a two-dimensional coordinate system, as shown in fig. 1, wherein: m and M respectively represent the mass of the trolley and the load, F represents power, l is the length of the lifting rope, and theta is a load swing angle;
in the process of transporting loads by the bridge crane, the length of the lifting rope is generally unchanged in order to ensure the transportation safety. Simplifying the model by the graph 1, and utilizing Lagrange kinetic equation under generalized coordinates[11]Establishing a two-dimensional bridge crane mathematical model with the following fixed rope length:
Figure GDA0002694953560000101
Figure GDA0002694953560000102
in the formula: f (t) represents the resultant force acting on the trolley, M and M represent the mass of the trolley and the load respectively, x (t) represents the displacement of the trolley in the horizontal direction, theta (t) represents the included angle of the load in the vertical direction, namely the swing angle,
Figure GDA0002694953560000103
and
Figure GDA0002694953560000104
respectively representing the angular velocity and the angular acceleration of the load swing, wherein l is the length of the lifting rope, and g is the gravity acceleration;
step 2: analyzing the model by using a phase plane analysis method, wherein the safe swing angle of the bridge crane is less than 5 degrees, so sin (theta (t)) ≈ theta (t), and cos (theta (t)) ≈ 1;
(2) can be simplified into
Figure GDA0002694953560000105
Solving a differential equation (3), and combining a phase plane analysis method to obtain a phase plane curve equation when the trolley runs at a constant acceleration a:
Figure GDA0002694953560000106
in the formula: θ (0) is 0 and
Figure GDA0002694953560000107
indicating the swing angle and the initial angular velocity in the initial state,
Figure GDA0002694953560000108
representing the natural oscillation frequency;
the formula (4) is represented by the formula (t) on the abscissa,
Figure GDA0002694953560000109
in a coordinate system of ordinate, can be expressed as [ -a/g, 0 [ - ]]Is used as the center of a circle,
Figure GDA00026949535600001010
a circle with a radius; the graph is shown in fig. 2, and when a ≠ 0, it can be known from the analysis of the motion of the bridge crane that the load has a fixed angular velocity ωnPerforming simple pendulum motion;when a is 0, the load and the trolley keep relatively static;
and step 3: three-section acceleration track control analysis, namely, establishing a symmetrical acceleration motion track, namely a three-section acceleration track, according to the phase plane analysis and by utilizing the swinging rule of the load in the running process, so as to ensure that the trolley can accurately reach a specified position and eliminate load swinging; the planned trajectory is shown in fig. 3, in which: a ismaxRepresenting maximum acceleration, taAnd tbRespectively representing the duration of the acceleration (deceleration) and the duration of the uniform speed;
the expression of the three-section type acceleration track is as follows:
Figure GDA0002694953560000111
within a given conveying distance, limiting various performance indexes, namely limiting maximum acceleration, maximum speed, rope length, maximum swing angle and the like; calculating a meeting the requirement according to the phase planemax、taAnd tcObtaining an accurate expression of the three-section acceleration trajectory, and ensuring that the bridge crane can reach the designated conveying position to eliminate swing within the safe operation range at the fastest speed;
and 4, step 4: the smooth track control design is adopted, the three-section acceleration track directly gives the maximum acceleration value to the actuating mechanism in the acceleration switching process, a smooth transition link is lacked, action response delay is caused, the impact on the trolley is large, and the phenomenon of slipping and shaking is easy to occur; in order to avoid the phenomenon and enable the transportation to be more stable and accurate, an acceleration smooth transition curve needs to be introduced into the three-section acceleration track; for this purpose, a new trajectory is planned as shown in fig. 4, in which: t is t1、t2、t3Respectively representing acceleration change acceleration (deceleration) stage time, acceleration constant acceleration (deceleration) stage time and uniform speed stage time;
in the case of a transport distance determination, i.e. a specified position displacement uxWhen x (t) is satisfied, the conveying displacement in the acceleration stage and the deceleration stage is the same, the acceleration trajectory curve is centrosymmetric, and the whole conveying process is satisfied withPerformance indexes are as follows:
1) safe swing angle index: maximum pivot angle u during operationθ≥|θ(t)|；
2) Maximum acceleration index: maximum acceleration during operation
Figure GDA0002694953560000121
3) Maximum speed index: maximum speed of operation
Figure GDA0002694953560000122
4) The steady state index is as follows: the swing angle theta (t) during uniform motion and stop motion is 0;
by using the track of FIG. 3, a smoothly varying trigonometric function curve of the acceleration is introduced in the acceleration stage, ensuring that the acceleration rate of change is at t1During the time interval, the acceleration is increased from small to large and then reaches the maximum acceleration, and t is operated at the acceleration2(ii) a Before the uniform motion is carried out, the acceleration change rate is controlled by adopting the same method, so that the acceleration is reduced to zero, the transportation speed is increased, the transportation time is shortened, and the slipping and shaking caused by overlarge acceleration change are avoided; similarly, similar control rules are adopted in the deceleration stage, so that the trolley can accurately reach the designated position, and the load stops swinging; the expression is as follows:
Figure GDA0002694953560000123
in the formula: ω pi/t1To avoid the load from oscillating back and forth, t1∈(0,π/2ωn)；
Then it is determined that,
Figure GDA0002694953560000124
substituting the expression of the time into (3) can obtain
Figure GDA0002694953560000131
The second-order heterogeneous differential equation can be solved
Figure GDA0002694953560000132
Then
Figure GDA0002694953560000133
According to (7) and (10), the compounds are obtained
Figure GDA0002694953560000134
From formula (11), when t is t ═ t1The end point of the variable acceleration motion is located in the third quadrant. The phase plane curve from which the acceleration trajectory can be smoothed based on the symmetry of the motion is shown in fig. 5, in which: o is1、O2Circle centers of an acceleration stage and a deceleration stage when the acceleration of the trolley is constant respectively, then | OO1|＝amax(ii)/g; A. b is the maximum load swing angle of the acceleration stage and the deceleration stage when the acceleration of the trolley is constant; c is the end point of the first segment of smooth over acceleration; d is the projection of C on the horizontal axis; OC represents a complex change phase plane curve of the first section of smooth transition acceleration, and O is a swing angle during uniform motion and stop motion;
the coordinates of C are given by the formulae (9) and (10)
Figure GDA0002694953560000135
From the coordinate of C, α is an acute angle, then
Figure GDA0002694953560000136
From the equation (12), according to the conclusion of FIG. 3, analyzing FIGS. 4 and 5, the
Figure GDA0002694953560000141
In the formula: T2T1+t2Representing the period of the whole acceleration stage, wherein the load swing period is half of the simple pendulum motion period;
the integration of (6) is carried out twice
ux＝vmax(2t1+t2+t3) (14)
Figure GDA0002694953560000142
From FIG. 5, it can be seen that
Figure GDA0002694953560000143
In the formula:
Figure GDA0002694953560000144
the C coordinate can be obtained.
According to (14), a
Figure GDA0002694953560000145
Under the limited performance indexes, the following performance indexes can be obtained from the formulas (14), (15) and (16):
1) maximum value of speed:
Figure GDA0002694953560000146
2) maximum value of acceleration:
Figure GDA0002694953560000147
at total delivery time TtoalA distance u from the transportxUnder known conditions, the specific expression of the smooth acceleration track can be obtained by combining the expressions (7), (13) and (17) with the performance indexes 1) and 2);
derivation of expression (6) gives
Figure GDA0002694953560000151
As can be seen from equation (18), the impact on the trolley under the smooth trajectory is greatly relieved compared with the three-stage acceleration trajectory, and the trajectory planning is completed.
In the embodiment, the positioning anti-swing performance of the planned smooth acceleration track is verified by using a three-dimensional crane experiment platform. According to the trajectory planning method, parameters of a three-section acceleration trajectory, a smooth transition trajectory and a trigonometric function trajectory are obtained, as shown in table 1, and parameters of an experimental platform are shown in table 2:
TABLE 1 trace parameter table
Figure GDA0002694953560000152
TABLE 2 platform parameters
Platform parameters M m l g ux uv ua uθ t
Numerical value 6.157 1 0.75 9.8 0.6 0.4 0.2 2 3.94
TABLE 3 data of experimental results
Figure GDA0002694953560000153
Wherein, the experimental results are shown in fig. 7-10 and table 3 above, in table 3: thetaresIndicating the residual swing angle. The experimental result shows that the actual displacement has smaller displacement difference compared with the planned displacement, and the actual displacement changes along with the planned displacement, which is beneficial to improving the positioning precision. On the other hand, in the whole transportation process, the actual change of the swing angle is within a safe range, the amplitude of the stable swing angle is small, and the purpose of restraining the swing angle is effectively achieved. In a word, the smooth transition track is superior to the trigonometric function track in the aspects of swing angle inhibition and quick positioning, the positioning precision and the swing angle are both small, and the method has a good application prospect.
In the invention, a smooth transition function is used, and a track equation under a limited performance index, namely a formula (18), is calculated according to an optimized phase plane curve; the load swing angle is in the safety range in guaranteeing the whole transportation process of the bridge crane, and the trolley can accurately reach the designated position and eliminate the load swing, so that the smoothness of the transportation process is improved. The influence that the track can reduce impact is verified through experiments, the shaking of the trolley is effectively reduced, the slipping phenomenon is avoided, the residual swing is smaller, and the working stability and the transportation efficiency of the bridge crane are improved. The smoothness of the track is very beneficial to the adoption of tracking control, and a theoretical basis is provided for the safe, rapid, accurate and stable transportation of goods by the automatic hoisting equipment.
The principal features, principles and advantages of the invention have been shown and described above. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to explain the principles of the invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the invention as expressed in the following claims. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (1)

1. A bridge crane positioning anti-swing control method based on dynamic smooth track is characterized in that: the method comprises the following steps:
s1: obtaining the displacement and swing angle information of the load and the control quantity of the rope length coupled to the displacement of the trolley;
s2: analyzing the relation between the displacement swing angle and the acceleration of the trolley in a two-dimensional coordinate system based on a two-dimensional bridge crane dynamic model, and establishing an acceleration control signal based on the displacement swing angle by combining a phase plane analysis method;
s21: establishing a two-dimensional bridge crane dynamic model: according to a two-dimensional bridge crane simplified model, under a generalized coordinate, a Lagrange dynamical equation is utilized to establish a two-dimensional bridge crane dynamical model with a fixed rope length:
Figure FDA0002694953550000011
Figure FDA0002694953550000012
wherein F (t) represents the resultant force acting on the trolley, M and M represent the mass of the trolley and the load respectively, x (t) represents the displacement of the trolley in the horizontal direction, theta (t) represents the included angle of the load in the vertical direction, namely the swing angle,
Figure FDA0002694953550000013
and
Figure FDA0002694953550000014
respectively representing the angular velocity and the angular acceleration of the load swing, wherein l is the length of the lifting rope, and g is the gravity acceleration;
s22: and (3) obtaining a phase plane curve equation when the trolley runs at the constant acceleration a by combining a phase plane analysis method:
Figure FDA0002694953550000015
wherein θ (0) is 0 and
Figure FDA0002694953550000016
indicating the swing angle and the initial angular velocity in the initial state,
Figure FDA0002694953550000017
representing the natural oscillation frequency;
s23: establishing a phase plane curve: based on step S22, at the abscissa of θ (t),
Figure FDA0002694953550000018
in a coordinate system of ordinate, expressed as [ -a/g, 0 [ - ]]Is used as the center of a circle,
Figure FDA0002694953550000021
a circle with a radius, namely a phase plane curve;
s24: according to the phase plane curve, the motion condition of the bridge crane is analyzed, and when a is not equal to 0, the load has a fixed angular speed omeganPerforming simple pendulum motion; when a is 0, the load and the trolley keep relatively static;
s3: establishing a motion control system, establishing a symmetrical acceleration motion track, namely a three-section acceleration track, by utilizing the swinging rule of the load in the running process, and setting various performance indexes to ensure that the trolley accurately reaches a specified position and eliminate load swinging;
s31: the expression of the three-section type acceleration track is as follows:
Figure FDA0002694953550000022
wherein, amaxRepresenting maximum acceleration, taIndicating the duration of acceleration or deceleration, tcIndicating the duration of the uniform speed;
within a given transport distance, various performance indicators are defined: limiting the maximum acceleration, the maximum speed, the rope length and the maximum swing angle, and calculating a meeting the requirement according to the phase plane curvemax、taAnd tcObtaining a three-section type acceleration track accurate expression, so that the bridge crane can reach the designated conveying position to eliminate swing within a safe operation range at the fastest speed;
the accurate expression of the three-section acceleration track is as follows:
Figure FDA0002694953550000031
wherein, ω is pi/t1To avoid the load from oscillating back and forth, t1∈(0,π/2ωn)，t1Acceleration or deceleration phase time, t, representing variation of acceleration2Acceleration or deceleration steps indicating constant accelerationPeriod of time, t3Representing the constant speed stage time;
s32: introducing an acceleration smooth transition curve: based on step S31, in case of a determination of the transport distance, i.e. the specified position displacement uxWhen x (t), the transport displacement in the acceleration stage is the same as that in the deceleration stage, the acceleration trajectory curve is centrosymmetric, and the whole transport process meets the following performance indexes:
(1) safe swing angle index: maximum pivot angle u during operationθ≥|θ(t)|；
(2) Maximum acceleration index: maximum acceleration during operation
Figure FDA0002694953550000032
(3) Maximum speed index: maximum speed of operation
Figure FDA0002694953550000033
(4) The steady state index is as follows: the swing angle theta (t) during uniform motion and stop motion is 0;
s4: by adjusting the displacement time functions of the load in an acceleration stage, a uniform motion stage and a deceleration stage, a dynamic smooth positioning anti-swing track of the load is constructed on the premise of not influencing positioning; obtaining a track equation under each performance index according to the three-section type acceleration track accurate expression; if the impact on the trolley under the smooth track is more relieved than the three-section acceleration track, the track planning is finished.
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