CN105867136A - Parameter identification based multi-motor servo system synchronization and tracking control method - Google Patents

Parameter identification based multi-motor servo system synchronization and tracking control method Download PDF

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CN105867136A
CN105867136A CN201610322184.2A CN201610322184A CN105867136A CN 105867136 A CN105867136 A CN 105867136A CN 201610322184 A CN201610322184 A CN 201610322184A CN 105867136 A CN105867136 A CN 105867136A
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motor
parameter
error
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normal number
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任雪梅
赵威
王树波
王敏林
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Beijing Institute of Technology BIT
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    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
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Abstract

The invention relates to a parameter identification based multi-motor servo system synchronization and tracking control method. The parameter identification based multi-motor servo system synchronization and tracking control method comprises the steps that 1, a multi-motor driven servo system containing unknown parameters is analyzed, and a mathematic model of the multi-motor driven servo system containing unknown parameters is established according to a motor structure and a physical law; 2, a load model established in the step 1 is analyzed, and unknown parameters in the load are estimated by utilizing a variable-gain self-adaptive parameter identification method; 3, synchronization and tracking control is conducted on the multi-motor driven servo system by utilizing neural network integral sliding-mode control algorithm according to a parameter identification result obtained in the step 2. The control method can ensure the steady-state accuracy of synchronization and tracking, effectively ensure transient-state and steady-state performance of parameter estimation, decrease the complexity and calculated quantity of algorithm design and effectively improves the response speed and robustness of the multi-motor driven servo system.

Description

Many motor servo systems based on parameter identification synchronize and tracking and controlling method
Technical field
The invention belongs to technical field of electromechanical control, in particular to a kind of many motor servos based on parameter identification System synchronization and tracking and controlling method.
Background technology
Along with society and industrial developing rapidly, high-power and large driving force equipment demand is also being continuously increased. Due to technology and the limitation of cost, powerful single electric system is difficult to manufacture, and this causes single motor to drive the most not High-power system demand in actual production can be met.In view of the feature that multi-motor driving overload capacity is strong, frequently with many Platform motor combines the method for driving load to solve the problems referred to above.In multi-motor driving servosystem, unknown systematic parameter The vibration of control system can be caused, have a strong impact on tracking accuracy and the performance of servosystem.This makes to utilize traditional controller It is difficult to ensure that many motor servo systems obtain good control effect.How to ensure many motor servo systems high precision tracking and Fast synchronization controls to have had become as a hot issue.
Unknown parameter is the problem being widely present in servosystem and has a negative impact accurate control of system.Unknown The existence of parameter can cause the shake of tracking signal thus affect the dynamic characteristic of system.Additionally, bigger tracking can be produced by mistake Differ from thus affect its steady-state characteristic.In order to solve unknown parameter, servosystem is followed the tracks of and the impact of synchronization accuracy, need design Parameter identification strategy.Research worker successively proposes many kinds of parameters discrimination method, such as classical gradient descent method, method of least square And particle swarm optimization etc..Wherein, method of least square is capable of accurately parameter estimation, it has also become be most frequently with in reality A kind of parameter identification method.But, existing these methods overwhelming majority the most only studies high-precision Parameter Estimation Problem, it is possible to Realize finite time simultaneously and high-precision discrimination method there is not yet invention and mentioned.
Synchronization Control, as a root problem of multi-motors drive system, is the principal element affecting systematic function.Electricity Asynchronous meeting between machine causes the collision of transmission link, thus produces bigger tracking error, and the damage of equipment even occurs.Often Synchronisation control means have master-slave synchronisation, cross-couplings synchronization etc..The output speed of master-slave synchronisation policy mandates mair motor is made For from the speed reference of motor, but when load is undergone mutation, the synchronization accuracy between each motor can not be guaranteed. Cross-coupling control be using motor between speed discrepancy as feedback signal back to the input of each motor, it is achieved same between motor Step.Compared to master & slave control, the method can quickly respond the change of each motor, thus it is same that high accuracy is better achieved Step controls.Li etc. propose a kind of Sliding mode controller based on cross-couplings strategy and achieve the synchronization driving between centers more. Cross-couplings strategy is combined by Xiao etc. with optimal algorithm, it is ensured that the energetic optimum of Synchronization Control.Although said method is all Achieve Synchronization Control, but they the most individually have studied the stationary problem driving between centers, and do not consider what system exported Accurate tracking.Therefore, the present invention proposes a kind of new control algolithm, and the method can efficiently solve load tracking and motor Coupled problem between synchronization, realizes accurate tracking and the Fast synchronization of motor of load simultaneously.
Summary of the invention
The invention aims to realize during many motor servo systems control the high precision tracking loaded and electricity The Synchronization Control of machine, proposes many motor servo systems based on parameter identification and synchronizes and tracking and controlling method.
The ultimate principle of the inventive method is: utilize variable-gain auto-adaptive parameter discrimination method to the unknown in load system Parameter carries out the estimation of finite time, thus preferably approaching to reality parameter, it is advantageously implemented accurately control.In order to solve load Follow the tracks of the coupled problem with motor in synchrony, utilize adjacency matrix to set up the synchronous error relation between motor, and devise broad sense coupling Close error.Propose integral sliding mode control on this basis, it is ensured that multi-machine system Fast synchronization and the high precision tracking of load Control.
For achieving the above object, the technical solution adopted in the present invention is as follows:
A kind of many motor servo systems based on parameter identification synchronize and tracking and controlling method, comprise the following steps: step 1, the multi-motor driving servosystem containing unknown parameter is analyzed, according to structure and the physical law of motor, sets up containing not Know the mathematical model of the multi-motor driving servosystem of parameter；Step 2, is analyzed the load module set up in step 1, And utilize variable-gain auto-adaptive parameter identification method that the unknown parameter in load is estimated；Step 3, joins according to step 2 gained Number identification result, utilizes neutral net integral sliding mode control algorithm, many motor servo systems is carried out synchronization and tracking control.
Further, step 1 includes: set up model
Wherein,
fi=β1(tanh(β2x4i)-tanh(β3x4i))+β4tanh(β5x4i)+β6x4i (3)
Wherein, x1=θl,x3i=θmi,θmi(i=1,2 ... n) and θlRespectively represent drive end and The corner of load end；WithRepresent drive end and the rotating speed of load end respectively；WithPoint Biao Shi drive end and the acceleration of load end；zi(t)=θi(t)-θmT () represents drive end and the differential seat angle of load end；J table Show the rotary inertia driving motor；JlRepresent the rotary inertia of load end；blFor connecting the viscosity of gear；a1=1/Jl,a2 =bl/Jl,a3=1/J；uiExpression system input torque；ω represents biasing moment；τiT () represents power of transmitting between motor and load Square；fiRepresent the moment of friction driving motor；T represents the time started from signal input；β1,β2,β3,β4,β5,β6It is unknown Constant；And ν is normal number.
Further, step 2 includes:
Step 21, load system is rewritten into the form of following linear parameterization
Wherein, δ=[a1k,a1kα,a2]TRepresent unknown parameter vector,Represent Know function；
Step 22, defines x respectively2It is x with the first-order filtering value of ρfAnd ρf, its expression formula is
Wherein, kfIt it is a normal number；
Design filtering matrix P ∈ R3×3With Q ∈ R3×1It is made to meet respectively
Wherein, O3With 03Representing 3 rank null matrix and null vectors respectively, l is normal number；Formula (6) is solved
Step 23, Design assistant error system S is:
Wherein, parameter estimating error isBy formula (8) it can be seen that the estimation difference of parameter can be by assisting System S represents；Therefore, the adaptive rate that design parameter is estimated is
Wherein, positive definite symmetric matrices Γ ∈ R3×3For permanent gain, l is time-varying gain
And reFor normal number；
Given normal numberAnd γ, work as vectorMeet persistent excitation condition,
Wherein, gain matrix Γ meets
Wherein, normal numberMeetAndThen it is capable of parameter estimation by mistake DifferenceFinite time convergence control, convergence time is
Wherein,
Further, step 3 includes:
Step 31, makes x1T () is the output signal of system, ydT () is reference signal, then tracking error et(t)=x1(t)- ydT (), obtains the differential of error, second differential is respectively as follows:
To tracking error etCarry out changing
Wherein, λ1For normal number, formula (16) can obtain, work as stWhen tending to 0, tracking error etT () converges to 0；
WhenTime, stConverge to 0, wherein, it is desirable to positionExpression formula is
And κ1,κ2＞ 0 is controller gain； WithIt is respectively parameter alpha, a1K and a2Estimated value；
Step 32, designs neutral net integral sliding mode control device, it is achieved the synchronization of motor and guarantee x3iT () converges onFirst definition motor position x3i(t) and desired locationsBetween error be
Additionally, the position synchronous error using Graph Theory to define motor is
Wherein, N is the set of motor, the adjacency matrix A=[a of connectionij]∈Rn×nFor describing the synchronization between motor Relation, it is defined as follows: aij＞ 0 represents that motor i and j exists relation, aij=0 represents that motor i and j is irrelevant, defines a in additionii =0；
Step 33, for ensure multi-machine system can Fast synchronization and realize high-precision load tracking, design broad sense Coupling error is
Wherein,biIt it is a normal number；
Can obtain according to Graph Theory, Generalized Coupled error σiWith anticipation error eiMeet following equalities
Wherein, B=diag{bi}∈Rn×n, L=[lij]∈Rn×nBe Laplacian Matrix andlij=- aij, i ≠ j, D ∈ Rn×nL=D-A is met for indegree matrix；
Step 34, for ensureing σi=0, design following Integral Sliding Mode face
And function phiiFor
Wherein, constant r ＞ 0 is storage gain,I=1,2,3 is normal number；
Neutral net integral sliding mode control device uiIt is expressed as
Wherein, κ3,κ4,∈i＞ 0 is controller gain,It is the estimation weights of neutral net, ΦiFor its basic function；
Additionally, the adaptivity turnover rate of neutral net is defined as
Wherein, κaIt it is a normal number；According to control law ui, multi-motor driving servosystem can be carried out synchronize with Track controls.
Control method of the present invention has the advantages that:
1, in many motor servo systems, the accurately control of system can be caused huge obstruction by the existence of unknown parameter. For solving this problem, the present invention devises auto-adaptive parameter identification algorithm based on variable-gain, it is achieved thereby that load the unknown The finite time of parameter is estimated.Additionally, this algorithm can ensure transient state and the steady-state behaviour of parameter estimation effectively, including: Big overshoot, minimum convergence rate and maximum steady state error.
2, the present invention is directed to motor in synchrony and the coupled problem of load tracking in multi-motor driving servosystem, based on adaptive Answer parameter identification method to devise integral sliding mode control device, merge synchronous error and with tracking error thus propose Generalized Coupled by mistake Difference σi, describe the degree synchronized and follow the tracks of well and solve multi-drive synchronization and the coordination problem of tracing control.By using Generalized Coupled error σi, original complicated coupling control problem (i.e. motor in synchrony and load tracking couple) is successfully converted For error σiConvergence problem, this significantly reduces algorithm design complexity and amount of calculation.
3, considering synchronization and the tracing control of many motor servo systems while carrying out parameter identification, design integration is sliding Modulo n arithmetic, effectively eliminates the singularity problem that general sliding formwork exists.Additionally, this algorithm ensure that the stable state synchronizing and following the tracks of Precision, realizes the tracing control of quick and little overshoot simultaneously.The present invention can make multi-machine system have preferable mapping, effectively Improve response speed and the robustness of multi-motor driving servosystem.
Reaching, compared to separately two kinds of controllers of design, the purpose synchronizing with following the tracks of, the method is for each motor only A controller need to be designed, thus be effectively reduced influencing each other between synchronization and tracing control, save the energy of controller Consumption.
Accompanying drawing explanation
The accompanying drawing of the part constituting the application is used for providing a further understanding of the present invention, and the present invention's is schematic real Execute example and illustrate for explaining the present invention, being not intended that inappropriate limitation of the present invention.In the accompanying drawings:
Fig. 1 is many motor servo control system structure chart of the present invention；
Fig. 2 is parameter a in detailed description of the invention1The identification curve chart of k；
Fig. 3 is parameter a in detailed description of the invention1The identification curve chart of k α；
Fig. 4 is parameter a in detailed description of the invention2Identification curve chart；
Fig. 5 is the tracking utilizing neutral net integral sliding mode control device in detailed description of the invention under auto-adaptive parameter identification Design sketch；
Fig. 6 is the tracking utilizing neutral net integral sliding mode control device in detailed description of the invention under auto-adaptive parameter identification Error Graph；
Fig. 7 is to utilize four drivings in neutral net integral sliding mode control device four motor servo system in detailed description of the invention The synchronous effect figure of motor；
Fig. 8 is to utilize four drivings in neutral net integral sliding mode control device four motor servo system in detailed description of the invention The synchronous error figure of motor.
Detailed description of the invention
In order to the purpose of the present invention and advantage are better described, below in conjunction with the accompanying drawings with embodiment to the method for the invention It is further elaborated.
A kind of many motor servo systems based on parameter identification synchronize and tracking and controlling method, comprise the following steps:
Step 1, is analyzed the multi-motor driving servosystem containing unknown parameter, and according to modelling by mechanism method, root According to structure and the physical law of motor, set up the mathematical model of the multi-motor driving servosystem containing unknown parameter.Specific as follows:
According to modelling by mechanism method, according to structure and the physical law of motor, set up the multi-motor driving containing unknown parameter The mathematical model of servosystem is as follows:
Wherein, θmi(i=1,2 ... n) and θlRepresent drive end and the corner of load end respectively；With Represent drive end and the rotating speed of load end respectively；WithRepresent drive end and the acceleration of load end respectively；J Represent the rotary inertia driving motor；JlRepresent the rotary inertia of load end；blFor connecting the viscosity of gear；uiRepresent system System input torque；ω represents biasing moment；τiT () represents transmission torque between motor and load；fiRepresent the friction driving motor Moment；T represents the time started from signal input；I=1,2 ... n represents driving motor 1 to the n of multi-machine system.
In formula (27), gear drive moment τiT () is represented by:
τi(t)=kf (zi(t))
(28)
Wherein, k is the torque coefficient of gear, f (zi(t)) it is dead-time voltage function, it is expressed as:
Wherein, α is backlash width, zi(t)=θmi(t)-θlT () is the differential seat angle of drive end and load end.Known functionIt is defined as
Wherein, ν is design parameter and ν ＞ 0.
Additionally, use continuous print friction model to describe moment of friction in formula (27)
Wherein, β1,β2,β3,β4,β5,β6It it is unknown constant.
Definition load and the position of motor and speed are state variable x respectively1,x2,x3i,x4i,
Then the state equation of system is rewritable is:
Wherein,
In said system, all systematic parameters are all unknown, including: a1,a2,a3,α,k,β1,β2,β3,β4, β5,β6.It is discussed below and how to utilize variable-gain auto-adaptive parameter discrimination method that the unknown parameter in load is estimated.
Step 2, utilizes the unknown parameter in variable-gain auto-adaptive parameter discrimination method load module set up to step 1 to enter Row identification；
Step 21, the load system in step 1 can be to be rewritten into the form of following linear parameterization
Wherein, δ=[a1k,a1kα,a2]TRepresent unknown parameter vector,Represent Know function.
Step 22, for system (34), defines x respectively2It is x with the first-order filtering value of ρfAnd ρf, its expression formula is
Wherein, kfIt it is a normal number.
Design filtering matrix P ∈ R3×3With Q ∈ R3×1It is made to meet respectively
Wherein, O3With 03Represent 3 rank null matrix and null vectors, constant l ＞ 0 respectively.Below, are quadratured in formula (36) both sides Can obtain
Convolution (34), (35), (36) and formula (37) are it can be seen that filtering matrix P and Q meets following equalities
Q=P δ (38)
Step 23, defined parameters estimation difference isAccording to the relation of P and Q, Design assistant error system S For:
By formula (39) it can be seen that the estimation difference of parameter indirectly can be represented by aid system S.Convolution (39) Take following auto-adaptive parameter Identification Strategy, it is achieved the finite time of parameter is estimated
Wherein, Γ ∈ R3×3Being positive definite symmetric matrices, l is time-varying gain
And reFor normal number.
Work as vectorMeet persistent excitation condition,
Wherein,It is normal number with γ, I3It is 3 rank unit matrixs.
Can be obtained by finite time convergence control theory, if selection gain matrix Γ is
Wherein, normal numberMeetAndThen the method is capable of parameter Estimation differenceFinite time convergence control, and convergence time is
Wherein,
Additionally, variable-gain adaptive parameter estimation algorithm (40) can ensure the transient state of parameter estimation and stability effectively Can, including the overshoot upper bound of estimation difference, the lower bound of rate of convergence and the maximum steady state error of parameter estimation.
The synchronization and the load output tracking that how to utilize integral sliding mode control device ensure motor is discussed below.
Step 3, the parameter identification result obtained according to step 2, utilize neutral net integral sliding mode control algorithm, it is achieved many Motor drives servosystem to synchronize and tracing control.
Parameter identification result based on step 2, the present invention use adjacency matrix definition Generalized Coupled error solve synchronize with The complicated coupling problem of tracing control.On this basis, utilize neutral net Integral Sliding Mode strategy, design multi-motor driving servo The control algolithm of system, so that multi-machine system both can guarantee that the speed sync of motor, can guarantee that again the accurate of load end Follow the tracks of.
Step 31, it is considered to the tracking performance of system, if x1T () is the output signal of system, ydT () is the reference letter of system Number, then tracking error et(t)=x1(t)-ydT (), obtains the differential of error, second differential is respectively as follows:
For the ease of design controller, to tracking error etCarry out changing
Wherein, λ1For normal number.Can be obtained by formula (47), work as stWhen tending to 0, tracking error etT () converges to 0.
In order to ensure transformed error stConverge to 0, formula (47) is solved and can obtain, works as x3iT () meets Time,I.e. reach stConverge to the purpose of 0, wherein, it is desirable to positionExpression formula is
And κ1,κ2＞ 0 is controller gain； WithIt is respectively parameter alpha, a1K and a2Estimated value, can be by step The parameter estimation of 2 draws.In addition, it is contemplated that external disturbance and the existence of parameter estimating error, by continuous function-κ2tanh(st) It is incorporated in formula (48) as robust item, to reach to eliminate Bounded Perturbations and the effect of estimation difference.
Step 32, as the above analysis, whenTime, the output tracking error of load converges to 0.Below, will Neutral net integral sliding mode control device is designed, it is achieved the synchronization of motor and guarantee x according to this result3iT () tends toFirst First definition motor position x3i(t) and desired locationsBetween error be
Additionally, in order to realize the synchronization between motor further, the position synchronous error using Graph Theory to define motor is
Wherein, N represents the set of motor, the adjacency matrix A=[a of connectionij]∈Rn×nSame for describe between motor Step relation, it is defined as follows: aij＞ 0 represents that motor i and j exists relation, aij=0 represents that motor i and j is irrelevant, defines in addition aii=0.
Step 33, in order to ensure multi-machine system Fast synchronization and realize high precision load tracing control, it would be desirable to by mistake Difference (49) and synchronization coupling error (50) combine, and design Generalized Coupled error is
Wherein,biIt it is a normal number.
Can obtain according to Graph Theory, Generalized Coupled error (51) and anticipation error (49) meet following equalities
Wherein, B=diag{bi}∈Rn×n, L=[lij]∈Rn×nBe Laplacian Matrix andlij=- aij, i ≠ j, D ∈ Rn×nL=D-A is met for indegree matrix.Due to adjacency matrix A be connection, can obtain matrix L+B be positive definite and Reversible.
By formula (53) it can be seen that Generalized Coupled error σiWith anticipation error eiIt is of equal value, i.e. works as σiWhen=0, eiConvergence To 0, then system can be realized as synchronizing and tracing control.Being changed by above-mentioned error, original complicated coupling problem is converted For Generalized Coupled error σiConvergence problem, this significantly reduces difficulty and the complexity of calculating.
Step 34, in order to ensure σi=0, design following Integral Sliding Mode face
And function phiiIt is defined as
Wherein, constant r ＞ 0,I=1,2,3 is normal number.
So, sliding formwork siFirst differential can be expressed as
Here, unknown nonlinear functionAnd there is footpath Meet to base neural net
Wherein, Wi *For neutral net ideal weight and meet | | Wi *||≤WN, Φi() represents RBF, εi It is approximate error, vector x3=[x31,…,x3n]T, x4=[x41,…,x4n]T。
The design of neutral net integral sliding mode control device presented below realizes sliding formwork siConvergence, control law uiIt is expressed as
Wherein, κ3,κ4,∈i＞ 0 is controller gain,It is Wi *Estimated value.In controller (58),For Neutral net item is used for approaching and compensate unknown nonlinear Ri, and robust item-κ4tanh(∈isi) be used for suppress external disturbance and The approximate error of neutral net.
Additionally, the adaptivity turnover rate of neutral net is defined as
Wherein, κaIt it is a normal number.
Work as siLevel off to 0 time, by choosing suitable parameterI=1,2,3, it is micro-that formula (54) can be changed into Nonlinear Tracking Divide the form of device, i.e. approximate velocity optimum control, thus realize σiThe quickly convergence of non-overshoot.According to control law ui, to many motors Drive servosystem to carry out synchronizing and tracing control, be achieved in the purpose of the present invention and original intention.
Above-mentioned result is emulated, obtains parameter identification, tracking effect and synchronous effect figure.Watch at four motors Take in the synchronized tracking emulation experiment of drive system, drive motor, load and the parameter that rubs is as shown in table 1.
Table 1 simulation parameter
To neutral net integral sliding mode control algorithm based on variable-gain auto-adaptive parameter identification under the above parameter of electric machine Emulate.To loading the identification result of unknown parameter as shown in Figure 2, Figure 3, Figure 4.Fig. 5 and Fig. 6 is sinusoidal signal tracking effect Figure, Fig. 7 and Fig. 8 is four motor in synchrony design sketchs.From analogous diagram, variable-gain auto-adaptive parameter discrimination method has quickly Estimating speed and the highest estimated accuracy, neutral net integral sliding mode control utensil has good mapping and stability Energy.From simulation result, the control algolithm of the present invention has the highest tracking performance and net synchronization capability, can make four electric systems Synchronize quickly and with high precision tracking input signal.
The present invention considers the many motor servo systems containing unknown parameter and synchronizes and tracking control problem.Design variable-gain Auto-adaptive parameter discrimination method, can estimate the unknown parameter in load well, and this model is possible not only to realize finite time Parameter estimation, and there is good transient state and steady-state behaviour.Neutral net Integral Sliding Mode is designed based on parameter identification result Controller, and Generalized Coupled error is proposed, can efficiently solve and simplify the coupled problem synchronizing with following the tracks of, and ensure simultaneously Multi-motor driving servosystem can Fast synchronization and high-precision tracking.Be can be seen that by emulation experiment, the inventive method has Well control performance.
The foregoing is only the preferred embodiments of the present invention, be not limited to the present invention, for the skill of this area For art personnel, the present invention can have various modifications and variations.All within the spirit and principles in the present invention, that is made any repaiies Change, equivalent, improvement etc., should be included within the scope of the present invention.

Claims (4)

1. many motor servo systems based on parameter identification synchronize and tracking and controlling method, it is characterised in that described method Comprise the following steps:
Step 1, is analyzed the multi-motor driving servosystem containing unknown parameter, according to structure and the physical law of motor, Set up the mathematical model of the multi-motor driving servosystem containing unknown parameter；
Step 2, is analyzed the mathematical model set up in step 1, and utilizes variable-gain auto-adaptive parameter identification method logarithm The unknown parameter learned in model is estimated；
Step 3, according to step 2 parameters obtained identification result, utilizes neutral net integral sliding mode control algorithm, to many motor servos System carries out synchronization and tracking control.
Control method the most according to claim 1, it is characterised in that described step 1 includes: set up model
Wherein,
fi=β1(tanh(β2x4i)-tanh(β3x4i))+β4tanh(β5x4i)+β6x4i (3)
Wherein,θmi(i=1,2 ... n) and θlRepresent drive end respectively and bear Carry the corner of end；WithRepresent drive end and the rotating speed of load end respectively；WithRespectively Represent drive end and the acceleration of load end；zi(t)=θi(t)-θmT () represents drive end and the differential seat angle of load end；J represents Drive the rotary inertia of motor；JlRepresent the rotary inertia of load end；blFor connecting the viscosity of gear；a1=1/Jl,a2= bl/Jl,a3=1/J；uiExpression system input torque；ω represents biasing moment；τiT () represents power of transmitting between motor and load Square；fiRepresent the moment of friction driving motor；T represents the time started from signal input；β1,β2,β3,β4,β5,β6It is unknown Constant；And ν is normal number.
Control method the most according to claim 1, it is characterised in that described step 2 includes:
Step 21, load system is rewritten into the form of following linear parameterization
Wherein, δ=[a1k,a1kα,a2]TRepresent unknown parameter vector,Represent known letter Number；
Step 22, defines x respectively2It is x with the first-order filtering value of ρfAnd ρf, its expression formula is
Wherein, kfIt it is a normal number；
Design filtering matrix P ∈ R3×3With Q ∈ R3×1It is made to meet respectively
Wherein, O3With 03Representing 3 rank null matrix and null vectors respectively, l is normal number；Formula (6) is solved
Step 23, Design assistant error system S is:
Wherein, parameter estimating error isBy formula (8) it can be seen that the estimation difference of parameter can be by aid system S represents；Therefore, the adaptive rate that design parameter is estimated is
Wherein, positive definite symmetric matrices Γ ∈ R3×3For permanent gain, l is time-varying gain
And reFor normal number；
Given normal numberAnd γ, work as vectorMeet persistent excitation condition,
Wherein, gain matrix Γ meets
Wherein, normal numberMeetAndThen it is capable of parameter estimating error Finite time convergence control, convergence time is
Wherein,
Control method the most according to claim 1, it is characterised in that described step 3 includes:
Step 31, makes x1T () is the output signal of system, ydT () is reference signal, then tracking error et(t)=x1(t)-yd T (), obtains the differential of error, second differential is respectively as follows:
To tracking error etCarry out changing
Wherein, λ1For normal number, formula (16) can obtain, work as stWhen tending to 0, tracking error etT () converges to 0；
WhenTime, stConverge to 0, wherein, it is desirable to positionExpression formula is
And κ1,κ2＞ 0 is controller gain；WithIt is respectively parameter alpha, a1K and a2Estimated value；
Step 32, designs neutral net integral sliding mode control device, it is achieved the synchronization of motor and guarantee x3iT () converges onFirst First definition motor position x3i(t) and desired locationsBetween error be
Additionally, the position synchronous error using Graph Theory to define motor is
Wherein, N is the set of motor, the adjacency matrix A=[a of connectionij]∈Rn×nFor describing the synchronized relation between motor, It is defined as follows: aij＞ 0 represents that motor i and j exists relation, aij=0 represents that motor i and j is irrelevant, defines a in additionii=0；
Step 33, for ensure multi-machine system can Fast synchronization and realize high-precision load tracking, design Generalized Coupled Error is
Wherein,biIt it is a normal number；
Can obtain according to Graph Theory, Generalized Coupled error σiWith anticipation error eiMeet following equalities
Wherein, B=diag{bi}∈Rn×n, L=[lij]∈Rn×nBe Laplacian Matrix andlij=-aij,i ≠ j, D ∈ Rn×nL=D-A is met for indegree matrix；
Step 34, for ensureing σi=0, design following Integral Sliding Mode face
And function phiiFor
Wherein, constant r ＞ 0 is storage gain,I=1,2,3 is normal number；
Neutral net integral sliding mode control device uiIt is expressed as
Wherein, κ3,κ4,εi＞ 0 is controller gain,It is the estimation weights of neutral net, ΦiFor its basic function；
Additionally, the adaptivity turnover rate of neutral net is defined as
Wherein, κaIt it is a normal number；According to control law ui, can carry out synchronizing to multi-motor driving servosystem and follow the tracks of control System.
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