CN111142385A - Bridge type traveling crane system control method based on sliding mode control theory - Google Patents

Bridge type traveling crane system control method based on sliding mode control theory Download PDF

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CN111142385A
CN111142385A CN202010006211.1A CN202010006211A CN111142385A CN 111142385 A CN111142385 A CN 111142385A CN 202010006211 A CN202010006211 A CN 202010006211A CN 111142385 A CN111142385 A CN 111142385A
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sliding mode
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杨玮林
陈佳瑜
许德智
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Jiangnan University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B66—HOISTING; LIFTING; HAULING
    • B66C—CRANES; LOAD-ENGAGING ELEMENTS OR DEVICES FOR CRANES, CAPSTANS, WINCHES, OR TACKLES
    • B66C13/00—Other constructional features or details
    • B66C13/18—Control systems or devices
    • B66C13/48—Automatic control of crane drives for producing a single or repeated working cycle; Programme control

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Abstract

The invention relates to a bridge type traveling crane system control method based on a layered sliding mode control theory, which establishes a sliding mode controller by applying the sliding mode control theory. Aiming at the under-actuated characteristic of a bridge type traveling crane system, a layered sliding mode control theory is selected for designing a controller. According to the under-actuated characteristic of the bridge type traveling crane system, a large trolley displacement error sliding mode function, a crane weight swing angle error sliding mode function and a total sliding mode function in the traveling direction of the large trolley and the small trolley are constructed, the effective control of the bridge type traveling crane system with the solid line of the equivalent control rate and the switching control rate is designed, and the effectiveness of the method is checked through simulation and comparison with the traditional PID control method.

Description

Bridge type traveling crane system control method based on sliding mode control theory
Technical Field
The invention relates to the field of bridge type traveling crane systems, in particular to a bridge type traveling crane system control method based on a sliding mode control theory.
Background
The bridge crane system is also called as a bridge crane and mainly comprises a bridge frame, a cart running mechanism, a hoisting trolley (a main hoisting mechanism, an auxiliary hoisting mechanism and a trolley running mechanism), an electrical control system and the like, has the advantages of less occupied land resources, strong load capacity, flexible operation and the like, and is widely applied to material handling in production workshops, warehouses, ports, nuclear waste treatment places and the like. At present, in the actual production, the anti-swing control of the hoisting weight of the bridge type traveling crane system is mainly completed by experienced operators, the efficiency is low, and the requirement on a crane driver is high. The swing control problem of the hoisting weight is solved, the automatic operation of the bridge crane is promoted, the labor intensity of operators is reduced, the carrying efficiency is improved, the safety of the hoisting weight and workers is guaranteed, and the swing control device has high practical value. Meanwhile, the bridge crane is a typical under-actuated nonlinear system, variables are mutually coupled, and the research on the under-actuated control and anti-swing problems of the bridge crane system has important theoretical significance.
Disclosure of Invention
The invention aims to provide a bridge type traveling crane system control method based on a sliding mode control theory.
In order to solve the technical problem, the invention provides a bridge crane system control method based on a layered sliding mode control theory, which comprises the following steps:
constructing a first-layer layered sliding-mode controller: according to a sliding mode control theory, constructing a first-layer layered sliding mode controller of a bridge type traveling crane system, wherein the controller comprises a large trolley displacement error sliding mode function, a small trolley displacement error sliding mode function and a hoisting swing angle error sliding mode function;
constructing a second-layer layered sliding-mode controller: and constructing a second-layer layered sliding mode controller of the bridge type traveling crane system according to a sliding mode control theory, wherein the controller comprises a total sliding mode function, an equivalent control rate and a switching control rate in the traveling direction of the big trolley and the small trolley.
In one embodiment, "build a first level hierarchical sliding-mode controller: according to the sliding mode control theory, a first-layer layered sliding mode controller of a bridge type traveling crane system is constructed, the controller comprises a large trolley displacement error sliding mode function and a small trolley displacement error sliding mode function, a hoisting swing angle error sliding mode function',
the large and small car displacement error sliding mode function is as follows: defining an equation:
Figure BDA0002355384080000021
is a sliding mode function of large and small car displacement error, wherein ssxIs a cart displacement error sliding mode function, ssyAs a function of the sliding mode of the car displacement error, ex＝x-xdIs the displacement error between the cart position and the cart target position, ey＝y-ydThe displacement error between the position of the small car and the target position of the small car, x and y are the position of the large car and the position of the small car respectively, and xd，ydRespectively a cart target position and a dolly target position, hsx，hsyRespectively sliding mode function coefficients.
In one embodiment, "build a first level hierarchical sliding-mode controller: according to the sliding mode control theory, a first-layer layered sliding mode controller of a bridge type traveling crane system is constructed, the controller comprises a large trolley displacement error sliding mode function and a small trolley displacement error sliding mode function, a hoisting swing angle error sliding mode function',
the hoisting swing angle error sliding mode function is as follows: defining an equation:
Figure BDA0002355384080000022
is a sliding mode function of the swing angle error of the hoist, where stxIs an error sliding mode function, s, of the swing angle of the hoisting weight in the running direction of the carttyAs a function of the slip form of the error of the swing angle of the hoist in the running direction of the trolley, etx＝θxIs the swing angle error between the swing angle component of the hoist in the running direction of the cart and the target, thetaxFor the swing angle component of the hoist in the direction of travel of the cart, ety＝θyIs the swing angle error between the swing angle component of the hoisting weight in the running direction of the trolley and the target thetayIs the swing angle component of the hoisting weight in the running direction of the trolley, htx，htyRespectively sliding mode function coefficients.
In one embodiment, the "build second level hierarchical sliding mode controller: constructing a second-layer layered sliding mode controller of the bridge type traveling crane system according to a sliding mode control theory, wherein the controller comprises a total sliding mode function, an equivalent control rate and a switching control rate in the traveling direction of a big car and a small car,
the total sliding mode function in the running direction of the big trolley and the small trolley is as follows: defining an equation:
Figure BDA0002355384080000031
is the sum of the big car and the small car in the running directionSliding mode function, wherein sxIs the total sliding mode function, s, of the cart in its direction of travelyAs a function of the overall sliding mode of the vehicle in its direction of travel, gsx，gtx，gsy，gtxRespectively sliding mode function coefficients.
In one embodiment, the "build second level hierarchical sliding mode controller: according to the sliding mode control theory, a second-layer layered sliding mode controller of the bridge type traveling crane system is constructed, the controller comprises a total sliding mode function, an equivalent control rate and a switching control rate in the traveling direction of the big trolley and the small trolley, and the sliding mode control rate u is set to be u ═ ueq1+ueq2+uswWherein u iseq1，ueq2To an equivalent control rate, uswTo switch control rates.
In one embodiment, the equivalent control rate is: definition of
Figure BDA0002355384080000032
Wherein, τ (θ)x,θy) In order to control the system function in a non-linear way,
Figure BDA0002355384080000033
for nonlinear control of the system coefficient matrix, es＝[exey]T，et＝[etxety]T， e＝[exeyetxety]TFor non-linear control of system function variables, D11，D12，D1，H1，D21，D22，D2，H2Are sliding mode function coefficient matrixes respectively.
In one embodiment, the switching control rate is: definition usw＝N[M2D21ueq1+M1D11ueq2+K1S+K2sgn(S)]Wherein N ═ M1D11+M2D21)-1For a non-linear control system coefficient matrix, ueq1，ueq2For equivalent control rate, sgn () is a sign function, S isGeneral sliding mode function in the running direction of big and small cars, M1，D11，M2，D21，K1，K2Are sliding mode function coefficient matrixes respectively.
Based on the same inventive concept, the present application also provides a computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the steps of any of the methods when executing the program.
Based on the same inventive concept, the present application also provides a computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out the steps of any of the methods.
Based on the same inventive concept, the present application further provides a processor for executing a program, wherein the program executes to perform any one of the methods.
The invention has the beneficial effects that:
on the basis of fully considering the under-actuated characteristic and the dynamic characteristic in the control process of the bridge traveling crane system, the invention establishes a layered sliding mode controller by using a layered sliding mode theory, and realizes the effective control of the bridge traveling crane by constructing a large trolley displacement error sliding mode function, a crane weight swing angle error sliding mode function, a total sliding mode function in the running direction of the large trolley and the small trolley, an equivalent control rate and a switching control rate. The effectiveness of the proposed method is checked by comparing the effects of the simulation with the traditional PID control approach.
Drawings
Fig. 1 is a four-degree-of-freedom bridge type traveling crane system model in the bridge type traveling crane system control method based on the sliding mode control theory.
Fig. 2 is a trolley space trajectory top view in the bridge traveling crane system control method based on the sliding mode control theory.
Fig. 3 is a graph of the movement path of the cart of fig. 1 along the target path in the travel direction.
Fig. 4 is a graph of the swing angle component of the sling of fig. 1 in the direction of travel of the cart.
Detailed Description
The present invention is further described below in conjunction with the following figures and specific examples so that those skilled in the art may better understand the present invention and practice it, but the examples are not intended to limit the present invention.
The sliding mode control is also called variable structure control, the non-linear characteristic of the sliding mode control is represented as control discontinuity, and the system track can be forced to gradually stabilize to a balance point according to a preset sliding mode by continuously changing the structure of the system according to the current state of the system. The sliding mode variable structure control problem can be decomposed into the comprehensive problems of two low-dimensional subsystems, namely the sliding mode control with good dynamic characteristics after the system enters the sliding mode motion is ensured by designing a variable structure control law to enable the system state to reach a selected sliding mode within a limited time and selecting a proper switching function, the sliding mode control has the advantages of order reduction, decoupling, simple algorithm, good robustness on system parameter change and external interference and the like, and the sliding mode control method is widely applied to the control of linear and nonlinear systems.
A bridge traveling crane system control method based on a layered sliding mode control theory
The model of the bridge crane system, as shown in figure 1,
Figure BDA0002355384080000051
[1]wherein q is [ x y θ ]xθy],qd＝[xd y d0 0]，
Figure BDA0002355384080000052
Figure BDA0002355384080000053
Figure BDA0002355384080000054
Wherein M represents the total mass of the large trolley, M represents the mass of the load and the rotating system thereof, and l represents
Length of watch rope, Mx,MyRespectively equivalent mass, g corresponding to gravitational acceleration, v, of a bridge crane coupled to a rotating member (e.g. an electric motor and its drive train) in respective corresponding directionsmCorresponding to load speed, Dx， DyRespectively, the viscous damping coefficients associated with the x, y directions. ThetaxIs theta at XMOZMComponent in the plane, θyIs theta at YMOZMThe component in the plane.
Rewriting the model into an error equation of state
Figure BDA0002355384080000061
Wherein e is q-qd＝[x-xdy-ydθxθy]T＝[exeyeθxeθy]T，
Figure BDA0002355384080000062
Wherein the content of the first and second substances,
Figure BDA0002355384080000063
the foregoing error state equation is rewritten as:
Figure BDA0002355384080000064
wherein the content of the first and second substances,
Figure 1
planning an ideal running track for the big car and the small car respectively:
Figure BDA0002355384080000066
wherein x isdIs the target track of the big car and the small car, PdTarget position of big or small car, kvThe maximum running speed of the big car and the small car, kaThe maximum acceleration of the big car and the small car, epsilon is a parameter for adjusting the initial acceleration of the big car and the small car, and t is a time variable.
According to the bridge type traveling crane system model, the rope length is fixed to be 10m, and the target position coordinates are (50, 20).
The method comprises the following steps:
step 1, respectively constructing a large trolley displacement error sliding mode function and a small trolley displacement error sliding mode function and a hoisting weight swing angle error sliding mode function according to the bridge type traveling crane system model.
(1) Trolley displacement error sliding mode function:
Figure BDA0002355384080000071
wherein s issxIs composed of
Cart displacement error sliding mode function, ssyAs a function of the sliding mode of the car displacement error, ex＝x-xdIs the displacement error between the cart position and the cart target position, x, y are the cart position and the cart position, respectively, ey＝y-ydIs the displacement error, x, between the car position and the car target positiond，ydRespectively a cart target position and a dolly target position, hsx，hsyRespectively sliding mode function coefficients.
(2) Hoisting swing angle error sliding mode function:
Figure BDA0002355384080000072
wherein s istxIs composed of
Error sliding mode function, s, of hoisting swing angle in running direction of carttyAs a function of the slip form of the error of the swing angle of the hoist in the running direction of the trolley, etx＝θxIs the swing angle error between the swing angle component of the hoist in the running direction of the cart and the target, thetaxFor the swing angle component of the hoist in the direction of travel of the cart, ety＝θyIs the swing angle error between the swing angle component of the hoisting weight in the running direction of the trolley and the target thetayIs the swing angle component of the hoisting weight in the running direction of the trolley, htx，htyRespectively sliding mode function coefficients.
Step 2, constructing a total sliding mode function in the running direction of the big trolley and the small trolley according to the bridge type traveling crane system model, and setting a sliding mode control rate u as ueq1+ueq2+uswWherein u iseq1，ueq2To an equivalent control rate, uswIn order to switch the control rate of the mobile terminal,
(1) the total sliding mode function in the running direction of the big car and the small car is as follows:
Figure BDA0002355384080000073
wherein s isxIs the total sliding mode function, s, of the cart in its direction of travelyAs a function of the overall sliding mode of the vehicle in its direction of travel, gsx，gtx，gsy，gtxRespectively sliding mode function coefficients.
(2) The equivalent control rate is: definition of
Figure BDA0002355384080000074
Wherein, τ (θ)x,θy) In order to control the system function in a non-linear way,
Figure BDA0002355384080000075
for nonlinear control of the system coefficient matrix, es＝[exey]T，et＝[etxety]T，e＝[exeyetxety]TFor non-linear control of system function variables, D11，D12，D1，H1，D21，D22，D2，H2Respectively are sliding mode function coefficient matrixes;
(3) the switching control rate is: definition usw＝N[M2D21ueq1+M1D11ueq2+K1S+K2sgn(S)]，
Wherein N is- (M)1D11+M2D21)-1For a non-linear control system coefficient matrix, ueq1，ueq2To an equivalent control rateSgn () is a sign function, S is a total sliding mode function in the traveling direction of the cart and the cart, M1，D11，M2， D21，K1，K2Are sliding mode function coefficient matrixes respectively.
According to the implementation steps, through simulation verification, the overhead curve chart of the space track of the trolley is shown in the figure
2, wherein the black dotted line is an original target track curve, and the black solid line is an actual running track of the trolley under the control of the layered sliding mode. Fig. 3 and 4 show the motion trajectory curve of displacement with respect to time and the fluctuation curve of the swing angle with respect to time in the running direction of the cart respectively, and simultaneously compare with the traditional PID control method. The black dotted line is a predetermined target track curve, the black dotted line is a displacement motion track curve relative to time and a swing angle fluctuation curve relative to time under the traditional PID control method, and the black solid line is a displacement motion track curve relative to time and a swing angle fluctuation curve relative to time under the layered sliding mode control.
The above-mentioned embodiments are merely preferred embodiments for fully illustrating the present invention, and the scope of the present invention is not limited thereto. The equivalent substitution or change made by the technical personnel in the technical field on the basis of the invention is all within the protection scope of the invention. The protection scope of the invention is subject to the claims.

Claims (10)

1. A bridge type traveling crane system control method based on a layered sliding mode control theory is characterized by comprising the following steps: the method comprises the following steps:
constructing a first-layer layered sliding-mode controller: according to the sliding mode control theory, a first-layer layered sliding mode controller of the bridge type traveling crane system is constructed, and the controller comprises a large trolley displacement error sliding mode function, a small trolley displacement error sliding mode function and a hoisting swing angle error sliding mode function.
Constructing a second-layer layered sliding-mode controller: and constructing a second-layer layered sliding mode controller of the bridge type traveling crane system according to a sliding mode control theory, wherein the controller comprises a total sliding mode function, an equivalent control rate and a switching control rate in the traveling direction of the big trolley and the small trolley.
2. The bridge traveling crane system control method based on the layered sliding mode control theory according to claim 1, characterized in that: "construct the first layer of layered sliding-mode controllers: according to the sliding mode control theory, a first-layer layered sliding mode controller of a bridge type traveling crane system is constructed, the controller comprises a large trolley displacement error sliding mode function and a small trolley displacement error sliding mode function, a hoisting swing angle error sliding mode function',
the large and small car displacement error sliding mode function is as follows: defining an equation:
Figure FDA0002355384070000011
is a sliding mode function of large and small car displacement error, wherein ssxIs a cart displacement error sliding mode function, ssyAs a function of the sliding mode of the car displacement error, ex＝x-xdIs the displacement error between the cart position and the cart target position, ey＝y-ydThe displacement error between the position of the small car and the target position of the small car, x and y are the position of the large car and the position of the small car respectively, and xd，ydRespectively a cart target position and a dolly target position, hsx，hsyRespectively sliding mode function coefficients.
3. The bridge traveling crane system control method based on the layered sliding mode control theory according to claim 1, characterized in that: "construct the first layer of layered sliding-mode controllers: according to the sliding mode control theory, a first-layer layered sliding mode controller of a bridge type traveling crane system is constructed, the controller comprises a large trolley displacement error sliding mode function and a small trolley displacement error sliding mode function, a hoisting swing angle error sliding mode function',
the hoisting swing angle error sliding mode function is as follows: defining an equation:
Figure FDA0002355384070000012
is a sliding mode function of the swing angle error of the hoist, where stxIs an error sliding mode function, s, of the swing angle of the hoisting weight in the running direction of the carttyIs a craneError sliding mode function of the yaw angle in the running direction of the trolley, etx＝θxIs the swing angle error between the swing angle component of the hoist in the running direction of the cart and the target, thetaxFor the swing angle component of the hoist in the direction of travel of the cart, ety＝θyIs the swing angle error between the swing angle component of the hoisting weight in the running direction of the trolley and the target thetayIs the swing angle component of the hoisting weight in the running direction of the trolley, htx，htyRespectively sliding mode function coefficients.
4. The bridge traveling crane system control method based on the layered sliding mode control theory according to claim 1, characterized in that: the step of building a second-layer layered sliding-mode controller comprises the following steps: constructing a second-layer layered sliding mode controller of the bridge type traveling crane system according to a sliding mode control theory, wherein the controller comprises a total sliding mode function, an equivalent control rate and a switching control rate in the traveling direction of a big car and a small car,
the total sliding mode function in the running direction of the big trolley and the small trolley is as follows: defining an equation:
Figure FDA0002355384070000021
is a total sliding mode function in the running direction of the big and small cars, wherein sxIs the total sliding mode function, s, of the cart in its direction of travelyAs a function of the overall sliding mode of the vehicle in its direction of travel, gsx，gtx，gsy，gtxRespectively sliding mode function coefficients.
5. The bridge traveling crane system control method based on the layered sliding mode control theory according to claim 1, characterized in that: the step of building a second-layer layered sliding-mode controller comprises the following steps: according to the sliding mode control theory, a second-layer layered sliding mode controller of the bridge type traveling crane system is constructed, the controller comprises a total sliding mode function, an equivalent control rate and a switching control rate in the traveling direction of the big trolley and the small trolley, and the sliding mode control rate u is set to be u ═ ueq1+ueq2+uswWherein u iseq1，ueq2To an equivalent control rate, uswFor switching controlAnd (5) preparing the rate.
6. The control method of the bridge traveling crane system based on the sliding mode control theory as claimed in claim 5, wherein the equivalent control rate is: definition of
Figure FDA0002355384070000022
Wherein, τ (θ)x,θy) In order to control the system function in a non-linear way,
Figure FDA0002355384070000023
for nonlinear control of the system coefficient matrix, es＝[exey]T，et＝[etxety]T，e＝[exeyetxety]TFor non-linear control of system function variables, D11，D12，D1，H1，D21，D22，D2，H2Are sliding mode function coefficient matrixes respectively.
7. The control method of the bridge traveling crane system based on the sliding mode control theory as claimed in claim 5, wherein the switching control rate is: definition usw＝N[M2D21ueq1+M1D11ueq2+K1S+K2sgn(S)]Wherein N ═ M1D11+M2D21)-1For a non-linear control system coefficient matrix, ueq1，ueq2For equivalent control rate, sgn () is a sign function, S is a total sliding mode function in the traveling direction of the big car and the small car, M1，D11，M2，D21，K1，K2Are sliding mode function coefficient matrixes respectively.
8. A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the steps of the method of any of claims 1 to 7 are implemented when the program is executed by the processor.
9. A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the steps of the method according to any one of claims 1 to 7.
10. A processor, characterized in that the processor is configured to run a program, wherein the program when running performs the method of any of claims 1 to 7.
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CN112051738A (en) * 2020-08-31 2020-12-08 五邑大学 Casting crane control method and device, computer readable storage medium
CN112068428A (en) * 2020-08-31 2020-12-11 五邑大学 Design method and system of double-pendulum PI type Terminal sliding mode controller of bridge crane
CN112061979A (en) * 2020-08-31 2020-12-11 五邑大学 Bridge crane control method, operation control device and computer readable storage medium
CN112061979B (en) * 2020-08-31 2022-09-30 五邑大学 Bridge crane control method, operation control device and computer readable storage medium
CN112551374A (en) * 2020-12-03 2021-03-26 东南大学 Rotary anti-swing control method of movable hoisting equipment
CN112875509A (en) * 2021-01-13 2021-06-01 南京工业大学 Positioning and swing eliminating method for under-actuated tower crane with load lifting motion
CN112875509B (en) * 2021-01-13 2022-02-22 南京工业大学 Positioning and swing eliminating method for under-actuated tower crane with load lifting motion
CN114967462A (en) * 2022-06-01 2022-08-30 南京工业大学 Sliding mode control method for suppressing output jitter of tower 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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Application publication date: 20200512