CN110526124B - Bridge crane anti-swing method, device and equipment based on sliding mode surface and storage medium - Google Patents
Bridge crane anti-swing method, device and equipment based on sliding mode surface and storage medium Download PDFInfo
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- CN110526124B CN110526124B CN201910818773.3A CN201910818773A CN110526124B CN 110526124 B CN110526124 B CN 110526124B CN 201910818773 A CN201910818773 A CN 201910818773A CN 110526124 B CN110526124 B CN 110526124B
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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
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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
- 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
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Abstract
The invention discloses a method, a device, equipment and a storage medium for preventing a bridge crane from swinging based on a sliding mode surface.A trolley position subsystem controller and a load swing angle subsystem controller are designed layer by layer based on an inversion control algorithm, then the trolley position subsystem controller and the load swing angle subsystem controller are combined to construct a position swing angle global sliding mode surface, and a time-varying function is introduced in the sliding mode surface design to construct a position swing angle controller; and designing the rope length controller layer by combining a state space function of the rope length with a Lyapunov function based on an inverse sliding mode control theory, so as to realize gradual stability of the lifting rope subsystem. The method provided by the embodiment of the invention can not only solve the problem of system non-matching uncertainty, eliminate buffeting in the traditional sliding mode control algorithm to the maximum extent, improve the robustness of crane system anti-swing control, enable the system to have anti-interference capability and further improve the stability and control performance of a bridge crane system.
Description
Technical Field
The invention relates to the technical field of bridge cranes, in particular to a method, a device, equipment and a storage medium for preventing a bridge crane from swinging based on a sliding mode surface.
Background
The bridge crane is widely applied to the assembly and transportation process of ports, warehouses, heavy industrial workshops, construction sites and other places as a large cargo handling mechanical device. The main goal of bridge crane system control is to achieve precise crane positioning and eliminate as much as possible the tilt angle of the load so that cargo can be transported to a designated location in a minimum amount of time without wobbling. The sliding mode control has good control performance on a nonlinear system, and is widely applied to system control of a bridge crane, but the sliding mode control of the bridge crane of the current mainstream has the following problems:
the traditional general sliding mode control algorithm cannot well solve the problem of system non-matching uncertainty, so that the buffeting phenomenon can occur, and the service life of the motor can be further influenced. In addition, when the system parameters are greatly changed by the traditional sliding mode control algorithm, the anti-swing control effect of the crane becomes worse, the robustness is poorer, and when the system is strongly interfered by the outside, the control algorithm cannot timely and accurately respond, so that the anti-swing effect of the bridge crane is further weakened.
Disclosure of Invention
In order to solve the problems, the invention aims to provide a method, a device, equipment and a storage medium for preventing a bridge crane from swinging based on a sliding mode surface, the advantage that the system is not matched with uncertainty can be processed by utilizing an inverse sliding mode control technology, and meanwhile, a time-varying sliding mode surface is introduced to enable the system to have stronger robustness, so that the stability and the control performance of a bridge crane system are further improved.
The technical scheme adopted by the invention for solving the problems is as follows:
in a first aspect, the invention provides a method for preventing a bridge crane from swinging based on a sliding mode surface, which comprises the following steps: constructing a mathematical model of a position swing angle system of a bridge crane, constructing a trolley position subsystem controller and a load swing angle subsystem controller based on an inverse sliding mode control theory, combining the trolley position subsystem controller and the load swing angle subsystem controller to construct a position swing angle global sliding mode surface, introducing a time-varying function into the position swing angle global sliding mode surface, and constructing a position swing angle sliding mode controller;
constructing a rope length system mathematical model of the bridge crane, and constructing a rope length sliding mode controller based on an inverse sliding mode control theory;
acquiring a trolley position parameter, a load swing angle parameter, a time parameter and a rope length parameter;
inputting the trolley position parameter, the load swing angle parameter and the time parameter into the position swing angle sliding mode controller, and inputting the rope length parameter into the rope length sliding mode controller;
and the position swing angle sliding mode controller and the rope length sliding mode controller respectively output horizontal traction force of the trolley and traction force along the rope.
Further, the method for constructing the trolley position subsystem controller based on the inverse sliding mode control theory comprises the following steps:
constructing a first layer of Lyapunov function of the trolley position subsystem;
performing first-order derivation on a first-layer Lyapunov function of the trolley position subsystem;
if the first derivative of the first-layer Lyapunov function of the trolley position subsystem is not more than 0, solving a trolley position subsystem controller;
if the first derivative of the first layer of the Lyapunov function of the trolley position subsystem is larger than 0, constructing a second layer of the Lyapunov function of the trolley position subsystem;
performing first-order derivation on a Lyapunov function of a second layer trolley position subsystem of the trolley position subsystem;
and (4) enabling a first derivative of a Lyapunov function of a second layer of trolley position subsystem of the trolley position subsystem to be not more than zero, and solving the controller of the trolley position subsystem.
Further, the method for constructing the load swing angle subsystem controller based on the inverse sliding mode control theory comprises the following steps:
constructing a first-layer Lyapunov function of a load swing angle subsystem;
carrying out first-order derivation on a first-layer Lyapunov function of the load swing angle subsystem;
if the first derivative of the first-layer Lyapunov function of the load swing angle subsystem is not more than 0, obtaining a load swing angle subsystem controller;
if the first-order derivative of the first-layer Lyapunov function of the load swing angle subsystem is larger than 0, constructing a second-layer Lyapunov function of the load swing angle subsystem;
performing first-order derivation on a second-layer Lyapunov function of the load swing angle subsystem;
and (4) enabling a first derivative of a second-layer Lyapunov function of the load swing angle subsystem to be not more than zero, and solving the load swing angle subsystem controller.
Further, the combining the trolley position subsystem controller and the load swing angle subsystem controller to construct a position swing angle global sliding mode surface, introducing a time-varying function into the position swing angle global sliding mode surface, and constructing the position swing angle sliding mode controller includes:
constructing a position swing angle global system sliding mode control function;
constructing a position swing angle global system time-varying sliding mode surface;
constructing a Lyapunov function of a position swing angle global system;
carrying out first-order derivation on a Lyapunov function of a position swing angle global system;
constructing a general index approach law to obtain a coupling switch control law of sliding mode control of a position swing angle global system;
and constructing an S-shaped saturation function as a position swing angle global system sliding mode control function to obtain a position swing angle sliding mode controller.
Further, the building of the rope length sliding mode controller based on the inverse sliding mode control theory comprises the following steps: constructing a first layer of Lyapunov function of the rope length system;
performing first-order derivation on a first-layer Lyapunov function of the rope length system;
if the first-order derivative of the first-layer Lyapunov function of the rope length subsystem is not larger than 0, the rope length subsystem controller is obtained;
if the first-order derivative of the first-layer Lyapunov function of the rope length subsystem is larger than 0, constructing a second-layer Lyapunov function of the rope length subsystem;
performing first-order derivation on a second layer of Lyapunov function of the rope length system;
and (4) making the first derivative of the second layer of the Lyapunov function of the rope length subsystem not greater than zero, and obtaining the rope length subsystem controller.
In a second aspect, the invention provides a sliding-form-surface-based anti-swing device for a bridge crane, which comprises: the system comprises a position swing angle sliding mode controller construction unit, a position swing angle sliding mode controller, a trolley position subsystem controller, a load swing angle subsystem controller, a position swing angle sliding mode controller and a control unit, wherein the position swing angle sliding mode controller construction unit is used for constructing a mathematical model of a position swing angle system of a bridge crane, constructing a trolley position subsystem controller and the load swing angle subsystem controller based on an inversion sliding mode control theory, combining the trolley position subsystem controller and the load swing angle subsystem controller to construct a position swing angle global sliding mode surface, introducing a time-varying;
the rope length sliding mode controller building unit is used for building a rope length system mathematical model of the bridge crane and building a rope length sliding mode controller based on an inverse sliding mode control theory;
the system comprises an acquisition unit, a control unit and a control unit, wherein the acquisition unit is used for acquiring a trolley position parameter, a load swing angle parameter, a time parameter and a rope length parameter;
the input unit is used for inputting the trolley position parameter, the load swing angle parameter and the time parameter into the position swing angle sliding mode controller and inputting the rope length parameter into the rope length sliding mode controller;
and the output unit is used for outputting the horizontal traction force and the traction force along the rope of the trolley by the position swing angle sliding mode controller and the rope length sliding mode controller respectively.
In a third aspect, the invention provides a bridge crane anti-swing device based on a sliding mode surface,
comprises at least one control processor and a memory for communicative connection with the at least one control processor; the memory stores instructions executable by the at least one control processor to enable the at least one control processor to perform the sliding mode surface based anti-sway method of the bridge crane as described above.
In a fourth aspect, the present invention provides a computer-readable storage medium storing computer-executable instructions for causing a computer to perform the method for preventing a bridge crane from swinging based on a sliding mode surface as described above.
In a fifth aspect, the present invention also provides a computer program product comprising a computer program stored on a computer readable storage medium, the computer program comprising program instructions which, when executed by a computer, cause the computer to perform the sliding mode surface based anti-sway method as described above.
One or more technical schemes provided in the embodiment of the invention have at least the following beneficial effects: after a trolley position subsystem controller and a load swing angle subsystem controller are designed layer by layer based on an inversion control algorithm, the trolley position subsystem controller and the load swing angle subsystem controller are combined to construct a position swing angle global sliding mode surface, and a time-varying function is introduced into the sliding mode surface design, so that the time for a state variable to reach the sliding mode surface is greatly reduced; and designing the rope length controller layer by combining a state space function of the rope length with a Lyapunov function based on an inverse sliding mode control theory, so as to realize gradual stability of the lifting rope subsystem. The method provided by the embodiment of the invention can not only solve the problem of system non-matching uncertainty, eliminate buffeting in the traditional sliding mode control algorithm to the maximum extent, improve the robustness of crane system anti-swing control, enable the system to have anti-interference capability and further improve the stability and control performance of a bridge crane system.
Drawings
The invention is further illustrated by the following figures and examples.
FIG. 1 is a flow chart of a method of an embodiment of the present invention;
FIG. 2 is a flowchart of a method for constructing a trolley position subsystem controller based on an inverse 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 an inverse sliding mode control theory according to an embodiment of the present invention;
fig. 4 is a flowchart of a method for constructing a position swing angle sliding mode controller by combining the trolley position subsystem controller and the load swing angle subsystem controller to construct a position swing angle global sliding mode surface, and introducing a time-varying function into the position swing angle global sliding mode surface according to an embodiment of the present invention;
FIG. 5 is a flow chart of a method for constructing a rope length sliding mode controller based on an inverse sliding mode control theory according to an embodiment of the invention;
FIG. 6 is a diagram of the effect of simulation experiments according to 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 in the simulation environment 1 according to the embodiment of the present invention;
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 in the simulation environment 2 according to the embodiment of the present invention;
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 in the simulation environment 3 according to the embodiment of the present invention;
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 in the simulation environment 4 according to the embodiment of the present invention;
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 in the simulation environment 5 according to the embodiment of the present invention;
FIG. 12 is a block diagram of a device according to an embodiment of the present invention;
FIG. 13 is a schematic illustration of the connections in the apparatus of an embodiment of the present invention;
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
It should be noted that, if not conflicted, the various features of the embodiments of the invention may be combined with each other within the scope of protection of the invention. Additionally, while functional block divisions are performed in apparatus schematics, with logical sequences shown in flowcharts, in some cases, steps shown or described may be performed in sequences other than block divisions in apparatus or flowcharts.
Referring to fig. 1, an embodiment of the present invention provides a method for preventing a bridge crane from swinging based on a sliding mode surface, including:
step S11, constructing a mathematical model of a position swing angle system of a bridge crane, constructing a trolley position subsystem controller and a load swing angle subsystem controller based on an inverse sliding mode control theory, combining the trolley position subsystem controller and the load swing angle subsystem controller to construct a position swing angle global sliding mode surface, introducing a time-varying function into the position swing angle global sliding mode surface, and constructing the position swing angle sliding mode controller;
step S12, constructing a rope length system mathematical model of the bridge crane, and constructing a rope length sliding mode controller based on an inverse sliding mode control theory;
step S13, obtaining a trolley position parameter, a load swing angle parameter, a time parameter and a rope length parameter;
step S14, inputting the trolley position parameter, the load swing angle parameter and the time parameter into the position swing angle sliding mode controller, and inputting the rope length parameter into the rope length sliding mode controller;
and step S15, the position swing angle sliding mode controller and the rope length sliding mode controller respectively output the horizontal traction force and the traction force along the rope of the trolley.
According to the embodiment of the invention, an original complex bridge crane dynamics model is converted into a general state space function form, a trolley position subsystem controller and a load swing angle subsystem controller are designed layer by using an inversion control algorithm, then the trolley position 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 into the sliding mode surface design, the sliding mode surface can be changed along with the change of time, the initial position of the sliding mode surface is close to a state variable as much as possible, and the time for the state variable to reach the sliding mode surface is greatly reduced; and constructing a rope length subsystem controller, and designing the state space function of the rope length in combination with the Lyapunov function layer by using an inverse sliding mode control theory to realize gradual stability of the lifting rope subsystem.
The bridge crane system is an under-actuated system, two state quantities of a trolley position and a load swing angle are driven by the same motor, namely one driving quantity causes the two state quantities to be changed simultaneously, so that in the design of the position swing angle subsystem controller, the anti-swing controllers of the trolley position and the load swing angle need to be taken into consideration simultaneously, the trolley position subsystem controller and the load swing angle subsystem controller are respectively built, and then a time-varying function is introduced by combining the trolley position subsystem controller and the load swing angle subsystem controller to build the position swing angle global system controller.
Referring to fig. 2, wherein the building of the trolley position subsystem controller based on the inverse sliding mode control theory further comprises the following steps:
step S21, constructing a first layer Lyapunov function of the trolley position subsystem;
step S22, first-order derivation is carried out on the first-layer Lyapunov function of the trolley position subsystem;
step S23, if the first derivative of the first-layer Lyapunov function of the trolley position subsystem is not more than 0, the controller of the trolley position subsystem is obtained;
step S24, if the first derivative of the first layer of the Lyapunov function of the trolley position subsystem is larger than 0, constructing a second layer of the Lyapunov function of the trolley position subsystem;
step S25, carrying out first order derivation on the Lyapunov function of the second layer trolley position subsystem of the trolley position subsystem;
and step S26, enabling a first derivative of the Lyapunov function of the second layer of trolley position subsystem to be not more than zero, and solving the trolley position subsystem controller.
In the embodiment of the invention, a trolley position subsystem controller is constructed based on an inversion sliding mode control theory and combined with a Lyapunov function to carry out stability design, the first layer of the Lyapunov function only contains trolley position parameters, and the trolley position subsystem controller is not enough for designing the trolley position controller, and the gradual stability of the trolley position controller cannot be ensured because the trolley position subsystem does not contain movement acceleration variables of a trolley, so the second layer of the Lyapunov function needs to be constructed for the trolley position subsystem, the trolley position subsystem tends to be stable, and the robustness and the control performance of the system are enhanced.
Referring to fig. 3, the construction of the load swing angle subsystem controller based on the inverse sliding mode control theory includes the following steps:
step S31, constructing a first layer of Lyapunov function of the load swing angle subsystem;
step S32, performing first-order derivation on the first-layer Lyapunov function of the load swing angle subsystem;
step S33, if the first derivative of the first layer of the Lyapunov function of the load swing angle subsystem is not more than 0, the controller of the load swing angle subsystem is obtained;
step S34, if the first derivative of the first-layer Lyapunov function of the load swing angle subsystem is larger than 0, constructing a second-layer Lyapunov function of the load swing angle subsystem;
step S35, performing first-order derivation on the second-layer Lyapunov function of the load swing angle subsystem;
and step S36, enabling the first derivative of the second-layer Lyapunov function of the load swing angle subsystem to be not more than zero, and obtaining the control of the load swing angle subsystem.
In the embodiment of the invention, a load swing angle subsystem controller is constructed based on an inversion sliding mode control theory and combined with a Lyapunov function to carry out stability design, the first layer of the Lyapunov function only contains a load swing angle parameter, and the first layer of the Lyapunov function is derived to obtain a load swing angle motion speed parameter, which is not enough for the design of the load swing angle controller, and the load swing angle subsystem tends to be stable because the load swing angle controller cannot be ensured to be gradually stable because the load swing angle controller does not contain a motion acceleration variable of a load swing angle, so that the second layer of the Lyapunov function needs to be constructed for the load swing angle subsystem, and the robustness and the control performance of the system are enhanced.
Referring to fig. 4, wherein the trolley position subsystem controller and the load swing angle subsystem controller are combined to construct a position swing angle global sliding mode surface, and a time-varying function is introduced into the position swing angle global sliding mode surface, the constructing of the position swing angle sliding mode controller comprises the following steps:
step S41, constructing a position swing angle global system sliding mode control function;
step S42, constructing a position swing angle global system time-varying sliding mode surface;
step S43, constructing a Lyapunov function of a position swing angle global system;
step S44, performing first-order derivation on the Lyapunov function of the position swing angle global system;
step S45, constructing a coupling switch control law of sliding mode control of the position swing angle global system by a general index approach law;
and step S46, constructing an S-shaped saturation function as a position swing angle global system sliding mode control function to obtain a position swing angle sliding mode controller.
The inversion sliding mode control design method comprises the steps of firstly dividing a system which is in a non-linear state and lacks complex driving quantity into subsystems which are not more than the number of system layers, then mutually combining a Lyapunov function and control quantity without practical physical meaning in the middle into subsystem design, introducing sliding mode variable structure control into virtual control quantity of a last layer of system, and ensuring gradual and stable progression of the last subsystem by utilizing the unchanged property of sliding mode control.
Referring to fig. 5, the building of the rope length sliding mode controller based on the inverse sliding mode control theory comprises the following steps:
step S51, constructing a first layer of Lyapunov function of the rope length system;
step S52, first-order derivation is carried out on the first layer of Lyapunov function of the rope length system;
step S53, if the first derivative of the first layer of the Lyapunov function of the rope length subsystem is not more than 0, the rope length subsystem controller is obtained;
step S54, if the first derivative of the first layer of the Lyapunov function of the rope length subsystem is larger than 0, constructing a second layer of the Lyapunov function of the rope length subsystem;
step S55, performing first-order derivation on the second layer Lyapunov function of the rope length system;
and step S56, enabling the first derivative of the second layer of the Lyapunov function of the rope length subsystem not to be larger than zero, and solving the rope length subsystem controller.
In the embodiment of the invention, based on an inversion sliding mode control theory and combined with a Lyapunov function to carry out stability design, the rope length subsystem controller is constructed, the first layer of the Lyapunov function only contains a rope length parameter, and the rope length motion speed parameter is obtained by derivation of the rope length parameter, which is not enough for the design of the rope length controller.
In a preferred embodiment, the building of the trolley position subsystem controller based on inverse sliding mode control theory comprises: a mathematical model of the trolley position subsystem is constructed, and the mathematical model formula of the bridge crane considers the degree of freedom of the trolley position and is rewritten into the following formula:
wherein x is1＝x，
x is the position where the trolley is moving,
speed of movement of the trolley, uxDerived from a mathematical model formula of a bridge crane for a trolley position subsystem controller
b1(x)＝1/[M+msin2(x3)]Wherein f is1Being a trolley position sub-systemState variable, b1Is the input variable of the trolley position subsystem, l is the rope length of the lifting rope, M is the crane mass, M is the load mass, g is the gravitational acceleration, x3＝θ，
Theta is the swing angle of the load,
angular velocity which is the load swing angle; defining trolley position tracking error e1＝x1-x1dWherein x is1dIs the target position of the trolley; to e1＝x1-x1dDerivation of derivatives
The first layer of Lyapunov function for constructing the position subsystem of the trolley is V1＝e1 22; to V1＝e1 2A/2 is obtained by first-order derivation
Order to
Wherein alpha is1Constructing a stable item alpha in an inversion sliding mode control algorithm for a virtual intermediate variable1＝k1e1Wherein k is1Error stability factor of the trolley position subsystem; will be alpha1＝k1e1Substitution into
In the formula
When e is2When the content is equal to 0, the content,
the stability of the system is judged by the stability of the Lyapunov function, but the system is generally in the motion processThe state quantity is unstable and will stabilize only when the target position is reached, so that when e2Not equal to 0, the position subsystem of the trolley needs to be further designed, and a second layer of Lyapunov function is defined as
Wherein S is1＝c1e1+e2，S1For the trolley position subsystem slip form face, c1Error coefficients for the trolley position subsystem; the first derivation of the lyapunov function of the second layer of trolley position subsystem comprises: to pair
Performing a first order derivation to obtain
Order to
Build trolley position subsystem controller uxIs composed of
Wherein h isxIs the sliding mode surface coefficient, beta, of the trolley position subsystemxGain is switched for the trolley position subsystem.
In the embodiment of the invention, the construction of the load swing angle subsystem controller based on the inverse sliding mode control theory comprises the following steps: the mathematical model formula of the bridge crane is changed into the following formula:
wherein x is3＝θ，
Theta is the swing angle of the load,
is the swing angular velocity of the load, uθIs a trolleyPosition subsystem controller derived from mathematical model formula of bridge crane
b2(x)＝[-cos(x3)]/{[M+msin2(x3)]l } in which f2As state variables of the swing angle sub-system, b2Is an input variable of the swing angle subsystem; defining load swing angle tracking error eθ1＝x3-θd，θdThe target load swing angle is 0 in an ideal state; to eθ1＝x3-θdDerivation of derivatives
The first layer of Lyapunov function for constructing the load swing angle subsystem is Vθ1＝eθ1 22; to Vθ1＝eθ1 2A/2 is obtained by first-order derivation
Order to
Construction of stable item alpha in inversion sliding mode control algorithmθ＝kθ1eθ1Wherein k isθThe error stability coefficient of the load swing angle subsystem; will be alphaθ＝kθ1eθ1Substitution into
In the formula
When e isθ2When the content is equal to 0, the content,
the stability of the system is judged to be stable by the Lyapunov function, but in general conditions, because the system is in the motion process, the state quantity is unstable, and the system can be stabilized only when reaching the target positionThus when eθ2Not equal to 0, the load swing angle subsystem needs to be further designed, and a second-layer Lyapunov function of the load swing angle subsystem is defined as Vθ2＝Vθ1+Sθ 2/2 wherein Sθ＝cθeθ1+eθ2，SθFor loading the sliding surface of the swing angle subsystem, cθThe error coefficient of the load swing angle subsystem; the first derivation of the second-level Lyapunov function of the load swing angle subsystem comprises: to Vθ2＝Vθ1+Sθ 2A/2 is obtained by first-order derivation
Order to
Constructing load swing angle subsystem controller uθIs composed of
Wherein h isθIs the sliding mode surface coefficient, beta, of the trolley position subsystemθGain is switched for the trolley position subsystem.
Notably, combining the trolley position subsystem controller and the load swing angle subsystem controller to construct a position swing angle global sliding mode surface, introducing a time-varying function into the position swing angle global sliding mode surface, and constructing the position swing angle sliding mode controller includes: because the two degrees of freedom of the position and the swing angle are input by one control, a trolley position subsystem controller and a load swing angle subsystem controller are combined to construct a global sliding mode controller u with u-ux+uθ+ucWherein u iscIs a coupling switch control law; constructing a time-varying sliding mode surface of a position swing angle global system aS aS1+S2+ωe-qtWhere a is a sliding mode surface weight coefficient, ω is an exponential function weight coefficient, e-qtIs a time-varying exponential function, q is an exponential function time-varying coefficient, and t is a system operation time variable; constructing a Lyapunov function of a position swing angle global system as V ═ S22; to position pendulumThe first derivation of the angular global system Lyapunov function comprises: for V ═ S22 first order derivation and simplification
Due to the position of the trolley, the subsystem controller uxAnd load swing angle subsystem controller uθAll the systems comprise the approximation law control of a sliding mode variable structure, so that the first derivative of the Lyapunov function of the position swing angle global system is simplified to obtain
According to the sliding mode control algorithm, selecting a general index approach law as a global sliding mode control law, wherein the specific formula of the general index approach law is
η>0, where-kS is an exponential approximation term, k is an approximation law, and η is a gain coefficient, thereby obtaining (ab)1uθ+b2ux)+uc(ab1+b2)-ωqe-qtThen, the coupled switch control law u is determinedcIs uc＝-[b2ux+ab1uθ+ηsgn(S)+kS-ωqe-qt]/(ab1+b2) (ii) a S-shaped saturation function is selected as the switching control function of the position swing angle global system to obtain a position swing angle global system controller u- [ ab ═1ux+b2uθ+ηsat(S)+kS]/(ab1+b2)。
It should be understood that constructing the rope length sliding mode controller based on the inverse sliding mode control theory comprises: the mathematical model formula of the rope length system is rewritten as
Wherein x is5＝l，
l is the length of the rope of the crane,
the rope length variation speed u of the cranelDeriving f for the trolley position subsystem controller based on a bridge crane mathematical model formula3(x)＝-x5D/m+g，b3(x) 1/m, wherein f3Is a state variable of the rope length system, b3The input variable of the rope length system is D, and the damping coefficient of the motion expansion of the lifting rope is D; defining rope length tracking error el1＝x5-ldWherein l isdThe target rope length; first order derivation is carried out on the tracking error of the rope length system, and e is obtainedl1＝x5-ldDerivation of derivatives
The first layer of Lyapunov function for constructing the rope length system is Vl1＝el1 22; to Vl1＝el1 2A/2 is obtained by first-order derivation
Order to
Construction of stable item alpha in inversion sliding mode control algorithml＝klel1Wherein k islThe error stability coefficient of the rope length system; will be alphal＝klel1Substitution into
In the formula
When e isl2When the content is equal to 0, the content,
the stability of the system is judged by the stability of the Lyapunov function, but the system is generally stable but is generally in motionDuring the moving process, the state quantity is unstable, and can be stabilized only when reaching the target position, so that when e is reachedl2Not equal to 0, the rope length system needs to be further designed, and a second layer of Lyapunov function of the rope length system is defined as Vl2＝Vl1+Sl 2/2 wherein Sl＝clel1+el2，SlIs a slip form surface of the rope length system, clThe error coefficient of the rope length system; to Vl2＝Vl1+Sl 2A/2 is obtained by first-order derivation
Order to
Building rope length system controller ulIs composed of
Wherein h islIs the slip form surface coefficient, beta, of the rope length systemlGain is switched for the rope length system.
According to the method of the embodiment of the invention, the anti-swing effect of the embodiment of the invention is tested through simulation experiments, the simulation time is set to be 15 seconds, and referring to fig. 6, wherein the time taken for the trolley position to move from 0 meter to the target position of 3 meters is 7 seconds, the maximum amplitude of the load swing angle is less than 0.03 radian, meanwhile, the time taken for the lifting rope to extend from 1 meter to 4 meters is 1 second when the lifting rope converges to 0 radian in 7 seconds, the lifting rope driving force converges to 0 newton soon after being generated, the convergence time is 1 second, the crane driving force drives the crane to move from about 45 newtons at the beginning and then converges to 0 newton quickly, the time taken is 7 seconds, and then no buffeting phenomenon is generated. The embodiment of the invention not only solves the problem of driving force buffeting in a time-varying sliding mode, but also solves the phenomenon of residual swing in an inversion sliding mode, so that the control effect of a bridge crane is optimal.
In order to further check the control effect of the control method of the embodiment of the invention on the bridge crane, five simulation environment experiments are set next, and the control effects of the control method of the embodiment of the invention on the bridge crane, the time-varying sliding mode control method and the inversion sliding mode control method in corresponding simulation environments are respectively compared, wherein a solid line represents the simulation result condition of the control method of the embodiment of the invention, a dotted line represents the simulation result condition of the time-varying sliding mode control method, a short dotted line represents the simulation result condition of the inversion sliding mode control method, and the five simulation environment conditions are as follows:
simulation environment 1: under the condition of light load, the target value of trolley displacement and the target value of rope length are respectively set to be 3 meters and 4 meters, the mass of the trolley and the mass of load are respectively set to be 10 kilograms and 5 kilograms, and other system model parameters are not changed.
Simulation environment 2: under heavy load conditions, the trolley displacement target value and the rope length target value are respectively set to be 3 meters and 4 meters, the trolley mass and the load mass are respectively set to be 500 kilograms and 100 kilograms, and other system model parameters are not changed.
Simulation environment 3: under the condition of a large target value, the trolley displacement target value and the rope length target value are respectively set to be 10 meters and 6 meters, the trolley mass and the load mass are respectively set to be 500 kilograms and 100 kilograms, and other system model parameters are not changed.
Simulation environment 4: under the condition of changing the system model, the trolley displacement target value and the rope length target value are respectively set to be 10 meters and 6 meters, the trolley mass and the load mass are respectively set to be 500 kilograms and 100 kilograms, the parameters of the two-dimensional bridge crane system model are changed, the air resistance coefficient of the crane is changed from 0.5 to 0.2, the air resistance coefficient of the load is changed from 0.5 to 0.6, and the friction coefficient of the crane is changed from 0.5 to 0.3.
Simulation environment 5: under the condition of external interference, a trolley displacement target value and a rope length target value are respectively set to be 10 meters and 6 meters, a trolley mass and a load mass are respectively set to be 500 kilograms and 100 kilograms, the air resistance coefficient of a crane is changed from 0.5 to 0.2, the air resistance coefficient of the load is changed from 0.5 to 0.6, the friction coefficient of the crane is changed from 0.5 to 0.3, the bridge crane moves from an initial position to a target position, and after the bridge crane converges and is stable, a force which is as long as 1 second is suddenly applied to the load to enable the bridge crane to swing from an angle of 0.15 radian.
Referring to fig. 7, the experimental result of the simulation environment 1 is: in the simulation result of the control method of the embodiment of the invention, the load swing angle amplitude is less than 0.031 radian, and no residual swing exists after convergence, while the simulation result of the time-varying sliding mode control method is that 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 the aspect of trolley position control performance, the position of the target is reached in 7 seconds without swinging in the embodiment of the invention, and the simulation result of the inversion sliding mode control method slightly swings; in the aspect of rope length control, the time for the lifting rope to stretch from 1 meter to 4 meters is 1 second, while the time for the time-varying sliding mode control method is 4 seconds, and the control effect of the embodiment of the invention is better. The above results show that compared with other two sliding mode control algorithms in the simulation environment 1, the control method of the embodiment of the invention has the advantages of smaller load swing angle amplitude, quicker achievement of stability and better control effect.
Referring to fig. 8, the experimental result of the simulation environment 2 is: when the mass of the trolley and the mass of the load are greatly increased, in a simulation result obtained by adopting the control method of the embodiment of the invention, the amplitude of the load swing angle is smaller than 0.03 radian, and no residual swing exists after convergence, while the simulation result obtained by adopting the time-varying sliding mode control method is that the amplitude of the load swing is larger, and the simulation result obtained by adopting the inverse sliding mode control method is that the amplitude of the load swing is larger and the residual swing exists; in the aspect of trolley position control performance, compared with other two control methods, the embodiment of the invention can reach the designated position more quickly and has no swing; in the aspect of rope length control, the time for the lifting rope to stretch from 1 meter to 4 meters is 1 second, while the time for the time-varying sliding mode control method is 4 seconds, and the control effect of the embodiment of the invention is better. The above results show that compared with other two sliding mode control algorithms in the simulation environment 2, the control method of the embodiment of the invention has the advantages of smaller load swing angle amplitude, quicker achievement of stability and better control effect.
Referring to fig. 9, the experimental result of the simulation environment 3 is: when the displacement target value and the rope length target value of the trolley are changed, the simulation result of the control method of the embodiment of the invention is that the load swing angle is 0.1 radian, no residual swing exists after convergence, while the load swing angle amplitude of time-varying sliding mode control exceeds 0.15 radian, the load swing angle amplitude of inversion sliding mode control exceeds 0.1 radian, and residual swing exists after convergence.
Referring to fig. 10, the experimental result of the simulation environment 4 is: when the air resistance coefficient and the friction coefficient on a two-dimensional bridge crane system model are changed, the simulation result of the control method of the embodiment of the invention is that the load swing angle is 0.1 radian, no residual swing exists after convergence, the load swing angle amplitude controlled by a time-varying sliding mode exceeds 0.15 radian, the load swing angle amplitude controlled by an inversion sliding mode exceeds 0.1 radian, and residual swing exists after convergence.
Referring to fig. 11, the experimental result of the simulation environment 5 is: under the condition of applying external interference, the trolley position recovery overshoot of the control method provided by the embodiment of the invention is smaller than that of other two sliding mode control algorithms, the output lifting rope driving force is obviously smaller than that of the other two sliding mode control algorithms, and the lifting rope driving force is close to 0. The above results show that the control method of the embodiment of the invention is superior to other two sliding mode control algorithms in the aspect of control torque output compared with other two sliding mode control algorithms in the simulation environment 5.
The embodiment of the invention also provides a sliding mode surface-based bridge crane anti-swing device, and the sliding mode surface-based bridge crane anti-swing device 1000 includes, but is not limited to: a position swing angle sliding mode controller constructing unit 1100, a rope length sliding mode controller constructing unit 1200, an obtaining unit 1300, an input unit 1400 and an output unit 1500.
The position swing angle sliding mode controller construction unit 1100 is used for constructing a position swing angle system mathematical model of a bridge crane, constructing a trolley position subsystem controller and a load swing angle subsystem controller based on an inverse sliding mode control theory, combining the trolley position subsystem controller and the load swing angle subsystem controller to construct a position swing angle global sliding mode surface, introducing a time-varying function into the position swing angle global sliding mode surface, and constructing the position swing angle sliding mode controller;
the rope length sliding mode controller building unit 1200 is used for building a rope length system mathematical model of the bridge crane and building a rope length sliding mode controller based on an inverse sliding mode control theory;
the acquiring unit 1300 is used for acquiring a trolley position parameter, a load swing angle parameter, a time parameter and a rope length parameter;
the input unit 1400 is used for inputting the trolley position parameter, the load swing angle parameter and the time parameter into the position swing angle sliding mode controller and inputting the rope length parameter into the rope length sliding mode controller;
and the output unit 1500 is used for outputting the horizontal traction force and the rope-following traction force of the trolley by the position swing angle sliding mode controller and the rope length sliding mode controller respectively.
It should be noted that, since the anti-swing device for a bridge crane based on a sliding mode surface in the present embodiment is based on the same inventive concept as the above-mentioned anti-swing method for a bridge crane based on a sliding mode surface, the corresponding contents in the method embodiments are also applicable to the present embodiment, and will not be described in detail here.
The embodiment of the invention also provides a sliding mode surface-based bridge crane anti-swing device, and the sliding mode surface-based bridge crane anti-swing device 2000 can be any type of intelligent terminal, such as a mobile phone, a tablet computer, a personal computer and the like.
Specifically, the sliding-mode-surface-based anti-swing device 2000 for a bridge crane includes: one or more control processors 2010 and memory 2020, one control processor 2010 being illustrated in fig. 13.
The control processor 2010 and the memory 2020 may be coupled by a bus or other means, such as by a bus as shown in FIG. 13.
The memory 2020, as a non-transitory computer-readable storage medium, may be used to store non-transitory software programs, non-transitory computer-executable programs, and modules, such as program instructions/modules corresponding to the sliding mode surface-based anti-sway method in the embodiment of the present invention, 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. 12. The control processor 2010 executes various functional applications and data processing of the sliding mode surface-based anti-sway device 1000 by running non-transitory software programs, instructions and modules stored in the memory 2020, that is, implements the sliding mode surface-based anti-sway method of the above-described method embodiment.
The memory 2020 may include a program storage area and a data storage area, wherein the program storage area may store an operating system, an application program required for at least one function; the stored data area may store data created according to the use of the sliding mode surface-based anti-sway device 1000, and the like. Further, the memory 2020 may include high-speed random access memory, and may also include non-transitory memory, such as at least one magnetic disk storage device, flash memory device, or other non-transitory solid state storage device. In some embodiments, memory 2020 optionally includes memory remotely located from control processor 2010, which may be connected to sliding mode surface based anti-sway apparatus 2000 via a network. Examples of such networks include, but are not limited to, the internet, 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, perform the sliding mode surface-based anti-sway method in the above-described method embodiments, for example, perform the above-described method steps S11-S15 in fig. 1, and implement the functions of the unit 1100-1500 in fig. 12.
Embodiments of the present invention further provide a computer-readable storage medium, where the computer-readable storage medium stores computer-executable instructions, which are executed by one or more control processors, for example, by one control processor 2010 in fig. 13, and may cause the one or more control processors 2010 to execute the sliding mode surface-based anti-sway method in the above method embodiment, for example, execute the above-described method steps S11 to S15 in fig. 1, and implement the functions of unit 1100-1500 in fig. 12.
The above-described embodiments of the apparatus are merely illustrative, and the units described as separate parts may or may not be physically separate, may be located in one place, or may be distributed over a plurality of network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment.
Through the above description of the embodiments, those skilled in the art can clearly understand that the embodiments can be implemented by software plus a general hardware platform. Those skilled in the art will appreciate that all or part of the processes of the methods of the above embodiments may be implemented by hardware related to instructions of a computer program, which may be stored in a computer readable storage medium, and when executed, may include the processes of the embodiments of the methods described above. The storage medium may be a magnetic disk, an optical disk, a Read Only Memory (ROM), a Random Access Memory (RAM), or the like.
While the preferred embodiments of the present invention have been described in detail, it will be understood by those skilled in the art that the foregoing and various other changes, omissions and deviations in the form and detail thereof may be made without departing from the scope of this invention.
Claims (7)
1. A bridge crane anti-swing method based on a sliding mode surface is characterized by comprising the following steps:
constructing a mathematical model of a position swing angle system of a bridge crane, constructing a trolley position subsystem controller and a load swing angle subsystem controller based on an inverse sliding mode control theory, combining the trolley position subsystem controller and the load swing angle subsystem controller to construct a position swing angle global sliding mode surface, introducing a time-varying function into the position swing angle global sliding mode surface, and constructing a position swing angle sliding mode controller;
constructing a rope length system mathematical model of the bridge crane, and constructing a rope length sliding mode controller based on an inverse sliding mode control theory;
acquiring a trolley position parameter, a load swing angle parameter, a time parameter and a rope length parameter;
inputting the trolley position parameter, the load swing angle parameter and the time parameter into the position swing angle sliding mode controller, and inputting the rope length parameter into the rope length sliding mode controller;
the position swing angle sliding mode controller and the rope length sliding mode controller respectively output trolley horizontal traction force and rope-following traction force;
wherein, the trolley position subsystem controller constructed based on the inversion sliding mode control theory comprises: constructing a first layer of Lyapunov function of the trolley position subsystem;
performing first-order derivation on a first-layer Lyapunov function of the trolley position subsystem;
if the first derivative of the first-layer Lyapunov function of the trolley position subsystem is not more than 0, solving a trolley position subsystem controller;
if the first derivative of the first layer of the Lyapunov function of the trolley position subsystem is larger than 0, constructing a second layer of the Lyapunov function of the trolley position subsystem;
performing first-order derivation on a Lyapunov function of a second layer trolley position subsystem of the trolley position subsystem;
and (4) enabling a first derivative of a Lyapunov function of a second layer of trolley position subsystem of the trolley position subsystem to be not more than zero, and solving the controller of the trolley position subsystem.
2. The method for preventing the swing of the bridge crane based on the sliding mode surface according to claim 1, is characterized in that: the load swing angle subsystem controller constructed based on the inversion sliding mode control theory comprises the following steps: constructing a first-layer Lyapunov function of a load swing angle subsystem;
carrying out first-order derivation on a first-layer Lyapunov function of the load swing angle subsystem;
if the first derivative of the first-layer Lyapunov function of the load swing angle subsystem is not more than 0, obtaining a load swing angle subsystem controller;
if the first-order derivative of the first-layer Lyapunov function of the load swing angle subsystem is larger than 0, constructing a second-layer Lyapunov function of the load swing angle subsystem;
performing first-order derivation on a second-layer Lyapunov function of the load swing angle subsystem;
and (4) enabling a first derivative of a second-layer Lyapunov function of the load swing angle subsystem to be not more than zero, and solving the load swing angle subsystem controller.
3. The method for preventing the swing of the bridge crane based on the sliding mode surface according to claim 1, is characterized in that: the trolley position 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 into the position swing angle global sliding mode surface, and the construction of the position swing angle sliding mode controller comprises the following steps:
constructing a position swing angle global system sliding mode control function;
constructing a position swing angle global system time-varying sliding mode surface;
constructing a Lyapunov function of a position swing angle global system;
carrying out first-order derivation on a Lyapunov function of a position swing angle global system;
constructing a general index approach law to obtain a coupling switch control law of sliding mode control of a position swing angle global system;
and constructing an S-shaped saturation function as a position swing angle global system sliding mode control function to obtain a position swing angle sliding mode controller.
4. The method for preventing the swing of the bridge crane based on the sliding mode surface according to claim 1, is characterized in that: the rope length sliding mode controller constructed based on the inversion sliding mode control theory comprises the following steps:
constructing a first layer of Lyapunov function of the rope length system;
performing first-order derivation on a first-layer Lyapunov function of the rope length system;
if the first-order derivative of the first-layer Lyapunov function of the rope length subsystem is not larger than 0, the rope length subsystem controller is obtained;
if the first derivative of the first layer of the Lyapunov function of the cord length system is greater than 0,
constructing a second layer of Lyapunov function of the rope length system;
performing first-order derivation on a second layer of Lyapunov function of the rope length system;
and (4) making the first derivative of the second layer of the Lyapunov function of the rope length subsystem not greater than zero, and obtaining the rope length subsystem controller.
5. The utility model provides a device is prevented putting by bridge crane based on slip form face which characterized in that: the method comprises the following steps:
the system comprises a position swing angle sliding mode controller construction unit, a position swing angle sliding mode controller, a trolley position subsystem controller, a load swing angle subsystem controller, a position swing angle sliding mode controller and a control unit, wherein the position swing angle sliding mode controller construction unit is used for constructing a mathematical model of a position swing angle system of a bridge crane, constructing a trolley position subsystem controller and the load swing angle subsystem controller based on an inversion sliding mode control theory, combining the trolley position subsystem controller and the load swing angle subsystem controller to construct a position swing angle global sliding mode surface, introducing a time-varying;
the rope length sliding mode controller building unit is used for building a rope length system mathematical model of the bridge crane and building a rope length sliding mode controller based on an inverse sliding mode control theory;
the system comprises an acquisition unit, a control unit and a control unit, wherein the acquisition unit is used for acquiring a trolley position parameter, a load swing angle parameter, a time parameter and a rope length parameter;
the input unit is used for inputting the trolley position parameter, the load swing angle parameter and the time parameter into the position swing angle sliding mode controller and inputting the rope length parameter into the rope length sliding mode controller;
and the output unit is used for outputting the horizontal traction force and the traction force along the rope of the trolley by the position swing angle sliding mode controller and the rope length sliding mode controller respectively.
6. The utility model provides a bridge crane prevents putting equipment based on slip form face which characterized in that: comprises at least one control processor and a memory for communicative connection with the at least one control processor; the memory stores instructions executable by the at least one control processor to enable the at least one control processor to perform the sliding mode surface based anti-sway method of any of claims 1-4.
7. A computer-readable storage medium characterized by: the computer-readable storage medium stores computer-executable instructions for causing a computer to perform the sliding-mode surface-based anti-sway method of a bridge crane of any one of claims 1-4.
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| CN112051740A (en) * | 2020-08-31 | 2020-12-08 | 五邑大学 | Parameter setting method and device for sliding mode controller and storage medium |
| CN112068428B (en) * | 2020-08-31 | 2022-05-17 | 五邑大学 | Design method and system of double-pendulum PI type Terminal sliding mode controller of bridge crane |
| CN113321123B (en) * | 2021-05-07 | 2023-08-29 | 武汉理工大学 | Layered quick terminal sliding mode control method for double-pendulum system of crane |
| CN113325715B (en) * | 2021-06-10 | 2022-05-24 | 浙江理工大学 | Feedforward control-based global continuous sliding mode control method for bridge crane |
| CN114967462B (en) * | 2022-06-01 | 2023-05-30 | 南京工业大学 | Sliding mode control method for inhibiting output jitter of tower crane |
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