CN113321123A - Layered rapid terminal sliding mode control method for double-pendulum system of crane - Google Patents
Layered rapid terminal sliding mode control method for double-pendulum system of crane Download PDFInfo
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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
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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
- B66C13/16—Applications of indicating, registering, or weighing devices
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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
- B66C13/18—Control systems or devices
- B66C13/46—Position indicators for suspended loads or for crane elements
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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
- B66C13/18—Control systems or devices
- B66C13/48—Automatic control of crane drives for producing a single or repeated working cycle; Programme control
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- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
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Abstract
The invention provides a layered rapid terminal sliding mode control method for a double-pendulum system of a crane, which comprises the following steps: s1, establishing a state equation of the double-pendulum system of the crane based on the dynamic analysis of the double-pendulum system of the distributed mass load crane; s2, respectively constructing a quick terminal sliding mode surface of a trolley or a cart, a lifting hook, a distributed mass load and a lifting mechanism by taking speed control as input; and S3, respectively obtaining a trolley or cart and a lifting mechanism control model formed by equivalent control and switching control by using an equivalent sliding mode control method. The invention is designed based on speed control, is easy for industrial application, can obviously improve the working efficiency of the crane, is suitable for the anti-swing control of the double-swing system of the crane under the condition of manual operation of the crane, is also suitable for the anti-swing control of the double-swing system of the crane under the condition of automatic control by setting the running speed track, and has the characteristics of wide application range, convenient application and the like.
Description
Technical Field
The invention belongs to the field of cranes, and particularly relates to a layered quick terminal sliding mode control method for a double-pendulum system of a crane.
Background
The bridge crane is used as an important logistics transportation tool and is widely applied to important industrial places such as workshop warehouses, metallurgical manufacturing, garbage disposal, production assembly workshops and the like. The structure of the bridge crane can be divided into a cart, a trolley and a hoisting mechanism. The hoisting mechanism realizes hoisting of the load through a flexible steel wire rope, and simultaneously realizes transportation of the load through translation of the cart and the trolley. Obviously, the crane is an under-actuated system, since the actuation degree of freedom is less than the system degree of freedom. Thus, during load transport, changes in cart and cart speeds will cause the load to swing.
In practical application of the crane, the long-time swinging of the load can seriously affect the working efficiency and the operation safety of the crane, and even threaten the safety of surrounding equipment and workers. Therefore, the anti-sway control technique has received a great deal of attention from researchers and crane manufacturers as a key technique for suppressing load sway. With regard to crane anti-sway control, researchers have conducted a great deal of research work, but most studies are now directed to cranes as point mass simple pendulum systems. However, in practical crane applications, the presence of the hook mass and the distributed mass load will cause a double pendulum effect of the crane.
In recent years, attention has been paid to anti-sway control of a crane double-pendulum system, and open-loop control methods including input shaping, offline trajectory planning, and the like have been proposed. Meanwhile, the closed-loop control is also applied to the anti-swing control of a crane double-swing system, including PID control, state feedback, fuzzy control and the like. In addition, the sliding mode control is also used for anti-swing control of a double-pendulum system of a crane, but most of the existing sliding mode control methods are based on displacement control and need to control through driving force, so the sliding mode control method is mostly suitable for automatic control conditions of load transportation displacement fixation, the driving force control is suitable for a servo control system, and the control system cost is high. In addition, most existing control methods are based on a point-mass crane double-pendulum system, namely, a lifting hook and a load are used as a non-volume point mass. When the load is hoisted by two or four steel wire ropes, the special load shape and the hoisting mechanism show more complicated double-pendulum effect of the crane. At the same time, anti-sway control of a crane double pendulum system will become more difficult when considering distributed mass load hoisting height variations.
Disclosure of Invention
The invention aims to provide a layered quick terminal sliding mode control method for a double-pendulum system of a crane, which realizes quick anti-swing control of the double-pendulum system of the distributed mass load crane under the conditions of speed control and hoisting rope length change through quick terminal sliding mode control, thereby obviously improving the working efficiency and the operation safety of the crane.
The technical scheme adopted by the invention is as follows:
a layered quick terminal sliding mode control method for a double-pendulum system of a crane comprises the following steps:
s1, establishing a state equation of the double-pendulum system of the crane based on the dynamic analysis of the double-pendulum system of the distributed mass load crane;
s2, respectively constructing a quick terminal sliding mode surface of a trolley or a cart, a lifting hook, a distributed mass load and a lifting mechanism by taking speed control as input;
and S3, respectively obtaining a trolley or cart and a lifting mechanism control model formed by equivalent control and switching control by using an equivalent sliding mode control method.
The invention has the beneficial effects that: the layered rapid terminal sliding mode control method of the double-pendulum system of the crane is characterized in that a state equation of the crane system is established based on the dynamic analysis of the double-pendulum system of the distributed mass load crane; on the basis, respectively establishing a trolley or a cart, a lifting hook, a distributed mass load and a quick terminal sliding mode surface of a lifting mechanism; and then obtaining a control model of the trolley or the cart and the hoisting mechanism, which consists of equivalent control and switching control, by using an equivalent sliding mode control method. The invention is designed based on speed control, is easy for industrial application, can obviously improve the working efficiency of the crane, is suitable for the anti-swing control of the double-swing system of the crane under the condition of manual operation of the crane, is also suitable for the anti-swing control of the double-swing system of the crane under the condition of automatic control by setting the running speed track, and has the characteristics of wide application range, convenient application and the like.
Further, in order to avoid high-frequency oscillation caused by the sign function in switching control, the control model adopts a saturation function to replace the sign function, so that the high-frequency oscillation is avoided.
Drawings
Fig. 1 is a schematic diagram of a layered rapid terminal sliding mode control system of a double-pendulum system of a crane according to an embodiment of the invention.
Fig. 2 is a model of a distributed mass loading crane double pendulum system according to an embodiment of the present invention.
FIG. 3 shows the track of the moving speed of the trolley or cart of the crane double-pendulum system according to the embodiment of the present invention.
Fig. 4 is a change track of the length of a hoisting rope of the double-pendulum system of the crane according to the embodiment of the invention.
Fig. 5 is a hook angle during layered fast terminal sliding mode control according to an embodiment of the present invention.
Fig. 6 is a distributed mass load angle in the layered fast terminal sliding mode control process according to an embodiment of the present invention.
Detailed Description
The invention will be further described with reference to the accompanying drawings in which:
the invention establishes a state equation of a distributed mass load crane double-pendulum system based on a Lagrange dynamics analysis method. And taking speed control as input, and constructing a rapid terminal sliding mode surface of the trolley, the lifting hook, the distributed mass load and the lifting mechanism subsystem. And respectively obtaining a trolley and a hoisting mechanism control model formed by equivalent control and switching control by using an equivalent sliding mode control method. At the same time, the sign function in the control model is replaced by a saturation function, so that high-frequency oscillation is avoided. And the stability of the design system is proved by adopting a Lyapunov method. The crane anti-swing control system can realize anti-swing control when the trolley or the cart and the hoisting mechanism run simultaneously, and can obviously improve the working efficiency of the crane. Meanwhile, the speed control mode is suitable for two conditions of manual operation and automatic control of the crane, and has the characteristics of wide application range, convenience in application and the like.
As shown in fig. 1, the control system adopted by the distributed mass load crane double-pendulum system fast terminal sliding mode control method of the present invention mainly includes hardware: the device comprises a speed measuring sensor 1, an angle measuring sensor 2, a weight measuring sensor 3, a rope length measuring sensor 4, an anti-swing controller 5, a cart driver 6, a trolley driver 7, a lifting driver 8, a cart running mechanism 9, a trolley running mechanism 10 and a lifting mechanism 11. The speed measuring sensor 1 is used for measuring the speed of the cart and the trolley in real time. The angle measuring sensor 2 may be a tilt sensor, a vision measuring system, etc. for measuring the swing angle of the hook and the distributed mass load. The weight sensor 3 is used for measuring the weight of the distributed mass load, and further obtaining the mass of the distributed mass load. The rope length measuring sensor 4 can realize the real-time measurement of the length of the hoisting rope. The anti-swing controller 5 can be an industrial personal computer, a PLC, an embedded control system and the like, and controls the operation of a cart, a trolley and a hoisting mechanism in real time through a driving system by utilizing a rapid terminal sliding mode control model according to the measured state information of the double-swing system of the crane, so that the distributed mass load swing suppression under the condition of the change of the length of the hoisting rope is realized. The cart frequency converter 6, the trolley frequency converter 7 and the lifting driver 8 can be servo drivers or frequency converters and are used for driving the cart, the trolley and the lifting mechanism to run.
The quick terminal sliding mode control method of the crane double-pendulum system in the embodiment of the invention comprises the following steps:
establishing a distributed mass load crane double-pendulum system model: as shown in FIG. 2, assume that l1For hoisting the rope length l2The length of the stay cable is m, and the mass of the lifting hook is m1The mass and length of the distributed mass load are respectively expressed as m2And lp。u1Acceleration of the car or wagon, u2Acceleration of the hoisting mechanism.
The dynamic differential equation of the double-pendulum system of the crane with the distributed mass load is as follows:
wherein,
θ1is the deflection angle of the lifting hook relative to the vertical lifting center,
is the angular velocity of the hook. Theta2Is the deflection angle of the load hoisting steel wire rope,
is the angular acceleration of the load, theta3Is the yaw angle of the load relative to the vertical hoisting center.
The vertical distance from the hook to the distributed mass load is
The mass ratio of the distributed mass load to the lifting hook is
Definition of
g is the gravitational acceleration constant.
The control targets of the trolley or the cart and the hoisting mechanism are as follows: in the invention, the swinging rules of the lifting hook and the distributed mass load in the moving directions of the cart and the trolley are similar, so that the control rules of the cart and the trolley are the same.
Assume that the control targets are: the car or cart moving to a desired speed ve1The swing angle of the distributed mass load and the lifting hook is minimum, and meanwhile, the distributed mass is horizontalThe beam is lifted to a set height xel. Then the error between the running speed of the small car or the big car and the expected speed is: e.g. of the typev＝x1-ve1And if the minimum swing angle of the hook and the distributed mass load is 0, the deviation of the swing angle is e3＝x2,e5＝x4The error between the distributed mass load hoisting height and the desired height is el＝x6-xel。
Establishing a quick terminal sliding mode control model of a trolley or a cart: according to the equivalent sliding mode control method, the quick terminal sliding mode control model of the trolley or the cart consists of two parts of equivalent control and switching control, and comprises the following steps:
u1＝ueq1+ueq2+ueq3+usw (2)
defining a rapid terminal sliding mode surface function of a small vehicle subsystem or a large vehicle subsystem as follows:
wherein, c1>0,c2>0, p and q are positive odd integers, 1 < p/q < 2, beta1>0。
Meanwhile, defining the fast terminal sliding mode surface functions of the lifting hook and the distributed mass load subsystem as follows:
in the formula, c3,c4,c5And c6Is a positive real number, p1,q1,p2And q is2Is a positive odd integer, 1 < p1/q1＜2,1＜p2/q2＜2，.β2>0,β3>0。
Equations (3) and (4) are derived over time t and calculated
Available cart or trolleyEquivalent control of the car, hook and distributed mass load subsystems is as follows:
the exponential approach rate is adopted to meet the arrival condition of the sliding mode surface, and the following conditions are provided:
in the formula, λ1And λ2Is a real number greater than zero, omega1＞0,ρ1＞0。
At the same time, the sign function is replaced by a saturation function, i.e.
Wherein i is 1,2, ΔiThe boundary layer thickness is described.
The simultaneous equations (1), (2), (5) and (6) can obtain the switching control model of the trolley or the cart as follows:
finally, simultaneous equations (5) and (7) are substituted into equation (2), and the obtained layered rapid terminal sliding mode control model of the trolley or the cart is as follows:
the above formula is the control of the speed control-based trolley or cart layered rapid terminal sliding mode controller. However, the negative exponential term in the above equivalent control
The singular phenomenon will be caused in the calculation process of practical application. For this purpose, the negative exponential terms in the equivalent control are uniformly biased by 1 x 10-nWherein n is>5. The offset form is as follows:
establishing a quick terminal sliding mode control model of a hoisting mechanism: defining the quick terminal sliding mode surface of a lifting mechanism subsystem as follows:
in the formula, is c7>0,p4And q is4Is a positive odd integer, 1 < p4/q4＜2，β4>0. Also, using the exponential approach rate, the following equation can be derived:
the formula (10) is derived for the time t and is driven into the formula (11), and the fast terminal sliding mode control model of the hoisting mechanism can be obtained as follows:
the stability proves that: defining a positive lyapunov function as:
differentiating the above equation yields:
substituting equations (5), (7), and (11) into the above equation can result:
due to the fact that
s1≡0，s2Equivalence 0, system stability was obtained according to the LaSalle's invariant lemma.
The method comprises the following concrete implementation steps:
(1) in the presetting stage, the maximum running speed v of the trolley or the cart is setmaxDesired load rise xelMaximum value of 4m, minimum value of 2m, mass m of hook1Length l of the diagonal wire rope2Length of distributed mass load lpNegative exponential term biased at 10-5。
(2) The data processing process of the anti-shaking controller comprises the following steps: hoisting rope length l measured in real time by using rope length sensor1Measuring the load mass m by means of a load cell2Meanwhile, the angle sensor acquires the swing angle of the lifting hook and the distributed mass load in real time, and the speed measuring sensor feeds back the running speed of the trolley and the cart.
(3) Determining parameters of a quick terminal sliding mode controller: determining c from system parameters1、c2、c3、c4、c5、c6、c7、ω1、ρ1、Δ1、λ1、λ2、p、q、p1、q1、p2、q2、p4、q4、β1、β2And beta3。
(4) Acceleration anti-shaking control process: when the cart or the trolley starts to accelerate with the hoisting mechanism, the expected running speed of the cart or the trolley is ve1＝vmaxThe expected lifting height of the distributed mass is xel4 m. According to the real-time measurement of the system parameters of the crane, the anti-swing controller respectively calculates the running speed errors e of the cart and the trolleyv＝x1-ve1Deviation e of the swing angle of the hook3＝x2Distributed mass load swing angle deviation e5＝x4And lifting height error el＝x6-xel. Then according to the equivalent control formula
Calculating equivalent control of the trolley or cart, the lifting hook and the distributed mass load subsystem. Finally, according to the layering of the trolley or the cart, the control model of the terminal sliding mode is rapidly controlled
Quick terminal sliding mode control model of hoisting mechanism
The acceleration operation of the trolley or the cart and the hoisting mechanism is driven, and the anti-swing control of the distributed mass load in the acceleration process of the double-pendulum system of the crane is realized. When the cart or the trolley runs to the maximum speed v in an accelerating waymaxAnd the distributed mass rises to the expected height of 4m, and the swing angle of the lifting hook and the distributed mass load is 0.
(5) Deceleration anti-swing control process: when the cart or the trolley starts to run at a reduced speed with the hoisting mechanism at the same time, the expected running speed of the cart or the trolley is v e10, the desired lift height of the distributed mass is xel2 m. According to the real-time measurement of the system parameters of the crane, the anti-swing controller respectively calculates the running speed errors e of the cart and the trolleyv＝x1-ve1Deviation e of the swing angle of the hook3＝x2Distributed mass load swing angle deviation e5＝x4And lifting height error el＝x6-xel. Then, using an equivalent control formula
Calculating equivalent control of the trolley or cart, the lifting hook and the distributed mass load subsystem. Finally, according to the quick terminal sliding mode control model of dolly or cart layering
And hoisting mechanism rapid terminationEnd sliding mode control model
The speed reduction operation of the trolley or the cart and the hoisting mechanism is driven, and the anti-swing control of the distributed mass load in the speed reduction process of the double-pendulum system of the crane is realized. When the cart or trolley runs to a stop at a reduced speed, the distributed mass is lowered to the desired height of 2m, and the swing angle of the hook and the distributed mass load is 0.
The implementation processes (1) to (5) of the fast terminal sliding mode control system of the double-pendulum system of the distributed mass load crane are only used for explaining the whole implementation process of the anti-swing control system, and only initial setting needs to be carried out in the installation and debugging process according to the use requirements in practical application.
Fig. 3 is a track of the running speed of a trolley or a cart of a double-pendulum system of a crane, fig. 4 is a track of the change of the length of a hoisting rope of the double-pendulum system of the crane, fig. 5 is a hook angle in a layered rapid terminal sliding mode control process, fig. 6 is a distributed mass load angle in the layered rapid terminal sliding mode control process, and it can be seen from the figure that in the acceleration process of the trolley, the change of the length of the hoisting rope is accompanied, namely, in the load descending process, and the swing angles of the hook and the distributed mass load are as shown in fig. 5 and fig. 6. Similarly, when the trolley or cart is decelerated, the hoisting line length changes as shown in fig. 4, and the hook and distributed mass load swing angle is also shown in fig. 5 and 6.
The above test cases are only for better illustrating the intrinsic nature of the present patent, and do not limit the scope of application of the present invention. A distributed mass load crane double-pendulum system quick terminal sliding mode control method is provided. By designing the trolley, the lifting hook, the distributed mass load and the quick terminal sliding mode surface of the lifting mechanism subsystem, the vibration suppression of the distributed mass beam of the crane system based on speed control and variable rope length is realized. In order to avoid high-frequency oscillation caused by a sign function in switching control, a saturation function is adopted to replace the saturation function in the control model. Based on the speed control method, the invention is simultaneously suitable for the manual operation of the crane, the anti-swing control of the double-swing system of the crane under the automatic control condition of setting the running speed track, and the cooperative control of the trolley or the cart and the hoisting mechanism, thereby obviously improving the working efficiency and the running safety of the crane.
It will be understood by those skilled in the art that the foregoing is merely a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included within the scope of the present invention.
Claims (4)
1. A layered quick terminal sliding mode control method for a double-pendulum system of a crane is characterized by comprising the following steps:
s1, establishing a state equation of the double-pendulum system of the crane based on the dynamic analysis of the double-pendulum system of the distributed mass load crane;
s2, respectively constructing a quick terminal sliding mode surface of a trolley or a cart, a lifting hook, a distributed mass load and a lifting mechanism by taking speed control as input;
and S3, respectively obtaining a trolley or cart and a lifting mechanism control model formed by equivalent control and switching control by using an equivalent sliding mode control method.
2. The layered rapid terminal sliding-mode control method for the double-pendulum system of the crane according to claim 1, wherein step S1 specifically comprises: let l1For hoisting the rope length l2The length of the stay cable is m, and the mass of the lifting hook is m1The mass and length of the distributed mass load are m respectively2And lp，u1Acceleration of the car or wagon, u2Acceleration of the hoisting mechanism is shown, and g is a gravity acceleration constant; the vertical distance of the hook to the distributed mass load is then
Defining the mass ratio of the distributed mass load to the hook as
Definition of
Wherein x is the displacement of the trolley or the cart, theta1Is the deflection angle of the lifting hook relative to the vertical lifting center,
angular velocity of the hook, θ2Is the yaw angle of the load,
is the angular acceleration of the load; the dynamic differential equation of the double-pendulum system of the crane with the distributed mass load is as follows:
3. the layered rapid terminal sliding-mode control method for the double-pendulum system of the crane according to claim 2, wherein the steps S2 and S3 specifically comprise:
s21, setting the expected running speed v of the trolley or the carte1The expected height of lift of the distributed mass load is xelAnd if the difference between the running speed of the trolley or the cart and the expected speed is as follows: e.g. of the typev＝x1-ve1And the minimum swing angle of the lifting hook and the distributed mass load is 0, the swing angle deviation is as follows: e.g. of the type3＝x2,e5＝x4The error between the distributed mass load hoisting height and the desired height is el＝x6-xel；
S22, establishing a quick terminal sliding mode control model of the trolley or the cart, wherein the quick terminal sliding mode control model of the trolley or the cart comprises equivalent control and switching control:
u1＝ueq1+ueq2+ueq3+usw
s23, defining a quick terminal sliding mode surface function of the trolley or the cart as follows:
wherein c1 is more than 0, c2 is more than 0, p and q are positive odd integers, 1 is more than p/q is less than 2, beta 1 is more than 0;
meanwhile, defining a quick terminal sliding mode surface function of the lifting hook and the distributed mass load as follows:
in the formula, c3,c4,c5And c6Is a positive real number, p1,q1,p2And q is2Is a positive odd integer, 1 < p1/q1＜2,1＜p2/q2＜2，β2>0,β3>0；
S24, derivation of the quick terminal sliding mode surface function of the trolley or the cart, the lifting hook and the distributed mass load to the time t, and calculation
Equivalent control of the trolley or cart, the lifting hook and the distributed mass load is obtained as follows:
the exponential approach rate is adopted to meet the arrival condition of the sliding mode surface, and the following conditions are provided:
in the formula, λ1And λ2Is a real number greater than zero, omega1＞0,ρ1>0, sgn is a sign function;
at the same time, the sign function is replaced by a saturation function, i.e.
Wherein i is 1,2, ΔiDescribing the thickness of the boundary layer;
the switching control model of the obtained trolley or cart is as follows:
and then the layered quick terminal sliding mode control model of the obtained trolley or cart is as follows:
s25, defining a quick terminal sliding mode surface function of the hoisting mechanism as follows:
in the formula, c7>0,p4And q is4Is a positive odd integer, 1 < p4/q4＜2，β4>0；
Also, using the exponential approach rate, the following equation can be derived:
the fast terminal sliding mode surface function of the hoisting mechanism is derived from the time t, and finally the fast terminal sliding mode control model of the hoisting mechanism is obtained as follows:
4. the layered rapid terminal sliding-mode control method for the double-pendulum system of the crane according to claim 3, wherein a negative exponential term in equivalent control
Unified bias 1 x 10-nWherein n is>And 5, the offset form is as follows:
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|---|---|---|---|---|
| DE4338444A1 (en) * | 1993-11-10 | 1995-05-11 | Univ Dresden Tech | Process for controlling the translatory movement sequence of a trolley with a load which is capable of swinging |
| CN106315414A (en) * | 2016-03-30 | 2017-01-11 | 南开大学 | Bridge crane control method based on sliding mode surface |
| CN110436347A (en) * | 2019-08-23 | 2019-11-12 | 武汉理工大学 | A kind of bridge crane double pendulum system optimization is anti-to shake control method |
| CN110526124A (en) * | 2019-08-30 | 2019-12-03 | 五邑大学 | A kind of anti-sway method, apparatus of bridge crane based on sliding-mode surface, equipment and storage medium |
| US20200270103A1 (en) * | 2018-01-22 | 2020-08-27 | Wuyi University | First-order dynamic sliding mode variable structure-based bridge crane anti-swing method |
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2021
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|---|---|---|---|---|
| DE4338444A1 (en) * | 1993-11-10 | 1995-05-11 | Univ Dresden Tech | Process for controlling the translatory movement sequence of a trolley with a load which is capable of swinging |
| CN106315414A (en) * | 2016-03-30 | 2017-01-11 | 南开大学 | Bridge crane control method based on sliding mode surface |
| US20200270103A1 (en) * | 2018-01-22 | 2020-08-27 | Wuyi University | First-order dynamic sliding mode variable structure-based bridge crane anti-swing method |
| CN110436347A (en) * | 2019-08-23 | 2019-11-12 | 武汉理工大学 | A kind of bridge crane double pendulum system optimization is anti-to shake control method |
| CN110526124A (en) * | 2019-08-30 | 2019-12-03 | 五邑大学 | A kind of anti-sway method, apparatus of bridge crane based on sliding-mode surface, equipment and storage medium |
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