WO2021036626A1 - 一种基于滑模面的桥吊防摆方法、装置、设备及存储介质 - Google Patents

一种基于滑模面的桥吊防摆方法、装置、设备及存储介质 Download PDF

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WO2021036626A1
WO2021036626A1 PCT/CN2020/104565 CN2020104565W WO2021036626A1 WO 2021036626 A1 WO2021036626 A1 WO 2021036626A1 CN 2020104565 W CN2020104565 W CN 2020104565W WO 2021036626 A1 WO2021036626 A1 WO 2021036626A1
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Prior art keywords
sliding mode
swing angle
subsystem
controller
rope length
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PCT/CN2020/104565
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English (en)
French (fr)
Inventor
王天雷
余焱江
伍智琴
张京玲
张宪文
李汶杰
邱炯智
郑宇杰
黄锦涛
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五邑大学
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Publication of WO2021036626A1 publication Critical patent/WO2021036626A1/zh

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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
    • B66C13/063—Auxiliary devices for controlling movements of suspended loads, or preventing cable slack for minimising or preventing longitudinal or transverse swinging of loads electrical
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B66—HOISTING; LIFTING; HAULING
    • B66C—CRANES; LOAD-ENGAGING ELEMENTS OR DEVICES FOR CRANES, CAPSTANS, WINCHES, OR TACKLES
    • B66C17/00—Overhead travelling cranes comprising one or more substantially horizontal girders the ends of which are directly supported by wheels or rollers running on tracks carried by spaced supports
    • B66C17/04—Overhead travelling cranes comprising one or more substantially horizontal girders the ends of which are directly supported by wheels or rollers running on tracks carried by spaced supports with lifting beams, e.g. slewable beams, carrying load-engaging elements, e.g. magnets, hooks

Definitions

  • the invention relates to the technical field of bridge cranes, in particular to an anti-sway method, device, equipment and storage medium of a bridge crane based on a sliding mold surface.
  • the traditional general sliding mode control algorithm can not deal with the problem of system non-matching uncertainty well, so chattering phenomenon will occur, which in turn will affect the service life of the motor.
  • the traditional sliding mode control algorithm greatly changes the system parameters, the anti-sway control effect of the crane will become poor, and the robustness will be poor.
  • the control algorithm cannot be accurately and timely. The response further weakens the anti-sway effect of the bridge crane.
  • the purpose of the present invention is to provide a method, device, equipment and storage medium for anti-swing of a bridge crane based on sliding mode surface, which can deal with the advantages of system non-matching uncertainty by using inversion sliding mode control technology.
  • the introduction of time-varying sliding mode surfaces makes the system more robust and further improves the stability and control performance of the overhead crane system.
  • the present invention provides an anti-sway method for a bridge crane based on a sliding surface, including:
  • the angle subsystem controller combines the construction of a position swing angle global sliding mode surface, and introduces a time-varying function into the position swing angle global sliding mode surface to construct a position swing angle sliding mode controller;
  • the position swing angle sliding mode controller and the rope length sliding mode controller respectively output the horizontal traction force of the trolley and the traction force along the rope.
  • constructing the trolley position subsystem controller based on the backstepping sliding mode control theory includes:
  • the trolley position subsystem controller is obtained;
  • the construction of the load swing angle subsystem controller based on the inversion sliding mode control theory includes:
  • the load swing angle subsystem controller is obtained
  • the first derivative of the second-level Lyapunov function of the load swing angle subsystem is not greater than zero, and the load swing angle subsystem controller is obtained.
  • the position swing angle sliding mode controller includes:
  • the S-shaped saturation function is constructed as the position swing angle global system sliding mode control function to obtain the position swing angle sliding mode controller.
  • the present invention provides an anti-sway device for a bridge crane based on a sliding surface, including:
  • the position swing angle sliding mode controller construction unit is used to construct the mathematical model of the position swing angle system of the bridge crane, and build the position subsystem controller and the load swing angle subsystem controller of the trolley based on the inversion sliding mode control theory.
  • the trolley position subsystem controller and the load swing angle subsystem controller combine to construct a position swing angle global sliding mode surface, and introduce a time-varying function into the position swing angle global sliding mode surface to construct a position swing angle sliding mode controller ;
  • the rope length sliding mode controller construction unit is used to construct the mathematical model of the rope length system of the bridge crane, and the rope length sliding mode controller is constructed based on the backstepping sliding mode control theory;
  • the acquisition unit is used to acquire trolley position parameters, load swing angle parameters, time parameters and rope length parameters;
  • An input unit for inputting the trolley position parameter, load swing angle parameter, and time parameter into the position swing angle sliding mode controller, and inputting the rope length parameter into the rope length sliding mode controller;
  • the output unit is used for the position swing angle sliding mode controller and the rope length sliding mode controller to respectively output the horizontal traction force of the trolley and the traction force along the rope.
  • the present invention provides a bridge crane anti-sway device based on a sliding surface
  • It includes at least one control processor and a memory for communicating with the at least one control processor; the memory stores instructions executable by the at least one control processor, and the instructions are executed by the at least one control processor to enable the at least one control processor.
  • the present invention provides a computer-readable storage medium, and the computer-readable storage medium stores computer-executable instructions, and the computer-executable instructions are used to make the computer execute the above-mentioned sliding-form surface-based bridge crane anti-sway method.
  • the present invention also provides a computer program product, the computer program product includes a computer program stored on a computer-readable storage medium, the computer program includes program instructions, when the program instructions are executed by a computer , Make the computer execute the above-mentioned method of anti-sway of the bridge crane based on the sliding surface.
  • One or more technical solutions provided in the embodiments of the present invention have at least the following beneficial effects: After the trolley position subsystem controller and the load swing angle subsystem controller are designed layer by layer based on the inversion control algorithm, the trolley position subsystem The controller and the load swing angle subsystem controller are combined to construct a position swing angle global sliding surface, and the time-varying function is introduced into the sliding surface design, which greatly reduces the time for state variables to reach the sliding surface; based on inversion sliding mode control The theory is based on the state space function of rope length combined with Lyapunov function to design the rope length controller layer by layer to realize the gradual stability of the rope sling subsystem.
  • the method of the embodiment of the present invention can not only deal with the system non-matching uncertainty problem, eliminate the chattering phenomenon existing in the traditional sliding mode control algorithm to the greatest extent, but also improve the robustness of the anti-sway control of the crane system, and make the system anti-interference. Ability to further improve the stability and control performance of the overhead crane system.
  • Fig. 1 is a flowchart of a method according to an embodiment of the present invention
  • FIG. 2 is a flowchart of a method for constructing a trolley position subsystem controller based on the inversion sliding mode control theory according to an embodiment of the present invention
  • FIG. 3 is a flowchart of a method for constructing a load swing angle subsystem controller based on the inversion sliding mode control theory according to an embodiment of the present invention
  • Figure 4 is an embodiment of the present invention combining the trolley position subsystem controller and the load swing angle subsystem controller to construct a position swing angle global sliding surface, when introduced into the position swing angle global sliding surface Variable function, flow chart of method for constructing position swing angle sliding mode controller;
  • FIG. 5 is a flowchart of a method for constructing a rope length sliding mode controller based on the inversion sliding mode control theory according to an embodiment of the present invention
  • Fig. 6 is a simulation experiment effect diagram of an embodiment of the present invention.
  • FIG. 7 is a simulation experiment effect diagram of the control method, the time-varying sliding mode control method, and the inversion sliding mode control method of the embodiment of the present invention in the simulation environment 1;
  • FIG. 8 is a simulation experiment effect diagram of the control method, the time-varying sliding mode control method, and the inversion sliding mode control method of the embodiment of the present invention in the simulation environment 2;
  • FIG. 9 is a simulation experiment effect diagram of the control method, the time-varying sliding mode control method, and the inversion sliding mode control method of the embodiment of the present invention in the simulation environment 3;
  • FIG. 10 is a simulation experiment effect diagram of the control method, the time-varying sliding mode control method, and the inversion sliding mode control method of the embodiment of the present invention in the simulation environment 4;
  • FIG. 11 is a simulation experiment effect diagram of the control method, the time-varying sliding mode control method, and the inversion sliding mode control method of the embodiment of the present invention in the simulation environment 5;
  • FIG. 12 is a schematic diagram of a unit architecture in a device according to an embodiment of the present invention.
  • Figure 13 is a schematic diagram of connections in a device according to an embodiment of the present invention.
  • an embodiment of the present invention provides a method for preventing swing of a bridge crane based on a sliding surface, including:
  • Step S11 construct the mathematical model of the position swing angle system of the overhead crane, construct the trolley position subsystem controller and the load swing angle subsystem controller based on the backstepping sliding mode control theory, and combine the trolley position subsystem controller and the total
  • the load swing angle subsystem controller is combined with the construction of a position swing angle global sliding mode surface, and a time-varying function is introduced into the position swing angle global sliding mode surface to construct a position swing angle sliding mode controller;
  • Step S12 constructing the mathematical model of the rope length system of the bridge crane, and constructing the rope length sliding mode controller based on the backstepping sliding mode control theory;
  • Step S13 Obtain trolley position parameters, load swing angle parameters, time parameters and rope length parameters;
  • Step S14 input the trolley position parameter, load swing angle parameter, and time parameter into the position swing angle sliding mode controller, and input the rope length parameter into the rope length sliding mode controller;
  • Step S15 the position swing angle sliding mode controller and the rope length sliding mode controller respectively output the horizontal traction force of the trolley and the traction force along the rope.
  • the embodiment of the present invention converts the originally complicated bridge crane dynamics model into the general state space function form, uses the inversion control algorithm to design the trolley position subsystem controller and the load swing angle subsystem controller layer by layer, and then the trolley position The subsystem controller and the load swing angle subsystem controller are combined to construct a position swing angle global sliding mode surface.
  • a time-varying function is introduced in the sliding mode surface design.
  • the sliding mode surface can change with time to make the sliding mode
  • the initial position of the surface is as close to the state variable as possible, which greatly reduces the time for the state variable to reach the sliding mode surface; the rope length subsystem controller is constructed, and the inversion sliding mode control theory is used to calculate the state space function of the rope length combined with the Lyapunov function.
  • Layer design to realize the gradual stability of the rope sling subsystem.
  • the bridge crane system is an under-driven system.
  • the two state variables of the trolley position and the load swing angle are driven by the same motor, that is, a driving variable causes the two state variables to change at the same time, so the design of the position swing angle subsystem controller It is necessary to consider the anti-sway controller of the trolley position and the load swing angle at the same time, construct the trolley position subsystem controller and the load swing angle subsystem controller respectively, and then combine the trolley position subsystem controller and the load swing angle subsystem.
  • the controller introduces a time-varying function to construct a global system controller for the position swing angle.
  • the construction of the trolley position subsystem controller based on the inversion sliding mode control theory also includes the following steps:
  • Step S21 construct the first-level Lyapunov function of the trolley position subsystem
  • Step S22 Perform first-order derivation on the first-level Lyapunov function of the trolley position subsystem
  • Step S23 If the first derivative of the first-level Lyapunov function of the trolley position subsystem is not greater than 0, obtain the trolley position subsystem controller;
  • Step S24 if the first derivative of the first-level Lyapunov function of the trolley position subsystem is greater than 0, construct the second-level Lyapunov function of the trolley position subsystem;
  • Step S25 Perform first-order derivation on the Lyapunov function of the second-level trolley position subsystem of the trolley position subsystem;
  • step S26 the first derivative of the Lyapunov function of the second-level trolley position subsystem of the trolley position subsystem is not greater than zero, and the trolley position subsystem controller is obtained.
  • the trolley position subsystem controller is constructed.
  • the first layer of Lyapunov function only contains the trolley position parameters.
  • the derivation to obtain the speed parameters of the trolley is not enough for the design of the trolley position controller. Because it does not include the motion acceleration variable of the trolley, the gradual stability of the trolley position controller cannot be guaranteed, so the position of the trolley needs to be adjusted.
  • the subsystem constructs the second-level Lyapunov function to stabilize the trolley position subsystem and enhance the robustness and control performance of the system.
  • the construction of the load swing angle subsystem controller based on the inversion sliding mode control theory includes the following steps:
  • Step S31 construct the first-level Lyapunov function of the load swing angle subsystem
  • Step S32 Perform first-order derivation on the first-level Lyapunov function of the load swing angle subsystem
  • Step S33 If the first derivative of the first-level Lyapunov function of the load swing angle subsystem is not greater than 0, obtain the load swing angle subsystem controller;
  • Step S34 if the first derivative of the first-level Lyapunov function of the load swing angle subsystem is greater than 0, construct the second-level Lyapunov function of the load swing angle subsystem;
  • Step S35 Perform first-order derivation on the second-level Lyapunov function of the load swing angle subsystem
  • step S36 the first derivative of the second-level Lyapunov function of the load swing angle subsystem is not greater than zero, and the load swing angle subsystem control is obtained.
  • the load swing angle subsystem controller is constructed.
  • the first layer of Lyapunov function only contains the load swing angle parameter.
  • the derivation of the load swing angle motion speed parameter is not enough for the load swing angle controller design. Because the motion acceleration variable of the load swing angle is not included, the gradual stability of the load swing angle controller cannot be guaranteed, so it is necessary to adjust the load swing angle.
  • the swing angle subsystem constructs the second-level Lyapunov function to stabilize the load swing angle subsystem and enhance the robustness and control performance of the system.
  • the construction of the position swing angle sliding mode controller includes the following steps:
  • Step S41 constructing a global system sliding mode control function of the position swing angle
  • Step S42 constructing a time-varying sliding mode surface of the position swing angle global system
  • Step S43 construct the Lyapunov function of the position swing angle global system
  • Step S44 Perform first-order derivation on the Lyapunov function of the global system of the position swing angle
  • Step S45 constructing a general exponential reaching law to obtain the coupled switch control law of the position swing angle global system sliding mode control
  • Step S46 constructing the S-shaped saturation function as the position swing angle global system sliding mode control function to obtain the position swing angle sliding mode controller.
  • the inversion sliding mode control design method first divides the complex non-linear system with lack of driving quantity into subsystems with no more than the number of system layers, and then combines the Lyapunov function with the control quantity without actual physical meaning in the middle. Introduced into the subsystem design, the sliding mode variable structure control is introduced into the virtual control value of the last layer of the system, and the immutability of sliding mode control is used to ensure the gradual stability of the final subsystem. In the embodiment of the present invention, it is first divided into stages. The vehicle position subsystem and the load swing angle subsystem construct controllers separately, and the time-varying sliding mode surface is introduced in the construction of the last layer of the system to construct a position swing angle global sliding mode controller.
  • the construction of a rope-length sliding mode controller based on the inversion sliding mode control theory includes the following steps:
  • Step S51 construct the first-level Lyapunov function of the rope length subsystem
  • Step S52 Perform first-order derivation on the first-level Lyapunov function of the rope length subsystem
  • Step S53 if the first derivative of the first-level Lyapunov function of the rope length subsystem is not greater than 0, obtain the rope length subsystem controller;
  • Step S54 if the first derivative of the first-level Lyapunov function of the rope length subsystem is greater than 0, construct the second-level Lyapunov function of the rope length subsystem;
  • Step S55 Perform first-order derivation on the second-level Lyapunov function of the rope length subsystem
  • step S56 the first derivative of the second-level Lyapunov function of the rope length subsystem is not greater than zero, and the rope length subsystem controller is obtained.
  • the rope length subsystem controller is constructed.
  • the first layer of Lyapunov function only contains the rope length parameter.
  • the rope length movement speed parameter is derived, which is not enough for the rope length controller design. Because the rope length motion acceleration variable is not included, the gradual stability of the rope length controller cannot be guaranteed. Therefore, a second layer of the rope length subsystem needs to be constructed.
  • the Lyapunov function stabilizes the rope length subsystem and enhances the robustness and control performance of the system.
  • constructing the trolley position subsystem controller based on the inversion sliding mode control theory includes: constructing a mathematical model of the trolley position subsystem, and the mathematical model formula of the overhead crane is rewritten as considering the degree of freedom of the trolley position
  • M is the crane mass
  • m the load mass
  • g the acceleration due to gravity
  • x 3 ⁇
  • ⁇ is the swing angle of the load, Is the angular velocity of the load swing angle
  • define the trolley position tracking error e 1 x 1 -x 1d
  • the first-order derivation of the Lyapunov function of the second-level trolley position subsystem of the trolley position subsystem includes: Perform a first-order derivative to get make Construct the trolley position subsystem controller u x as Among them, h x is the sliding surface coefficient of the trolley position subsystem, and ⁇ x is the switching gain of the trolley position subsystem.
  • the trolley position subsystem controller and the load swing angle subsystem controller are combined to construct a position swing angle global sliding surface, and a time-varying function is introduced into the position swing angle global sliding surface.
  • the anti-swing effect of the embodiment of the present invention is tested through simulation experiments.
  • the simulation time is set to 15 seconds. Refer to Figure 6, where the time taken for the trolley to move from 0 meters to the target position of 3 meters It is 7 seconds, the maximum amplitude of the load swing angle is less than 0.03 radians, and at the same time it converges to 0 radians in 7 seconds, the time it takes for the rope to extend from 1 meter to 4 meters in length is 1 second, and the driving force of the rope is quickly converged When it reaches 0 Newton, the convergence time is 1 second. From the beginning, the driving force of the crane is about 45 Newton to drive the crane movement, and then it quickly converges to 0 Newton.
  • the time it takes is 7 seconds, after which there is no chattering phenomenon.
  • the embodiment of the present invention not only overcomes the driving force chattering problem caused by the time-varying sliding mode, but also overcomes the residual swing phenomenon of the inversion sliding mode, so that the control effect of the bridge crane is optimized.
  • Simulation environment 1 Under light load conditions, set the target value of the trolley displacement and rope length to 3 meters and 4 meters, respectively, and set the weight of the trolley and load to 10 kg and 5 kg respectively. Other system model parameters do not change.
  • Simulation environment 2 Under heavy load conditions, set the target value of the trolley displacement and rope length to 3 meters and 4 meters, respectively, and set the weight of the trolley and load to 500 kg and 100 kg, respectively, and other system model parameters do not change.
  • Simulation environment 3 Under the condition of large target value, set the target value of trolley displacement and rope length to 10 meters and 6 meters, respectively, and set the weight of the trolley and load to 500 kg and 100 kg respectively, other system models The parameters are not changed.
  • Simulation environment 4 Under the condition of changing the system model, set the target value of trolley displacement and rope length to 10 meters and 6 meters, respectively, and set the weight of the trolley and load to 500 kg and 100 kg, respectively.
  • the model parameters of the overhead crane system were changed.
  • the air resistance coefficient of the crane was changed from 0.5 to 0.2
  • the air resistance coefficient of the load was changed from 0.5 to 0.6
  • the friction coefficient of the crane was changed from 0.5 to 0.3.
  • Simulation environment 5 Under the condition of external interference, set the target value of trolley displacement and rope length to 10 meters and 6 meters, respectively, set the weight of the trolley and load to 500 kg and 100 kg, respectively, and the air resistance of the crane The coefficient changes from 0.5 to 0.2, the load air resistance coefficient changes from 0.5 to 0.6, and the crane friction coefficient changes from 0.5 to 0.3.
  • the overhead crane moves from the initial position to the target position. After it has converged and stabilized, the load is suddenly applied for a long period of time. The force of 1 second causes it to swing from an angle of 0.15 radians.
  • the experimental result of simulation environment 1 is: in the simulation result of the control method using the embodiment of the present invention, the load swing angle amplitude is less than 0.031 radians, and there is no residual swing after convergence, and the simulation result of the time-varying sliding mode control method is The load swing amplitude is large, and the simulation result of the inversion sliding mode control method is that the load swing angle has residual swing; in terms of the position control performance of the trolley, the embodiment of the present invention reaches the index position in 7 seconds without swinging, while the inversion sliding mode control
  • the simulation result of the method has a slight swing; in terms of rope length control, it takes 1 second for the sling in the embodiment of the invention to extend from 1 meter to 4 meters, while the time-varying sliding mode control method takes 4 seconds.
  • the control effect is better.
  • the above results show that, in the simulation environment 1 of the control method of the embodiment of the present invention, compared with the other two sliding mode control algorithms, the load swing angle is smaller, the stability is reached faster, and the control effect is better
  • the experimental results of simulation environment 2 are: when the mass of the trolley and the load are greatly increased, in the simulation result of the control method using the embodiment of the present invention, the amplitude of the load swing angle is less than 0.03 radians, and there is no residual swing after convergence, and
  • the simulation result of the time-varying sliding mode control method is that the load swing is larger, and the simulation result of the inversion sliding mode control method is that the load swing is larger and there is residual swing; in terms of the trolley position control performance, the embodiment of the present invention is better than others.
  • the two control methods reach the designated position faster without swinging; in terms of rope length control, it takes 1 second for the sling in the embodiment of the present invention to extend from 1 meter to 4 meters, while the time-varying sliding mode control method takes 4 minutes. Second, the control effect of the embodiment of the present invention is better.
  • the above results show that in the simulation environment 2 of the control method of the embodiment of the present invention, compared with the other two sliding mode control algorithms, the load swing angle is smaller, the stability is reached faster, and the control effect is better.
  • the experimental result of simulation environment 3 is: when the target value of trolley displacement and the target value of rope length are changed, the simulation result of the control method using the embodiment of the present invention is that the load swing angle is 0.1 radians, and there is no residual swing after convergence, and The load swing angle amplitude of the time-varying sliding mode control exceeds 0.15 radians, and the load swing angle amplitude of the inversion sliding mode control exceeds 0.1 radians and there is residual swing after convergence.
  • the above results show that the control method of the embodiment of the present invention is compared in the simulation environment 3. With the other two sliding mode control algorithms, the amplitude of the load swing angle is smaller, the stability is reached faster, and the control effect is better.
  • the experimental result of simulation environment 4 is: when the air resistance coefficient and friction coefficient on the two-dimensional bridge crane system model are changed, the simulation result of the control method of the embodiment of the present invention is that the load swing angle is 0.1 radians, which converges After that, there is no residual swing, but the load swing angle amplitude of the time-varying sliding mode control exceeds 0.15 radians, and the load swing angle amplitude of the inversion sliding mode control exceeds 0.1 radians and there is residual swing after convergence.
  • the above results show that the control method of the embodiment of the present invention Compared with the other two sliding mode control algorithms in the simulation environment 4, the load swing angle is smaller, the stability is reached faster, and the control effect is better.
  • the experimental results of simulation environment 5 are: under the condition of external interference, the position recovery overshoot of the trolley using the control method of the embodiment of the present invention is smaller than that of the other two sliding mode control algorithms, and the output rope driving force is obvious Less than the other two sliding mode control algorithms, the driving force of the sling is close to zero.
  • the above results show that the control method of the embodiment of the present invention compares the other two sliding mode control algorithms in the simulation environment 5, and is superior to the other two sliding mode control algorithms in terms of control torque output.
  • the embodiment of the present invention also provides a bridge crane anti-sway device based on a sliding mode surface.
  • the bridge crane anti-sway device 1000 based on a sliding mode surface includes, but is not limited to: a position swing angle sliding mode controller construction unit 1100 , Rope length sliding mode controller construction unit 1200, acquisition unit 1300, input unit 1400 and output unit 1500.
  • the position swing angle sliding mode controller construction unit 1100 is used to construct the mathematical model of the position swing angle system of the bridge crane, and the trolley position subsystem controller and the load swing angle subsystem controller are constructed based on the inversion sliding mode control theory.
  • the trolley position subsystem controller and the load swing angle subsystem controller are combined to construct a position swing angle global sliding surface, and a time-varying function is introduced into the position swing angle global sliding surface to construct a position swing angle sliding surface.
  • the rope length sliding mode controller construction unit 1200 is used to construct the mathematical model of the rope length system of the bridge crane, and the rope length sliding mode controller is constructed based on the inversion sliding mode control theory;
  • the obtaining unit 1300 is used for obtaining trolley position parameters, load swing angle parameters, time parameters, and rope length parameters;
  • the input unit 1400 is configured to input the trolley position parameter, load swing angle parameter, and time parameter into the position swing angle sliding mode controller, and input the rope length parameter into the rope length sliding mode controller;
  • the output unit 1500 is used for the position swing angle sliding mode controller and the rope length sliding mode controller to respectively output the horizontal traction force of the trolley and the traction force along the rope.
  • the embodiment of the present invention also provides a bridge crane anti-sway device based on a sliding mode surface.
  • the bridge crane anti-sway device 2000 based on a sliding mode surface can be any type of intelligent terminal, such as a mobile phone, a tablet computer, a personal computer, and the like.
  • the bridge crane anti-sway device 2000 based on a sliding mode surface includes: one or more control processors 2010 and a memory 2020.
  • one control processor 2010 is taken as an example.
  • control processor 2010 and the memory 2020 may be connected through a bus or in other ways, and connection through a bus is taken as an example in FIG. 13.
  • the memory 2020 can be used to store non-transitory software programs, non-transitory computer executable programs and modules, such as the anti-sway of the bridge crane based on the sliding mode surface in the embodiment of the present invention.
  • the program instructions/modules corresponding to the method for example, the position swing angle sliding mode controller construction unit 1100, the rope length sliding mode controller construction unit 1200, the acquisition unit 1300, the input unit 1400, and the output unit 1500 shown in FIG.
  • the control processor 2010 executes various functional applications and data processing of the bridge crane anti-sway device 1000 based on the sliding mode surface by running the non-transient software programs, instructions and modules stored in the memory 2020, that is, the above method embodiments are realized An anti-sway method of bridge crane based on sliding surface.
  • the memory 2020 may include a storage program area and a storage data area.
  • the storage program area can store an operating system and an application program required by at least one function; The created data, etc.
  • the memory 2020 may include a high-speed random access memory, and may also include a non-transitory memory, such as at least one magnetic disk storage device, a flash memory device, or other non-transitory solid-state storage devices.
  • the memory 2020 may optionally include memories remotely provided with respect to the control processor 2010, and these remote memories may be connected to the bridge crane anti-sway device 2000 based on the sliding mode surface through a network. Examples of the aforementioned networks include, but are not limited to, the Internet, corporate intranets, local area networks, mobile communication networks, and combinations thereof.
  • the one or more modules are stored in the memory 2020, and when executed by the one or more control processors 2010, the method for preventing swing of the bridge crane based on the sliding surface in the above method embodiment is executed, for example, The steps S11 to S15 of the method in FIG. 1 described above are executed to realize the functions of the units 1100-1500 in FIG. 12.
  • An embodiment of the present invention also provides a computer-readable storage medium that stores computer-executable instructions, and the computer-executable instructions are executed by one or more control processors, for example, as shown in FIG. 13
  • One of the control processors 2010 executes the above-mentioned one or more control processors 2010, which can make the above-mentioned one or more control processors 2010 execute the method of anti-sway of the bridge crane based on the sliding mode surface in the above-mentioned method embodiment, for example, execute the above-described method step S11 in FIG. 1 To S15, the functions of the units 1100-1500 in FIG. 12 are realized.
  • the device embodiments described above are merely illustrative, and the units described as separate components may or may not be physically separated, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules can be selected according to actual needs to achieve the objectives of the solutions of the embodiments.
  • each implementation manner can be implemented by means of software plus a general hardware platform.
  • All or part of the processes in the methods of the above embodiments can be implemented by computer programs instructing relevant hardware.
  • the programs can be stored in a computer readable storage medium. At this time, it may include the flow of the embodiment of the above-mentioned method.
  • the storage medium may be a magnetic disk, an optical disc, a read-only memory (Read Only Memory, ROM), or a random access memory (Random Access Memory, RAM), etc.

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Abstract

一种基于滑模面的桥吊防摆方法、装置、设备及存储介质，基于反演控制算法逐层设计台车位置子系统控制器和负载摆角子系统控制器后，将台车位置子系统控制器和负载摆角子系统控制器进行结合，构建一个位置摆角全局滑模面，在滑模面设计中引入时变函数，构建位置摆角控制器；基于反演滑模控制理论对绳长的状态空间函数结合李雅普诺夫函数对绳长控制器进行逐层设计，实现吊绳子系统的渐进稳定。本方法不仅可以处理系统非匹配不确定性问题，最大限度消除传统滑模控制算法中存在的抖振现象，而且可以提高吊车系统防摆控制的鲁棒性，同时使系统具有抗干扰能力，进一步提高桥式吊车系统的稳定性和控制性能。

Description

一种基于滑模面的桥吊防摆方法、装置、设备及存储介质 技术领域
本发明涉及桥式起重机技术领域，特别是一种基于滑模面的桥吊防摆方法、装置、设备及存储介质。
背景技术
桥式吊车作为一种大型货物装卸机械装置，被广泛应用于港口、仓库、重工业车间、建筑工地等场所的装配运输过程。桥式吊车系统控制的主要目标是实现精确的吊车定位并尽可能地消除负载的摆角，以便在最短时间内将货物运输到指定位置而不产生摆动。滑模控制对非线性系统的有良好的控制性能，被广泛应用到桥式吊车的系统控制中，但是当前主流的桥式吊车滑模控制存在以下问题：
传统的一般滑模控制算法不能很好地处理系统非匹配不确定性的问题，因而会出现抖振现象，这一问题进而会影响到电机的使用寿命。此外，传统的滑模控制算法在大幅度改变系统参数时，吊车的防摆控制效果会变得较差，鲁棒性较差，当系统受到外部强烈干扰时，控制算法无法及时准确地做出响应，进一步削弱了桥吊防摆效果。
发明内容
为解决上述问题，本发明的目的在于提供一种基于滑模面的桥吊防摆方法、装置、设备及存储介质，利用反演滑模控制技术能处理系统非匹配不确定性的优点，同时引入时变滑模面使系统具有更强的鲁棒性，进一步提高桥式吊车系统的稳定性和控制性能。
本发明解决其问题所采用的技术方案是：
第一方面，本发明提供了一种基于滑模面的桥吊防摆方法，包括：
构建桥式吊车的位置摆角系统数学模型，基于反演滑模控制理论构建台车位置子系统控制器和负载摆角子系统控制器，将所述台车位置子系统控制器和所述负载摆角子系统控制器结合构建位置摆角全局滑模面，在所述位置摆角全局滑模面中引入时变函数，构建位置摆角滑模控制器；
构建桥式吊车的绳长系统数学模型，基于反演滑模控制理论构建绳长滑模控制器；
获取台车位置参数、负载摆角参数、时间参数和绳长参数；
将所述台车位置参数、负载摆角参数、时间参数输入所述位置摆角滑模控制器中，将所述绳长参数输入到绳长滑模控制器中；
所述位置摆角滑模控制器和绳长滑模控制器分别输出台车水平牵引力和沿绳牵引力。
进一步，基于反演滑模控制理论构建台车位置子系统控制器包括：
构建台车位置子系统的第一层李雅普诺夫函数；
对台车位置子系统的第一层李雅普诺夫函数进行一阶求导；
若所述台车位置子系统的第一层李雅普诺夫函数的一阶导数不大于0，则求得台车位置子系统控制器；
若所述台车位置子系统的第一层李雅普诺夫函数的一阶导数大于0，则构建台车位置子系统的第二层台车位置子系统李雅普诺夫函数；
对台车位置子系统的第二层台车位置子系统李雅普诺夫函数进行一阶求导；
令台车位置子系统的第二层台车位置子系统李雅普诺夫函数的一阶导数不大于零，求得台车位置子系统控制器。
进一步，所述基于反演滑模控制理论构建负载摆角子系统控制器包括：
构建负载摆角子系统的第一层李雅普诺夫函数；
对负载摆角子系统的第一层李雅普诺夫函数进行一阶求导；
若所述负载摆角子系统的第一层李雅普诺夫函数的一阶导数不大于0，则求得负载摆角子系统控制器；
若所述负载摆角子系统的第一层李雅普诺夫函数的一阶导数大于0，
则构建负载摆角子系统的第二层李雅普诺夫函数；
对负载摆角子系统的第二层李雅普诺夫函数进行一阶求导；
令负载摆角子系统的第二层李雅普诺夫函数的一阶导数不大于零，求得负载摆角子系统控制器。
进一步，所述将所述台车位置子系统控制器和所述负载摆角子系统控制器结合构建位置摆角全局滑模面，在所述位置摆角全局滑模 面中引入时变函数，构建位置摆角滑模控制器包括：
构建位置摆角全局系统滑模控制函数；
构建位置摆角全局系统时变滑模面；
构建位置摆角全局系统李雅普诺夫函数；
对位置摆角全局系统李雅普诺夫函数进行一阶求导；
构建一般指数趋近律求得位置摆角全局系统滑模控制的耦合开关控制律；
构建S型饱和函数为位置摆角全局系统滑模控制函数求得位置摆角滑模控制器。
进一步，所述基于反演滑模控制理论构建绳长滑模控制器包括：
构建绳长子系统的第一层李雅普诺夫函数；
对绳长子系统的第一层李雅普诺夫函数进行一阶求导；
若所述绳长子系统的第一层李雅普诺夫函数的一阶导数不大于0，则求得绳长子系统控制器；
若所述绳长子系统的第一层李雅普诺夫函数的一阶导数大于0，
则构建绳长子系统的第二层李雅普诺夫函数；
对绳长子系统的第二层李雅普诺夫函数进行一阶求导；
令绳长子系统的第二层李雅普诺夫函数的一阶导数不大于零，求得绳长子系统控制器。
第二方面，本发明提供了一种基于滑模面的桥吊防摆装置，包括：
位置摆角滑模控制器构建单元，用于构建桥式吊车的位置摆角系统数学模型，基于反演滑模控制理论构建台车位置子系统控制器和负载摆角子系统控制器，将所述台车位置子系统控制器和所述负载摆角子系统控制器结合构建位置摆角全局滑模面，在所述位置摆角全局滑模面中引入时变函数，构建位置摆角滑模控制器；
绳长滑模控制器构建单元，用于构建桥式吊车的绳长系统数学模型，基于反演滑模控制理论构建绳长滑模控制器；
获取单元，用于获取台车位置参数、负载摆角参数、时间参数和绳长参数；
输入单元，用于将所述台车位置参数、负载摆角参数、时间参数输入所述位置摆角滑模控制器中，将所述绳长参数输入到绳长滑模控制器中；
输出单元，用于所述位置摆角滑模控制器和绳长滑模控制器分别输出台车水平牵引力和沿绳牵引力。
第三方面，本发明提供了一种基于滑模面的桥吊防摆设备，
包括至少一个控制处理器和用于与至少一个控制处理器通信连接的存储器；存储器存储有可被至少一个控制处理器执行的指令，指令被至少一个控制处理器执行，以使至少一个控制处理器能够执行如上所述的基于滑模面的桥吊防摆方法。
第四方面，本发明提供了一种计算机可读存储介质，计算机可读存储介质存储有计算机可执行指令，计算机可执行指令用于使计算机执行如上所述的基于滑模面的桥吊防摆方法。
第五方面，本发明还提供了一种计算机程序产品，所述计算机程序产品包括存储在计算机可读存储介质上的计算机程序，所述计算机程序包括程序指令，当所述程序指令被计算机执行时，使计算机执行如上所述的基于滑模面的桥吊防摆方法。
本发明实施例中提供的一个或多个技术方案，至少具有如下有益效果：基于反演控制算法逐层设计台车位置子系统控制器和负载摆角子系统控制器后，将台车位置子系统控制器和负载摆角子系统控制器进行结合，构建一个位置摆角全局滑模面，在滑模面设计中引入时变函数，大大减少状态变量到达滑模面的时间；基于反演滑模控制理论对绳长的状态空间函数结合李雅普诺夫函数对绳长控制器进行逐层设计，实现吊绳子系统的渐进稳定。本发明实施例方法不仅可以处理系统非匹配不确定性问题，最大限度消除传统滑模控制算法中存在的抖振现象，而且可以提高吊车系统防摆控制的鲁棒性，同时使系统具有抗干扰能力，进一步提高桥式吊车系统的稳定性和控制性能。
附图说明
下面结合附图和实施例对本发明作进一步说明。
图1是本发明实施例的方法流程图；
图2是本发明实施例的基于反演滑模控制理论构建台车位置子系统控制器的方法流程图；
图3是本发明实施例的基于反演滑模控制理论构建负载摆角子系统控制器的方法流程图；
图4是本发明实施例的将所述台车位置子系统控制器和所述负载摆角子系统控制器结合构建位置摆角全局滑模面，在所述位置摆角全局滑模面中引入时变函数，构建位置摆角滑模控制器的方法流程图；
图5是本发明实施例的基于反演滑模控制理论构建绳长滑模控制器的方法流程图；
图6是本发明实施例的仿真实验效果图；
图7是本发明实施例控制方法与时变滑模控制方法、反演滑模控制方法在仿真环境1中的仿真实验效果图；
图8是本发明实施例控制方法与时变滑模控制方法、反演滑模控制方法在仿真环境2中的仿真实验效果图；
图9是本发明实施例控制方法与时变滑模控制方法、反演滑模控制方法在仿真环境3中的仿真实验效果图；
图10是本发明实施例控制方法与时变滑模控制方法、反演滑模控制方法在仿真环境4中的仿真实验效果图；
图11是本发明实施例控制方法与时变滑模控制方法、反演滑模控制方法在仿真环境5中的仿真实验效果图；
图12是本发明实施例的装置中单元架构示意图；
图13是本发明实施例的设备中的连接示意图；
具体实施方式
为了使本发明的目的、技术方案及优点更加清楚明白，以下结合附图及实施例，对本发明进行进一步详细说明。应当理解，此处所描述的具体实施例仅用以解释本发明，并不用于限定本发明。
需要说明的是，如果不冲突，本发明实施例中的各个特征可以相互结合，均在本发明的保护范围之内。另外，虽然在装置示意图中进行了功能模块划分，在流程图中示出了逻辑顺序，但是在某些情况下，可以以不同于装置中的模块划分，或流程图中的顺序执行所示出或描述的步骤。
参照图1，本发明的一个实施例提供了一种基于滑模面的桥吊防摆方法，包括：
步骤S11,构建桥式吊车的位置摆角系统数学模型，基于反演滑模控制理论构建台车位置子系统控制器和负载摆角子系统控制器，将所述台车位置子系统控制器和所述负载摆角子系统控制器结合构建位置摆角全局滑模面，在所述位置摆角全局滑模面中引入时变函数，构建位置摆角滑模控制器；
步骤S12,构建桥式吊车的绳长系统数学模型，基于反演滑模控制理论构建绳长滑模控制器；
步骤S13,获取台车位置参数、负载摆角参数、时间参数和绳长参数；
步骤S14,将所述台车位置参数、负载摆角参数、时间参数输入所述位置摆角滑模控制器中，将所述绳长参数输入到绳长滑模控制器中；
步骤S15,所述位置摆角滑模控制器和绳长滑模控制器分别输出台车水平牵引力和沿绳牵引力。
本发明实施例将原本复杂的桥式吊车动力学模型转换成一般状态空间函数形式，运用反演控制算法逐层设计台车位置子系统控制器和负载摆角子系统控制器后，将台车位置子系统控制器和负载摆角子系统控制器进行结合，构建一个位置摆角全局滑模面，在滑模面设计中引入时变函数，滑模面可随着时间的改变而改变，使滑模面的初始位置尽可能地接近状态变量，大大减少状态变量到达滑模面的时间；构建绳长子系统控制器，利用反演滑模控制理论对绳长的状态空间函数结合李雅普诺夫函数进行逐层设计，实现吊绳子系统的渐进稳定。
桥式吊车系统为欠驱动系统，台车位置和负载摆角两个状态量为同一个电机所驱动，也就是一个驱动量引起两个状态量同时改变，因此在位置摆角子系统控制器的设计中需要将台车位置和负载摆角的防摆控制器同时考虑进来，分别构建台车位置子系统控制器和负载摆角子系统控制器，再结合台车位置子系统控制器和负载摆角子系统控制器，引入时变函数，构建出位置摆角全局系统控制器。
参照图2，其中，基于反演滑模控制理论构建台车位置子系统控制器还包括以下步骤：
步骤S21，构建台车位置子系统的第一层李雅普诺夫函数；
步骤S22，对台车位置子系统的第一层李雅普诺夫函数进行一阶求导；
步骤S23,若所述台车位置子系统的第一层李雅普诺夫函数的一阶导数不大于0，则求得台车位置子系统控制器；
步骤S24，若所述台车位置子系统的第一层李雅普诺夫函数的一阶导数大于0，则构建台车位置子系统的第二层台车位置子系统李雅普诺夫函数；
步骤S25，对台车位置子系统的第二层台车位置子系统李雅普诺夫函数进行一阶求导；
步骤S26,令台车位置子系统的第二层台车位置子系统李雅普诺夫函数的一阶导数不大于零，求得台车位置子系统控制器。
本发明实施例中，基于反演滑模控制理论，并结合李雅普诺夫函数进行稳定性设计，构建台车位置子系统控制器，第一层李雅普诺夫函数中仅包含台车位置参数，对其求导得到台车运动速度参数，这对于台车位置控制器设计来说是不够的，因为不包含台车的运动加速度变量，无法保证台车位置控制器渐进稳定，所以需要对台车位置子系统构建第二层李雅普诺夫函数，使台车位置子系统趋于稳定，增强系统的鲁棒性和控制性能。
参照图3，其中，基于反演滑模控制理论构建负载摆角子系统控制器包括以下步骤：
步骤S31，构建负载摆角子系统的第一层李雅普诺夫函数；
步骤S32，对负载摆角子系统的第一层李雅普诺夫函数进行一阶求导；
步骤S33,若所述负载摆角子系统的第一层李雅普诺夫函数的一阶导数不大于0，则求得负载摆角子系统控制器；
步骤S34，若所述负载摆角子系统的第一层李雅普诺夫函数的一阶导数大于0，则构建负载摆角子系统的第二层李雅普诺夫函数；
步骤S35，对负载摆角子系统的第二层李雅普诺夫函数进行一阶求导；
步骤S36，令负载摆角子系统的第二层李雅普诺夫函数的一阶导数不大于零，求得负载摆角子系统控制。
本发明实施例中，基于反演滑模控制理论，并结合李雅普诺夫函数进行稳定性设计，构建负载摆角子系统控制器，第一层李雅普诺夫函数中仅包含负载摆角角度参数，对其求导得到负载摆角运动速度参数，这对于负载摆角控制器设计来说是不够的，因为不包含负载摆角的运动加速度变量，无法保证负载摆角控制器渐进稳定，所以需要对负载摆角子系统构建第二层李雅普诺夫函数，使负载摆角子系统趋于稳定，增强系统的鲁棒性和控制性能。
参照图4，其中，将所述台车位置子系统控制器和所述负载摆角子系统控制器结合构建位置摆角全局滑模面，在所述位置摆角全局滑模面中引入时变函数，构建位置摆角滑模控制器包括以下步骤：
步骤S41，构建位置摆角全局系统滑模控制函数；
步骤S42，构建位置摆角全局系统时变滑模面；
步骤S43，构建位置摆角全局系统李雅普诺夫函数；
步骤S44，对位置摆角全局系统李雅普诺夫函数进行一阶求导；
步骤S45，构建一般指数趋近律求得位置摆角全局系统滑模控制的耦合开关控制律；
步骤S46，构建S型饱和函数为位置摆角全局系统滑模控制函数求得位置摆角滑模控制器。
反演滑模控制设计方法首先对复杂的驱动量缺失的不呈线性状态的系统分隔成不多于系统层数的子系统，然后将李雅普诺夫函数与中间无实际物理含义的控制量相互结合引入到子系统设计中，在最后一层系统的虚拟控制量引入滑模变结构控制，利用滑模控制的不改变性来保证最后子系统的渐进平稳，在本发明实施例中是先分成台车位置子系统和负载摆角子系统分别构建控制器，在最后一层系统的构建中引入时变滑模面，从而构建出位置摆角全局滑模控制器。
参照图5，其中，基于反演滑模控制理论构建绳长滑模控制器包括以下步骤：
步骤S51，构建绳长子系统的第一层李雅普诺夫函数；
步骤S52，对绳长子系统的第一层李雅普诺夫函数进行一阶求导；
步骤S53，若所述绳长子系统的第一层李雅普诺夫函数的一阶导数不大于0，则求得绳长子系统控制器；
步骤S54，若所述绳长子系统的第一层李雅普诺夫函数的一阶导数大于0，则构建绳长子系统的第二层李雅普诺夫函数；
步骤S55，对绳长子系统的第二层李雅普诺夫函数进行一阶求导；
步骤S56，令绳长子系统的第二层李雅普诺夫函数的一阶导数不大于零，求得绳长子系统控制器。
本发明实施例中，基于反演滑模控制理论，并结合李雅普诺夫函数进行稳定性设计，构建绳长子系统控制器，第一层李雅普诺夫函数中仅包含绳长长度参数，对其求导得到绳长运动速度参数，这对于绳长控制器设计来说是不够的，因为不包含绳长的运动加速度变量，无法保证绳长控制器渐进稳定，所以需要对绳长子系统构建第二层李雅普诺夫函数，使绳长子系统趋于稳定，增强系统的鲁棒性和控制性能。
在一种优选的实施方式中，基于反演滑模控制理论构建台车位置子系统控制器包括：构建台车位置子系统数学模型，桥式吊车的 数学模型公式考虑台车位置自由度改写成如下公式：
Figure PCTCN2020104565-appb-000001
其中，x 1＝x，
Figure PCTCN2020104565-appb-000002
x为台车移动的位置，
Figure PCTCN2020104565-appb-000003
为台车移动的速度，u x为台车位置子系统控制器，基于桥式吊车的数学模型公式推导得出
Figure PCTCN2020104565-appb-000004
b 1(x)＝1/[M+m sin 2(x 3)]，其中，f 1为台车位置子系统的状态变量，b 1为台车位置子系统的输入变量，l为吊绳的绳长，M为吊车质量，m为负载质量，g为重力加速度，x 3＝θ，
Figure PCTCN2020104565-appb-000005
θ为负载的摆角，
Figure PCTCN2020104565-appb-000006
为负载摆角的角速度；定义台车位置跟踪误差e 1＝x 1-x 1d，其中，x 1d为台车目标位置；对e 1＝x 1-x 1d求导数得到
Figure PCTCN2020104565-appb-000007
构建台车位置子系统的第一层李雅普诺夫函数为V 1＝e 1 2/2；对V 1＝e 1 2/2进行一阶求导得到
Figure PCTCN2020104565-appb-000008
令
Figure PCTCN2020104565-appb-000009
其中α 1为虚拟中间变量，在反演滑模控制算法中构建稳定项α 1＝k 1e 1，其中k 1为台车位置子系统的误差稳定系数；将α 1＝k 1e 1代入
Figure PCTCN2020104565-appb-000010
式子中得到
Figure PCTCN2020104565-appb-000011
当e 2＝0时，
Figure PCTCN2020104565-appb-000012
由李雅普诺夫函数稳定性判断系统趋于稳定，但一般情况下由于系统处在运动过程中，状态量是不稳定的，只有到达目标位置才会稳定下来，因此当e 2≠0，需要对台车位置子系统进一步设计，定义第二层李雅普诺夫函数为V 2＝V 1+S 1 2/2，其中，S 1＝c 1e 1+e 2，S 1为台车位置子系统滑模面，c 1为台车位置子系统的误差系数；对台车位置子系统的第二层台车位置子系统李雅普诺夫函数进行一阶求导包括：对
Figure PCTCN2020104565-appb-000013
进行一阶求导得到
Figure PCTCN2020104565-appb-000014
令
Figure PCTCN2020104565-appb-000015
构建台车位置子系统控制器u x为
Figure PCTCN2020104565-appb-000016
其中，h x为台车位置子系统滑模面系数，β x为台车位置子系统切换增益。
在本发明实施例中，基于反演滑模控制理论构建负载摆角子系统控制器包括：桥式吊车的数学模型公式负载摆角自由度改写成如下公式：
Figure PCTCN2020104565-appb-000017
其中，x 3＝θ，
Figure PCTCN2020104565-appb-000018
θ为负载的摆动角度，
Figure PCTCN2020104565-appb-000019
为负载的摆动角速度，u θ为台车位置子系统控制器，基于桥式吊车的数学模型公式推导得出
Figure PCTCN2020104565-appb-000020
b 2(x)＝[-cos(x 3)]/{[M+m sin 2(x 3)]l}，其中，f 2为摆角子系统的状态变量，b 2为摆角子系统的输入变量；定义负载摆角跟踪误差e θ1＝x 3-θ d，θ d为目标负载摆角大小，理想状态应为0；对e θ1＝x 3-θ d求导数得到
Figure PCTCN2020104565-appb-000021
构建负载摆角子系统的第一层李雅普诺夫函数为V θ1＝e θ1 2/2；对V θ1＝e θ1 2/2进行一阶求导得到
Figure PCTCN2020104565-appb-000022
令
Figure PCTCN2020104565-appb-000023
在反演滑模控制算法中构建稳定项α θ＝k θ1e θ1，其中k θ为负载摆角子系统的误差稳定系数；将α θ＝k θ1e θ1代入
Figure PCTCN2020104565-appb-000024
式子中得到
Figure PCTCN2020104565-appb-000025
当e θ2＝0时，
Figure PCTCN2020104565-appb-000026
由李雅普诺夫函数稳定性判断系统趋于稳定，但一般情况下但一般情况下由于系统处在运动过程中，状态量是不稳定的，只有到达目标位置才会稳定下来，因此当e θ2≠0，需要对负载摆角子系统进一步设计，定义负载摆角子系统的第二层李雅普诺夫函数为V θ2＝V θ1+S θ 2/2，其中，S θ＝c θe θ1+e θ2，S θ为负载摆角子系统滑模面，c θ为负载摆角子系统的误差系数；对负载摆角子系统的第二层李雅普诺夫函数进行一阶求导包括：对 V θ2＝V θ1+S θ 2/2进行一阶求导得到
Figure PCTCN2020104565-appb-000027
令
Figure PCTCN2020104565-appb-000028
构建负载摆角子系统控制器u θ为
Figure PCTCN2020104565-appb-000029
其中，h θ为台车位置子系统滑模面系数，β θ为台车位置子系统切换增益。
值得注意的是，将所述台车位置子系统控制器和所述负载摆角子系统控制器结合构建位置摆角全局滑模面，在所述位置摆角全局滑模面中引入时变函数，构建位置摆角滑模控制器包括：因为位置和摆角两自由度皆由一个控制输入，所以需要将台车位置子系统控制器和负载摆角子系统控制器结合，构建一个全局滑模控制器u为u＝u x+u θ+u c，其中u c为耦合开关控制律；构建位置摆角全局系统时变滑模面为S＝aS 1+S 2+ωe -qt，其中，a为滑模面权重系数，ω为指数函数加权系数，e -qt为时变指数函数，q为指数函数时变系数，t为系统运行时间变量；构建位置摆角全局系统李雅普诺夫函数为V＝S 2/2；对位置摆角全局系统李雅普诺夫函数进行一阶求导包括：对V＝S 2/2进行一阶求导并化简得到
Figure PCTCN2020104565-appb-000030
由于台车位置子系统控制器u x和负载摆角子系统控制器u θ中均包含了滑模变结构的趋近律控制，因此对位置摆角全局系统李雅普诺夫函数的一阶导数进行化简，得到
Figure PCTCN2020104565-appb-000031
根据滑模控制算法，选择一般指数趋近律作为全局滑模控制律，一般指数趋近律具体公式为
Figure PCTCN2020104565-appb-000032
η＞0，其中，-kS为指数趋近项，k为趋近律，η是增益系数，由此得到(ab 1u θ+b 2u x)+u c(ab 1+b 2)-ωqe -qt＝-ηsgn(S)-kS，继而求得耦合开关控制律u c为u c＝-[b 2u x+ab 1u θ+ηsgn(S)+kS-ωqe -qt]/(ab 1+b 2)；位置摆角全局系统的切换控制函数选用S型饱和函数，得到位置摆角全局系统控制器u＝-[ab 1u x+b 2u θ+ηsat(S)+kS]/(ab 1+b 2)。
应理解，基于反演滑模控制理论构建绳长滑模控制器包括：绳长子系统的数学模型公式改写为
Figure PCTCN2020104565-appb-000033
Figure PCTCN2020104565-appb-000034
其中，x 5＝l，
Figure PCTCN2020104565-appb-000035
l为吊车的绳长，
Figure PCTCN2020104565-appb-000036
为吊车的绳长变化速度，u l为台车位置子系统控制器，基于桥式吊车的数学模型公式推导得出f 3(x)＝-x 5D/m+g，b 3(x)＝1/m，其中，f 3为绳长子系统的状态变量，b 3为绳长子系统的输入变量，D为吊绳运动伸缩的阻尼系数；定义绳长跟踪误差e l1＝x 5-l d，其中l d为目标绳长；对绳长子系统跟踪误差进行一阶求导，对e l1＝x 5-l d求导数得到
Figure PCTCN2020104565-appb-000037
构建绳长子系统的第一层李雅普诺夫函数为V l1＝e l1 2/2；对V l1＝e l1 2/2进行一阶求导得到
Figure PCTCN2020104565-appb-000038
令
Figure PCTCN2020104565-appb-000039
在反演滑模控制算法中构建稳定项α l＝k le l1，其中k l为绳长子系统的误差稳定系数；将α l＝k le l1代入
Figure PCTCN2020104565-appb-000040
式子中得到
Figure PCTCN2020104565-appb-000041
当e l2＝0时，
Figure PCTCN2020104565-appb-000042
由李雅普诺夫函数稳定性判断系统趋于稳定，但一般情况下但一般情况下由于系统处在运动过程中，状态量是不稳定的，只有到达目标位置才会稳定下来，因此当e l2≠0，需要对绳长子系统进一步设计，定义绳长子系统的第二层李雅普诺夫函数为V l2＝V l1+S l 2/2，其中，S l＝c le l1+e l2，S l为绳长子系统滑模面，c l为绳长子系统的误差系数；对V l2＝V l1+S l 2/2进行一阶求导得到
Figure PCTCN2020104565-appb-000043
令
Figure PCTCN2020104565-appb-000044
构建绳长子系统控制器u l为
Figure PCTCN2020104565-appb-000045
其中，h l为绳长子系统滑模面系数，β l为绳长子系统切换增益。
根据本发明实施例的方法，通过仿真实验来检验本发明实施例的防摆效果，仿真时长设置为15秒，参照图6，其中，台车位置从 0米运动到3米目标位置所花费时间为7秒，负载摆角的最大幅度小于0.03弧度，同时在7秒收敛到0弧度，吊绳从1米伸长到4米长度所花费时间为1秒，吊绳驱动力产生后很快收敛到0牛顿，收敛时间为1秒，吊车驱动力从一开始约45牛顿驱动吊车运动，随后快速收敛到0牛顿，所耗费时间为7秒，之后再无抖振现象产生。本发明实施例不仅克服了时变滑模出现的驱动力抖振问题，而且克服了反演滑模出现残余摆动现象，使桥式吊车的控制效果达到最优。
为了进一步检验本发明实施例控制方法对桥式吊车的控制效果，接下来设置了五种仿真环境实验，分别对比本发明实施例控制方法与时变滑模控制方法、反演滑模控制方法在相应仿真环境中对桥式吊车的控制效果，其中实线代表本发明实施例控制方法的仿真结果情况，方点虚线代表时变滑模控制方法的仿真结果情况，短虚线代表反演滑模控制方法的仿真结果情况，五种仿真环境条件如下：
仿真环境1：轻型负载条件下，将台车位移目标值和绳长目标值分别设定为3米和4米，台车质量和负载质量分别设定为10千克和5千克，其他系统模型参数不改变。
仿真环境2：重型负载条件下，将台车位移目标值和绳长目标值分别设定为3米和4米，台车质量和负载质量分别设定为500千克和100千克，其他系统模型参数不改变。
仿真环境3：大目标值条件下，将台车位移目标值和绳长目标值分别设定为10米和6米，台车质量和负载质量分别设定为500千克和100千克，其他系统模型参数不改变。
仿真环境4：系统模型改变条件下，将台车位移目标值和绳长目标值分别设定为10米和6米，台车质量和负载质量分别设定为500千克和100千克，对二维桥式吊车系统模型参数进行改变，吊车空气阻力系数从0.5变为0.2，负载空气阻力系数从0.5变为0.6，吊车摩擦系数从0.5变为0.3。
仿真环境5：有外界干扰条件下，将台车位移目标值和绳长目标值分别设定为10米和6米，台车质量和负载质量分别设定为500千克和100千克，吊车空气阻力系数从0.5变为0.2，负载空气阻力系数从0.5变为0.6，吊车摩擦系数从0.5变为0.3，桥式吊车由初始位置运动到目标位置，待其收敛稳定后，对负载突然施加一个长达1秒的力使其从0.15弧度的角度开始摆动。
参照图7，仿真环境1实验结果为：采用本发明实施例控制方法的仿真结果中，负载摆角幅度小于0.031弧度，并且在收敛后无残余摆动，而时变滑模控制方法的仿真结果为负载摆动幅度较大，反演滑模控制方法的仿真结果为负载摆角有残余摆动；在台车位置控制性能方面，本发明实施例7秒到达指标位置且没有摆动，而反演滑模控制方法的仿真结果有轻微摆动；在绳长控制方面，本发明实施例吊绳从1米伸长到4米耗时为1秒，而时变滑模控制方法耗时4秒，本发明实施例控制效果较好。以上结果表明，本发明实施例控制方法在仿真环境1中对比其他两种滑模控制算法，负载摆角幅度较小，更快达到稳定，控制效果较佳。
参照图8，仿真环境2实验结果为：当台车质量与负载质量大幅度增加时，采用本发明实施例控制方法的仿真结果中，负载摆角幅度小于0.03弧度，收敛后无残余摆动，而时变滑模控制方法的仿真结果为负载摆动幅度较大，反演滑模控制方法的仿真结果为负载摆动幅度较大并且有残余摆动；在台车位置控制性能方面，本发明实施例较其他两种控制方法更快达到指定位置，并且没有摆动；在绳长控制方面，本发明实施例吊绳从1米伸长到4米耗时为1秒，而时变滑模控制方法耗时4秒，本发明实施例控制效果较好。以上结果表明，本发明实施例控制方法在仿真环境2中对比其他两种滑模控制算法，负载摆角幅度较小，更快达到稳定，控制效果较佳。
参照图9，仿真环境3实验结果为：当改变台车位移目标值和绳长目标值时，采用本发明实施例控制方法的仿真结果为负载摆角为0.1弧度，收敛后无残余摆动，而时变滑模控制的负载摆角幅度超过0.15弧度，反演滑模控制的负载摆角幅度超过0.1弧度并且收敛后存在残余摆动，以上结果表明，本发明实施例控制方法在仿真环境3中对比其他两种滑模控制算法，负载摆角幅度较小，更快达到稳定，控制效果较佳。
参照图10，仿真环境4实验结果为：当改变改变二维桥式吊车系统模型上的空气阻力系数和摩擦系数时，采用本发明实施例控制方法的仿真结果为负载摆角为0.1弧度，收敛后无残余摆动，而时变滑模控制的负载摆角幅度超过0.15弧度，反演滑模控制的负载摆角幅度超过0.1弧度并且收敛后存在残余摆动，以上结果表明，本发明实施例控制方法在仿真环境4中对比其他两种滑模控制算法，负载摆角幅度较小，更快达到稳定，控制效果较佳。
参照图11，仿真环境5实验结果为：在施加外界干扰条件下，采用本发明实施例控制方法的台车位置恢复超调比其他两种滑模控制算法小，并且输出的吊绳驱动力明显小于其他两种滑模控制算法，吊绳驱动力接近于0。以上结果表明，本发明实施例控制方法在仿真环境5中对比其他两种滑模控制算法，在控制力矩输出方面优于其他两种滑模控制算法。
本发明实施例还提供了一种基于滑模面的桥吊防摆装置，在该基于滑模面的桥吊防摆装置1000中，包括但不限于：位置摆角滑模 控制器构建单元1100、绳长滑模控制器构建单元1200、获取单元1300、输入单元1400和输出单元1500。
其中，位置摆角滑模控制器构建单元1100，用于构建桥式吊车的位置摆角系统数学模型，基于反演滑模控制理论构建台车位置子系统控制器和负载摆角子系统控制器，将所述台车位置子系统控制器和所述负载摆角子系统控制器结合构建位置摆角全局滑模面，在所述位置摆角全局滑模面中引入时变函数，构建位置摆角滑模控制器；
绳长滑模控制器构建单元1200，用于构建桥式吊车的绳长系统数学模型，基于反演滑模控制理论构建绳长滑模控制器；
获取单元1300，用于获取台车位置参数、负载摆角参数、时间参数和绳长参数；
输入单元1400，用于将所述台车位置参数、负载摆角参数、时间参数输入所述位置摆角滑模控制器中，将所述绳长参数输入到绳长滑模控制器中；
输出单元1500，用于所述位置摆角滑模控制器和绳长滑模控制器分别输出台车水平牵引力和沿绳牵引力。
需要说明的是，由于本实施例中的一种基于滑模面的桥吊防摆装置与上述的一种基于滑模面的桥吊防摆方法基于相同的发明构思，因此，方法实施例中的相应内容同样适用于本装置实施例，此处不再详述。
本发明实施例还提供了一种基于滑模面的桥吊防摆设备，该基于滑模面的桥吊防摆设备2000可以是任意类型的智能终端，例如手机、平板电脑、个人计算机等。
具体地，该基于滑模面的桥吊防摆设备2000包括：一个或多个控制处理器2010和存储器2020，图13中以一个控制处理器2010为例。
控制处理器2010和存储器2020可以通过总线或者其他方式连接，图13中以通过总线连接为例。
存储器2020作为一种非暂态计算机可读存储介质，可用于存储非暂态软件程序、非暂态性计算机可执行程序以及模块，如本发明实施例中的基于滑模面的桥吊防摆方法对应的程序指令/模块，例如，图12中所示的位置摆角滑模控制器构建单元1100、绳长滑模控制器构建单元1200、获取单元1300、输入单元1400和输出单元1500。控制处理器2010通过运行存储在存储器2020中的非暂态软件程序、指令以及模块，从而执行基于滑模面的桥吊防摆装置1000的各种功能应用以及数据处理，即实现上述方法实施例的基于滑模面的桥吊防摆方法。
存储器2020可以包括存储程序区和存储数据区，其中，存储程序区可存储操作系统、至少一个功能所需要的应用程序；存储数据区可存储根据基于滑模面的桥吊防摆装置1000的使用所创建的数据等。此外，存储器2020可以包括高速随机存取存储器，还可以包括非暂态存储器，例如至少一个磁盘存储器件、闪存器件、或其他非暂态固态存储器件。在一些实施方式中，存储器2020可选包括相对于控制处理器2010远程设置的存储器，这些远程存储器可以通过网络连接至该基于滑模面的桥吊防摆设备2000。上述网络的实例包括但不限于互联网、企业内部网、局域网、移动通信网及其组合。
所述一个或者多个模块存储在所述存储器2020中，当被所述一个或者多个控制处理器2010执行时，执行上述方法实施例中的基于滑模面的桥吊防摆方法，例如，执行以上描述的图1中的方法步骤S11至S15，实现图12中的单元1100-1500的功能。
本发明实施例还提供了一种计算机可读存储介质，所述计算机可读存储介质存储有计算机可执行指令，该计算机可执行指令被一个或多个控制处理器执行，例如，被图13中的一个控制处理器2010执行，可使得上述一个或多个控制处理器2010执行上述方法实施例中的基于滑模面的桥吊防摆方法，例如，执行以上描述的图1中的方法步骤S11至S15，实现图12中的单元1100-1500的功能。
以上所描述的装置实施例仅仅是示意性的，其中所述作为分离部件说明的单元可以是或者也可以不是物理上分开的，即可以位于一个地方，或者也可以分布到多个网络单元上。可以根据实际的需要选择其中的部分或者全部模块来实现本实施例方案的目的。
通过以上的实施方式的描述，本领域技术人员可以清楚地了解到各实施方式可借助软件加通用硬件平台的方式来实现。本领域技术人员可以理解实现上述实施例方法中的全部或部分流程是可以通过计算机程序来指令相关的硬件来完成，所述的程序可存储于一计算机可读取存储介质中，该程序在执行时，可包括如上述方法的实施例的流程。其中，所述的存储介质可为磁碟、光盘、只读存储记忆体(ReadOnly Memory,ROM)或随机存储记忆体(Random Access Memory,RAM)等。
以上是对本发明的较佳实施进行了具体说明，但本发明并不局限于上述实施方式，熟悉本领域的技术人员在不违背本发明精神的前提下还可作出种种的等同变形或替换，这些等同的变形或替换均包含在本申请权利要求所限定的范围内。

Claims (8)

  1. 一种基于滑模面的桥吊防摆方法，其特征在于包括以下步骤：
    构建桥式吊车的位置摆角系统数学模型，基于反演滑模控制理论构建台车位置子系统控制器和负载摆角子系统控制器，将所述台车位置子系统控制器和所述负载摆角子系统控制器结合构建位置摆角全局滑模面，在所述位置摆角全局滑模面中引入时变函数，构建位置摆角滑模控制器；
    构建桥式吊车的绳长系统数学模型，基于反演滑模控制理论构建绳长滑模控制器；
    获取台车位置参数、负载摆角参数、时间参数和绳长参数；
    将所述台车位置参数、负载摆角参数、时间参数输入所述位置摆角滑模控制器中，将所述绳长参数输入到绳长滑模控制器中；
    所述位置摆角滑模控制器和绳长滑模控制器分别输出台车水平牵引力和沿绳牵引力。
  2. 根据权利要求1所述的一种基于滑模面的桥吊防摆方法，其特征在于：基于反演滑模控制理论构建台车位置子系统控制器包括：
    构建台车位置子系统的第一层李雅普诺夫函数；
    对台车位置子系统的第一层李雅普诺夫函数进行一阶求导；
    若所述台车位置子系统的第一层李雅普诺夫函数的一阶导数不大于0，则求得台车位置子系统控制器；
    若所述台车位置子系统的第一层李雅普诺夫函数的一阶导数大于0，则构建台车位置子系统的第二层台车位置子系统李雅普诺夫函数；
    对台车位置子系统的第二层台车位置子系统李雅普诺夫函数进行一阶求导；
    令台车位置子系统的第二层台车位置子系统李雅普诺夫函数的一阶导数不大于零，求得台车位置子系统控制器。
  3. 根据权利要求1所述的一种基于滑模面的桥吊防摆方法，其特征在于：所述基于反演滑模控制理论构建负载摆角子系统控制器包括：
    构建负载摆角子系统的第一层李雅普诺夫函数；
    对负载摆角子系统的第一层李雅普诺夫函数进行一阶求导；
    若所述负载摆角子系统的第一层李雅普诺夫函数的一阶导数不大于0，则求得负载摆角子系统控制器；
    若所述负载摆角子系统的第一层李雅普诺夫函数的一阶导数大于0，
    则构建负载摆角子系统的第二层李雅普诺夫函数；
    对负载摆角子系统的第二层李雅普诺夫函数进行一阶求导；
    令负载摆角子系统的第二层李雅普诺夫函数的一阶导数不大于零，求得负载摆角子系统控制器。
  4. 根据权利要求1所述的一种基于滑模面的桥吊防摆方法，其特征在于：所述将所述台车位置子系统控制器和所述负载摆角子系统控制器结合构建位置摆角全局滑模面，在所述位置摆角全局滑模面中引入时变函数，构建位置摆角滑模控制器包括：
    构建位置摆角全局系统滑模控制函数；
    构建位置摆角全局系统时变滑模面；
    构建位置摆角全局系统李雅普诺夫函数；
    对位置摆角全局系统李雅普诺夫函数进行一阶求导；
    构建一般指数趋近律求得位置摆角全局系统滑模控制的耦合开关控制律；
    构建S型饱和函数为位置摆角全局系统滑模控制函数求得位置摆角滑模控制器。
  5. 根据权利要求1所述的一种基于滑模面的桥吊防摆方法，其特征在于：所述基于反演滑模控制理论构建绳长滑模控制器包括：
    构建绳长子系统的第一层李雅普诺夫函数；
    对绳长子系统的第一层李雅普诺夫函数进行一阶求导；
    若所述绳长子系统的第一层李雅普诺夫函数的一阶导数不大于0，则求得绳长子系统控制器；
    若所述绳长子系统的第一层李雅普诺夫函数的一阶导数大于0，
    则构建绳长子系统的第二层李雅普诺夫函数；
    对绳长子系统的第二层李雅普诺夫函数进行一阶求导；
    令绳长子系统的第二层李雅普诺夫函数的一阶导数不大于零，求得绳长子系统控制器。
  6. 一种基于滑模面的桥吊防摆装置，其特征在于：包括：
    位置摆角滑模控制器构建单元，用于构建桥式吊车的位置摆角系统数学模型，基于反演滑模控制理论构建台车位置子系统控制器和负载摆角子系统控制器，将所述台车位置子系统控制器和所述负载摆角子系统控制器结合构建位置摆角全局滑模面，在所述位置摆角全局滑模面中引入时变函数，构建位置摆角滑模控制器；
    绳长滑模控制器构建单元，用于构建桥式吊车的绳长系统数学模型，基于反演滑模控制理论构建绳长滑模控制器；
    获取单元，用于获取台车位置参数、负载摆角参数、时间参数和绳长参数；
    输入单元，用于将所述台车位置参数、负载摆角参数、时间参数输入所述位置摆角滑模控制器中，将所述绳长参数输入到绳长滑模控制器中；
    输出单元，用于所述位置摆角滑模控制器和绳长滑模控制器分别输出台车水平牵引力和沿绳牵引力。
  7. 一种基于滑模面的桥吊防摆设备，其特征在于：包括至少一个控制处理器和用于与所述至少一个控制处理器通信连接的存储器；所述存储器存储有可被所述至少一个控制处理器执行的指令，所述指令被所述至少一个控制处理器执行，以使所述至少一个控制处理器能够执行如权利要求1-5任一项所述的基于滑模面的桥吊防摆方法。
  8. 一种计算机可读存储介质，其特征在于：所述计算机可读存储介质存储有计算机可执行指令，所述计算机可执行指令用于使计算机执行如权利要求1-5任一项所述的基于滑模面的桥吊防摆方法。
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CN108427280A (zh) * 2018-03-21 2018-08-21 南京邮电大学 一种基于滑模控制理论的桥式吊车防摆控制方法
CN110526124A (zh) * 2019-08-30 2019-12-03 五邑大学 一种基于滑模面的桥吊防摆方法、装置、设备及存储介质

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