CN108828959A - A kind of novel bridge crane is anti-sway with position control method and device - Google Patents
A kind of novel bridge crane is anti-sway with position control method and device Download PDFInfo
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B66—HOISTING; LIFTING; HAULING
- B66C—CRANES; LOAD-ENGAGING ELEMENTS OR DEVICES FOR CRANES, CAPSTANS, WINCHES, OR TACKLES
- B66C13/00—Other constructional features or details
- B66C13/04—Auxiliary devices for controlling movements of suspended loads, or preventing cable slack
- B66C13/06—Auxiliary devices for controlling movements of suspended loads, or preventing cable slack for minimising or preventing longitudinal or transverse swinging of loads
- B66C13/063—Auxiliary devices for controlling movements of suspended loads, or preventing cable slack for minimising or preventing longitudinal or transverse swinging of loads electrical
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B66—HOISTING; LIFTING; HAULING
- B66C—CRANES; LOAD-ENGAGING ELEMENTS OR DEVICES FOR CRANES, CAPSTANS, WINCHES, OR TACKLES
- B66C13/00—Other constructional features or details
- B66C13/18—Control systems or devices
- B66C13/22—Control systems or devices for electric drives
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Abstract
A kind of novel bridge crane is anti-sway and position control method, including：Establish T-S nonlinear fuzzy model；According to T-S nonlinear fuzzy model, design of Fuzzy Controller is designed using parallel distributed compensation control (PDC) structure, obtains PDC control law u (t)；Feedback gain matrix F is calculated using the LMI with attenuation ratei.The controller can guarantee the closed loop asymptotic stability of system, have preferable positioning, anti-pendulum and interference free performance.The maximum pendulum angle loaded during trolley travelling is smaller, and payload is swung to be inhibited well, and pivot angle rapidly disappears after trolley reaches target position, and interference free performance does not change with the variation of desired locations and load quality, and robustness is stronger.
Description
Technical field
The present invention relates to crane technical fields, and in particular to a kind of novel bridge crane is anti-sway with location control side
Method and device.
Background technique
Bridge crane is the important work that production process mechanization, automation is realized in modern industrial production and lifting transport
Tool and equipment, are widely used in the places such as indoor and outdoor warehouse, workshop, port and pier, outdoor bin stock.The positioning of bridge crane and
Anti-swing control target is driving trolley, will load quickly, it is accurate, be safely transported to desired point, and reduce or eliminate as far as possible
The remaining pivot angle of load pivot angle and trolley stop motion back loading during transport, in case crane and surrounding objects touch
It hits, causes huge economic loss.
Bridge crane positioning and anti-sway control strategy are many kinds of, crane model when according to design controller,
Control method can be divided into two major classes：One kind is the control method based on linear mathematical model；One kind is based on nonlinear model
The control method of type.
Control method based on linear mathematical model is to design controller, this Linear Control plan according to linear control theory
It is slightly simple and be easily achieved, but since controller is designed based on linear mathematical model, system control performance is depended critically upon
The levels of precision of model, it is more sensitive to model parameter (such as rope length, magnitude of load) variation, in addition, it needs trolley lower
The speed of service and unpractical limitation is applied to crane operation.In order to overcome this deficiency, many other Linear Control sides
Method control strategy such as sliding formwork control, model-free fuzzy control, ANN Control are used in crane control.Although these
Control method helps to obtain better response characteristic, but there is also some disadvantages, tremble as controlled to export to exist in sliding formwork control
Vibration, system stability analysis is relatively difficult etc. when encountering particular constraints in model-free fuzzy logic control.
With the development of nonlinear control techniques, some researchers are on the basis of analysis crane nonlinear mathematical model
On, a series of non-linear control strategies are proposed, such as based on the control of energy/passivity, Non-linear coupling control method, feedback
Linearization technique, gain scheduling Nonlinear Model Predictive Control etc..However, the control effect of these control methods is different degrees of
On there are still certain deficiencies, such as：The maximum pendulum angle loaded in operational process is larger, overshoot is larger, anti-interference is not strong etc.
Disadvantage.
Summary of the invention
In view of the shortcomings of the prior art, the application provide a kind of novel bridge crane it is anti-sway with position control method with
Device has preferably positioning, anti-pendulum and interference free performance.
According in a first aspect, the application provides, a kind of novel bridge crane is anti-sway and position control method, including：
Establish T-S nonlinear fuzzy model；
According to T-S nonlinear fuzzy model, T-S design of Fuzzy Controller is carried out using parallel distributed compensation method, is obtained
PDC
Control law u (t)；
Feedback gain matrix F is calculated using the LMI with attenuation ratei。
In some embodiments, the control law
In some embodiments, the control rule is：
IF z1(t)is Nj and z2(t)is Rk；
THEN ui(t)=- FixmI=1 ... r, r=8.
In some embodiments, including：T-S nonlinear fuzzy model, the system mode of model are established using sector nonlinear
Equation is：
In some embodiments, feedback gain matrix Fi=QiP-1, P is positive definite matrix, P, QiMeet：
PAi T+AiP-Qi T Bi T-BiQi+ 2 α P < 0；α > 0, i=1,2 ..., r；；
In some embodiments,
According to second aspect, the application provides that a kind of novel bridge crane is anti-sway and position control device, including：
For establishing the module of T-S nonlinear fuzzy model；
For carrying out T-S design of Fuzzy Controller using parallel distributed compensation method according to T-S nonlinear fuzzy model,
It obtains
The module of PDC control law u (t)；
For feedback gain matrix F to be calculated using the LMI with attenuation rateiModule.
According to the third aspect, the application provides a kind of computer readable storage medium, which is characterized in that including program, institute
Stating program can be executed by processor to realize such as the described in any item methods of first aspect.
It is based on according to above-described embodiment since the present processes establish bridge crane T-S nonlinear fuzzy model
T-S nonlinear fuzzy model, using sector nonlinear modelling PDC fuzzy controller, and using the LMI meter with attenuation rate
Calculation obtains feedback gain matrix Fi, which ensure that the closed loop asymptotic stability of model, so that this method has preferably
Control effect has preferable positioning, anti-pendulum and interference free performance.The maximum pendulum angle loaded in operational process is smaller, effectively carries
Lotus swings to be inhibited well, and pivot angle rapidly disappears after trolley reaches target position, and interference free performance is not with desired position
The variation set and change, robustness is stronger.
Detailed description of the invention
Fig. 1 is two-dimentional bridge crane simplified model schematic diagram；
Fig. 2 is that the novel bridge crane of the application is anti-sway with position control method flow chart；
Fig. 3 is the former piece variable z of the embodiment of the present application1(t) subordinating degree function figure；
Fig. 4 is the former piece variable z of the embodiment of the present application2(t) category degree functional arrangement；
Fig. 5 is the former piece variable z of the embodiment of the present application3(t) subordinating degree function figure；
Fig. 6 is the simulation model figure of the bridge crane of the embodiment of the present application；
Fig. 7 is the displacement of trolley and the pivot angle of payload under the conditions of differential declines rate
Fig. 8 is that the fuzzy PD C controller and the fuzzy PD C based on sector nonlinear model based on Local approximation model control
The control effect simulation comparison figure of device；
Fig. 9 is traditional LMI based on linear model and the control of the LMI based on sector nonlinear model with attenuation rate effect
Fruit simulation comparison figure；
Figure 10 is the different expectation target x of trolleydUnder the conditions of simulation result；
Figure 11 is the simulation result diagram of payload mass variation；
Figure 12 is the simulation result diagram of rope lengths variation.
Specific embodiment
Below by specific embodiment combination attached drawing, invention is further described in detail.Wherein different embodiments
Middle similar component uses associated similar element numbers.In the following embodiments, many datail descriptions be in order to
The application is better understood.However, those skilled in the art can recognize without lifting an eyebrow, part of feature
It is dispensed, or can be substituted by other elements, material, method in varied situations.In some cases, this Shen
Please it is relevant it is some operation there is no in the description show or describe, this is the core in order to avoid the application by mistake
More descriptions are flooded, and to those skilled in the art, these relevant operations, which are described in detail, not to be necessary, they
Relevant operation can be completely understood according to the general technology knowledge of description and this field in specification.
It is formed respectively in addition, feature described in this description, operation or feature can combine in any suitable way
Kind embodiment.Meanwhile each step in method description or movement can also can be aobvious and easy according to those skilled in the art institute
The mode carry out sequence exchange or adjustment seen.Therefore, the various sequences in the description and the appended drawings are intended merely to clearly describe a certain
A embodiment is not meant to be necessary sequence, and wherein some sequentially must comply with unless otherwise indicated.
It is at present largely linear Design of Mathematical Model to the control method of Intelligent crane, it is this based on linear
The linear control strategies of model are simple and are easily achieved, but system control performance depends critically upon the levels of precision of model, to mould
Shape parameter (such as rope length, magnitude of load) variation is more sensitive.T-S fuzzy model can approach nonlinear system with arbitrary accuracy, can
The analysis and synthesis method in linear control theory to be applied wherein, so that external disturbance and Parameters variation are to control effect
Effect is significantly reduced, the robustness enhancing of system.Therefore there is important reality to the research of the fuzzy system based on T-S model
Meaning.
The application establishes T-S nonlinear fuzzy model on the basis of analyzing crane system nonlinear mathematical model, for
This nonlinear fuzzy model is based on PDC controlling plan design fuzzy controller, and is counted using linear matrix inequality (LMI)
Feedback gain matrix is calculated, to realize that bridge crane is anti-sway and positions.
With reference to Fig. 1, for two-dimentional bridge crane simplified model figure, in figure, M and m respectively indicate trolley quality and load matter
Amount, l are lifting rope length, and x is trolley displacement, and θ is the pivot angle loaded in the vertical direction, and F indicates to act on outer on crane
Power, FxAnd FlIt is to act in the horizontal direction with the external force on rope length direction respectively, g is acceleration of gravity.
With reference to Fig. 2, the application provide a kind of bridge crane based on LM I it is anti-sway with positioning nonlinear control method, should
Method includes：
Step 100：Establish T-S nonlinear fuzzy model；
Step 200：According to T-S nonlinear fuzzy model, T-S fuzzy controller is carried out using parallel distributed compensation method and is set
Meter, obtains PDC control law u (t)；
Step 300：Feedback gain matrix F is calculated using the LMI with attenuation ratei。
For step 100, the kinetic model of crane, the side Lagrange being established using Euler-Lagrange method
Journey is as follows：
Q in formulaiThe power being applied in system, xiIt is generalized coordinates or state variable, L is Lagrangian L=T-U,
T and U is the total kinetic energy and total potential energy of system respectively.
Consider movement of the bridge crane on two-dimensional surface, the total kinetic energy of system can be expressed as
Total potential energy is expressed as
U=mg (h-l cos θ) (3)
Wherein, ignore the quality and rigidity of wirerope, load is considered as a point mass.If rope length remains unchanged,
Bridge crane non-linear dynamic model is as follows：
Take state vectorThen state equation is as follows：
As can be seen from the above equation, bridge crane is a nonlinear system.The state side of any one nonlinear system
Journey can be expressed as follows：
In formula, x (t) indicates state vector, and u (t) indicates that dominant vector, A indicate that state matrix, B indicate control matrix.
T-S fuzzy model approximate representation is
In formula,
Z (t) refers to that system inputs, and is former piece variable；ωiRepresent the weight of the i-th rule, i=1,2 ... r, hiGeneration
The corresponding normalized weight of table, wherein
T-S nonlinear fuzzy model is established using sector nonlinear in the step 100 of some embodiments, the present embodiment.Formula
(6) there are five nonlinear terms in, are sinx respectively3, cosx3, x4 2, sinx3cosx3, 1/ ((M+m)-mcos2x3), using T-S mould
Fuzzy model needs 25Rule.In order to simplify mathematical model, the nonlinear terms in model are reduced, are enabled
F=(M+msin2x3)u-mg sin x3 cos x3-mlx4 2 sin x3 (10)
U is new control input in formula.
The mathematical model of formula (6) is reduced to
As can be seen from the above formula that nonlinear terms are respectively defined as z as former piece variable there are three in model1=sinx3,
z2=cos x3WithMeeting restrictive condition With sector nonlinear theory
In the case of, the corresponding subordinating degree function of former piece variable can be determined by following formula.
In formula
Again
By formula (12)-formula (15), it is as follows subordinating degree function can be calculated：
Fig. 3-Fig. 5 provides former piece variable z1(t)、z2(t) and z3(t) subordinating degree function figure.
According to formula (16)-(21), the kinetic model (6) of bridge crane existsWithConstraint
Under can be described as following formula：
In formula,Mi, NjAnd PkIt is former piece variable z respectively1(t)、z2(t) and z3(t) degree of membership letter
Number, u (t) is input quantity.
Assuming that all state variables of crane system can measure, it can be anti-for each sub-fuzzy system design point
Controller is presented, step 200 carries out T-S design of Fuzzy Controller using parallel distributed compensation (PDC) method, calculates using LMI anti-
Feedforward gain Fi.In PDC design, every control rule is designed according to the respective rule of T-S fuzzy model, i.e., designed
The former piece part of fuzzy controller and fuzzy model have identical fuzzy set.
If xdThe desired locations of trolley, xx-xdIt is position deviation, if xm=[x1-xd x2 x3 x4] ', is in order to enable trolley
It gets at up to desired position, control rule is as follows：
IF z1(t)is Nj and z2(t)is Rk,
THEN ui(t)=- FixmI=1 ... r, r=8. (23)
PDC control law is obtained by the weighted array of above-mentioned rule：
In some specific embodiments, 8 rules that can establish T-S fuzzy model are as follows：
Rule 1：
Rule 2：
Rule 3：
Rule4：
Rule 5：
Rule 6：
Rule 7：
Rule 8：
In the rule, each LINEAR CONTINUOUS equationReferred to as one " subsystem ", subsystem
Coefficient matrix is represented by respectively：
Formula (24) are substituted into formula (8), it is as follows to obtain closed-loop control system equation：
In formula, Gij=Ai-BiFj
Each " subsystem " to control controllability as follows：
(1) rank of matrix can be controlled
rank[Bi Ai*Bi Ai 2*Bi Ai 3*Bi]=4
(2) rank of matrix can be seen
rank[C*Bi C*Ai*Bi C*Ai 2*Bi C*Ai 3*Bi]=2
It can be seen that system is to control see, therefore can add feed back control system to system, so that system closed loop is steady
It is fixed.
In step 300, when determining feedback gain matrix using linear matrix inequality (LMI), in order to ensure system is steady
It is fixed, according to existing literature：The Fuzzy control systems of the K.Tanaka published and H.O.Wang chief editor in 2001
Design and analysis is directed to the following theorem that continuous control system provides.
Theorem 1：If there is a positive definite matrix P, meet with lower inequality
The then Continuous-time Fuzzy Control Systems asymptotically stable in the large of formula (25) description.
Above-mentioned inequality is not due to being linear matrix inequality there are unknown matrix/vector variable product
(LMI).In order to which the stable condition using theorem determines that the feedback oscillator Fi of control system, equation (26) are left and right respectively multiplied by P-1,
Redefine variable P=P-1With a new variable Qi=FiP, available linear matrix inequality below：
Matrix P and vector QiIt can be solved and be obtained by linear matrix inequality (27).If symmetric positive definite can be obtained
Matrix P can then guarantee the stability of system.
Feedback gain matrix can be calculated by following formula：
Fi=QiP-1 (28)
Using the LMIs and formula (28) feedback gain matrix can be readily available, but obtained feedback oscillator in formula (27)
Matrix be it is unique, it is different that system is surely made to obtain preferable control performance.In order to meet the actual requirement of system, the application is adopted
With the LMIs with attenuation rate α.The response speed of T-S Fuzzy control system is related with attenuation rate, can by changing attenuation rate parameter
So that system is preferably controlled out effect
Definition：For system (25), the Lyapunov function of selection is V (x (t))=xT(t) Px (t), P > 0, if it exists
Real number α > 0 meetsThen claim the system with attenuation rate α asymptotically stable in the large.
Theorem 2：For system (25), if real number α > 0, for all i, meet
With to all i < j, s.t hi∩hj≠ φ meets
Then claim the system with attenuation rate α asymptotically stable in the large.
Inequality (29) and (30) are left and right respectively multiplied by P-1, redefine variable P=P-1With a new variable Qi=
FiP, available linear matrix inequality below：
PAi T+AiP-Qi T Bi T-BiQi0 α > 0, i=1,2 ..., r of+2 α P <；(31)
Matrix P and vector QiUseable linear MATRIX INEQUALITIES (31) and (32), which solve, to be obtained.
Correspondingly, the application also provides that a kind of novel bridge crane is anti-sway and position control device, the device include：
For establishing the module of T-S nonlinear fuzzy model；
For carrying out T-S design of Fuzzy Controller using parallel distributed compensation method according to T-S nonlinear fuzzy model,
Obtain the module of PDC control law u (t)；
For feedback gain matrix F to be calculated using the LMI with attenuation rateiModule.
Correspondingly, the application also provides a kind of computer readable storage medium, including program, and described program can be processed
Device is executed to realize that the bridge crane based on LM I is anti-sway with positioning nonlinear control method.
In order to prove the validity of the application method, below with existing based on Local approximation model control method and being based on
Traditional LMI of linear model is compared.
Wherein, based on Local approximation model control method be at 0 ° and ± 45 ° of three operating points it is non-linear to crane
Model is linearized, and corresponding linearized state-space model is obtained.For formula (7),
State-space model at 0 ° isWherein
The state-space model of bridge crane at 45 °：
Using Triangleshape grade of membership function, the Local approximation model of bridge crane is as follows：
The application is emulated using MATLAB, and verifying provides the validity of method.Fig. 6 gives the bridge of formula (6) expression
The simulation model for the fuzzy PD C controller that formula crane dynamic model and formula (24) indicate, in simulations, the target position of trolley
It is arranged to xd=0.6m.In order to verify the interference free performance of system, trolley gives system one impulse disturbances of increase after stablizing.Under
Face is discussed by the simulation result in the case of four kinds.
Situation 1：The case where differential declines rate α value is discussed.
Response speed is related with attenuation rate α, and the position of the trolley in different α values is set forth in Fig. 7 (a) and Fig. 7 (b)
Move the pivot angle with payload.As can be seen that α value is bigger in Fig. 7, dynamic respond speed is faster, and anti-interference ability is stronger, but has
It is bigger to imitate load pivot angle.Therefore, the application selects α=0.53.
Situation 2：Comparative studies.
Firstly, by according to Local approximation modelling with 2 rules the fuzzy PD C controller with it is non-thread based on sector
Property modelling the control effect of the fuzzy PD C controller with 8 rules be compared, two kinds of situations are all made of band decaying
The LMI of rate calculates feedback gain matrix, is according to the feedback oscillator that formula (31) and (32) calculate 8 rules
F1=[17.7510 32.9452-175.0808-1.7266]
F2=[17.7554 32.9467-175.1205-1.7257]
F3=[18.5326 34.7355-190.4480-4.2406]
F4=[18.5275 34.7206-190.4016-4.2411] (34)
F5=[19.1524 35.4767-188.3394-1.3522]
F6=[19.1548 35.4745-188.3598-1.3512]
F7=[20.9061 39.0106.-212.2236-3.5317]
F8=[20.8961 38.9868-212.1307-3.5330]
The gain matrix of two rules is
F1=[24.4625 30.4433-63.5695-14.4929]
F2=[37.9780 47.7883-183.1461-18.1274] (35)
Simulation result in the case of two kinds is as shown in Figure 8.Fig. 8 show trolley displacement, speed and load pivot angle and
Pivot angle velocity-response curve figure, table 1 provide specific comparison result.
1 performance indicator of table compares
It can be seen from the graph that there are 2 rule the fuzzy PD C controller phases with based on Local approximation modelling
Than, when using based on sector nonlinear modelling with 8 rule the fuzzy PD C controller, when the trolley travelling time is the same,
The maximum pendulum angle loaded in operational process is smaller, and does not have overshoot.
Secondly, by being obtained using traditional LMI based on linear model and based on sector nonlinear model with the LMI of attenuation rate
To feedback oscillator be respectively used to bridge crane nonlinear system control in be compared research, simulation result such as Fig. 9 institute
Show.Detailed quantification result when table 2 is provided using two methods.
The comparison that system responds in the case of 2 two kinds of table
Simulation result shows that two kinds of LMI control methods can guarantee that there is no Residual oscillations in target position load.So
And compared with traditional linear LMI, the controller of the application design has preferably positioning, anti-pendulum and interference free performance.
Situation 3：Different transportation ranges.
In order to verify control performance of the present processes under different transportation ranges, x has been selected respectivelyd=0.4m, xd=
0.6m and xd=0.8m, xd=1.0m.Figure 11 gives the simulation result in the case of four kinds.
Simulation result shows that during transportation trolley can accurately achieve predetermined position, and payload swings to obtain
Inhibit well, pivot angle is between [- 5 °, 5 °], and pivot angle rapidly disappears after trolley reaches target position, and interference free performance is not
Change with the variation of desired locations.
Situation 4：Robustness Study when load quality variation and long change of rope.
Load quality and rope length are two important parameters for influencing system performance, in practical application in industry, different fortune
Defeated task needs to change load quality or rope lengths.Therefore need to consider the Shandong of the controller in the two Parameters variations
Stick.The application gives payload mass in Figure 11 and Figure 12 respectively and changes to 8kg from 2kg, and rope lengths are from 0.5m
Change to the simulation result of 0.85m.
As seen from Figure 11, when load quality changes, the rapidity and payload swing angle of trolley all do not have
It changes.As can see from Figure 12, when rope length reduces, the rapidity variation of trolley is little, payload swing angle
Increase, but angle is in the range of control performance allows.But when two Parameters variations, AF panel performance does not change.
The result shows that this method has stronger robustness to the variation of payload mass and rope lengths, have in practical applications
It is significant.
In conclusion the present processes establish bridge crane T-S nonlinear fuzzy model, it is non-linear based on T-S
Fuzzy model is calculated instead using sector nonlinear modelling PDC fuzzy controller, and using the LMI with attenuation rate
Feedforward gain matrix Fi, which ensure that the closed loop asymptotic stability of model, have a preferable control effect, in operational process
The maximum pendulum angle of load is smaller, has preferably positioning, anti-pendulum and interference free performance, payload is swung to be pressed down well
System, pivot angle rapidly disappears after trolley reaches target position, and interference free performance does not change, robust with the variation of desired locations
Property is stronger.Simulation results show the validity of this method.
It will be understood by those skilled in the art that all or part of function of various methods can pass through in above embodiment
The mode of hardware is realized, can also be realized by way of computer program.When function all or part of in above embodiment
When being realized by way of computer program, which be can be stored in a computer readable storage medium, and storage medium can
To include：It is above-mentioned to realize to execute the program by computer for read-only memory, random access memory, disk, CD, hard disk etc.
Function.For example, program is stored in the memory of equipment, when executing program in memory by processor, can be realized
State all or part of function.In addition, when function all or part of in above embodiment is realized by way of computer program
When, which also can store in storage mediums such as server, another computer, disk, CD, flash disk or mobile hard disks
In, through downloading or copying and saving into the memory of local device, or version updating is carried out to the system of local device, when logical
When crossing the program in processor execution memory, all or part of function in above embodiment can be realized.
Use above specific case is illustrated the present invention, is merely used to help understand the present invention, not to limit
The system present invention.For those skilled in the art, according to the thought of the present invention, can also make several simple
It deduces, deform or replaces.
Claims (8)
1. a kind of novel bridge crane is anti-sway and position control method, which is characterized in that including：
Establish T-S nonlinear fuzzy model；
According to T-S nonlinear fuzzy model, T-S design of Fuzzy Controller is carried out using parallel distributed compensation method, obtains PDC control
System rule u (t)；
Feedback gain matrix F is calculated using the LMI with attenuation ratei。
2. the method as described in claim 1, which is characterized in that the control law
3. the method as described in claim 1, which is characterized in that the control rule is：
IF z1(t) is Nj and z2(t) is Rk；
THEN ui(t)=- FixmI=1 ... r, r=8.
4. the method as described in claim 1, which is characterized in that including：T-S nonlinear smearing mould is established using sector nonlinear
The system state equation of type, model is：
5. the method as described in claim 1, which is characterized in that feedback gain matrix Fi=QiP-1, P is positive definite matrix, P, QiIt is full
Foot:
PAi T+AiP-Qi TBi T-BiQi+ 2 α P < 0；α > 0, i=1,2 ..., r；；
PAi T+AiP+PAj T+AjP-Qi TBj T-BiQj-Qj TBi T-BjQi+4αP≤0；s.t.hi∩hj≠φ。
6. apparatus/method as claimed in claim 6, which is characterized in that
P is positive definite symmetric matrices.
7. a kind of novel bridge crane is anti-sway and position control device, it is characterised in that including：
For establishing the module of T-S nonlinear fuzzy model；
For carrying out T-S design of Fuzzy Controller using parallel distributed compensation method, obtaining according to T-S nonlinear fuzzy model
The module of PDC control law u (t)；
For feedback gain matrix F to be calculated using the LMI with attenuation rateiModule.
8. a kind of computer readable storage medium, which is characterized in that including program, described program can be executed by processor with reality
Now such as method of any of claims 1-6.
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| CN112160864A (en) * | 2020-10-28 | 2021-01-01 | 山东科技大学 | Classic inhibition formula wind turbine blade structure and inhibition system that flutters |
| CN113595387A (en) * | 2021-07-30 | 2021-11-02 | 厦门理工学院 | Buck-type converter sliding mode prediction control method, terminal equipment and storage medium |
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