CN116573557A - Amplitude saturation nonlinear output feedback control method and system for tower crane - Google Patents
Amplitude saturation nonlinear output feedback control method and system for tower crane Download PDFInfo
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- 238000005259 measurement Methods 0.000 claims description 20
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- 238000005859 coupling reaction Methods 0.000 claims description 6
- 238000013461 design Methods 0.000 claims description 6
- 238000006073 displacement reaction Methods 0.000 claims description 6
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Classifications
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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
- B66C23/00—Cranes comprising essentially a beam, boom, or triangular structure acting as a cantilever and mounted for translatory of swinging movements in vertical or horizontal planes or a combination of such movements, e.g. jib-cranes, derricks, tower cranes
- B66C23/88—Safety gear
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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
- B66C13/18—Control systems or devices
- B66C13/22—Control systems or devices for electric drives
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
- Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
- Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]
Abstract
The application discloses a tower crane amplitude saturation nonlinear output feedback control method and system, comprising the following steps: constructing a dynamic model of the tower crane based on the Lagrangian method and the actual working state of the tower crane; taking the data difference between the expected position of the dynamic model of the tower crane and actual feedback data as an error signal, and designing a rope-length-variable PD controller according to the error signal; combining the designed rope-length-variable PD controller with a pseudo speed signal constructed based on system driving information to obtain a speed-measurement-free rope-length-variable PD controller; the speed-measurement-free rope-measuring and length-changing PD controller is based on a saturation function bounded principle, and forms a five-degree-of-freedom amplitude saturation nonlinear output feedback controller of the speed-measurement-free tower crane to control the tower crane. The application constructs the pseudo speed signal by the system driving information, can effectively acquire the system speed information in the actual working condition, limits the output torque of the controller, and improves the efficiency and the performance of the controller.
Description
Technical Field
The application relates to the technical field of tower crane anti-shake motion control, in particular to a tower crane amplitude saturation nonlinear output feedback control method and system.
Background
The crane plays an increasingly important role in our daily life, is also used in more and more occasions, and has the problem that a speed signal is difficult to measure when a complex measuring device is used due to the fact that the working place of the crane is complex. In actual working conditions, the motor output also has certain amplitude limiting, so how to effectively solve the problems that the speed signal is difficult to obtain and the motor is protected from being influenced by larger output is one of the primary consideration of improving the transportation efficiency of the crane. Therefore, by utilizing the dynamic model of the tower crane, a good control effect on the tower crane is achieved according to the pseudo speed signal and the amplitude limiting function.
Disclosure of Invention
This section is intended to outline some aspects of embodiments of the application and to briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this section as well as in the description of the application and in the title of the application, which may not be used to limit the scope of the application.
The present application has been made in view of the above-described problems occurring in the prior art.
Therefore, the application provides a tower crane amplitude saturation nonlinear output feedback control method and a system, which solve the problems that the existing crane control method does not consider the problems that the speed signal is difficult to measure and the motor output is limited.
In order to solve the technical problems, the application provides the following technical scheme:
in a first aspect, an embodiment of the present application provides a method for controlling amplitude saturation nonlinear output feedback of a tower crane, including:
constructing a dynamic model of the tower crane based on the Lagrangian method and the actual working state of the tower crane;
according to the data difference between the expected position of the dynamic model of the tower crane and actual feedback data, the dynamic model of the tower crane is used as an error signal, and a rope length variable PD controller is designed according to the error signal;
combining the designed variable rope length PD controller with a pseudo speed signal constructed based on system driving information to obtain a variable rope length PD controller without speed measurement;
the speed-measurement-free rope-measuring and length-changing PD controller is based on a saturation function bounded principle, and forms a five-degree-of-freedom amplitude saturation nonlinear output feedback controller of the speed-measurement-free tower crane to control the tower crane.
As a preferable scheme of the amplitude saturation nonlinear output feedback control method of the tower crane, the application comprises the following steps: the dynamic model of the tower crane is expressed as follows:
wherein M is the mass of the trolley, M is the mass of the load, l is the rope length between the trolley and the load, x is the positioning of the trolley, alpha is the rotation angle of the cantilever, and theta 1 And theta 2 The angle projected onto the vertical plane parallel to the boom and the angle projected onto the vertical plane perpendicular to the boom are respectively J 0 For moment of inertia in the direction of rotation T a For driving force in cantilever direction F x F is the driving force in the direction of the trolley l Is the driving force in the rope direction.
As a preferable scheme of the amplitude saturation nonlinear output feedback control method of the tower crane, the application comprises the following steps: the data difference between the expected position of the dynamic model of the tower crane and the actual feedback data is used as an error signal, and the method comprises the following steps: a trolley position error, a cantilever angle error, a rope length error, an angle error projected onto a vertical plane parallel to the boom, and an angle error projected onto a vertical plane perpendicular to the cantilever;
the vector form of the error signal is expressed as:
e 1 ＝q 1 -q 1d ,e 2 ＝q 2 -q 2d ,e 3 ＝q 3 -q 3d ,e 4 ＝q 4 -q 4d ,e 5 ＝q 5 -q 5d
wherein q 1 For cantilever angle, q 1d Target position for cantilever angle, q 2 For trolley position, q 2d For the target position of the trolley, q 3 Length of rope, q 3d Target position for rope length, q 4 For projection to an angle on a vertical plane parallel to the boom, q 4d For projection to an angular target position on a vertical plane parallel to the boom, q 5 Q for projection to an angle on a vertical plane perpendicular to the cantilever 5d To project to a target location at an angle on a vertical plane perpendicular to the cantilever.
As a preferable scheme of the amplitude saturation nonlinear output feedback control method of the tower crane, the application comprises the following steps: designing a variable rope length PD controller according to the error signal, comprising: introducing a coupling item for strengthening positioning and eliminating swing into a variable rope length PD controller;
the coupling terms for enhanced positioning and shimmy cancellation are expressed as:
-k γ γ i (γ 1 β 1 -γ 2 β 2 -γ 3 β 3 )
-k δi [(e 4 2 +e 5 2 )β i ]
wherein k is γ ＞0，γ i ＞0，k δi ＞0，(i＝1，2，3)。
As a preferable scheme of the amplitude saturation nonlinear output feedback control method of the tower crane, the application comprises the following steps: combining the designed variable rope length PD controller with a pseudo speed signal constructed based on system drivable information to obtain a speed-measurement-free variable rope length PD controller, comprising:
pseudo speed signal, expressed as:
β 1 ＝η 1 +k β1 α
β 2 ＝η 2 +k β2 x
β 3 ＝η 3 +k β3 l
wherein alpha is the rotation angle of the cantilever, x is the displacement of the trolley, l is the length of the suspension rope, and k β1 ＞0，k β2 ＞0，k β3 ＞0。
As a preferable scheme of the amplitude saturation nonlinear output feedback control method of the tower crane, the application comprises the following steps: further comprises:
the speed-free measuring rope length-variable PD controller is expressed as:
T a ＝-k α1 e 1 -k γ γ 1 (γ 1 β 1 -γ 2 β 2 -γ 3 β 3 )-k β1 β 1 -k δ1 [(e 4 2 +e 5 2 )β 1 ]
F x ＝-k α2 e 2 -k γ γ 2 (γ 1 β 1 -γ 2 β 2 -γ 3 β 3 )-k β2 β 2 -k δ2 [(e 4 2 +e 5 2 )β 2 ]
F l ＝-mg-k α3 e 3 -k γ γ 3 (γ 1 β 1 -γ 2 β 2 -γ 3 β 3 )-k β3 β 3 -k δ3 [(e 4 2 +e 5 2 )β 3 ]
wherein m is the load mass, g is the gravitational acceleration, k αi ＞0，k βi ＞0，k δi ＞0，k γ ＞0，γ i ＞0，(i＝1，2，3)。
As a preferable scheme of the amplitude saturation nonlinear output feedback control method of the tower crane, the application comprises the following steps: the five-degree-of-freedom tower crane amplitude saturation nonlinear output feedback controller without speed measurement is designed, and the five-degree-of-freedom tower crane amplitude saturation nonlinear output feedback controller comprises: introducing a representation mechanism of a saturation function into the PD controller without the speed measurement rope, and designing based on a bounded principle of the saturation function;
the expression mechanism of the saturation function is expressed as:
the five-degree-of-freedom tower crane amplitude saturation nonlinear output feedback controller without speed measurement is expressed as:
T a ＝-k α1 arctane 1 -k γ γ 1 arctan(γ 1 β 1 -γ 2 β 2 -γ 3 β 3 )-k β1 arctanβ 1 -k δ1 arctan[(e 4 2 +e 5 2 )β 1 ]
F x ＝-k α2 arctane 2 -k γ γ 2 arctan(γ 1 β 1 -γ 2 β 2 -γ 3 β 3 )-k β2 arctanβ 2 -k δ2 arctan[(e 4 2 +e 5 2 )β 2 ]
F l ＝-k α3 arctane 3 -k γ γ 3 arctan(γ 1 β 1 -γ 2 β 2 -γ 3 β 3 )-mg-k β3 arctanβ 3 -k δ3 arctan[(e 4 2 +e 5 2 )β 3 ]
wherein k is αi ＞0,k βi ＞0,k δi ＞0,k γ ＞0,γ i ＞0,(i＝1,2,3)。。
In a second aspect, the present application provides a tower crane amplitude saturation nonlinear output feedback control system, comprising:
the model building module is used for building a dynamic model of the tower crane based on the Lagrangian method and the actual working state of the tower crane;
the first design module is used for taking the data difference between the expected position of the dynamic model of the tower crane and actual feedback data as an error signal and designing a rope length-variable PD controller according to the error signal;
the second design module is used for combining the designed rope-length-variable PD controller with a pseudo speed signal constructed based on system driving information to obtain a speed-measurement-free rope-measuring PD controller;
and the control module is used for forming a five-degree-of-freedom amplitude saturation nonlinear output feedback controller of the speed-free measurement tower crane based on a saturation function bounded principle by the speed-free measurement rope-changing PD controller and controlling the tower crane.
In a third aspect, the present application provides a computing device comprising:
a memory and a processor;
the memory is used for storing computer executable instructions, and the processor is used for executing the computer executable instructions, and the computer executable instructions realize the steps of the amplitude saturation nonlinear output feedback control method of the tower crane when being executed by the processor.
In a fourth aspect, the present application provides a computer readable storage medium storing computer executable instructions that when executed by a processor implement the steps of the tower crane amplitude saturation nonlinear output feedback control method.
Compared with the prior art, the application has the beneficial effects that: according to the application, the pseudo speed signal is constructed only through the system drivable information, so that the situation that the system speed information cannot be acquired in the actual working condition is effectively avoided; meanwhile, the upper output limit of the motor driving system in actual use is considered, so that the efficiency and performance of the controller are improved in order to protect the motor from limiting the output torque of the controller.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are needed in the description of the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present application, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art. Wherein:
FIG. 1 is a schematic diagram of a tower crane structure according to a method and system for controlling amplitude saturation nonlinear output feedback of a tower crane according to an embodiment of the present application;
FIG. 2 is a schematic flow chart of a method and system for controlling amplitude saturation nonlinear output feedback of a tower crane according to an embodiment of the application;
FIG. 3 is a logic diagram of a simulation platform encoder of a method and system for controlling amplitude saturation nonlinear output feedback of a tower crane according to an embodiment of the present application;
fig. 4 is a diagram showing a comparison of simulation effects of a method and a system for controlling amplitude saturation nonlinear output feedback of a tower crane according to an embodiment of the present application.
Detailed Description
So that the manner in which the above recited objects, features and advantages of the present application can be understood in detail, a more particular description of the application, briefly summarized above, may be had by reference to the embodiments, some of which are illustrated in the appended drawings. All other embodiments, which can be made by one of ordinary skill in the art based on the embodiments of the present application without making any inventive effort, shall fall within the scope of the present application.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present application, but the present application may be practiced in other ways other than those described herein, and persons skilled in the art will readily appreciate that the present application is not limited to the specific embodiments disclosed below.
Further, reference herein to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic can be included in at least one implementation of the application. The appearances of the phrase "in one embodiment" in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments.
While the embodiments of the present application have been illustrated and described in detail in the drawings, the cross-sectional view of the device structure is not to scale in the general sense for ease of illustration, and the drawings are merely exemplary and should not be construed as limiting the scope of the application. In addition, the three-dimensional dimensions of length, width and depth should be included in actual fabrication.
Also in the description of the present application, it should be noted that the orientation or positional relationship indicated by the terms "upper, lower, inner and outer", etc. are based on the orientation or positional relationship shown in the drawings, are merely for convenience of describing the present application and simplifying the description, and do not indicate or imply that the apparatus or elements referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus should not be construed as limiting the present application. Furthermore, the terms "first, second, or third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
The terms "mounted, connected, and coupled" should be construed broadly in this disclosure unless otherwise specifically indicated and defined, such as: can be fixed connection, detachable connection or integral connection; it may also be a mechanical connection, an electrical connection, or a direct connection, or may be indirectly connected through an intermediate medium, or may be a communication between two elements. The specific meaning of the above terms in the present application will be understood in specific cases by those of ordinary skill in the art.
Example 1
Referring to fig. 1-2, in one embodiment of the present application, there is provided a method for controlling amplitude saturation nonlinear output feedback of a tower crane, including:
s1, constructing a dynamic model of the tower crane based on a Lagrangian method and an actual working state of the tower crane;
still further, the tower crane dynamic model is expressed as:
wherein M is the mass of the trolley, M is the mass of the load, l is the rope length between the trolley and the load, x is the positioning of the trolley, alpha is the rotation angle of the cantilever, and theta 1 And theta 2 The angle projected onto the vertical plane parallel to the boom and the angle projected onto the vertical plane perpendicular to the boom are respectively J 0 For moment of inertia in the direction of rotation T a For driving force in cantilever direction F x F is the driving force in the direction of the trolley l Is the driving force in the rope direction.
It should be noted that the characteristics of moment of inertia and the like of a load in practical application are considered in the establishment of the dynamic model of the tower crane, and the nonlinear characteristics of the dynamic model of the tower crane are fully fitted with the practical crane.
S2, taking the data difference between the expected position of the dynamic model of the tower crane and actual feedback data as an error signal, and designing a rope-length-variable PD controller according to the error signal;
further, the expected position of the dynamic model of the tower crane is expressed as:
q 1d ＝α d ＝-30[deg],q 2d ＝x d ＝0.3[m],q 3d ＝l d ＝0.5[m]
q 4d ＝θ 1d ＝0[deg],q 5d ＝θ 2d ＝0[deg]
wherein q 1d Target position for cantilever angle, q 2d For the target position of the trolley, q 3d Target position for rope length, q 4d For projection to an angular target position on a vertical plane parallel to the boom, q 5d To project to a target location at an angle on a vertical plane perpendicular to the cantilever.
Further, the error signal is a data difference between the expected position of the dynamic model of the tower crane and the actual feedback data, and includes: a trolley position error, a cantilever angle error, a rope length error, an angle error projected onto a vertical plane parallel to the boom, and an angle error projected onto a vertical plane perpendicular to the cantilever;
the vector form of the error signal is expressed as:
e 1 ＝q 1 -q 1d ,e 2 ＝q 2 -q 2d ,e 3 ＝q 3 -q 3d ,e 4 ＝q 4 -q 4d ,e 5 ＝q 5 -q 5d
wherein q 1 For cantilever angle, q 1d Target position for cantilever angle, q 2 For trolley position, q 2d For the target position of the trolley, q 3 Length of rope, q 3d Target position for rope length, q 4 For projection to an angle on a vertical plane parallel to the boom, q 4d For projection to an angular target position on a vertical plane parallel to the boom, q 5 Q for projection to an angle on a vertical plane perpendicular to the cantilever 5d To project to a target location at an angle on a vertical plane perpendicular to the cantilever.
Still further, designing a variable rope length PD controller based on the error signal, comprising: introducing a coupling item for strengthening positioning and eliminating swing into a variable rope length PD controller;
the coupling terms for enhanced positioning and shimmy cancellation are expressed as:
-k γ γ i (γ 1 β 1 -γ 2 β 2 -γ 3 β 3 )
-k δi [(e 4 2 +e 5 2 )β i ]
wherein k is γ ＞0，γ i ＞0，k δi ＞0，(i＝1，2，3)。
S3: combining the designed variable rope length PD controller with a pseudo speed signal constructed based on system driving information to obtain a variable rope length PD controller without speed measurement;
further, combining the designed variable rope length PD controller with a pseudo speed signal constructed based on system drivable information to obtain a speed-free measured variable rope PD controller, comprising:
pseudo speed signal, expressed as:
β 1 ＝η 1 +k β1 α
β 2 ＝η 2 +k β2 x
β 3 ＝η 3 +k β3 l
wherein alpha is the rotation angle of the cantilever, x is the displacement of the trolley, l is the length of the suspension rope, and k β1 ＞0，k β2 ＞0，k β3 ＞0。
Still further, still include:
the speed-free measuring rope length-variable PD controller is expressed as:
T a ＝-k α1 e 1 -k γ γ 1 (γ 1 β 1 -γ 2 β 2 -γ 3 β 3 )-k β1 β 1 -k δ1 [(e 4 2 +e 3 2 )β 1 ]
F x ＝-k α2 e 2 -k γ γ 2 (γ 1 β 1 -γ 2 β 2 -γ 3 β 3 )-k β2 β 2 -k δ2 [(e 4 2 +e 5 2 )β 2 ]
F l ＝-mg-k α3 e 3 -k γ γ 3 (γ 1 β 1 -γ 2 β 2 -γ 3 β 3 )-k β3 β 3 -k δ3 [(e 4 2 +e 5 2 )β 3 ]
wherein m is the load mass, g is the gravitational acceleration, k αi ＞0，k βi ＞0，k δi ＞0，k γ ＞0，γ i ＞0，(i＝1，2，3)。
S4: the PD controller forms a five-degree-of-freedom amplitude saturation nonlinear output feedback controller of the tower crane without speed measurement based on a saturation function bounded principle, and controls the tower crane;
furthermore, a five-degree-of-freedom tower crane amplitude saturation nonlinear output feedback controller without speed measurement is designed, comprising: introducing a representation mechanism of a saturation function into the PD controller without the speed measurement rope, and designing based on a bounded principle of the saturation function;
the expression mechanism of the saturation function is expressed as:
the five-degree-of-freedom tower crane amplitude saturation nonlinear output feedback controller without speed measurement is expressed as:
T a ＝-k α1 arctane 1 -k γ γ 1 arctan(γ 1 β 1 -γ 2 β 2 -γ 3 β 3 )-k β1 arctanβ 1 -k δ1 arctan[(e 4 2 +e 5 2 )β 1 ]
F x ＝-k α2 arctane 2 -k γ γ 2 arctan(γ 1 β 1 -γ 2 β 2 -γ 3 β 3 )-k β2 arctanβ 2 -k δ2 arctan[(e 4 2 +e 5 2 )β 2 ]
F l ＝-k α3 arctane 3 -k γ γ 3 arctan(γ 1 β 1 -γ 2 β 2 -γ 3 β 3 )-mg-k β3 arctanβ 3 -k δ3 arctan[(e 4 2 +e 5 2 )β 3 ]
wherein k is αi ＞0,k βi ＞0,k δi ＞0,k γ ＞0,γ i ＞0,(i＝1,2,3)。
Further, the tower crane is analyzed according to the pseudo speed signal and the amplitude limiting function, and when the positioning distance and the cantilever positioning distance are fixed, the angle theta on the vertical plane parallel to the suspension arm is obtained through coordinate transformation projection of a coordinate system 1 And an angle θ projected onto a vertical plane perpendicular to the cantilever 2 And the amplitude of (2) determines the swing angle suppressing effect.
It should be noted that, in combination with the constructed pseudo-speed signal, the output torque of the controller is limited by introducing the expression mechanism of the saturation function, so that the motor loss caused by the overlarge motor output value is protected; meanwhile, the rope length changing model is considered, so that the working efficiency of the system is improved, and the safety of operation is improved.
The above is a schematic scheme of the amplitude saturation nonlinear output feedback control method of the tower crane in this embodiment. It should be noted that, the technical solution of the amplitude saturation nonlinear output feedback control system of the tower crane and the technical solution of the amplitude saturation nonlinear output feedback control method of the tower crane belong to the same concept, and details of the technical solution of the amplitude saturation nonlinear output feedback control system of the tower crane in this embodiment, which are not described in detail, can be referred to the description of the technical solution of the amplitude saturation nonlinear output feedback control method of the tower crane.
In this embodiment, an amplitude saturation nonlinear output feedback control system of a tower crane includes:
the model building module is used for building a dynamic model of the tower crane based on the Lagrangian method and the actual working state of the tower crane;
the first design module is used for taking the data difference between the expected position of the dynamic model of the tower crane and actual feedback data as an error signal and designing a rope length-variable PD controller according to the error signal;
the second design module is used for combining the designed rope-length-variable PD controller with a pseudo speed signal constructed based on system driving information to obtain a speed-measurement-free rope-measuring PD controller;
and the control module is used for forming a five-degree-of-freedom amplitude saturation nonlinear output feedback controller of the speed-free measurement tower crane based on a saturation function bounded principle by the speed-free measurement rope-changing PD controller and controlling the tower crane.
The embodiment also provides a computing device, which is suitable for the situation of the tower crane amplitude saturation nonlinear output feedback control method, and comprises the following steps:
a memory and a processor; the memory is used for storing computer executable instructions, and the processor is used for executing the computer executable instructions to realize the method for realizing the amplitude saturation nonlinear output feedback control of the tower crane according to the embodiment.
The present embodiment also provides a storage medium having stored thereon a computer program which, when executed by a processor, implements a method for implementing nonlinear output feedback control of amplitude saturation of a tower crane as proposed in the above embodiment.
The storage medium proposed in the present embodiment belongs to the same inventive concept as the method for implementing amplitude saturation nonlinear output feedback control of a tower crane proposed in the above embodiment, and technical details not described in detail in the present embodiment can be seen in the above embodiment, and the present embodiment has the same beneficial effects as the above embodiment.
Example 2
Referring to fig. 3 to 4, for one embodiment of the present application, a simulation experiment of amplitude saturation nonlinear output feedback control of a five-degree-of-freedom tower crane without speed measurement is provided, and scientific demonstration is performed through the simulation experiment, so as to verify the beneficial effects of the present application.
Based on the working state of an actual crane, a motion control board, an industrial computer and a crane are utilized, an upper computer is utilized to build a hardware simulation platform of the tower crane, and in combination with the internal logic of a simulation platform encoder shown in fig. 3, the embodiment of the application utilizes four absolute encoders, including a hook angle encoder 100, a load angle encoder 101, a displacement encoder 102 and a cantilever rotation angle encoder 103, to measure the angle values of the hook and the load in real time, the displacement of a trolley and a guide rail and the rotation angle of the cantilever, and the first driving unit 104 and the second driving unit 105 in the embodiment of the application use an absolute encoder for feeding back the displacement of the trolley and an encoder for feeding back the rotation angle of the cantilever.
The data interaction of the tower crane hardware simulation platform is completed by a motion control board 106 and an industrial personal computer 107, the data measured by the three encoders are input into the motion control board 106, the data are transmitted into the industrial personal computer 107 through the motion control board 106, the feedback data are integrated by utilizing a MATLAB simulation module at the end of the industrial personal computer 107, the sampling period is 0.005s, a real-time control signal is formed, and the motion control board 106 feeds back the generated signal to the first driving unit 104 and the second driving unit 105 to drive the crane to move.
The initial position of the system is set as follows:
q 1 (0)＝0[deg],q 2 (0)＝0[m],q 3 (0)＝0.3[m],q 4 (0)＝q 5 (0)＝0[deg]。
the saturation value of the motor is set as:
T a ∈[-10 10](N·m),F x ∈[-5 5](N),F l ∈[-5 5](N)
the controller parameters are set as follows:
experiments are carried out by using a traditional saturation controller and a variable rope length controller and a controller of the method, wherein the formula of the traditional saturation controller is as follows:
T a ＝-k α1 tanh(ε α )-k β1 tanh(ξ α )
F x ＝-k α2 tanh(ε x )-k β2 tanh(ξ x )
F l ＝-mg-k α3 tanh(ε l )-k β3 tanh(ξ l )
the formula of the rope length variable controller is as follows:
it should be noted that, in order to ensure fairness of experiment verification, the values of the parameters adopted by the comparison controller are consistent with those of the application.
The amplitudes of the methods of the present application and the conventional saturation controller and variable rope length controller were calculated using the experimental platform constructed as described above, and the comparison results are shown in table 1:
table 1 effect comparison
As can be seen from table 1 and referring to fig. 4, under the condition that the positioning distances are the same, both the conventional saturation controller and the variable rope length controller exceed the limiting range set by the system, and the suppression effect on the two swing angles is obviously not excellent in the proposed controller, and the maximum swing angle of the load under the comparative controller exceeds the proposed controller. By adopting the controller provided by the application, the system state can quickly reach the target position, the set output amplitude limit cannot be exceeded, and meanwhile, a good swing eliminating effect can be achieved.
It should be noted that the above embodiments are only for illustrating the technical solution of the present application and not for limiting the same, and although the present application has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the technical solution of the present application may be modified or substituted without departing from the spirit and scope of the technical solution of the present application, which is intended to be covered in the scope of the claims of the present application.
Claims (10)
1. The amplitude saturation nonlinear output feedback control method for the tower crane is characterized by comprising the following steps of:
constructing a dynamic model of the tower crane based on the Lagrangian method and the actual working state of the tower crane;
according to the data difference between the expected position of the dynamic model of the tower crane and actual feedback data, the dynamic model of the tower crane is used as an error signal, and a rope length variable PD controller is designed according to the error signal;
combining the designed variable rope length PD controller with a pseudo speed signal constructed based on system driving information to obtain a variable rope length PD controller without speed measurement;
the speed-measurement-free rope-measuring and length-changing PD controller is based on a saturation function bounded principle, and forms a five-degree-of-freedom amplitude saturation nonlinear output feedback controller of the speed-measurement-free tower crane to control the tower crane.
2. The tower crane amplitude saturation nonlinear output feedback control method as claimed in claim 1, wherein: the dynamic model of the tower crane is expressed as follows:
wherein M is the mass of the trolley, M is the mass of the load, l is the rope length between the trolley and the load, x is the positioning of the trolley, alpha is the rotation angle of the cantilever, and theta 1 And theta 2 The angle projected onto the vertical plane parallel to the boom and the angle projected onto the vertical plane perpendicular to the boom are respectively J 0 For moment of inertia in the direction of rotation T a For driving force in cantilever direction F x F is the driving force in the direction of the trolley l Is the driving force in the rope direction.
3. The tower crane amplitude saturation nonlinear output feedback control method as claimed in claim 2, wherein a data difference between a desired position of the tower crane dynamic model and actual feedback data is used as an error signal, comprising: a trolley position error, a cantilever angle error, a rope length error, an angle error projected onto a vertical plane parallel to the boom, and an angle error projected onto a vertical plane perpendicular to the cantilever;
the vector form of the error signal is expressed as:
e 1 ＝q 1 -q 1d ,e 2 ＝q 2 -q 2d ,e 3 ＝q 3 -q 3d ,e 4 ＝q 4 -q 4d ,e 5 ＝q 5 -q 5d
wherein q 1 For cantilever angle, q 1d Is a cantileverTarget position of angle, q 2 For trolley position, q 2d For the target position of the trolley, q 3 Length of rope, q 3d Target position for rope length, q 4 For projection to an angle on a vertical plane parallel to the boom, q 4d For projection to an angular target position on a vertical plane parallel to the boom, q 5 Q for projection to an angle on a vertical plane perpendicular to the cantilever 5d To project to a target location at an angle on a vertical plane perpendicular to the cantilever.
4. The tower crane amplitude saturation nonlinear output feedback control method as set forth in claim 3, wherein designing a variable rope length PD controller based on the error signal comprises: introducing a coupling item for strengthening positioning and eliminating swing into a variable rope length PD controller;
the coupling terms for enhanced positioning and shimmy cancellation are expressed as:
-k γ γ i (γ 1 β 1 -γ 2 β 2 -γ 3 β 3 )
wherein k is γ ＞0，γ i ＞0，k δi ＞0，(i＝1，2，3)。
5. The method for amplitude saturation nonlinear output feedback control of a tower crane according to claim 4, wherein combining the designed variable rope length PD controller with a pseudo speed signal constructed based on system drivable information to obtain a speed-free variable rope length PD controller comprises:
pseudo speed signal, expressed as:
β 1 ＝η 1 +k β1 α
β 2 ＝η 2 +k β2 x
β 3 ＝η 3 +k β3 l
wherein alpha is the rotation angle of the cantilever, x is the displacement of the trolley, l is the length of the suspension rope, and k β1 ＞0,k β2 ＞0,k β3 ＞0。
6. The tower crane amplitude saturation nonlinear output feedback control method as set forth in claim 5, further comprising:
the speed-free measuring rope length-variable PD controller is expressed as:
T a ＝-k α1 e 1 -k γ γ 1 (γ 1 β 1 -γ 2 β 2 -γ 3 β 3 )-k β1 β 1 -k δ1 [(e 4 2 +e 5 2 )β 1 ]
F x ＝-k α2 e 2 -k γ γ 2 (γ 1 β 1 -γ 2 β 2 -γ 3 β 3 )-k β2 β 2 -k δ2 [(e 4 2 +e 5 2 )β 2 ]
F l ＝-mg-k α3 e 3 -k γ γ 3 (γ 1 β 1 -γ 2 β 2 -γ 3 β 3 )-k β3 β 3 -k δ3 [(e 4 2 +e 5 2 )β 3 ]
wherein m is the load massG is the acceleration of gravity, k αi ＞0,k βi ＞0,k δi ＞0,k γ ＞0,γ i ＞0,(i＝1,2,3)。
7. The method for amplitude saturation nonlinear output feedback control of a tower crane according to claim 6, wherein designing a five-degree-of-freedom tower crane amplitude saturation nonlinear output feedback controller without speed measurement comprises: introducing a representation mechanism of a saturation function into the PD controller without the speed measurement rope, and designing based on a bounded principle of the saturation function;
the expression mechanism of the saturation function is expressed as:
the five-degree-of-freedom tower crane amplitude saturation nonlinear output feedback controller without speed measurement is expressed as:
T a ＝-k α1 arctane 1 -k γ γ 1 arctan(γ 1 β 1 -γ 2 β 2 -γ 3 β 3 )-k β1 arctanβ 1 -k δ1 arctan[(e 4 2 +e 5 2 )β 1 ]
F x ＝-k α2 arctane 2 -k γ γ 2 arctan(γ 1 β 1 -γ 2 β 2 -γ 3 β 3 )-k β2 arctanβ 2 -k δ2 arctan[(e 4 2 +e 5 2 )β 2 ]
F l ＝-k α3 arctane 3 -k γ γ 3 arctan(γ 1 β 1 -γ 2 β 2 -γ 3 β 3 )-mg-k β3 arctanβ 3 -k δ3 arctan[(e 4 2 +e 5 2 )β 3 ]
wherein k is αi ＞0,k βi ＞0,k δi ＞0,k γ ＞0,γ i ＞0,(i＝1,2,3)。。
8. An amplitude saturation nonlinear output feedback control system of a tower crane, which is characterized by comprising:
the model building module is used for building a dynamic model of the tower crane based on the Lagrangian method and the actual working state of the tower crane;
the first design module is used for taking the data difference between the expected position of the dynamic model of the tower crane and actual feedback data as an error signal and designing a rope length-variable PD controller according to the error signal;
the second design module is used for combining the designed rope-length-variable PD controller with a pseudo speed signal constructed based on system driving information to obtain a speed-measurement-free rope-measuring PD controller;
and the control module is used for forming a five-degree-of-freedom amplitude saturation nonlinear output feedback controller of the speed-free measurement tower crane based on a saturation function bounded principle by the speed-free measurement rope-changing PD controller and controlling the tower crane.
9. An electronic device, comprising:
a memory and a processor;
the memory is configured to store computer executable instructions that, when executed by the processor, implement the steps of the tower crane amplitude saturation nonlinear output feedback control method of any one of claims 1 to 7.
10. A computer readable storage medium storing computer executable instructions which when executed by a processor perform the steps of the tower crane amplitude saturation nonlinear output feedback control method in accordance with any one of claims 1 to 7.
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