CN113321123B - Layered quick terminal sliding mode control method for double-pendulum system of crane - Google Patents

Layered quick terminal sliding mode control method for double-pendulum system of crane Download PDF

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CN113321123B
CN113321123B CN202110493428.4A CN202110493428A CN113321123B CN 113321123 B CN113321123 B CN 113321123B CN 202110493428 A CN202110493428 A CN 202110493428A CN 113321123 B CN113321123 B CN 113321123B
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cart
trolley
sliding mode
crane
control
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CN113321123A (en
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汪小凯
吴庆祥
夏明辉
华林
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Wuhan University of Technology WUT
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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
    • B66C13/16—Applications of indicating, registering, or weighing devices
    • 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
    • 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
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

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  • Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Automation & Control Theory (AREA)
  • Control And Safety Of Cranes (AREA)

Abstract

The invention provides a layering quick terminal sliding mode control method of a crane double-pendulum system, which comprises the following steps: s1, establishing a crane double pendulum system state equation based on dynamic analysis of a distributed mass load crane double pendulum system; s2, taking speed control as input, respectively constructing a trolley or a cart, a lifting hook, a distributed mass load and a quick terminal sliding die surface of a lifting mechanism; s3, utilizing an equivalent sliding mode control method to respectively obtain a trolley or a cart and a lifting mechanism control model which are formed by equivalent control and switching control. 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

Layered quick terminal sliding mode control method for double-pendulum system of crane
Technical Field
The invention belongs to the field of cranes, and particularly relates to a layering rapid terminal sliding mode control method of a crane double-pendulum system.
Background
The bridge crane is used as an important logistics transport tool and is widely applied to important industrial places such as workshop warehouses, metallurgical manufacturing, garbage disposal, production assembly workshops and the like. The bridge crane structure can be divided into three parts of a cart, a trolley and a lifting mechanism. The lifting mechanism realizes the lifting of the load through the flexible steel wire rope, and simultaneously realizes the transportation of the load through the translation of the cart and the trolley. Obviously, a crane is an underactuated system, since the degree of freedom of actuation is less than the degree of freedom of the system. Thus, during load transport, both the cart and cart speed variations 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 staff. Therefore, the anti-roll control technique is receiving extensive attention from researchers and crane manufacturers as a key technique for suppressing load hunting. Regarding the crane anti-swing control, researchers have conducted a lot of research work, but most of the current researches have been conducted on a single pendulum system using a crane as a point mass. However, during practical use of the crane, the presence of hook mass and distributed mass loading will cause a double pendulum effect of the crane.
In recent years, the anti-swing control of a crane double swing system has been attracting attention, and an open loop control method including input shaping, off-line trajectory planning, and the like has been proposed. Meanwhile, the closed-loop control is also applied to the anti-swing control of the crane double-swing system, and comprises PID control, state feedback, fuzzy control and the like. In addition, the sliding mode control is also used for the anti-swing control of the double-swing system of the crane, but the current sliding mode control method is mostly based on displacement control and needs to be controlled through driving force, so that the sliding mode control method is mostly suitable for the automatic control condition of fixed load transportation displacement, driving force control is suitable for a servo control system, and the control system cost is high. In addition, the existing control method is based on a double-pendulum system of the crane with point mass, namely, a lifting hook and a load are used as the point mass without volume. And when the load is lifted by two or four steel wire ropes, the special load shape and the lifting mechanism show more complex double-swing effect of the crane. At the same time, anti-roll control of the crane double pendulum system will become more difficult when considering distributed mass loading elevation changes.
Disclosure of Invention
The invention aims to provide a layering rapid terminal sliding mode control method of a double-pendulum system of a crane, which realizes rapid anti-swing control of the double-pendulum system of the distributed mass load crane under the condition of speed control and hoisting rope length change by rapid terminal sliding mode control, thereby remarkably improving the working efficiency and the operation safety of the crane.
The technical scheme adopted by the invention is as follows:
a layering quick terminal sliding mode control method of a double-pendulum system of a crane comprises the following steps:
s1, establishing a crane double pendulum system state equation based on dynamic analysis of a distributed mass load crane double pendulum system;
s2, taking speed control as input, respectively constructing a trolley or a cart, a lifting hook, a distributed mass load and a quick terminal sliding die surface of a lifting mechanism;
s3, utilizing an equivalent sliding mode control method to respectively obtain a trolley or a cart and a lifting mechanism control model which are formed by equivalent control and switching control.
The beneficial effects of the invention are as follows: according to the layered rapid terminal sliding mode control method for the double pendulum system of the crane, a crane system state equation is established based on 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 die surface of a lifting mechanism; and then, an equivalent sliding mode control method is utilized to obtain a trolley or a cart and lifting mechanism control model consisting of equivalent control and switching control. 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 symbol function in the switching control, the symbol function is replaced by the saturated function in the control model, 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 crane double pendulum system according to an embodiment of the invention.
FIG. 2 is a distributed mass-loaded crane double pendulum system model of an embodiment of the present invention.
Fig. 3 is a trolley or cart travel speed trajectory for a crane double pendulum system of an embodiment of the present invention.
Fig. 4 is a hoisting rope length variation trace of the crane double pendulum system according to an embodiment of the present invention.
Fig. 5 is a view of hook angle during a layered quick terminal slip-form control process in accordance with an embodiment of the present invention.
Fig. 6 is a distributed mass loading angle during a layered fast terminal sliding mode control process in accordance with an embodiment of the present invention.
Detailed Description
The invention will be further described with reference to the accompanying drawings:
the invention establishes a state equation of a double pendulum system of a distributed mass load crane based on a Lagrangian dynamics analysis method. Taking speed control as input, a quick terminal sliding mode surface of a trolley, a lifting hook, a distributed mass load and a lifting mechanism subsystem is constructed. And respectively obtaining a trolley and a lifting mechanism control model formed by equivalent control and switching control by using an equivalent sliding mode control method. And simultaneously, the saturation function is used for replacing a sign function in the control model, 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 lifting 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 main hardware adopted by the rapid terminal sliding mode control method of the double pendulum system of the distributed mass load crane comprises the following components: a speed measuring sensor 1, an angle measuring sensor 2, a weight measuring sensor 3, a rope length measuring sensor 4, an anti-remote control 5, a cart driver 6, a cart driver 7, a lifting driver 8, a cart running mechanism 9, a cart running mechanism 10 and a lifting mechanism 11. The speed measuring sensor 1 is used for real-time measurement of the speed of the cart and the trolley. The angle measuring sensor 2 may be an inclination sensor, a vision measuring system, etc. for measuring the swing angle of the hook and the distributed mass load. The weighing 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 real-time measurement of the length of the lifting rope. The anti-swing controller 5 can be an industrial personal computer, a PLC, an embedded control system and the like, and utilizes a quick terminal sliding mode control model to control the operation of a cart, a trolley and a lifting mechanism in real time through a driving system according to measured state information of a double-swing system of the crane, so that distributed mass load swing inhibition under the condition of the length change of the lifting 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 for driving the operation of the cart, the trolley and the lifting mechanism.
The quick terminal sliding mode control method of the crane double-pendulum system provided by the embodiment of the invention comprises the following steps:
establishing a double-pendulum system model of the distributed mass load crane: as shown in fig. 2, assume l 1 For lifting rope length l 2 For the length of the inclined pull rope, the weight of the lifting hook is m 1 The mass and length of the distributed mass load are denoted as m, respectively 2 And l p 。u 1 For the acceleration of the trolley or the cart, u 2 Acceleration of the lifting mechanism.
The dynamic differential equation of the double pendulum system with distributed mass loading crane is:
wherein, the liquid crystal display device comprises a liquid crystal display device,θ 1 is the deflection angle of the lifting hook relative to the vertical lifting center, < ->Is the angular velocity of the hook. θ 2 Is the deflection angle of the load hoisting steel wire rope, < + >>Is the angular acceleration of the load, θ 3 Is the deflection angle of the load relative to the vertical lifting center. /> The vertical distance of the hook to the distributed mass load is +.>The mass ratio of the distributed mass load to the lifting hook is +.>Definitions->g is a gravitational acceleration constant.
Trolley or cart and hoisting mechanism control target: according to the invention, the swinging rules of the lifting hook and the distributed mass load in the moving direction of the cart and the cart are similar, so that the cart and the cart have the same control rule.
Assume that the control target is: the trolley or cart being moved to a desired speed v e1 During the process, the swing angle of the distributed mass load and the lifting hook is minimum, and meanwhile, the distributed mass beam is lifted to a set height x el . There is an error between the trolley or cart operating speed and the desired speed of: e, e v ＝x 1 -v e1 The minimum swing angle of the lifting hook and the distributed mass load is 0, and the swing angle deviation is e 3 ＝x 2 ,e 5 ＝x 4 The error between the distributed mass-loading elevation and the desired elevation is e l ＝x 6 -x el 。
Establishing a trolley or cart quick terminal sliding mode control model: according to the equivalent sliding mode control method, the trolley or cart quick terminal sliding mode control model consists of two parts, namely equivalent control and switching control, and comprises the following parts:
u 1 ＝u eq1 +u eq2 +u eq3 +u sw (2)
defining a quick terminal sliding mode surface function of a trolley or a trolley subsystem as follows:
wherein c 1 >0,c 2 >0, p and q are positive odd integers, p/q is 1 < 2, beta 1 >0。
Meanwhile, a quick terminal sliding mode surface function of the lifting hook and the distributed mass load subsystem is defined as follows:
wherein, c 3 ,c 4 ,c 5 And c 6 Is a positive real number, p 1 ,q 1 ,p 2 And q 2 Is a positive odd integer, 1 < p 1 /q 1 ＜2,1＜p 2 /q 2 ＜2，.β 2 >0,β 3 >0。
Equations (3) and (4) derivative the time t, calculateEquivalent control of the available cart or trolley, hooks and distributed mass loading subsystem is as follows:
the index approach rate is adopted to meet the arrival condition of the sliding mode surface, and the following steps are:
wherein lambda is 1 And lambda (lambda) 2 Is a real number greater than zero, ω 1 ＞0,ρ 1 ＞0。
At the same time, the sign function is replaced by a saturation function, i.eWherein i=1, 2, Δ i Boundary layer thickness is described.
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 brought into equation (2), and the layered rapid terminal sliding mode control model of the trolley or the cart can be obtained as follows:
the control of the trolley or the large trolley layering rapid terminal sliding mode controller based on speed control is achieved. However, the negative index term in the above equivalent controlThe singular phenomenon will be caused in the calculation process of practical application. For this purpose, the negative exponential term in the equivalent control is uniformly biased by 1×10 -n Wherein n is>5. The post-bias version is as follows:
establishing a quick terminal sliding mode control model of the lifting mechanism: the quick terminal sliding die surface defining the lifting mechanism subsystem is as follows:
wherein is c 7 >0,p 4 And q 4 Is a positive odd integer, 1 < p 4 /q 4 ＜2，β 4 >0. Also, using the exponential approach rate, the following equation can be obtained:
and (3) deriving the time t from the formula (10) and bringing the time t into the formula (11), so that a quick terminal sliding mode control model of the lifting mechanism is obtained as follows:
stability demonstration: the positive lyapunov function is defined as:
the differentiation of the above can be obtained:
bringing equations (5), (7) and (11) into the above equation yields:
due tos 1 ≡0，s 2 Identical to 0, the system is stabilized according to LaSalle's invariant theory.
The specific implementation steps of the invention are as follows:
(1) A preset stage, setting the maximum running speed v of the trolley or the cart max Load desired elevation x el Maximum value is 4m, minimum value is 2m, and lifting hook mass m 1 Length l of diagonal cable 2 Distributed mass load length l p Negative exponential term bias of 10 -5 。
(2) The data processing process of the anti-shake controller comprises the following steps: lifting rope length l measured in real time by using rope length sensor 1 Measuring with a load cellLoad mass m 2 Meanwhile, the angle sensor acquires swing angles of the lifting hook and the distributed mass load in real time, and the speed measuring sensor feeds back the running speeds of the trolley and the cart.
(3) And (3) determining parameters of a quick terminal sliding mode controller: determining c from system parameters 1 、c 2 、c 3 、c 4 、c 5 、c 6 、c 7 、ω 1 、ρ 1 、Δ 1 、λ 1 、λ 2 、p、q、p 1 、q 1 、p 2 、q 2 、p 4 、q 4 、β 1 、β 2 And beta 3 。
(4) Accelerating the anti-shaking control process: when the cart or trolley starts to accelerate with the lifting mechanism, the expected running speed of the cart or trolley is v e1 ＝v max The desired elevation of the distributed mass is x el =4m. According to real-time measurement of crane system parameters, the anti-swing controller calculates the running speed errors e of the cart and the trolley respectively v ＝x 1 -v e1 Deviation e of swing angle of lifting hook 3 ＝x 2 Distributed mass load swing angle deviation e 5 ＝x 4 And a lifting height error e l ＝x 6 -x el . Then according to the equivalent control formulaAnd calculating equivalent control of the trolley or the cart, the lifting hook and the distributed mass load subsystem. Finally layering and rapid terminal sliding mode control model according to trolley or cartAnd quick terminal sliding mode control model of lifting mechanismAnd driving the trolley or the cart and the lifting mechanism to accelerate, so as to realize the anti-swing control of the distributed mass load in the acceleration process of the double-pendulum system of the crane. When the cart or trolley is accelerated to the maximum speed v max At this time, the distributed mass is lifted to the desired height of 4m, and the swing angle of the hook and the distributed mass load is 0.
(5) The deceleration and anti-shaking control process comprises the following steps: when the cart or trolley starts to run at the same time as the lifting mechanism, the expected running speed of the cart or trolley is v e1 =0, distributed mass expected rise height x el =2m. According to real-time measurement of crane system parameters, the anti-swing controller calculates the running speed errors e of the cart and the trolley respectively v ＝x 1 -v e1 Deviation e of swing angle of lifting hook 3 ＝x 2 Distributed mass load swing angle deviation e 5 ＝x 4 And a lifting height error e l ＝x 6 -x el . Then, an equivalent control formula is utilizedAnd calculating equivalent control of the trolley or the cart, the lifting hook and the distributed mass load subsystem. Finally, according to the layered rapid terminal sliding mode control model of the trolley or the cartAnd quick terminal sliding mode control model of lifting mechanismThe trolley or the cart and the lifting mechanism are driven to run in a decelerating mode, and the anti-shaking control of the distributed mass load in the decelerating process of the double-pendulum system of the crane is realized. When the cart or trolley is run down to a stop, the distributed mass drops to the desired height 2m and the swing angle of the hook and the distributed mass load is 0.
The implementation processes (1) - (5) of the quick terminal sliding mode control system of the double-pendulum system of the distributed mass load crane are understood to be only for illustrating the whole implementation process of the anti-swing control system, and in practical application, only initial setting is needed in the installation and debugging process according to the use requirement.
Fig. 3 is a track of the running speed of a trolley or a cart of the crane double-pendulum system, fig. 4 is a track of the change of the length of a lifting rope of the crane double-pendulum system, fig. 5 is a lifting hook angle in the process of layering rapid terminal sliding mode control, fig. 6 is a distributed mass load angle in the process of layering rapid terminal sliding mode control, and it can be seen from the figure that the change of the length of the lifting rope, namely, the load falling process is accompanied in the process of accelerating the trolley, and the swinging angles of the lifting hook and the distributed mass load are shown in fig. 5 and 6. Likewise, when the trolley or cart is decelerating, the hoist rope 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 patent of the present invention, and are not intended to limit the scope of application of the present invention. A rapid terminal sliding mode control method for a double-pendulum system of a distributed mass load crane. The vibration suppression of the distributed mass beam of the crane system based on speed control and rope length change is realized by designing the trolley, the lifting hook, the distributed mass load and the quick terminal sliding die surface of the lifting mechanism subsystem. In order to avoid high-frequency oscillation caused by a symbol function in switching control, a saturation function is adopted to replace the saturation function in a control model. The invention is simultaneously suitable for the manual operation of the crane and the anti-swing control of the double-swing system of the crane under the automatic control condition of setting the running speed track based on the speed control method, and the cooperative control of the trolley or the cart and the lifting mechanism obviously improves the working efficiency and the running safety of the crane.
It will be readily appreciated by those skilled in the art that the foregoing is merely a preferred embodiment of the invention and is not intended to limit the invention, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.

Claims (2)

1. The layering rapid terminal sliding mode control method of the double-pendulum system of the crane is characterized by comprising the following steps of:
s1, establishing a crane double pendulum system state equation based on dynamic analysis of a distributed mass load crane double pendulum system;
s2, taking speed control as input, respectively constructing a trolley or a cart, a lifting hook, a distributed mass load and a quick terminal sliding die surface of a lifting mechanism;
s3, utilizing an equivalent sliding mode control method to respectively obtain a trolley or a cart and a lifting mechanism control model which are formed by equivalent control and switching control;
the step S1 specifically includes:
let 1 1 For lifting rope length l 2 For the length of the inclined pull rope, the weight of the lifting hook is m 1 The mass and length of the distributed mass load are respectively m 2 And l p ，u 1 For the acceleration of the trolley or the cart, u 2 Acceleration of the lifting mechanism, g is a gravity acceleration constant; the vertical distance of the hook to the distributed mass load is
Defining the mass ratio of the distributed mass load to the lifting hook as
Definition of the definitionWherein x is the displacement of the trolley or the cart, theta 1 Is the deflection angle of the lifting hook relative to the vertical lifting center, < ->For angular velocity of hook, θ 2 Is the deflection angle of the load, +.>Angular acceleration of the load; there is a distributed mass-loaded crane double pendulumThe kinetic differential equation of the system is:
the steps S2 and S3 specifically include:
s21, setting the expected running speed of the trolley or the cart as v e1 The lifting expected height of the distributed mass load is x el There is an error between the trolley or cart running speed and the desired speed as: e, e v ＝x 1 -v e1 The minimum swing angle of the lifting hook and the distributed mass load is 0, and the swing angle deviation is as follows: e, e 3 ＝x 2 ,e 5 ＝x 4 The error between the distributed mass-loading elevation and the desired elevation is e l ＝x 6 -x el ；
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:
u 1 ＝u eq1 +u eq2 +u eq3 +u sw
s23, defining a quick terminal sliding mode surface function of a trolley or a cart as follows:
wherein c1>0, c2>0, p and q are positive odd integers, 1 < p/q < 2, beta 1>0;
meanwhile, a quick terminal sliding mode surface function of the lifting hook and the distributed mass load is defined as follows:
wherein, c 3 ,c 4 ,c 5 And c 6 Is a positive real number, p 1 ,q 1 ,p 2 And q 2 Is of the positive odd typeInteger of 1 < p 1 /q 1 ＜2,1＜p 2 /q 2 ＜2，β 2 >0,β 3 >0；
S24, deriving the time t by using a quick terminal sliding mode surface function of the trolley or the cart, the lifting hook and the distributed mass load, and calculatingThe equivalent control of the trolley or cart, hook and distributed mass load is obtained as follows:
the index approach rate is adopted to meet the arrival condition of the sliding mode surface, and the following steps are:
wherein lambda is 1 And lambda (lambda) 2 Is a real number greater than zero, ω 1 >0,ρ 1 >0, sgn is a sign function;
at the same time, the sign function is replaced by a saturation function, i.e
Where i=1, 2, # is delta i Describing the boundary layer thickness;
the obtained switching control model of the trolley or the cart is as follows:
and then the layered quick terminal sliding mode control model of the trolley or the cart is obtained as follows:
s25, defining a quick terminal sliding mode surface function of a lifting mechanism as follows:
wherein, c 7 >0,p 4 And q 4 Is a positive odd integer, 1 < p 4 q 4 ＜2，β 4 >0；
Also, using the exponential approach rate, the following equation can be obtained:
the quick terminal sliding mode surface function of the lifting mechanism is led out for the time t, and finally the quick terminal sliding mode control model of the lifting mechanism is obtained as follows:
2. the method for controlling a layered quick terminal sliding mode of a double pendulum system of a crane according to claim 1, wherein the negative exponential term in the equivalent controlUnified offset 1 x 10 -n Wherein n is>5, the biased version is as follows:
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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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CN108303883A (en) * 2018-01-22 2018-07-20 五邑大学 The anti-pendular regime of bridge crane based on first-order dynamic sliding moding structure

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
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

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