CN107809113A - Complementary sliding-mode surface inverting Adaptive radial basis function neural network Design of Observer method - Google Patents
Complementary sliding-mode surface inverting Adaptive radial basis function neural network Design of Observer method Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
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Abstract
The invention discloses a kind of complementary sliding-mode surface inverting Adaptive radial basis function neural network Design of Observer method, it is characterised in that comprises the following steps：Virtual controlling amount in step 1, design back stepping control, further combined with complementary sliding-mode surface, real controllers are obtained, and the stability of sliding-mode surface is proved by liapunov function；Step 2, design RBF neural observer, the observation system Nonlinear perturbations d upper bounds, improve the control accuracy and performance of system.Compared to traditional sliding-mode control, the controller of design improves system response time and steady-state tracking precision using a kind of complementary sliding-mode surface；At the same time, back-stepping sliding mode control method can solve the problems, such as the non-linear of system, Parameters variation and interference；RBF neural can be used for the upper bound of approximation system interference and eliminate chattering phenomenon with this due to good approximation capability itself.
Description
Technical field
The present invention relates to a kind of complementary sliding-mode surface inverting Adaptive radial basis function neural network Design of Observer method.
Background technology
With the progress and development of society, the living standard of people increasingly improves, and substantial amounts of electrical equipment is put into daily
Production and living in, the thing followed is exactly to occur the pollution of substantial amounts of harmonic wave and reactive power in power network, and this has a strong impact on
The quality of electric energy.Harmonic voltage or harmonic current in power network be present can increase the added losses of power system device, cause to survey
The problems such as amount and apparatus for automatic control failure, the service efficiency of equipment is have impact on, may be because of the excessively thermally-induced fire of circuit when serious
Calamity.
At present mainly using outside harmonic compensation device come compensation harmonic, wave filter is divided into passive filter and active filter
Two kinds of ripple device.Passive filter is influenceed very big on the control effect of harmonic wave by the impedance operator of system, is highly prone to temperature, humorous
Ripple and the influence of nonlinear load change, its filtering performance are unstable.In addition, passive filter can only filter out specific rank
Secondary harmonic wave, therefore it is not particularly suited for the complicated place of harmonic wave situation.The defects of in the presence of particular harmonic can only be compensated, so existing
Active filter is concentrated mainly in the improvement to electric energy problem.Compared to passive filter, active filter realizes dynamic
Compensation, fast response time；Required energy-storage travelling wave tube capacity is little；Influenceed little, will not be occurred with electric network impedance by electric network impedance
Resonance etc..
At present, the advanced control theory system of the Active Power Filter-APF of system, active filter are not yet formed both at home and abroad
Modeling method vary with each individual, the control method of use is also varied, causes the stability of system and reliability relatively low.
The content of the invention
To solve the deficiencies in the prior art, it is an object of the invention to provide a kind of complementary sliding-mode surface inverting self_adaptive RBF
Neural Network Observer design method, instruction current real-time tracking can be compensated, reliability is high, to Parameters variation robustness
High, stability height.
In order to realize above-mentioned target, the present invention adopts the following technical scheme that：
A kind of complementary sliding-mode surface inverting Adaptive radial basis function neural network Design of Observer method, it is characterized in that, including it is as follows
Step：
Virtual controlling amount in step 1) design back stepping control；
With reference to complementary sliding-mode surface, real controllers are obtained；
Step 2) designs RBF neural observer, and non-linear dry using the observation system online approximating of the observer
The upper bound disturbed.
A kind of foregoing complementary sliding-mode surface inverting Adaptive radial basis function neural network Design of Observer method, it is characterized in that, institute
The virtual controlling amount for the back stepping control based on complementary sliding-mode surface that step 1) obtains and true control law are stated, by designing Li Ya
Pu Nuofu functions prove its stability.
A kind of foregoing complementary sliding-mode surface inverting Adaptive radial basis function neural network Design of Observer method, it is characterized in that, tool
Body step is：
Step 11) defines the virtual controlling amount of back stepping controlWherein z1For tracking error, x1dTo refer to
Make electric current, k1For the normal number of non-zero；
Step 12) designs complementary sliding-mode surface sc：Wherein, coefficient k2＞ 0 determines state error s's
Bandwidth,
According to APF mathematical modeling, to sliding-mode surface s along the derivation of time τ
Ignore interference d, orderThe equivalent controller of system is
Design switching functionWherein δ >=| d |, system controller can obtain
Step 13) is by using liapunov functionChecking is transported on the basis of complementary sliding-mode surface
The asymptotically stability of system can be ensured with back stepping control.
A kind of foregoing complementary sliding-mode surface inverting Adaptive radial basis function neural network Design of Observer method, it is characterized in that, institute
State the interference in step 2) and be expressed as d=ω*Thi(x)+ε,Wherein, x is network
Input, i represent the input of i-th of network input layer, and h (x) is Gaussian function, ω*TFor ideal network weights, ε approaches for network
Error；
Assuming that interference d estimated value table is shown asWherein,It is the real-time weights of RBF neural, h
(x) it is Gaussian function,It is ε estimate.
A kind of foregoing complementary sliding-mode surface inverting Adaptive radial basis function neural network Design of Observer method, it is characterized in that, institute
The particular content for stating step 2) is：
Define neural network weight errorFor
Design obtains Adaptive radial basis function neural network back-stepping sliding mode control rule
Design Lyapunov functions：Wherein γ1,γ2For positive number,
And to the function derivation；
Design adaptive law：Wherein, γ1,γ2For learning rate；Design is obtained adaptive
Rule substitutes into Lyapunov functions and carries out verifying whether to meet the requirements.
A kind of foregoing complementary sliding-mode surface inverting Adaptive radial basis function neural network Design of Observer method, it is characterized in that, institute
Stating the standard of checking is：
Can designed controller can ensure that the derivative of Lyapunov functions is negative semidefinite；According to Lyapunov
The stability of stability second method decision-making system.
The beneficial effect that the present invention is reached：
In the Active Power Filter-APF inverting RBF neural observer based on complementary sliding formwork, complementary sliding-mode surface can
The response speed of raising system, quickly realize tracking；
The controller of design is able to ensure that the robustness of the real-time tracking and strengthening system to instruction current；
Active Power Filter-APF can be carried out effectively, reliable control, can be with the case of unknown to systematic parameter
The parameters of system effectively are estimated, and ensure the global stability of system；
, can be by the basis of the Active Power Filter-APF RBF neural based on complementary sliding-mode surface approaches the design of device
Step obtains dynamic control law and adaptive law；Conventional Sliding mode variable structure control is mainly utilized in the design of sliding formwork control,
It can overcome the uncertainty of system, have very strong robustness to interference, and the especially control to nonlinear system has very
Strong control effect.
Brief description of the drawings
Fig. 1 is the model schematic of Active Power Filter-APF in the specific embodiment of the invention；
Fig. 2 is the system structure diagram of control method of the present invention；
Fig. 3 is the nonlinear load current waveform schematic diagram of system access；
Fig. 4 is the network wave schematic diagram after access design controller；
Fig. 5 is instruction current and compensation current tracking waveform diagram；
Fig. 6 is compensation current track error waveform diagram；
Fig. 7 is DC voltage waveform diagram；
Fig. 8 is the current spectrum figure of access controller.
Embodiment
The invention will be further described below in conjunction with the accompanying drawings.Following examples are only used for clearly illustrating this hair
Bright technical scheme, and can not be limited the scope of the invention with this.
In the present embodiment, Vs1,Vs2,Vs3Represent three-phase mains voltage；is1,is2,is3Represent three phase mains electric current；iL1,iL2,
iL3Represent load current；v1, v2, v3Represent three phase active electric power filter terminal voltage；i1,i2,i3Represent three-phase compensation electric current；
LcRepresent AC inductance；RcRepresent direct current side resistance.v1M,v2M,v3M,vMNCorrespond respectively and represent M points to a, b, c, N point
Voltage.
The design method mainly includes following two steps：
Virtual controlling amount in step 1, design back stepping control, further combined with complementary sliding-mode surface, is truly controlled
Device, and pass through the stability of liapunov function proof sliding-mode surface；
Step 2, design RBF neural observer, observation and the approximation system Nonlinear perturbations upper bound, improve system
Control accuracy and performance.
It is specifically addressed with reference to background：
First, the basic functional principle of Active Power Filter-APF is in APF dynamic models, by entering to power network current
Row collection in real time, the related compensation component of quick obtaining, by the control to high-performance current transformer, produce PWM ripples and inject
Into Active Power Filter-APF, corresponding compensation electric current, and then harmonic carcellation electric current are produced.
Following three formula can obtain according to Circuit theory and Kirchhoff's theoremIts
In, v1, v2, v3Respectively power network and the voltage of APF junctions, i1, i2, i3The compensation electric current of power network, L are injected for APFcFor electricity
Sense, RcFor resistance, V1M, V2M, V3M, VMNFor the voltage of M points to a, b, c, N point.
Assuming that v1+v2+v3=0, i1+i2+i3=0, and then can obtain
In order to identify IGBT switch situation, function c is introducedk, it is specific as follows
Meanwhile VkM=CkVdc, obtain
In order to obtain the Strict-feedback form of Active Power Filter-APF, Based Inverse Design Method is facilitated the use, does and enters
The derivation conversion of one step：
Define dnkForWherein, n is integer, represents IGBT switching mode, and span is
0~7, k are then the number of phases, and span is 1~3.D can be obtained by calculatingnkWith ckBetween relation：
Can further it be transformed to：
Define two new state variable x1For instruction current, x2For x1Derivative, i.e.,：
Respectively to x1And x2Time is differentiated, can be obtained：
Consider extraneous unknown disturbances, APF mathematical modeling, which can adjust, to be converted to：
Wherein,D is extraneous unknown dry
Disturb, it is a bounded normal number.This paper mathematical modeling is (10) derived.
On the basis of this method is more than, the purpose using back stepping control method is the suitable virtual controlling rule x of design2d
Make the x in (10) with actual control law u1Required command signal x can be tracked1d
Step 11)：Definition status error z1=x1-x1d, z2=x2-x2d；
Tracking error z1Time is differentiated：
It is following form to choose virtual controlling amount：Wherein k1For the normal number of non-zero.
Design first Lyapunov function
To V1Obtained along time derivation：
If state error z2In finite time convergence control to 0, thenThat is z1It is asymptotically stability
, so as to x1X can be trackedd。
Step 12)：Sliding formwork control has very strong robustness for system parameter variations and external interference.In order to improve sound
Speed and steady-state tracking precision are answered, we devise a kind of complementary synovial membrane face sc, to improve the effect of traditional sliding-mode surface.
Do not consider that interference and indeterminate, controlled system object factory are first：
Traditional sliding-mode surface s and complementary sliding-mode surface scExpression it is as follows；
S=z2+k2∫z2dτ (18)
sc=z2-k2∫z2dτ (19)
Wherein, k2＞ 0, determine state error s bandwidth.
S and scBetween relation, can be expressed as：
To (20) along time derivation：
Designing equivalent controller u is：
In order to ensure that sliding formwork reaching condition is set up, design switching control is as follows：Its
In, δ >=| d |.
Sliding formwork control ratio is made up of equivalent control term and switching control item, i.e.,：
Step 13) designs second liapunov function：
(26) two edge time derivations can be obtained：
(20) and (25) are substituted into, (23) can be further represented as：
Now, the control law (24) of design can be substituted into (28), be represented by：
Thus, it is possible to find, in the presence of true control law u, system can keep stable.
However, systematic parameter and the continuous change of interference, δ will become very big, and this is produced inevitable seriously
Tremble, as function δ sgn (s+sc) when switching over action.It would therefore be desirable to by further studying, to reduce interference
Influence to control system.
Step 2) improves the performance of system to solve the problem of trembling of control system, when designing controller, this step
Suddenly d is disturbed come online approximating using a kind of Adaptive radial basis function neural network.
Due to the ability that the RBF overall situation is approached, the network being capable of accurate Nonlinear Function Approximation.
Therefore, interference d can be expressed as：
D=ω*Th(x)+ε (30)
Wherein, x is network inputs, and i represents the input of i-th of network input layer, and h (x) is Gaussian function, ω*TFor ideal
Network weight, ε are network approximate error.
Assuming that interference d estimated value table is shown as：Wherein,It is that RBF neural is real-time
Weights,It is Gaussian function,It is ε estimate.
Define neural network weight errorFor：
Definition more than, RBF neural can be utilized to carry out On-line Estimation, this and adaptive inverting to interference d
Sliding formwork item in sliding mode controller (21) serves the same role, and design obtains self_adaptive RBF Neural Network Inversion sliding formwork control
Restrain and be：
This control law is designed to the problem of trembling that δ sgn (s) are brought to system in avoidance (21) well.
Design the 3rd Lyapunov function：Wherein
γ1,γ2For positive number.
(31) derivation can be obtained
Obtained control law u substitutions (32) will be designed, Lee's function can be further represented as：
Due to ω*It is a fixed value, therefore following expression formula can be obtained：
Then (36) can be rewritten as：
Therefore, adaptive law can be designed：Wherein, γ1,γ2For learning rate.
Then it can will design obtained adaptive law (40) substitution (39)：
Therefore, designed controller can ensure that the derivative of Lyapunov functions is negative semidefinite；According to Lyapunov
Stability second method, it is possible to determine that the stability of system.
It is negative semidefinite expression, system can reach sliding-mode surface in finite time, and S is bounded.According to
Barbalat lemma and its inference, it can proveThat is S can converge to 0, in sliding-mode surface function
Error and derivative can all converge to 0.
Based on the controller of above-mentioned design, Matlab emulation experiments are carried out：
With reference to the dynamic model of Active Power Filter-APF and the self_adaptive RBF amphineura network control of fractional order sliding formwork control
The design method of device processed, main program is gone out by Matlab/Simulink Software for Design.
Compensation circuit access switch closure, active filter are started working during 0.04S (S represents the second), and in 0.1S and
An identical extra nonlinear load is accessed during 0.2S, change procedure can be will become apparent from from Fig. 3.In Fig. 4, can be with
It was found that after the controller that the access present invention designs, the harmonic wave of system is significantly compensated, target waveform of the power network into sine.,
At the same time, it can be found that involved controller compensation precision is higher in Fig. 5, Fig. 6 and Fig. 7, tracking error is small.Most
Eventually, in fig. 8 it can be found that the total harmonic distortion of system falls below 1.15%, ideal control effect has been reached.
Therefore using the active of the adaptively Compensating Current Control Method of complementary sliding formwork inverting RBF neural observer
Electric-power filter can not only eliminate the harmonic wave as caused by nonlinear load well, and stability also meets higher want
Ask.
The present invention is applied to the inverting Adaptive radial basis function neural network based on complementary sliding formwork control of Active Power Filter-APF
Observer, this method carry out effectively, reliably controlling to Active Power Filter-APF, can in the case of unknown to systematic parameter
Effectively to estimate the parameters of system, and ensure the global stability of system；In base based on the anti-of complementary sliding formwork control
Drill Adaptive radial basis function neural network to approach on the basis of the design of device, can progressively obtain dynamic control law and adaptive law；In cunning
It is to utilize complementary Sliding mode variable structure control in the design of mould control, it can overcome the uncertainty of system, have very to interference
Strong robustness, there is very strong control effect to nonlinear system；Adaptive radial basis function neural network controller is used for having approached
Non-linear partial in active power filter.Adaptive back stepping control device is able to ensure that the real-time tracking to instruction current and added
The robustness of strong system.The present invention is able to ensure that the real-time tracking to instruction current, and the dynamic property of strengthening system, carries
High system robustness and insensitive to Parameters variation.
Described above is only the preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art
For member, without departing from the technical principles of the invention, some improvement and deformation can also be made, these improve and become
Shape also should be regarded as protection scope of the present invention.
Claims (6)
1. a kind of complementary sliding-mode surface inverting Adaptive radial basis function neural network Design of Observer method, it is characterized in that, including following step
Suddenly：
Virtual controlling amount in step 1) design back stepping control；
With reference to complementary sliding-mode surface, real controllers are obtained；
Step 2) designs RBF neural observer, and utilize the observation system online approximating Nonlinear perturbations of the observer
The upper bound.
2. a kind of complementary sliding-mode surface inverting Adaptive radial basis function neural network Design of Observer method according to claim 1, its
It is characterized in, the virtual controlling amount for the back stepping control based on complementary sliding-mode surface that the step 1) obtains and true control law, passes through
Design liapunov function proves its stability.
3. a kind of complementary sliding-mode surface inverting Adaptive radial basis function neural network Design of Observer method according to claim 2, its
It is characterized in, concretely comprises the following steps：
Step 11) defines the virtual controlling amount of back stepping controlWherein z1For tracking error, x1dFor instruction electricity
Stream, k1For the normal number of non-zero；
Step 12) designs complementary sliding-mode surface sc：Wherein, coefficient k2＞ 0 determines state error s bandwidth,
According to APF mathematical modeling, to sliding-mode surface s along the derivation of time τ
Ignore interference d, orderThe equivalent controller of system is
Design switching functionWherein δ >=| d |, system controller can obtain
Step 13) is by using liapunov functionInverting is used in checking on the basis of complementary sliding-mode surface
Control can ensure the asymptotically stability of system.
4. a kind of complementary sliding-mode surface inverting Adaptive radial basis function neural network Design of Observer method according to claim 1, its
It is characterized in, the interference in the step 2) is expressed as d=ω*Thi(x)+ε,Wherein,
X is network inputs, and i represents the input of i-th of network input layer, and h (x) is Gaussian function, ω*TFor ideal network weights, ε is net
Network approximate error；
Assuming that interference d estimated value table is shown asWherein,It is the real-time weights of RBF neural, h (x) is high
This function,It is ε estimate.
5. a kind of complementary sliding-mode surface inverting Adaptive radial basis function neural network Design of Observer method according to claim 4, its
It is characterized in, the particular content of the step 2) is：
Define neural network weight errorFor
Design obtains Adaptive radial basis function neural network back-stepping sliding mode control rule
Design Lyapunov functions：Wherein γ1,γ2For positive number, and it is right
The function derivation；
Design adaptive law：Wherein, γ1,γ2For learning rate；Obtained adaptive law substitution will be designed
Carry out verifying whether to meet the requirements in Lyapunov functions.
6. a kind of complementary sliding-mode surface inverting Adaptive radial basis function neural network Design of Observer method according to claim 5, its
It is characterized in, the standard of the checking is：
Can designed controller can ensure that the derivative of Lyapunov functions is negative semidefinite；According to Lyapunov stability
The stability of second method decision-making system.
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| CN111736617A (en) * | 2020-06-09 | 2020-10-02 | 哈尔滨工程大学 | Speed observer-based benthonic underwater robot preset performance track tracking control method |
| CN111736617B (en) * | 2020-06-09 | 2022-11-04 | 哈尔滨工程大学 | Track tracking control method for preset performance of benthonic underwater robot based on speed observer |
| CN113156825A (en) * | 2021-05-28 | 2021-07-23 | 大连海事大学 | Design method of self-adaptive backstepping sliding mode controlled ship-based photoelectric tracking system |
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