CN111762688B - Bridge crane controller generation method, control method and controller generation system - Google Patents

Bridge crane controller generation method, control method and controller generation system Download PDF

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CN111762688B
CN111762688B CN202010627922.0A CN202010627922A CN111762688B CN 111762688 B CN111762688 B CN 111762688B CN 202010627922 A CN202010627922 A CN 202010627922A CN 111762688 B CN111762688 B CN 111762688B
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control
controller
bridge crane
crane
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CN111762688A (en
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黄静雯
吕展坤
康博涵
孙建桥
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Beijing University of Chemical Technology
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B66—HOISTING; LIFTING; HAULING
    • B66C—CRANES; LOAD-ENGAGING ELEMENTS OR DEVICES FOR CRANES, CAPSTANS, WINCHES, OR TACKLES
    • B66C13/00—Other constructional features or details
    • B66C13/04—Auxiliary devices for controlling movements of suspended loads, or preventing cable slack
    • B66C13/06—Auxiliary devices for controlling movements of suspended loads, or preventing cable slack for minimising or preventing longitudinal or transverse swinging of loads
    • B66C13/063—Auxiliary devices for controlling movements of suspended loads, or preventing cable slack for minimising or preventing longitudinal or transverse swinging of loads electrical
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B66—HOISTING; LIFTING; HAULING
    • B66C—CRANES; LOAD-ENGAGING ELEMENTS OR DEVICES FOR CRANES, CAPSTANS, WINCHES, OR TACKLES
    • B66C13/00—Other constructional features or details
    • B66C13/16—Applications of indicating, registering, or weighing devices
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B66—HOISTING; LIFTING; HAULING
    • B66C—CRANES; LOAD-ENGAGING ELEMENTS OR DEVICES FOR CRANES, CAPSTANS, WINCHES, OR TACKLES
    • B66C13/00—Other constructional features or details
    • B66C13/18—Control systems or devices
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B66—HOISTING; LIFTING; HAULING
    • B66C—CRANES; LOAD-ENGAGING ELEMENTS OR DEVICES FOR CRANES, CAPSTANS, WINCHES, OR TACKLES
    • B66C2700/00—Cranes
    • B66C2700/08—Electrical assemblies or electrical control devices for cranes, winches, capstans or electrical hoists

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

Abstract

The invention relates to a bridge crane controller generation method, a bridge crane controller generation method and a bridge crane controller generation system, which relate to the technical field of bridge crane control, and are characterized in that a model to be observed under a dynamic structure is established according to a bridge crane structure; designing an optimal feedback full-state observer based on the measurement variables, and obtaining an estimation model; carrying out inversion design according to a control design target, and obtaining an actual controller based on the estimation model; and obtaining a bridge crane control method by using an actual controller, and further obtaining a control model acquisition module to be observed, an estimation model acquisition module and an actual controller generation module by using the controller generation method, thereby generating a controller system. Compared with the prior art, the method and the device realize the tracking control of the motion state of the bridge crane and have the effect of high conveying efficiency.

Description

Bridge crane controller generation method, control method and controller generation system
Technical Field
The invention relates to the technical field of bridge crane control, in particular to a bridge crane controller generation method, a bridge crane controller control method and a bridge crane controller generation system.
Background
The bridge crane is a hoisting device which is transversely arranged above workshops, warehouses and material yards to hoist materials. The bridge crane is a typical under-actuated nonlinear system, from the perspective of a control theory, the limitation of the control input of the under-actuated system is a challenging control problem, and in recent decades, how to realize accurate full-automatic control on the bridge crane so as to improve the conveying efficiency, the positioning accuracy and the safety factor is a research hotspot problem in the current industrial field.
At present, in the research of crane anti-swing and positioning control on a bridge crane system, an under-actuated bridge crane anti-swing tracking control method is provided in an article 'under-actuated bridge crane anti-swing tracking control' published by Sun-Ning, Fangyong pure and Chenhe in 'control theory and application', a bridge crane dynamic equation is subjected to partial feedback linearization treatment and coordinate transformation, a novel nonlinear controller is designed on the basis of the transformation to realize the tracking control on the bridge crane, so that the operation and control quantity of the crane are smoother, and the control effect is shown in figure 1.
The traditional under-actuated control method mostly depends on a specific mathematical model of a system, however, in the working process of the bridge crane, due to mutual influence among crane displacement, rope pendulum length and pendulum angle, load change among different transportation batches and interference of external uncertain factors such as wind direction, collision and the like, the system accurate parameter model of the bridge crane is difficult to obtain, so that the crane displacement tracking effect and the rope pendulum angle stability are poor, and the transportation efficiency is caused.
Disclosure of Invention
The invention aims to provide a bridge crane controller generation method which has the characteristic of being beneficial to improving the conveying efficiency of a bridge crane.
The above object of the present invention is achieved by the following technical solutions:
a bridge crane controller generation method comprises the following steps,
the control model to be observed is obtained, and according to the bridge crane structure, the dynamics analysis is carried out on the bridge crane, and the control model to be observed under the system dynamics structure is established:
Figure GDA0003007993620000021
wherein, y1(t) represents a rope swing angle, y2(t) shows crane displacement, f1(t) model to be observed including model uncertainty and disturbance information in the yaw angle system, f2(t) representing a model to be observed containing model uncertainty and disturbance information in the displacement system, u (t) representing the control input of the system, and b being a known control coefficient;
estimation model acquisition based on the measured variable y1(t) and y2(t) obtaining an estimation model based on an optimal feedback full-state observer; and the number of the first and second groups,
and generating a controller, performing inversion design according to a control design target, and obtaining an actual controller based on the estimation model.
By adopting the technical scheme, the optimal feedback full-state observer is set, and all state information in the observer is fully utilized; the displacement speed and the rope swinging angle are estimated by the aid of the feedback of the crane displacement and the rope swinging angle in combination with the estimation model, and then combined with a control design target to further carry out control design on the model to obtain an actual bridge crane controller, so that the next displacement speed adjustment of the bridge crane is realized according to the obtained bridge crane controller, the stability of the rope swinging angle is guaranteed, and the conveying efficiency of the crane is improved.
The invention is further configured to: the specific method for obtaining the estimation model comprises the following steps:
carrying out system expansion on the control model to be observed to obtain an expanded state space model; defining a system observer based on the extended state space model;
defining an all-state virtual controller based on the system observer, and defining a performance index J based onvObtaining a quadratic optimal feedback rate k, and obtaining an optimal feedback all-state observer of the bridge crane by combining the quadratic optimal feedback rate k and the all-state virtual controller; and the number of the first and second groups,
and obtaining a bridge crane model based on the optimal feedback full-state observer.
By adopting the technical scheme, the virtual controller has good observation performance based on the whole observability of the self variable in the optimal feedback full-state observer, and the stability and the optimality of the performance index of the bridge crane observer can be considered by adopting a linear quadratic optimal feedback function.
The invention is further configured to: the specific acquisition method of the bridge crane estimation model comprises the following steps,
moving the crane by y2(t) and the rope swing angle y1(t) substituting the control model to be observed as an observation variable to obtain an extended state space model:
Figure GDA0003007993620000031
wherein the content of the first and second substances,
Figure GDA0003007993620000032
C2＝[C1,C1]，
Figure GDA0003007993620000036
and is
Figure GDA0003007993620000034
y(t)＝[y1(t)，y2(t)]U (t) is the same as the control input shown in formula (1), h1(t) and h2(t) are each f1(t) and f2(t), where x (t) is [ x [ ]1(t),x2(t),x3(t),x4(t),x5(t),x6(t),x7(t),x8(t)]T；
Equation (3) is equivalent to
Figure GDA0003007993620000035
Thereby having
x4(t)＝f1(t) (5)
x8(t)＝f2(t) (6)
Defining the extended state vector as:
z＝[z1,z2,z3,z4,z5,z6,z7,z8]T (7)
wherein z is1Representing a measured variable y1(t) estimate of (z)5Representing measurement y2(t) estimate of (z)2Representing a measured variable y1(t) using the estimated value of the derivative, z6Representing a measured variable y2(t) using the estimated value of the derivative, z3And z7Representing integral feedback, z, for constructing an optimal feedback all-state observer4Representation system model f1(t) estimation of z8Representation system model f2(t) estimation;
based on C in the formula (3)1And C2Is defined by y1(t)＝x1(t)，y2(t)＝x5(t) subsequent sections each displacing the crane by x1(t) and rope pendulum angle x5(t) directly as a measured variable;
defining the optimal feedback full-state observer of the bridge crane as follows:
Figure GDA0003007993620000041
wherein v is a 8 × 1 dimensional virtual controller for designing and configuring optimal feedback full state observer parameters, and the bridge crane observer coefficients are set as:
Figure 100002_1
Bv＝eye(8)，Dv＝zeros(8,8)，
Figure GDA0003007993620000043
by defining the following performance indicators
Figure GDA0003007993620000044
Obtaining the optimal feedback rate of linear quadratic form
k＝lqry(Av,Bv,Cv,Dv,Qv,Rv) (9)
The full-state estimation controller is designed as
v＝-kz+k(1:4)ref1+k(5:8)ref2 (10)
Wherein ref1＝[x1(t),r12,0,r14]TAnd is provided with
Figure GDA0003007993620000045
ref2＝[x5(t),r22,0,r24]TAnd is provided with
Figure GDA0003007993620000046
Figure GDA0003007993620000047
Are respectively as
Figure GDA0003007993620000048
Figure GDA0003007993620000049
Is obtained by a derivative estimation method.
Through an optimal feedback full-state observer, a system model f can be obtained1(t) and f2(t) estimation:
Figure GDA0003007993620000051
Figure GDA0003007993620000052
by adopting the technical scheme, the crane displacement and the rope swinging angle are used as measurement variables, the bridge crane observer is obtained by combining the extended state space model and the optimal feedback full-state observer, the bridge crane observer can observe the state variables of the bridge crane, the observation of the motion state of the bridge crane is realized, and the improvement of the conveying efficiency is facilitated.
The present invention in a preferred example may be further configured to: the control design objectives in the controller generation include crane displacement tracking error, minimized yaw displacement and speed.
By adopting the technical scheme, the rope swinging angle can be changed in the moving process of the crane, which brings difficulty to the acquisition of an accurate parameter model of the system, so that the minimized swinging angle displacement and the minimized swinging angle speed are used as control design targets of the controller, the control of the rope swinging angle is realized, and the stability of the swinging angle is favorably ensured.
The invention is further configured to: the specific method for generating the controller comprises the following steps:
according to the formula (3) configuration of the system expansion matrix, the kinetic model to be observed (1) is equivalent to the formula (4) and can be expressed in the following form:
Figure GDA0003007993620000053
wherein s is1(t)＝y2(t)，s2(t)＝y1(t)，
Figure GDA0003007993620000054
f1(t) and f2(t) may be estimated by an optimal feedback full state observer;
defining crane displacement and virtual controller tracking error:
Figure GDA0003007993620000055
wherein the content of the first and second substances,
Figure GDA0003007993620000056
y2d(T) is the expected reference track of crane displacement, T is the [0, T ]]，αiThe method is characterized in that the method is a virtual controller, T is a target operation time length, i is a natural number which is more than or equal to 2 and less than or equal to n, and n is the total level number of inversion design;
defining the following Lyapunov functions, carrying out inversion design and obtaining an actual controller:
in the first-stage inversion design, the tracking effect output by the crane control system is obtained:
Figure GDA0003007993620000061
the derivative is:
Figure GDA0003007993620000062
wherein the content of the first and second substances,
Figure GDA0003007993620000063
is y2d(t) derivative of;
in the second-stage and third-stage inversion design, based on the under-actuated characteristic of a crane control system, the swing angle displacement s is minimized2(t) and minimum yaw rate s3(t) obtaining a stable rope sway angle as one of control design targets other than trajectory tracking, adding a target of minimizing the sway angle to the lyapunov function design, thereby defining:
Figure GDA0003007993620000064
Figure GDA0003007993620000065
the derivative is:
Figure GDA0003007993620000066
Figure GDA0003007993620000067
lyapunov function V for defining fourth-order inversion design4Comprises the following steps:
Figure GDA0003007993620000068
the derivative is:
Figure GDA0003007993620000069
using the model estimation, based on equations (13) (16) (18) (20), on the premise that the respective order derivatives of the lyapunov function are negative, the virtual controller is designed to:
Figure 2
Figure 4
get the actual controller
Figure GDA0003007993620000072
Wherein, c1、c2、c3And c4To control the gain, m is 2w2+α2，n＝2w3+α3。
By adopting the technical scheme, the estimation model is obtained by combining the full feedback state observer and the model estimation, and then the estimation model is introduced into the inversion control to realize the control of the bridge crane, so that the control of the bridge crane is improved to a certain extent, and the displacement tracking control effect of the bridge crane is improved.
The invention is further configured to: the specific method for estimating the derivative comprises the following steps:
defining a derivative estimation variable and passing the derivative estimator
Figure GDA0003007993620000073
A derivative estimation method is implemented.
Wherein the content of the first and second substances,
Figure GDA0003007993620000074
r＝[r1,r2,r3]Tr is a derivative estimate variable, and vrA virtual controller being an estimator for designing parameters required for derivative estimation;
vr＝-krr+krErx1(t) (32)
wherein the content of the first and second substances,
Figure GDA0003007993620000075
kris obtained by defining a performance index JrObtaining a secondary optimal feedback rate;
Figure GDA0003007993620000076
kr＝lqr(Ar,Br,Qr,Rr) (34)
wherein Q isrAnd RrFor the coefficient to be adjusted, kr＝[kr1,kr2,kr3]。
By adopting the technical scheme, the derivative controller is designed and combined with the virtual controller, so that the derivative is obtained, the error is favorably reduced, and the derivative error is almost zero to a certain extent, so that the control effect is favorably improved.
The invention also aims to provide a bridge crane manufacturing method which has the characteristic of improving the conveying efficiency of the bridge crane.
The above object of the present invention is achieved by the following technical solutions:
a bridge crane control method is realized based on an actual controller generated by a controller generation method.
By adopting the technical scheme, the actual controller generated based on the controller generation method is used for controlling the movement of the crane, the accurate control of the displacement of the bridge crane is realized to a certain extent, the swing angle is ensured to be basically stable, and the improvement of the conveying efficiency is facilitated.
The invention aims to provide a bridge crane controller generation system which has the characteristic of being beneficial to improving the conveying efficiency of a bridge crane.
The above object of the present invention is achieved by the following technical solutions:
a bridge crane controller generation system, the generation system comprising,
wait to observe control model and acquire the module, according to the bridge crane structure, carry out the dynamics analysis to the bridge crane, establish the control model of waiting to observe under the crane control system dynamics structure:
Figure GDA0003007993620000081
wherein, y1(t) represents a rope swing angle, y2(t) shows crane displacement, f1(t) model to be observed including model uncertainty and disturbance information in the yaw angle system, f2(t) representing a model to be observed containing model uncertainty and disturbance information in the displacement system, u (t) representing the control input of the system, and b being a known control coefficient;
estimation model acquisition module based on measured variable y1(t) and y2(t) obtaining an estimation model based on an optimal feedback full-state observer;
and the actual controller generation module is used for carrying out inversion design according to a control design target and obtaining an actual controller based on the estimation model.
By adopting the technical scheme, the optimal feedback full-state observer is set, and all state information in the observer is fully utilized; the crane displacement and the rope pendulum angle are estimated by combining the estimation model through the feedback of the crane displacement and the rope pendulum angle, and then are combined with a control design target to further control and design the control model to be observed to obtain a controller generation system, so that the following displacement speed adjustment of the bridge crane is realized, the stability of the rope pendulum angle is ensured, and the conveying efficiency of the crane is improved.
In summary, the invention includes at least one of the following beneficial technical effects:
1. according to the method for generating the bridge crane controller, the optimal feedback full-state observer is arranged, and all state information in the observer is fully utilized; the method has the advantages that the displacement and the rope swinging angle are estimated by the aid of feedback of crane displacement and the rope swinging angle and the combination of an estimation model, and further combined with a control design target, the model is further controlled and designed, and an actual bridge crane controller is obtained, so that the next displacement speed adjustment of the bridge crane can be realized according to the obtained bridge crane controller, the rope swinging angle is guaranteed to be stable, and the conveying efficiency of the crane is improved;
2. according to the bridge crane control method, the obtained actual controller is utilized to realize the control of the motion state of the bridge crane, the displacement tracking control effect is improved, the stability of the rope swinging angle is ensured, and therefore the conveying efficiency of the bridge crane is improved;
3. according to the bridge crane controller generation system, the controller generation method is utilized to obtain the control model acquisition module to be observed, the estimation model acquisition module and the actual controller generation module, so that the controller system is generated, tracking control over the motion state of the bridge crane is facilitated, and the conveying efficiency of the bridge crane is further facilitated to be improved.
Drawings
FIG. 1 is a graph of the effect of prior art control;
FIG. 2 is a schematic view of a bridge crane;
FIG. 3 is a flow chart illustrating a method for generating a bridge crane controller according to an embodiment of the present invention;
fig. 4 is a control effect diagram of the practical controller 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.
Any feature disclosed in this specification (including any accompanying drawings) may be replaced by alternative features serving equivalent or similar purposes, unless expressly stated otherwise. That is, unless expressly stated otherwise, each feature is only an example of a generic series of equivalent or similar features.
Referring to fig. 2, a bridge crane on a bridge is movable along the bridge, with a load connected to the crane by long ropes of fixed length. Uncertainty in the control system is caused by the interplay between trolley displacement, rope pendulum length and pendulum angle during the operation of the bridge crane.
As a specific embodiment of the method for generating the bridge crane controller, as shown in fig. 3, the method for generating includes,
the model of the control to be observed is obtained 101, as shown in fig. 2, according to the bridge crane structure, the dynamics analysis is carried out on the bridge crane, and the model of the control to be observed under the system dynamics structure is established:
Figure GDA0003007993620000101
wherein, y1(t) represents a rope swing angle, y2(t) shows crane displacement, f1(t) model to be observed including model uncertainty and disturbance information in the yaw angle system, f2(t) represents a model to be observed containing model uncertainty and disturbance information in the displacement system, u (t) represents the control input of the system, and b is a known control coefficient and is determined by relevant factors such as the output torque of the motor and the gear transmission ratio.
The analysis shows that the crane control system has y1(t) and y2(t) two degrees of freedom, but only one controller u (t), and thus this is a typical under-actuated system. Meanwhile, the control accuracy lower than that of the model method can be reduced due to the accuracy of a crane control system, external disturbance, load change and the like. For this purpose, based on the real-time measurement data y1(t) and y2(t) estimating the model, and performing further control design according to the estimated model to become a current more practical control method.
Estimation model acquisition 102, based on the measured variable y1(t) and y2(t) obtaining an estimation model based on an optimal feedback full-state observer.
And the controller generates 103, performs inversion design according to a control design target, and obtains an actual controller based on the estimation model.
By the method for generating the bridge crane controller, the optimal feedback full-state observer is arranged, and all state information in the observer is fully utilized; through the feedback of the crane displacement and the rope swinging angle, the displacement and the rope swinging angle are estimated by combining the estimation model, and then combined with a control design target, the model is further controlled and designed, and an actual bridge crane controller is obtained, so that the following displacement adjustment of the bridge crane is realized according to the obtained bridge crane controller, the stability of the rope swinging angle is ensured, and the conveying efficiency of the crane is improved.
As an implementation manner of estimation model acquisition, the specific method includes:
carrying out system expansion on a control model to be observed to obtain an expanded state space model; defining a system observer based on the extended state space model;
defining an all-state virtual controller based on a system observer, defining a performance index J based onvObtaining a quadratic optimal feedback rate k, and obtaining an optimal feedback all-state observer of the bridge crane by combining the quadratic optimal feedback rate k and the all-state virtual controller; and the number of the first and second groups,
and obtaining an estimation model of the bridge crane based on the optimal feedback full-state observer.
The specific method of system expansion is not definite, and the obtained expanded state space model is theoretically equivalent representation of the control model to be observed and can be used as structural reference and error proof of the bridge crane observer.
In the embodiment of the estimation model acquisition, the virtual controller has good observation performance based on the whole observability of the self variable in the optimal feedback full-state observer, and the linear quadratic optimal feedback function can give consideration to the stability and optimality of the performance index of the bridge crane observer.
As an implementation mode of the control model system to be observed, the specific method comprises the following steps:
moving the crane by y2(t) substituting as an observation variable into the control model to be observed can be expanded to
Figure GDA0003007993620000111
Wherein the content of the first and second substances,
Figure GDA0003007993620000112
then simultaneously displacing the crane by y2(t) and the rope swing angle y1(t) substituting the control model to be observed as an observation variable to obtain an extended state space model:
Figure GDA0003007993620000113
wherein the content of the first and second substances,
Figure GDA0003007993620000114
C2＝[C1,C1]，
Figure GDA0003007993620000115
y(t)＝[y1(t)，y2(t)]u (t) is the same as the control input shown in formula (1), h1(t) and h2(t) are each f1(t) and f2(t), and at this time, x (t) ═ x1(t),x2(t),x3(t),x4(t),x5(t),x6(t),x7(t),x8(t)]T；
Equation (3) is equivalent to
Figure GDA0003007993620000121
Thereby having
x4(t)＝f1(t) (5)
x8(t)＝f2(t) (6)
Only the crane displacement y in the crane control system2(t) and the rope swing angle y1(t) two degrees of freedom, so that the crane control system is controlled, and the crane motion state can be adjusted in time according to the state information of observing the crane displacement and the rope swinging angle.
For one embodiment of defining an optimal feedback full state observer, the extended state vector is defined as
z＝[z1,z2,z3,z4,z5,z6,z7,z8]T (7)
Wherein z is1Representing a measured variable y1(t) estimate of (z)5Representing measurement y2(t) estimate of (z)2Representing a measured variable y1(t) using the estimated value of the derivative, z6Representing a measured variable y2(t) using the estimated value of the derivative, z3And z7Representing integral feedback, z, for constructing an optimal feedback all-state observer4Representation system model f1(t) estimation of z8Representation system model f2(t) estimation.
Based on C in the formulas (2) and (3)1And C2Definition of (2), swinging the rope by an angle x1(t) and Crane Displacement x5(t) as a measurement variable, based on which, as an embodiment of obtaining the bridge crane observer, the bridge crane observer is defined as:
Figure GDA0003007993620000122
and v is an 8 x 1 dimensional full feedback estimation controller used for designing and configuring optimal feedback full state observer parameters.
The bridge crane observer coefficients are set as:
Figure GDA0003007993620000131
Figure GDA0003007993620000132
Bv＝eye(8)，Dv＝zeros(8,8)，B2the same as the definition in the formula (3).
By defining the following performance indicators
Figure GDA0003007993620000133
Obtaining the optimal feedback rate of linear quadratic form
k＝lqry(Av,Bv,Cv,Dv,Qv,Rv) (9)
Wherein Q isvAnd RvIs the coefficient to be adjusted.
The formula (9) is further designed to
v＝-kz+k(1:4)ref1+k(5:8)ref2 (10)
A virtual controller is obtained, i.e., equation (10) is a virtual controller. Wherein ref1＝[x1(t),r12,0,r14]TAnd is provided with
Figure GDA0003007993620000134
Figure GDA0003007993620000135
ref2＝[x5(t),r22,0,r24]TAnd is provided with
Figure GDA0003007993620000136
Figure GDA0003007993620000137
Figure GDA0003007993620000138
Are respectively as
Figure GDA0003007993620000139
The estimate of (c) can be derived by a derivative estimation method.
Finally, combining the virtual controller (10) with the bridge crane observer (8) to obtain an estimation model, wherein the model f1(t) and f2(t) estimation
Figure GDA00030079936200001310
And
Figure GDA00030079936200001311
：
Figure GDA00030079936200001312
Figure GDA00030079936200001313
the obtained estimation model can estimate the following motion state of the bridge crane, thereby realizing the prejudgment of the crane motion.
The control target of the bridge crane is to keep the stability of the rope swinging angle while realizing the crane displacement tracking. However, due to the coupling characteristics among system variables, load variation among different conveying batches and interference of external uncertain factors such as wind direction, collision and the like, an accurate parameter model of the bridge crane system is difficult to obtain, so that the tracking control effect of the bridge crane position is poor, the swing angle is too large, the conveying efficiency of the bridge crane is reduced, inversion design is carried out according to a control design target, an actual controller is obtained based on an estimation model, the obtained actual controller can realize tracking control of crane displacement, and meanwhile the stability of the rope swing angle is guaranteed.
As an embodiment generated by an actual controller, the specific method is as follows:
the configuration of the system expansion matrix according to equation (3), the control model to be observed (1) is equivalent to equation (4) and can be represented in the form:
Figure GDA0003007993620000141
wherein s is1(t)＝y2(t)，s2(t)＝y1(t)，
Figure GDA0003007993620000142
f1(t) and f2(t) may be estimated by an optimal feedback full state observer;
defining crane displacement and virtual controller tracking error:
Figure GDA0003007993620000143
wherein the content of the first and second substances,
Figure GDA0003007993620000144
y2d(T) is the expected reference track of crane displacement, T is the [0, T ]]，αiThe method is characterized in that the method is a virtual controller, T is a target operation time length, i is a natural number which is more than or equal to 2 and less than or equal to n, and n is the total level number of inversion design;
defining the following Lyapunov functions, carrying out inversion design and obtaining an actual controller:
in the first-stage inversion design, the tracking effect output by the crane control system is obtained:
Figure GDA0003007993620000145
the derivative is:
Figure GDA0003007993620000146
wherein the content of the first and second substances,
Figure GDA0003007993620000151
is y2d(t) derivative of;
in the second-stage and third-stage inversion design, based on the under-actuated characteristic of a crane control system, the swing angle displacement s is minimized2(t) and minimum yaw rate s3(t) obtaining a stable rope sway angle as one of control design targets other than trajectory tracking, adding a target of minimizing the sway angle to Lyapunov (Lyapunov) function design, thereby defining:
Figure GDA0003007993620000152
Figure GDA0003007993620000153
the derivative is:
Figure GDA0003007993620000154
Figure GDA0003007993620000155
lyapunov function V defining a fourth order inversion design4Comprises the following steps:
Figure GDA0003007993620000156
the derivative is:
Figure GDA0003007993620000157
by using model estimation (12), based on equations (13), (16), (18) and (20), the virtual controller is designed to satisfy the condition that the respective order derivatives of the Lyapunov function are negative:
Figure 6
finally obtaining the actual controller
Figure GDA0003007993620000159
Wherein, c1、c2、c3And c4To control the gain, m is 2w2+α2，n＝2w3+α3Thereby obtaining:
Figure GDA00030079936200001510
Figure GDA0003007993620000161
Figure GDA0003007993620000162
Figure GDA0003007993620000163
Δf1and Δ f2To estimate the error, it can be expressed as:
Figure GDA0003007993620000164
the crane control system has an overall Lyapunov function of
Figure GDA0003007993620000165
The derivative is:
Figure GDA0003007993620000166
based on the geometric mean inequality, the above equation can be expressed as:
Figure GDA0003007993620000167
for the acquisition of the derivative estimation, a traditional derivation method can be adopted, but in the traditional derivation method, the situation that the derivative error is large exists, the derivative obtained by the traditional derivation method in the virtual controller can influence the result of the estimation model, and in order to reduce the error of the derivative, a new derivative estimation method is provided, which is used in the following steps
Figure GDA0003007993620000168
Specific embodiments of derivative estimation are described.
In the derivative estimation acquisition, a derivative estimation variable is defined and passes through a derivative estimator
Figure GDA0003007993620000169
A derivative estimation method is implemented.
Wherein the content of the first and second substances,
Figure GDA00030079936200001610
r＝[r1,r2,r3]Tr is a derivative estimate variable, and vrA virtual controller being an estimator for designing parameters required for derivative estimation;
vr＝-krr+krErx1(t) (32)
wherein the content of the first and second substances,
Figure GDA00030079936200001611
kris obtained by defining a performance index JrObtaining a secondary optimal feedback rate;
Figure GDA00030079936200001612
kr＝lqr(Ar,Br,Qr,Rr) (34)
wherein Q isrAnd RrFor the coefficient to be adjusted, kr＝[kr1,kr2,kr3]。
Substituting the formula (32) into the formula (31) to obtain
Figure GDA0003007993620000171
Further written as
Figure GDA0003007993620000172
As can be seen from equations (35) and (36), the feedback matrix k is configured by equation (34)rThe method can obtain the state that the pole of the closed-loop system reaches the expected state, and can also take the stability and the optimality of the performance indexes of the crane observer system into consideration, so that the design based on the virtual controller can ensure that x is obtained1(t)-r 10, thereby obtaining
Figure GDA0003007993620000173
Figure GDA0003007993620000174
Is estimated as
Figure GDA0003007993620000175
Figure GDA0003007993620000176
And can ensure that the tracking error is zero, which is beneficial to improving ref1And ref2The accuracy of (2).
In order to prove the stability and the observation error convergence of the full feedback state observer, the virtual controller (10) is substituted into the bridge crane observer (8) by the following steps:
Figure GDA0003007993620000177
(4) - (37) and definition e ═ x (t) -z, then
Figure GDA0003007993620000181
Accurate derivative estimates can be obtained by derivative estimation methods, including
Figure GDA0003007993620000182
Therefore, r14-z4(t)＝x4(t)-z4＝e4(t)。
In the same way, because
Figure GDA0003007993620000183
Therefore, r24-z8＝x8(t)-z8＝e8Thereby to make
Figure GDA0003007993620000184
Namely, it is
Figure GDA0003007993620000185
Therefore, the characteristic root of the error system can be determined by the linear quadratic form all-state feedback control rate k, and the coefficient h is obtained in the model1(t) and h2And (t) under the condition of being bounded, the stability of the error system can be guaranteed to be bounded.
To demonstrate the stability of the actual control, a guarantee that the derivative estimation error in equation (36) is zeroEquation (40) may ensure that the estimated error value Δ fiIs bounded, so ε can be defined as
Figure GDA0003007993620000186
Selection c1＞0,c2＞0,
Figure GDA0003007993620000187
And order
Figure GDA0003007993620000191
Can obtain
Figure GDA0003007993620000192
And
Figure GDA0003007993620000193
from equation (25), the crane control system response converges within the limited proximity when t → ∞:
Figure GDA0003007993620000194
by selecting an appropriate filter time constant τixAnd control gain ciThe size of the limited neighborhood that determines the stability of the system may be set.
As an implementation mode of a bridge crane control method, an actual controller obtained in a bridge crane controller generation method is utilized to carry out displacement tracking control on a bridge crane, so that information such as displacement and swing angle of the bridge crane is tracked, the following motion state of the bridge crane is pre-judged according to the tracked motion state information, if the problem that the swing angle amplitude is too large and unstable is pre-judged, the actual controller timely adjusts the displacement speed of the bridge crane and the like, the stability of the rope swing angle is guaranteed, and the conveying efficiency of the bridge crane is further improved.
As one embodiment of a bridge crane controller generation system, includes,
wait to observe control model and acquire the module, according to the bridge crane structure, carry out the dynamics analysis to the bridge crane, establish the control model of waiting to observe under the system dynamics structure:
Figure GDA0003007993620000195
wherein, y1(t) represents a rope swing angle, y2(t) shows crane displacement, f1(t) model to be observed including model uncertainty and disturbance information in the yaw angle system, f2(t) represents a model to be observed comprising model uncertainty and disturbance information in the displacement system, u (t) represents the control input of the system, and b is a known control coefficient.
Estimation model acquisition module based on measured variable y1(t) and y2(t) obtaining an estimation model based on an optimal feedback full-state observer.
And the actual controller generation module is used for carrying out inversion design according to a control design target and obtaining an actual controller based on the estimation model.
By utilizing the controller generation method, the control model acquisition module to be observed, the estimation model acquisition module and the actual controller generation module are obtained, so that a controller system is generated, the tracking control of the motion state of the bridge crane is facilitated, and the conveying efficiency of the bridge crane is facilitated to be improved.
Referring to fig. 4, the control parameter of the actual controller is set to c1＝200，c2＝100，c3＝1000，c4The control effect shown in fig. 4 is obtained as 100, the target curves are all set as black dotted lines, the actual response curve is a black solid line, and the crane displacement curve y2(t) it can be seen that the controller outputs the tracking target which can be accurately and rapidly controlled by the rope pendulumSwing angle curve y1(t) it can be seen that the rope swing angle output by the controller is stable and fluctuates substantially around zero degrees.
Compared with the control effect of the prior art shown in FIG. 1, the angle response curve y of the two graphs1(t) it can be seen that the output angle of the embodiment of the invention is more stable, the output angle fluctuates around zero basically, and the control performance is superior to that of the methods of the documents in the background art. Meanwhile, as can be seen from the control curve u (t), the energy consumed by the embodiment of the present invention is lower than the energy consumed by the methods of the documents in the background art.
The present embodiment is only for explaining the present invention, and it is not limited to the present invention, and those skilled in the art can make modifications of the present embodiment without inventive contribution as needed after reading the present specification, but all of them are protected by patent law within the scope of the claims of the present invention.

Claims (7)

1. A bridge crane controller generation method is characterized by comprising the following steps,
the method comprises the following steps of obtaining (101) a control model to be observed, carrying out dynamics analysis on a bridge crane according to the bridge crane structure, and establishing the control model to be observed under the dynamics structure of a crane control system:
Figure FDA0003007993610000011
Figure FDA0003007993610000012
wherein, y1(t) represents a rope swing angle, y2(t) shows crane displacement, f1(t) model to be observed including model uncertainty and disturbance information in the yaw angle system, f2(t) representing a model to be observed containing model uncertainty and disturbance information in the displacement system, u (t) representing the control input of the system, and b being a known control coefficient;
estimation modelObtaining (102) a measurement variable y1(t) and y2(t) obtaining an estimation model based on an optimal feedback full-state observer; and the number of the first and second groups,
generating (103) an actual controller, performing inversion design according to a control design target, and obtaining the actual controller based on the estimation model;
the specific method for obtaining the estimation model (102) comprises the following steps:
carrying out system expansion on the control model to be observed to obtain an expanded state space model; defining a system observer based on the extended state space model;
defining an all-state virtual controller based on the system observer, and defining a performance index J based onvObtaining a quadratic optimal feedback rate k, and obtaining an optimal feedback all-state observer of the bridge crane by combining the quadratic optimal feedback rate k and the all-state virtual controller; and obtaining an estimation model of the bridge crane based on the optimal feedback full-state observer.
2. The controller generation method according to claim 1, wherein the specific acquisition method of the estimation model of the bridge crane comprises,
moving the crane by y2(t) and the rope swing angle y1(t) substituting the control model to be observed as an observation variable to obtain an extended state space model:
Figure FDA0003007993610000013
wherein the content of the first and second substances,
Figure FDA0003007993610000021
C2＝[C1,C1]，
Figure FDA0003007993610000022
and is
Figure FDA0003007993610000023
y(t)＝[y1(t)，y2(t)]U (t) is the same as the control input shown in formula (1), h1(t) and h2(t) are each f1(t) and f2(t), where x (t) is [ x [ ]1(t),x2(t),x3(t),x4(t),x5(t),x6(t),x7(t),x8(t)]T；
Equation (3) is equivalent to
Figure FDA0003007993610000024
Figure FDA0003007993610000025
Figure FDA0003007993610000026
Figure FDA0003007993610000027
Figure FDA0003007993610000028
Figure FDA0003007993610000029
Figure FDA00030079936100000210
Figure FDA00030079936100000211
Thereby having
x4(t)＝f1(t) (5)
x8(t)＝f2(t) (6)
Defining the extended state vector as:
z＝[z1,z2,z3,z4,z5,z6,z7,z8]T (7)
wherein z is1Representing a measured variable y1(t) estimate of (z)5Representing measurement y2(t) estimate of (z)2Representing a measured variable y1(t) using the estimated value of the derivative, z6Representing a measured variable y2(t) using the estimated value of the derivative, z3And z7Representing integral feedback, z, for constructing an optimal feedback all-state observer4Representation system model f1(t) estimation of z8Representation system model f2(t) estimation;
based on C in the formula (3)1And C2Is defined by y1(t)＝x1(t)，y2(t)＝x5(t) subsequent sections each displacing the crane by x1(t) and rope pendulum angle x5(t) directly as a measured variable;
defining the optimal feedback full-state observer of the bridge crane as follows:
Figure FDA0003007993610000031
wherein v is a 8 × 1 dimensional virtual controller for designing and configuring optimal feedback full state observer parameters, and the bridge crane observer coefficients are set as:
Figure 3
Bv＝eye(8)，Dv＝zeros(8,8)，
Figure FDA0003007993610000033
by defining the following performance indicators
Figure FDA0003007993610000034
Obtaining the optimal feedback rate of linear quadratic form
k＝lqry(Av,Bv,Cv,Dv,Qv,Rv) (9)
The full-state estimation controller is designed as
v＝-kz+k(1：4)ref1+k(5：8)ref2 (10)
Wherein ref1＝[x1(t)，r12，0，r14]TAnd is provided with
Figure FDA0003007993610000035
ref2＝[x5(t)，r22，0，r24]TAnd is provided with
Figure FDA0003007993610000036
Are respectively as
Figure FDA0003007993610000037
Figure FDA0003007993610000038
Can be obtained by a derivative estimation method;
through an optimal feedback full-state observer, a system model f can be obtained1(t) and f2(t) estimation
Figure FDA0003007993610000039
Figure FDA00030079936100000310
3. The controller generation method according to claim 1, wherein the control design objectives in the actual controller generation (103) include minimizing crane displacement tracking error, minimizing yaw displacement and speed.
4. The controller generation method according to claim 2, wherein the specific method of actual controller generation (103) comprises:
according to the formula (3) configuration of the system expansion matrix, the control model to be observed is equivalent to the formula (4), and can be expressed in the following form:
Figure FDA0003007993610000041
wherein s is1(t)＝y2(t)，s2(t)＝y1(t)，
Figure FDA0003007993610000042
f1(t) and f2(t) may be estimated by an optimal feedback full state observer;
defining crane displacement and virtual controller tracking error:
Figure FDA0003007993610000043
wherein the content of the first and second substances,
Figure FDA0003007993610000044
y2d(T) is the expected reference track of crane displacement, T is the [0, T ]]，αiIs a virtualA controller, wherein T is the length of target operation time, i is a natural number which is more than or equal to 2 and less than or equal to n, and n is the total level number of inversion design;
defining the following Lyapunov functions, carrying out inversion design and obtaining an actual controller:
in the first-stage inversion design, the tracking effect output by the crane control system is obtained:
Figure FDA0003007993610000045
the derivative is:
Figure FDA0003007993610000046
wherein the content of the first and second substances,
Figure FDA0003007993610000047
is y2d(t) derivative of;
in the second-stage and third-stage inversion design, based on the under-actuated characteristic of a crane control system, the swing angle displacement s is minimized2(t) and minimum yaw rate s3(t) obtaining a stable rope sway angle as one of control design targets other than trajectory tracking, adding a target of minimizing the sway angle to the lyapunov function design, thereby defining:
Figure FDA0003007993610000048
Figure FDA0003007993610000051
the derivative is:
Figure FDA0003007993610000052
Figure FDA0003007993610000053
lyapunov function V for defining fourth-order inversion design4Comprises the following steps:
Figure FDA0003007993610000054
the derivative is:
Figure FDA0003007993610000055
with the model estimation, based on equation (13), equation (16), equation (18), and equation (20), on the premise that each order derivative of the lyapunov function is negative, the virtual controller is designed to:
Figure 1
get the actual controller
Figure FDA0003007993610000057
Wherein, c1、c2、c3And c4To control the gain, m is 2w2+α2，n＝2w3+α3。
5. The controller generation method according to claim 2, wherein the specific method of derivative estimation comprises:
defining a derivative estimation variable and passing the derivative estimator
Figure FDA0003007993610000058
Implementing a derivative estimation method;
wherein the content of the first and second substances,
Figure FDA0003007993610000061
r＝[r1,r2,r3]Tr is a derivative estimate variable, and vrIs a virtual controller of the estimator for designing the parameters required for the derivative estimation,
vr＝-krr+krErx1(t) (32)
wherein the content of the first and second substances,
Figure FDA0003007993610000062
kris obtained by defining a performance index JrObtaining a secondary optimal feedback rate;
Figure FDA0003007993610000063
kr＝lqr(Ar,Br,Qr,Rr) (34)
wherein Q isrAnd RrFor the coefficient to be adjusted, kr＝[kr1,kr2,kr3]。
6. A bridge crane control method, characterized in that the control method is implemented based on the actual controller generated by the controller generation method according to one of claims 1 to 5.
7. A bridge crane controller generation system, characterized in that the generation system comprises,
wait to observe control model and acquire the module, according to the bridge crane structure, carry out the dynamics analysis to the bridge crane, establish the control model of waiting to observe under the crane control system dynamics structure:
Figure FDA0003007993610000064
Figure FDA0003007993610000065
wherein, y1(t) represents a rope swing angle, y2(t) shows crane displacement, f1(t) model to be observed including model uncertainty and disturbance information in the yaw angle system, f2(t) representing a model to be observed containing model uncertainty and disturbance information in the displacement system, u (t) representing the control input of the system, and b being a known control coefficient;
estimation model acquisition module based on measured variable y1(t) and y2(t) obtaining an estimation model based on an optimal feedback full-state observer;
the actual controller generation module is used for carrying out inversion design according to a control design target and obtaining an actual controller based on the estimation model;
the specific method for obtaining the estimation model comprises the following steps:
carrying out system expansion on a control model to be observed to obtain an expanded state space model; defining a system observer based on the extended state space model;
defining an all-state virtual controller based on the system observer, and defining a performance index J based onvObtaining a quadratic optimal feedback rate k, and obtaining an optimal feedback all-state observer of the bridge crane by combining the quadratic optimal feedback rate k and the all-state virtual controller; and obtaining an estimation model of the bridge crane based on the optimal feedback full-state observer.
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