CN114084800B - Self-adaptive fuzzy control method and system for double-pendulum bridge crane - Google Patents
Self-adaptive fuzzy control method and system for double-pendulum bridge crane Download PDFInfo
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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
- B66C13/00—Other constructional features or details
- B66C13/16—Applications of indicating, registering, or weighing devices
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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
- B66C13/18—Control systems or devices
- B66C13/22—Control systems or devices for electric drives
Abstract
The invention provides a self-adaptive fuzzy control method and a self-adaptive fuzzy control system for a double-pendulum bridge crane, wherein the self-adaptive fuzzy control method for the double-pendulum bridge crane comprises the following steps: determining a control target of the double-swing bridge crane system; determining an uncertainty item containing an actuator dead zone in the double-pendulum bridge crane system based on the control target and a kinematic model of the double-pendulum bridge crane system; fitting an uncertainty term by using an adaptive fuzzy control system to construct an adaptive fuzzy controller; and (3) calculating in real time by using the self-adaptive controller to obtain corresponding control driving force, driving the double-pendulum bridge crane to move, and completing a control target. The invention compensates the uncertainty item containing the dead zone of the actuator by utilizing the idea of fitting the nonlinear function by the fuzzy logic system, and can improve the control precision of the double-pendulum bridge crane system.
Description
Technical Field
The invention belongs to the technical field of automatic control of nonlinear under-actuated electromechanical systems, and particularly relates to a self-adaptive fuzzy control method and system for a double-pendulum bridge crane.
Background
The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.
Under-actuated mechanical systems refer to a class of systems in which the number of independent control inputs is less than the number of system degrees of freedom. Compared with a full-drive system, the underactuated system has the advantages of energy conservation, cost reduction, system quality reduction and the like. With the development of modern industrialization, a crane, which is one of under-actuated systems, plays an important role in various fields such as disaster relief, industrial production, construction sites and the like. The cranes may be classified into tower cranes, bridge cranes, mast cranes, etc. according to the mechanical structure. Bridge cranes are one of the most widely used, and like other crane systems, the control objective is to quickly and accurately transport a load to a designated location. However, the load can swing due to acceleration and deceleration movements of the trolley during transportation, which can have a certain influence on safe production and working efficiency. Currently, most cranes are manually operated by workers, often with positioning errors and residual swing. In addition, in a severe working environment and in a long-time hard work, an operator may malfunction, thereby affecting the working efficiency and even causing a safety accident. Therefore, it is necessary to design an automatic control method for a crane system for safe production and improved work efficiency.
Over the past decades, students have proposed some high performance control methods for crane systems, which can be categorized into open loop control, closed loop control, and intelligent control. The open loop control method has the advantages of low cost, simple structure, easy realization and the like, and can obtain good control effect under the condition of no external interference. However, in practical applications, the crane is inevitably affected by external disturbances such as wind or internal factors such as dead zones of the actuator, which may deteriorate the control performance of the open loop control method to some extent. With the continuous development of devices such as sensors, the running state of the system can be detected in real time, which not only provides an important reference basis for the operation of staff, but also lays a solid foundation for the development of a closed-loop control method. Compared with an open-loop control method, the closed-loop control method has better robustness and is more suitable for an environment with external interference. Some intelligent control methods have outstanding performances in terms of model inaccuracy or parameter optimization, but many intelligent control methods can only verify control performance through simulation or experiments, and cannot ensure the stability of a closed-loop system in theory. In addition, when the system parameters change, the control method has to be redesigned, which is very inconvenient in practical application.
While scholars have devised some effective control methods for double pendulum cranes, there are still some challenging problems. In particular, most control methods are designed for constant rope length, but in order to increase the work efficiency, both trolley translation and load lifting are typically considered. In addition, many control methods ignore control input uncertainty of actuators such as dead zones. However, the input dead zone may degrade control performance and even cause instability in some cases.
Disclosure of Invention
In order to solve the above problems, a first aspect of the present invention provides a self-adaptive fuzzy control method for a double-pendulum bridge crane, which considers trolley translation and load lifting, and compensates for an actuator dead zone by using the idea of fitting a nonlinear function by a fuzzy logic system, so as to improve the control accuracy of the double-pendulum bridge crane system.
In order to achieve the above object, the present invention mainly includes the following aspects:
in a first aspect, an embodiment of the present invention provides a self-adaptive fuzzy control method for a double-swing bridge crane, including:
determining a control target of the double-swing bridge crane system;
determining an uncertainty item containing an actuator dead zone in the double-pendulum bridge crane system based on the control target and a kinematic model of the double-pendulum bridge crane system;
fitting the uncertainty term by using an adaptive fuzzy control system to construct an adaptive fuzzy controller;
and calculating in real time by using the self-adaptive controller to obtain corresponding control driving force to drive the double-pendulum bridge crane to move so as to complete a control target.
In one possible embodiment, the control target is that the trolley position and the lifting rope length are respectively converged to corresponding expected values, and two-stage swing angles are restrained; the two-stage swing angle comprises a lifting hook swing angle and a load swing angle.
In one possible implementation, the fitting of the uncertainty term using an adaptive fuzzy control system constructs an adaptive fuzzy controller comprising:
defining an error signal and determining a sliding mode surface based on the control target;
and fitting the uncertainty term by using an adaptive fuzzy control system, and constructing an adaptive fuzzy controller based on the fitted uncertainty term and a sliding mode surface.
In one possible embodiment, the kinematic model of the double-pendulum bridge crane system is of the form:
wherein q a ＝[x l 1 ] Τ Representing a vector of states that can be driven,is q a Second derivative of>Represents a positive definite symmetric matrix, u= [ u ] 1 u 2 ] Τ Represents the driving force vector, u 1 Represents the driving force for translating the trolley, u 2 Represents a driving force for lifting and lowering a load, h= [ H ] 1 h 2 ] Τ Representing a vector of measurable components, T representing the lumped uncertainty vector of the system, and superscript T representing the transpose of the matrix.
In one possible embodiment, the kinematic model of the double-pendulum bridge crane system is calculated as:
d is determined as an uncertainty term in the double pendulum bridge crane system that contains the dead zone of the actuator.
In one possible implementation, the uncertainty term is fitted using an adaptive fuzzy control system, the fitted uncertainty term having the form:
wherein,represents a weight vector Γ ij (i=1, 2, j=1, 2,., 7) represents weights in the fuzzy logic system, are parameters to be estimated,represents the fuzzy basis function vector, ζ ij (i=1, 2, j=1, 2,.,. 7) represents a fuzzy basis function, τ represents a stateState vector, epsilon 1 ,ε 2 Represents approximation errors, and the upper bounds of the errors are +.>
In one possible implementation, the expression of the adaptive fuzzy controller is as follows:
wherein,respectively is gamma 1 ，Γ 2 Estimated value of ∈10->For slip form surface area, k 1 ，k 2 ，k p1 ，k p2 ，k v1 ，k v2 All positive control gains.
In a second aspect, an embodiment of the present invention provides a dual swing bridge crane adaptive fuzzy control system, including:
a control target determining unit for determining a control target of the double-swing bridge crane system;
an uncertainty item determining unit, configured to determine an uncertainty item including an actuator dead zone in the double-swing bridge crane system based on the control target and a kinematic model of the double-swing bridge crane system;
the construction unit is used for fitting the uncertain term by using an adaptive fuzzy control system and constructing an adaptive fuzzy controller;
and the driving unit is used for calculating corresponding control driving force in real time by utilizing the self-adaptive controller to drive the double-pendulum bridge crane to move so as to finish a control target.
In a third aspect, an embodiment of the present invention provides a computer apparatus, including: a processor, a memory and a bus, said memory storing machine readable instructions executable by said processor, said processor and said memory communicating via the bus when the computer device is running, said machine readable instructions when executed by said processor performing the steps of the double pendulum bridge crane adaptive fuzzy control method as described in any one of the possible embodiments of the first aspect above.
In a fourth aspect, the present embodiment provides a computer readable storage medium having stored thereon a computer program which, when executed by a processor, performs the steps of the double pendulum bridge crane adaptive fuzzy control method as described in any one of the possible embodiments of the first aspect.
The beneficial effects of the invention are as follows:
the self-adaptive fuzzy control method of the double-pendulum bridge crane is provided by analyzing a kinematic model of the bridge crane system with load lifting and double-pendulum effects and compensating dead zone characteristics of an actuator by utilizing a fuzzy logic system, and the self-adaptive fuzzy control method of the double-pendulum bridge crane is used for completing control targets of the crane system, improving control accuracy of the system, and improving working efficiency of the crane system by applying the control targets to a crane platform for experiments.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention.
FIG. 1 is a flow chart of a double-swing bridge crane adaptive fuzzy control method provided by an embodiment of the invention;
FIG. 2 is a diagram of experimental results of a double-swing bridge crane adaptive fuzzy control method provided by an embodiment of the invention;
fig. 3 is a diagram showing an adaptive parameter Γ of a dual-swing bridge crane adaptive fuzzy control method according to an embodiment of the present invention 1 A trend graph of change over time;
fig. 4 is a diagram showing an adaptive parameter Γ of a dual-swing bridge crane adaptive fuzzy control method according to an embodiment of the present invention 2 A trend graph of change over time;
FIG. 5 is a schematic diagram of a dual swing bridge crane adaptive fuzzy control system according to an embodiment of the present invention;
fig. 6 is a schematic diagram of a computer device according to an embodiment of the present invention.
Detailed Description
The invention will be further described with reference to the drawings and examples.
It should be noted that the following detailed description is illustrative and is intended to provide further explanation of the invention. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the present invention. As used herein, the singular is also intended to include the plural unless the context clearly indicates otherwise, and furthermore, it is to be understood that the terms "comprises" and/or "comprising" when used in this specification are taken to specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof.
In the present day, most crane operations are performed by a worker, and the transportation efficiency of the crane system is mainly determined by the proficiency of operators, that is, the operators need to be trained for a long period of time to grasp the related skills and operating rules. In addition, the manual operation has the defects of poor positioning precision, low efficiency, easy occurrence of safety accidents and the like. Furthermore, some specific applications (e.g., nuclear material transport, etc.) are not amenable to manual handling. It is therefore necessary to design automatic control strategies for bridge crane systems to replace manual operations. Unlike available method, the present invention can treat dead zone of the executor in the system, raise the conveying speed of the bogie and inhibit the swinging of load, and raise the control precision and safety of the whole control system.
For the convenience of understanding the present embodiment, first, a detailed description is given of a dual-swing bridge crane adaptive fuzzy control method disclosed in the present embodiment, and an execution main body of the dual-swing bridge crane adaptive fuzzy control method provided in the present embodiment may be a cloud platform or a server that interacts with a user terminal. The following describes the self-adaptive fuzzy control method of the double-pendulum bridge crane provided by the embodiment of the invention with the execution main body as a server.
Example 1
Referring to fig. 1, fig. 1 is a flowchart of a dual-swing bridge crane adaptive fuzzy control method according to an embodiment of the present invention, as shown in fig. 1, the dual-swing bridge crane adaptive fuzzy control method includes steps S101 to S104, wherein:
s101: a control objective of the double pendulum bridge crane system is determined.
As an alternative embodiment, the control targets are that the trolley position and the lifting rope length are respectively converged to corresponding expected values, and two-stage swing angles are restrained; the two-stage swing angle comprises a lifting hook swing angle and a load swing angle.
In a specific implementation, control targets of a crane system, a trolley position x (t) and a lifting rope length l are analyzed 1 (t) convergence to a corresponding desired value x d And/l 1d And suppresses the two-stage swing angle theta 1 (t),θ 2 (t) wherein θ 1 (t),θ 2 (t) represents the hook swing angle and the load swing angle, respectively, t in brackets represents time, and the variable following (t) represents that the variable is a variable with respect to time, and (t) following most of the variables is omitted for convenience of representation.
S102: and determining an uncertainty item containing an actuator dead zone in the double-swing bridge crane system based on the control target and a kinematic model of the double-swing bridge crane system.
In a specific implementation, the dynamics model of the two-dimensional double-pendulum bridge crane system is specifically as follows:
wherein m, m 1 ,m 2 Respectively representing the mass of the trolley, the mass of the lifting hook and the mass of the load, x (t) represents the displacement of the trolley, and l 1 (t),l 2 Respectively represent the length of the lifting rope, the distance between the center of the lifting hook and the center of the load, theta 1 (t),θ 2 (t) respectively represents the swing angle of the lifting hook and the swing angle of the load, g represents the acceleration of gravity, and d 1 ,d 2 Respectively representing the air resistance coefficients of the lifting hook and the load, and the air resistance coefficients are positive numbers, f 1 ,f 2 Representing the actual output of the actuator for translating the trolley and elevating the load, respectively, is as follows:
wherein u is 1 ,u 2 S represents the theoretical output of an actuator for translating the trolley and elevating the load, respectively l (·),s r (. Cndot.) represent respectively unknown nonlinear functions related to actuator dead zone, b l ,b r Representing the upper and lower bounds of the dead zone, respectively. For convenience of representation, f will be 1 ,f 2 Denoted as f 1 ＝u 1 +Δu 1 ,f 2 ＝u 2 +Δu 2 ，Δu 1 ,Δu 2 Representing the difference between the actual output of the actuator and the theoretical output. Before analysis of the crane system, the following shorthand notations are defined:
s i ＝sinθ i ,c i ＝cosθ i ,s i±j ＝sin(θ i ±θ j ),c i±j ＝cos(θ i ±θ j ),i,j＝1,2(i≠j)
calculating the formulas (3) and (4),can be expressed as:
definition of drivable state vector q a ＝[x l 1 ] Τ Substitution of formulas (6) and (7) into formulas (1) and (2) can result in:
wherein,represents a positive definite symmetric matrix, u= [ u ] 1 u 2 ] Τ Represents the driving force vector, h= [ H ] 1 h 2 ] Τ Representing a vector consisting of measurable parts, t= [ T ] 1 t 2 ] Τ Representing lumped uncertainty vector of system, P 0 ,h 1 ,h 2 ,t 1 ,t 2 The specific definition of (2) is as follows:
taking into account the working conditions of the actual crane system, the following assumptions are made here:
suppose 1: in the conveying process, the lifting hook is always positioned below the bridge, and the load is always positioned below the lifting hook, namely
-π/2<θ 1 (t),θ 2 (t)<π/2，t≥0
The control objective of the bridge crane system is to converge the trolley position and the hoist rope length to the corresponding target positions, respectively, and to suppress the swinging of the load and the hoist hook, i.e. for a limited time
S103: and fitting the uncertainty term by using an adaptive fuzzy control system to construct an adaptive fuzzy controller.
As an alternative embodiment, the adaptive fuzzy controller is constructed by fitting the uncertainty term using an adaptive fuzzy control system, comprising:
defining an error signal and determining a sliding mode surface based on the control target;
and fitting the uncertainty term by using an adaptive fuzzy control system, and constructing an adaptive fuzzy controller based on the fitted uncertainty term and a sliding mode surface.
In practice, the terms to be fitted by the fuzzy logic system are determined prior to controller design. The calculation of formula (8) yields:
where D represents an uncertainty term in the system that includes the dead zone of the actuator. Next, a fuzzy logic system (fuzzy logic system, FLS) is designed to estimate and compensate D. The fuzzy rule base consists of fuzzy rules formed by If-Then sentences, and the relation between the input set and the output set can be expressed as by using a Mamdani direct reasoning method
If-Then Rules：R i :if x 1 is F 1 i and...and x n isthen y is Y i ,i＝1,...,N.
According to If-Then rules, the FLS may be expressed as
Wherein,and Y i Representing fuzzy sets Γ i Representation function->Maximum value achieved, +_>Representing membership functions>The fuzzy base function is represented, and N and N respectively represent the number of control inputs and the number of fuzzy rules. The weight vector Γ and the fuzzy basis function vector ζ (x) are defined as Γ= [ Γ), respectively 1 Γ 2 ...Γ N ] Τ ，ξ(x)＝[ζ 1 (x)ζ 2 (x)...ζ N (x)] Τ Then formula (10) can be written as:
y(x)＝Γ Τ ξ(x)
for any continuous function f (x) on the compact set W, the output y (x) of the FLS satisfies
Where ε is a sufficiently small positive constant. Using equation (11), the continuous function F (x) can be expressed as
F(x)＝Γ Τ ξ(x)+ε (12)
Through the above analysis, D in the formula (9) can be approximated as
Wherein,represents a weight vector Γ ij (i=1, 2, j=1, 2,., 7) represents weights in the fuzzy logic system, are parameters to be estimated,represents the fuzzy basis function vector, ζ ij (i=1, 2, j=1, 2,., 7) represents a fuzzy basis function,/->Representing state vectors, ε 1 ,ε 2 Is an approximation error, and the upper bounds of the errors are +.>
Defining the position error signal of the trolley and the length error signal of the lifting rope as respectivelyThe method comprises the following steps:
structure sliding formPlane vector And its derivative->Has the following form:
wherein k is 1 ,k 2 Indicating a positive control gain. Substitution of formulas (9) and (13) into formula (14) can result in:
the adaptive fuzzy controller is designed according to the form of the formula (15), and is specifically as follows:
wherein,respectively represent Γ 1 ,Γ 2 Is a function of the estimated value of (2); k (k) p1 ,k p2 ,k v1 ,k v2 Control gain is positive and satisfies:
wherein,as will be given in the subsequent analysis. The update rate of the design controller is as follows:
wherein alpha, beta 1 ,β 2 Indicating positive control gain, pi 1 ＝diag{w 11 w 22 ... w 77 },Π 2 ＝diag{b 11 b 22 ... b 77 And represents a positive diagonal matrix, w ii ,b ii (i=1, 2,., 7) represents the parameter to be positive.The estimation error of the representative weight vector is obtained by deriving the estimation error:
to facilitate subsequent analysis, substituting the controller (16) and the update rate (18) into equation (15) may yield:
s104: and calculating in real time by using the self-adaptive controller to obtain corresponding control driving force to drive the double-pendulum bridge crane to move so as to complete a control target.
In a specific implementation, the trolley position x (t) and the lifting rope length l are obtained on line by means of a sensor 1 (t) hook swing angle θ 1 (t) angular velocity of hook swingLoad swing angle θ 2 (t) and load-swing angular velocity +.>And (3) calculating in real time according to the formula (16) to obtain corresponding control signals, and controlling a driver and a motor of the crane system to output control force so as to realize a control target.
Next, it will be demonstrated by rigorous mathematical analysis that the controller (16) ensures that the trolley position and the hoist rope length, respectively, converge to the desired value x d And/l 1d And the hook and load pivot angles converge to zero, i.e
Wherein t is f Representing a finite time.
To demonstrate equation (21), consider the following Lyapunov candidate function V 1 (t)：
The formula (22) is derived with respect to time and is simplified by the formulas (18) and (20), and the obtained products are arranged
Taking into account k p1 ,k p2 Positive control gain and equation (17) can be obtainedThus (2)
Can be obtained by using the Barbara theory and (23)
Based on formulas (14) and (25), the following can be concluded:
to demonstrate that the slip plane Φ can converge to 0 in a finite time, consider the following Lyapunov candidate function V 2 (t)：
For convenience of representation, Λ will be 1 ,Λ 2 Is defined asΛ can be derived based on equation (24) 1 ,Λ 2 Respectively have upper bounds->I.e.
Deriving formula (27) about time, V 2 Derivative of (t)Can be expressed in the following form:
wherein k representsIntegrating equation (29) over time and using equation (27) can be obtained:
let the state variable be at t f Converging to the sliding surface phi at the moment, i.e. V 2 (t f ) =0. Can be obtained from the formula (30)
I.e. t f There is an upper bound. Using formula (29), the time t is greater than or equal to t f When the sliding mode surface phi is unchanged, namely
Can be obtained based on the formulas (14) and (31)
Next, the convergence of the hook swing angle and the load swing angle is analyzed. For convenience of representation, an underactuated state vector q is defined u ＝[θ 1 θ 2 ] Τ Actuator output vector u a ＝[f 1 f 2 ] Τ Air resistance vectorWhere dt represents integrating. Formulas (1) - (4) may be represented as follows:
wherein M is ij ,C ij ,G i (i, j=1, 2) has the following definition:
for M in formula (33) 22 And C 22 The following properties are always true:
using formula (33), formulas (3) and (4) can be organized as follows:
next, consider a third Lyapunov candidate function V 3 (t)
Deriving and sorting equation (36) with respect to time is available:
based on formula (32), when t is greater than or equal to t f When it comes to the following conclusion:
/>
substituting the conclusion of formula (38) into formulas (1) and (2) yields
Based on formula (35), willWritten in the form:
defining virtual control input u v1 ,u v2 The method comprises the following steps:
consider the zero input kinetic equation, where u v1 ＝0,u v2 =0, and equation (40) can be expressed as:
i.e.Can be rewritten into the following form:
the time integral for equation (43) is available:
taking into account thatFor->Using fractional integration methods:
from the following componentsIt can be derived that:
/>
by using the fractional integration method, the following can be obtained:
the last term in equation (47) is calculated:
from the following componentsThe method can obtain:
using formulas (44), (46) and (49), the following can be concluded:
i.e.
Using the ballet theorem for formulas (38), (39) and (51) are available:
through calculation, can be used forWritten in the form:
wherein delta 1 ,δ 2 ,σ 1 ,σ 2 The method comprises the following steps:
for delta 1 ,δ 2 The derivative about time is available:
can be obtained from formula (54)I.e. delta 1 ,δ 2 Consistent continuous by the method of sigma 1 ,σ 2 The calculation can be as follows:
using the extended ballet theorem, formulas (52), (53) and (55) can be obtained:
the calculation of equation (56) can be obtained:
the calculations for equations (58) and (59) can be made:
thus, the equilibrium point of the "zero input" dynamic system in equation (41) is asymptotically stable, and considering the conclusion in equation (32), one can get:
due toThe unexcited kinematic model (40) satisfies the properties of the input bounded convergence state (converging input bounded state, CIBS). Based on equation (61) and system (42) being asymptotically stable, it can be derived that the overall undriven kinematic model (40) is satisfied:
similar to the above, using the extended ballet theorem, it is known that:
according to equations (32), (62) and (63), equation (21) is verified.
In order to verify the effectiveness of the control method proposed by the present invention, experiments were performed on a crane experimental platform according to the above steps. Through measurement, the trolley mass, the lifting hook mass, the load mass, the distance between the lifting hook and the load and the gravity acceleration in the experimental platform are respectively as follows:
m＝7kg,m 1 ＝0.263kg,m 2 ＝0.25kg,l 2 ＝0.15m,g＝9.8m/s 2
the initial value and the expected value of the trolley displacement and the lifting rope length are respectively set as follows:
x(0)＝0m,l 1 (0)＝0.45m,x d ＝0.5m,l 1d ＝0.2m
wherein x (0) represents the initial position of the trolley, l 1 (0) An initial value representing the length of the hoist rope. In the experiment, 7 membership functions were chosen as follows:
after debugging, the control parameters of the controller (16) are selected as follows:
k 1 ＝2.5,k p1 ＝35,k v1 ＝15,k 2 ＝10,k p2 ＝40,k v2 ＝35,α＝0.005,β 1 ＝0.05,β 2 ＝8
∏ 1 ＝diag{8,8,8,8,8,8,8},∏ 2 ＝diag{1.5,1.5,1.5,1.5,1.5,1.5,1.5}
further, the control period of the system is 5 milliseconds.
The experimental results are shown in fig. 2 to 4. The solid line in fig. 2 shows the curves of trolley displacement, sling displacement, hook swing angle, and load swing angle over time. The dashed line of sub-graph 1 in fig. 2 represents the target position of the trolley, the dashed line of sub-graph 2 in fig. 2 represents the target position of the length of the lifting rope, and the units of load swing angle are converted from radians to angles in the figure for visual representation.
As can be seen from fig. 2, the control method provided by the invention can enable the trolley position and the lifting rope length to converge to the corresponding target positions within 2 seconds, the final positioning errors are all within 2 millimeters, and the load swing can be rapidly eliminated. As can be seen from fig. 3 and 4, the control method adaptation parameters proposed by the present invention are always bounded and eventually converge to a constant. From the experimental results, the control method designed by the invention has good effects on load positioning and swing inhibition.
Example two
Referring to fig. 5, fig. 5 is a schematic structural diagram of a dual-swing bridge crane adaptive fuzzy control system according to an embodiment of the present invention. As shown in fig. 5, the present embodiment provides a dual swing bridge crane adaptive fuzzy control system 500 including:
a control target determining unit 510 for determining a control target of the double swing bridge crane system;
an uncertainty item determination unit 520 configured to determine an uncertainty item including an actuator dead zone in the double-swing bridge crane system based on the control target and a kinematic model of the double-swing bridge crane system;
a constructing unit 530 for fitting the uncertainty term using an adaptive fuzzy control system to construct an adaptive fuzzy controller;
and the driving unit 540 is used for calculating corresponding control driving force in real time by using the self-adaptive controller to drive the double-pendulum bridge crane to move so as to complete the control target.
Example III
Referring to fig. 6, fig. 6 is a schematic diagram of a computer device according to an embodiment of the invention. As shown in fig. 6, the computer device 600 includes a processor 610, a memory 620, and a bus 630.
The memory 620 stores machine-readable instructions executable by the processor 610, when the computer device 600 is running, the processor 610 communicates with the memory 620 through the bus 630, and when the machine-readable instructions are executed by the processor 610, the steps of the adaptive fuzzy control method of the double-swing bridge crane in the method embodiment shown in fig. 1 can be executed, and the specific implementation can be referred to the method embodiment and will not be described herein.
Example IV
Based on the same application conception, the embodiment of the present invention further provides a computer readable storage medium, where a computer program is stored on the computer readable storage medium, and when the computer program is executed by a processor, the steps of the double-swing bridge crane adaptive fuzzy control method described in the above method embodiment are executed, and specifically, reference may be made to the above method embodiment, and details are not repeated herein.
It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of a hardware embodiment, a software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, magnetic disk storage, optical storage, and the like) having computer-usable program code embodied therein.
The above description is only of the preferred embodiments of the present invention and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (5)
1. The self-adaptive fuzzy control method for the double-pendulum bridge crane is characterized by comprising the following steps of:
determining a control target of the double-swing bridge crane system;
the control targets are that the trolley position and the lifting rope length are respectively converged to corresponding expected values, and two-stage swing angles are restrained; the two-stage swing angle comprises a lifting hook swing angle and a load swing angle;
determining an uncertainty item containing an actuator dead zone in the double-pendulum bridge crane system based on the control target and a kinematic model of the double-pendulum bridge crane system;
the kinematic model of the double pendulum bridge crane system is as follows:
wherein q a ＝[x l 1 ] Τ Represents a drivable state vector, x (t) represents trolley displacement, l 1 (t) represents the length of the hoist rope, the variable followed by (t) means that the variable is a time-dependent variable, most of the variables followed by (t) are omitted for ease of presentation,is q a Second derivative of>Represents a positive definite symmetric matrix, u= [ u ] 1 u 2 ] Τ Represents the driving force vector, u 1 Represents the driving force for translating the trolley, u 2 Represents a driving force for lifting and lowering a load, h= [ H ] 1 h 2 ] Τ Representing a vector of measurable components, T representing the lumped uncertainty vector of the system;
the kinematic model of the double-pendulum bridge crane system is calculated to be:
determining D as an uncertainty term containing an actuator dead zone in the double-pendulum bridge crane system;
fitting the uncertainty term by using an adaptive fuzzy control system to construct an adaptive fuzzy controller;
fitting the uncertainty term using an adaptive fuzzy control system, the fitted uncertainty term having the form:
wherein,represents a weight vector Γ ij (i=1, 2, j=1, 2,., 7) represents weights in the fuzzy logic system, are parameters to be estimated,represents the fuzzy basis function vector, ζ ij (i=1, 2, j=1, 2,.,. 7) represents a fuzzy basis function, τ represents a state vector, ε 1 ,ε 2 Represents approximation errors, and the upper bounds of the errors are +.>
The expression of the adaptive fuzzy controller is as follows:
wherein,respectively is gamma 1 ，Γ 2 Estimated value of ∈10->For slip form surface area, k 1 ，k 2 ，k p1 ，k p2 ，k v1 ，k v2 Control gain, which are positive +.>The position error signal of the trolley and the length error signal of the lifting rope are respectively;
and calculating in real time by using the self-adaptive fuzzy controller to obtain corresponding control driving force to drive the double-pendulum bridge crane to move so as to complete a control target.
2. The double-pendulum bridge crane adaptive fuzzy control method of claim 1, wherein fitting the uncertainty term with an adaptive fuzzy control system constructs an adaptive fuzzy controller comprising:
defining an error signal and determining a sliding mode surface based on the control target;
and fitting the uncertainty term by using an adaptive fuzzy control system, and constructing an adaptive fuzzy controller based on the fitted uncertainty term and a sliding mode surface.
3. The utility model provides a double pendulum bridge crane self-adaptation fuzzy control system which characterized in that includes:
a control target determining unit for determining a control target of the double-swing bridge crane system;
the control targets are that the trolley position and the lifting rope length are respectively converged to corresponding expected values, and two-stage swing angles are restrained; the two-stage swing angle comprises a lifting hook swing angle and a load swing angle;
an uncertainty item determining unit, configured to determine an uncertainty item including an actuator dead zone in the double-swing bridge crane system based on the control target and a kinematic model of the double-swing bridge crane system;
the kinematic model of the double pendulum bridge crane system is as follows:
wherein q a ＝[x l 1 ] Τ Represents a drivable state vector, x (t) represents trolley displacement, l 1 (t) represents the length of the hoist rope, the variable followed by (t) means that the variable is a time-dependent variable, most of the variables followed by (t) are omitted for ease of presentation,is q a Second derivative of>Represents a positive definite symmetric matrix, u= [ u ] 1 u 2 ] Τ Represents the driving force vector, u 1 Represents the driving force for translating the trolley, u 2 Represents a driving force for lifting and lowering a load, h= [ H ] 1 h 2 ] Τ Representing a vector of measurable components, T representing the lumped uncertainty vector of the system;
the kinematic model of the double-pendulum bridge crane system is calculated to be:
determining D as an uncertainty term containing an actuator dead zone in the double-pendulum bridge crane system;
the construction unit is used for fitting the uncertain term by using an adaptive fuzzy control system and constructing an adaptive fuzzy controller;
fitting the uncertainty term using an adaptive fuzzy control system, the fitted uncertainty term having the form:
wherein,represents a weight vector Γ ij (i=1, 2, j=1, 2,., 7) represents weights in the fuzzy logic system, are parameters to be estimated,represents the fuzzy basis function vector, ζ ij (i=1, 2, j=1, 2,.,. 7) represents a fuzzy basis function, τ represents a state vector, ε 1 ,ε 2 Represents approximation errors, and the upper bounds of the errors are +.>
The expression of the adaptive fuzzy controller is as follows:
wherein,respectively is gamma 1 ，Γ 2 Estimated value of ∈10->For slip form surface area, k 1 ，k 2 ，k p1 ，k p2 ，k v1 ，k v2 Control gain, which are positive +.>The position error signal of the trolley and the length error signal of the lifting rope are respectively;
and the driving unit is used for calculating corresponding control driving force in real time by utilizing the self-adaptive fuzzy controller to drive the double-pendulum bridge crane to move so as to finish a control target.
4. A computer device, comprising: a processor, a memory and a bus, said memory storing machine readable instructions executable by said processor, said processor and said memory communicating via the bus when the computer device is running, said machine readable instructions when executed by said processor performing the steps of the double swing bridge crane adaptive fuzzy control method of any of claims 1 to 2.
5. A computer readable storage medium, characterized in that the computer readable storage medium has stored thereon a computer program which, when executed by a processor, performs the steps of the double pendulum bridge crane adaptive fuzzy control method of any one of claims 1 to 2.
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