CN103441499A - Linearization feedback neural sliding-mode control method for three-phase parallel-connection active power filter - Google Patents

Linearization feedback neural sliding-mode control method for three-phase parallel-connection active power filter Download PDF

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CN103441499A
CN103441499A CN2013103136780A CN201310313678A CN103441499A CN 103441499 A CN103441499 A CN 103441499A CN 2013103136780 A CN2013103136780 A CN 2013103136780A CN 201310313678 A CN201310313678 A CN 201310313678A CN 103441499 A CN103441499 A CN 103441499A
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王哲
费峻涛
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Changzhou Campus of Hohai University
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Abstract

The invention discloses a linearization feedback neural sliding-mode control method for a three-phase parallel-connection active power filter. According to the control method, the method of RBF neural network approach and self-adaptation control is adopted, the linearization feedback technology is utilized, a self-adaptation neural sliding-mode controller is designed, and a control law of an output linearization feedback neural sliding-mode of the controller is used for approaching a switch function of the three-phase parallel-connection active power filter, so that connection and disconnection of a main circuit switch of the active power filter is controlled. The control method integrates advantages of a linearization feedback method, sliding-mode control, a self-adaptation algorithm and an RBF neural network, can detect and track harmonic waves in power source currents constantly, and achieves the purposes of eliminating the harmonic waves and improving quality of electric energy by generating offset currents equal in magnitude and opposite in direction. As the self-adaptation law is designed on the basis of the lyapunov function, the control method can regulate the weight of the neural network on line, so that a system has stability and robustness.

Description

The Linearization Feedback neural network sliding mode control method of Three Phase Shunt Active Filter
Technical field
The present invention relates to the Linearization Feedback neural network sliding mode control method of Three Phase Shunt Active Filter, belong to Active Power Filter-APF control technology field.
Background technology
Along with the extensive application of nonlinear load, the harmonic content in electrical network increases day by day, causes the quality of power supply worse and worse.Harmonic wave can cause must be suppressed a series of harm such as apparatus overheat, loss increase, electric current be excessive.With respect to passive power filter, Active Power Filter-APF (APF) is the humorous power factor that involves of processing variation load more effectively, and it has the work characteristics of real-time and accuracy, is acknowledged as the most effective means of the comprehensive regulation " electric network pollution ".
The control technology of APF is one of key technology of APF, the control effect of APF depends on the performance of its controller to a great extent, and the development along with industrial technology, designing requirement to control system improves day by day, in order to improve better the quality of power supply, the research of the control strategy of APF is had to great theory and realistic meaning.Because real system exists complexity, non-linear, time distortion, the factor such as uncertain, can't obtain accurate Mathematical Modeling, traditional control theory can not meet the requirement of industrial development, so advanced control theory is proposed and develops.ANN Control is a new branch of Based Intelligent Control, for solving complicated control problem non-linear, uncertain, that be uncertain of system, has opened up new way.
RBF (RBF) neuron network simulation the local neural network structure of adjusting, mutually covering acceptance region in the human brain, it has three layers of feedforward network of single hidden layer, the hidden layer action function adopts the gaussian basis function, the RBF network is the neural net of partial approximation, need only in theory abundant neuron, the RBF neural net can be approached the arbitrary continuation function with arbitrary accuracy.The RBF network is nonlinear by the mapping that is input to output, and the hidden layer space is linear to the mapping of output region, therefore adopts the RBF network greatly to accelerate pace of learning and avoids the local minimum problem, is suitable for the requirement that APF controls in real time.
Sliding mode variable structure control is a kind of control strategy of variable structure control system.This control strategy is the discontinuity of controlling, i.e. a kind of time dependent switching characteristic of system " structure " that makes with the conventional fundamental difference of controlling.This control characteristic can force that system state trajectory along regulation under certain characteristic is done by a small margin, high-frequency moving up and down, i.e. so-called " sliding formwork motion ".This sliding formwork motion can design, and irrelevant with parameter and the interference of system.Like this, the system in the sliding formwork motion just has good robustness.
The Linearization Feedback neural network sliding mode control is the combination of Linearization Feedback technology, sliding formwork control, RBF ANN Control and adaptive control, combine the advantage of various controls, be a kind of Novel Control that solves parameter uncertain system control problem, improved the combination property of system.In recent years, the Linearization Feedback neural network control theory has obtained a series of impressive progress, and because the method has good accuracy, robustness and adaptivity have good application prospect on engineering.
Summary of the invention
The present invention is by adopting neural net to approach and the method for adaptive control, utilize the Linearization Feedback technology, designed a kind of adaptive neural network sliding mode controller, Linearization Feedback method, adaptive sliding mode are controlled to the method combined with the RBF neural net APF system is controlled, the impact of uncertain factor and external interference in can the elimination system, improve stability and the robustness of APF system.
The technical scheme that technical solution of the present invention adopts is:
The Linearization Feedback neural network sliding mode control method of Three Phase Shunt Active Filter comprises the following steps:
1) set up the Mathematical Modeling of controlled device Three Phase Shunt Active Filter;
2) Linearization Feedback method, sliding formwork control, adaptive algorithm and RBF neural net are combined, design linearisation feedback adaptive RBF neural network sliding mode control device, Linearization Feedback neural network sliding mode control rule is acted on to the switch function of Three Phase Shunt Active Filter, be specially
2-1) utilize the Linearization Feedback method, the design sliding mode controller, obtain the sliding formwork control law, be specially,
Definition sliding formwork function s is: s (t)=ce
Wherein, c is the sliding formwork coefficient, and e is tracking error
The mathematical modulo pattern of active filter is:
Figure BDA00003559579900021
According to the Linearization Feedback technology, design sliding formwork control law u 1for:
Figure BDA00003559579900022
Wherein, R=ξ (x)-ρ sgn (s)
Figure BDA00003559579900023
x mfor given signal, ρ is the Linearization Feedback parameter, ρ>0
2-3) design self_adaptive RBF neural network sliding mode control device, with the output of neural net replace f (x), obtain Linearization Feedback neural network sliding mode control rule u, realize described controller approaching the Three Phase Shunt Active Filter switch function, thereby control the break-make of active filter main circuit switch, produce the offset current with harmonic current equal and opposite in direction, opposite direction, offset harmonic wave, be specially
At first, suppose to exist neural network weight w, make the output of neural net
Figure BDA00003559579900031
approach time-varying function f (x), its approximation accuracy is ε, that is:
max | | f ^ ( x ) - f ( x ) | | ≤ ϵ
Definition w tfor neural network weight w at t estimated value constantly
Output by neural net
Figure BDA00003559579900033
replace time-varying function f (x), obtain Linearization Feedback neural network sliding mode control rule u and be, u = R - f ^ ( x ) b
Wherein,
Figure BDA00003559579900035
the input that x is the RBF neural net, h (x) is Gaussian function, output
Figure BDA00003559579900036
estimated value for unknown nonlinear function f (x);
3) according to lyapunov function design adaptive law, guarantee the stability of Linearization Feedback self_adaptive RBF neural network sliding mode control device,
Described lyapunov function V is chosen for,
Figure BDA00003559579900037
Described adaptive law
Figure BDA00003559579900038
be designed to,
Figure BDA00003559579900039
Wherein,
Figure BDA000035595799000310
for neural network weight at t error constantly, w t *for neural network weight, in the t optimal value in the moment, p is auto-adaptive parameter.
Aforesaid step 1) is set up the Mathematical Modeling of controlled device Three Phase Shunt Active Filter, is specially
1-1) according to Circuit theory and Kirchhoff's theorem, the Mathematical Modeling of active filter is expressed as
i . c = - r L i c + V s L + V dc L β - - - ( 4 )
Wherein, i cfor active filter offset current, V dcfor DC capacitor voltage, V sfor the active filter terminal voltage, r is resistance, and L is inductance, and β is switch function;
1-2) definition parameter x, parameter u, time-varying function f (x), constant term b,
Make x=i c, f ( x ) = - r L x + V s L , b = V dc L , u=β
The mathematical modulo pattern (4) of active filter becomes: x . = f ( x ) + bu - - - ( 5 )
Using this basis as the Linearization Feedback neural network sliding mode control.
Aforesaid step 1-1), in, the operating state of switch function indication IGBT, be defined as β = 1 Q N = 1 0 Q N = 0 , Conducting is 1, and shutoff is 0.
Compared with the prior art, beneficial effect of the present invention is embodied in:
At first, the distinguishing feature of neural net is without carrying out system modelling, take full advantage of neuronic association search and learning ability and realize controlling purpose, make the present invention not rely on accurate APF model, to harmonic wave, can compensate preferably, effectively improve stability and the dynamic property of APF system, improve power transmission and distribution, power grid security guarantee and the quality of power supply.
Secondly, the present invention combines Linearization Feedback technology, sliding formwork control, RBF ANN Control and adaptive control advantage separately, make the APF system there is higher accuracy, robustness and adaptivity, can effectively reduce the impact of error and external interference, thereby guarantee that APF can work normally in actual environment, with respect to tradition, control and there is range of application widely.
The accompanying drawing explanation
The schematic diagram that Fig. 1 is Linearization Feedback neural network sliding mode control of the present invention;
The offset current trace command current waveform figure that Fig. 2 is APF output in the embodiment of the present invention;
Fig. 3 is tracing deviation oscillogram in the real-time example of the present invention.
Embodiment
Below in conjunction with accompanying drawing, the invention will be further described:
Referring to Fig. 1, controlled device of the present invention is the Three-Phase Parallel Active Power Filter-APF, and the Linearization Feedback neural network sliding mode control method of Three Phase Shunt Active Filter, comprise the following steps
One, set up the Mathematical Modeling of Three Phase Shunt Active Filter
According to Circuit theory and Kirchhoff's theorem, the Mathematical Modeling of active filter is expressed as:
i . ca = - ri ca + V sa L + V dc L β - - - ( 1 )
i . cb = - ri cb + V sb L + V dc L β - - - ( 2 )
i . cc = - ri cc + V sc L + V dc L β - - - ( 3 )
Wherein, β is switch function, and the operating state of indication IGBT, be defined as β = 1 Q N = 1 0 Q N = 0 , Conducting is 1, and shutoff is 0; i ca, i cb, i ccbe respectively the three-phase offset current of active filter, V sa, V sb, V scbe respectively three-phase active filter terminal voltage, V dcfor DC capacitor voltage, r is resistance, and L is inductance,
Can be by above-mentioned component equation with being write as following form:
i . c = - r L i c + V s L + V dc L β - - - ( 4 )
Wherein, i c=(i ca, i cb, i cc), V s=(V sa, V sb, V sc)
Definition parameter x, parameter u, time-varying function f (x), constant term b,
Formula (4) can be write as
x . = f ( x ) + bu - - - ( 5 )
Wherein, x=i c, f ( x ) = - r L x + V s L , b = V dc L , u=β
Using this basis as the neural sliding formwork of Linearization Feedback.
Two, Linearization Feedback method, sliding formwork control, adaptive algorithm and RBF neural net are combined, design linearisation feedback adaptive RBF neural network sliding mode control device, linearization feedback neural sliding formwork control law is acted on to the switch function of Three Phase Shunt Active Filter, realize described controller approaching the Three Phase Shunt Active Filter switch function, thereby control the break-make of active filter main circuit switch, produce the offset current with harmonic current equal and opposite in direction, opposite direction, offset harmonic wave, be specially
1, the Linearization Feedback theory is:
Consider following SISO system:
x . = f 0 ( x ) + g 0 ( x ) τ y = h ( x ) - - - ( 6 )
Wherein, x ∈ R nfor state variable, function f 0(x), g 0(x) meet: R n→ R n(be input as n dimension constant, output is also n dimension constant so), function h (x) meets: R n→ R n, and f 0(0)=0, h 0(0)=0
y . = ∂ h ∂ x x . = ∂ h ∂ x f 0 ( x ) + ∂ h ∂ x g 0 ( x ) τ - - - ( 7 )
Will
Figure BDA00003559579900057
be defined as f 1(x),
Figure BDA00003559579900058
be defined as g 1(x),
y . = f 1 ( x ) + g 1 ( x ) τ
Suppose g 1(x) ≠ 0, design linearisation Feedback Control Laws τ is:
τ = R - f 1 ( x ) g 1 ( x ) - - - ( 8 )
Formula (7) becomes linear system
Figure BDA00003559579900062
If position command is y d, get R and be
R = y . d - α ( y - y d ) - - - ( 9 )
Wherein, α>0, be proportionality coefficient, and formula (9) becomes
e . + αe = 0 - - - ( 10 )
Wherein e is error function, e=y-y d.
Obviously formula (10) is the error dynamics equation, and e (t) levels off to zero with exponential form, if
Figure BDA00003559579900065
e (t) is zero in institute free (t>=0).
2, utilize the Linearization Feedback theory, the design sliding mode controller, obtain the sliding formwork control law
Known that the Mathematical Modeling of APF can be write as
Figure BDA00003559579900066
the target of controlling makes x follow the tracks of a given signal x exactly m,
Defining tracking error function e is, e=x-x m,
Definition sliding formwork function s is s (t)=ce (11)
Wherein, c is the sliding formwork coefficient,
According to the Linearization Feedback technology, by sliding formwork control law u 1be designed to
u 1 = R - f ( x ) b - - - ( 12 )
Wherein, R=ξ (x)-ρ sgn (s) (13)
ξ ( x ) = x . m - - - ( 14 )
ρ is the Linearization Feedback parameter, ρ>0
Stability proves:
Definition Lyapunov function V 1
V 1 = 1 2 s 2 - - - ( 15 )
To its differentiate, obtain
V . 1 = s s . = sc e . = sc ( x . - x . m ) - - - ( 16 )
= sc ( f ( x ) + bu - x . m )
By sliding formwork control law u 1as switch function u substitution formula (16), obtain
V . 1 = - scρsgn ( s ) - - - ( 17 )
V . 1 = - cρ | s | - - - ( 18 )
So V . 1 ≤ 0
Thus can be according to the stability of Lyapunov Theory of Stability proof APF system.
3, design self_adaptive RBF neural network sliding mode control device, obtain Linearization Feedback neural network sliding mode control rule u,
Due to time-varying function f (x) the unknown, sliding formwork control law formula (12) is difficult to realize, utilize the RBF neural net unknown nonlinear function f (x) to be approached with the function of arbitrary accuracy Approximation of Arbitrary Nonlinear Function, with the output of RBF neural net
Figure BDA00003559579900077
replace f (x), realize the control of adaptive neural network sliding formwork, concrete grammar is:
Suppose to exist neural network weight w, make
Figure BDA00003559579900078
approach f (x), its approximation accuracy is ε, that is:
max | | f ^ ( x ) - f ( x ) | | ≤ ϵ
Definition w tfor weight w at t estimated value constantly,
Obtaining Linearization Feedback neural network sliding mode control rule u is,
u = R - f ^ ( x ) b - - - ( 19 )
Wherein,
f ^ ( x ) = w t h ( x ) - - - ( 20 )
The input that x is the RBF neural net, h (x) is Gaussian function, output estimated value for unknown nonlinear function f (x).
4, according to lyapunov function design adaptive law, guarantee the stability of Linearization Feedback self_adaptive RBF neural network sliding mode control device,
The design adaptive law for
w . t = pcsh ( x ) - - - ( 20 )
P is auto-adaptive parameter.
If neural network weight in the optimal value in the t moment is
w t * = arg min w t ∈ Ω t [ sup | f ^ ( x | w t x ∈ R n ) - f ( x ) | ] - - - ( 21 )
Wherein, Ω tbe respectively w tset.
Definition minimum approximation error m is
m = f ( x ) - f ^ ( x | w t * ) - - - ( 22 )
|m|≤m max (23)
M maxthe upper bound for minimum approximation error
Sliding formwork function derivative
s . = c e . = c ( x . - x . m ) = c [ f ( x ) + bu - x . m ]
= c [ f ( x ) + R - f ^ ( x ) - x . m ]
= c [ f ^ ( x / w * t ) + m + ξ ( x ) - ρsgn ( s ) - f ^ ( x ) - x . m ] - - - ( 24 )
= c [ f ^ ( x / w * t ) - f ^ ( x ) + m - ρsgn ( s ) ]
= c [ w t * h ( x ) - w t h ( x ) + m - ρsgn ( s ) ]
= c [ w ~ h ( x ) + m - ρsgn ( s ) ]
Wherein,
Figure BDA000035595799000811
for neural network weight at t error constantly.
Choosing lyapunov function V is
V = 1 2 ( s 2 + 1 p w ~ T w ~ ) - - - ( 25 )
Wherein, p is auto-adaptive parameter.
To lyapunov function V, differentiate obtains
V . = s s . + 1 p w ~ T w ~ .
= sc [ w ~ T h ( x ) + m - ρsgn ( s ) ] + 1 p w ~ T w ~ . - - - ( 26 )
= sc w ~ T h ( x ) + 1 p w ~ T w ~ . + sc ( m - ρsgn ( s ) )
= 1 p w ~ T ( pcsh ( x ) + w ~ . ) + sc ( m - ρsgn ( s ) )
Wherein, because w t *for constant, therefore
Figure BDA00003559579900095
Adaptive law formula (20) substitution formula (26) is obtained
V . = sc ( m - ρsgn ( s ) ) - - - ( 27 )
When minimum approximation error m is substantially equal to 0, formula (27) can be write as
V . = - scρsgn ( s ) = - cρ | s | - - - ( 28 )
We just can obtain so
V . ≤ 0 .
Now meet Lyapunov stability condition, can prove that thus Linearization Feedback self_adaptive RBF neural network sliding mode control device is stable.
Through above-mentioned steps, realize the control constantly to the Three-Phase Shunt Active Power electric-power filter of RBF neural network sliding mode control device based on Linearization Feedback, thereby realized the compensation to harmonic wave, reduced current distortion rate, improved grid supply quality.
Finally, by emulation experiment, verify the inventive method
In the present embodiment, self_adaptive RBF neural network sliding mode control device played a role since 0.05 second, and emulation in 0.16 second finishes.Parameter designing is as follows:
Parameter in the RBF neural net: the number of hidden nodes m=21, center vector c=-20:2:20, sound stage width parameter b=4;
Sliding formwork coefficient: c=10000;
Linearization Feedback parameter: ρ=50;
The PI controller is controlled DC voltage, the parameter of PI controller: k p=0.03, k i=0.02;
Constant term: b=170000; Auto-adaptive parameter: p=1
APF parameter: Inductor L=5mH, DC capacitor voltage V dc=100uF
Result as shown in Figures 2 and 3,
What Fig. 2 described is the oscillogram of the offset current trace command electric current of APF output, what Fig. 3 described is the oscillogram of offset current and instruction current deviation, as can be seen from the figure, 0.05 introduce self_adaptive RBF neural network sliding mode control device during second, switch function to APF is controlled, 0.06 a second precompensation electric current can trace into instruction current, both deviations level off to 0, tracking effect is better, so just effectively eliminated harmonic wave, adopt adaptive algorithm to adjust the weights of RBF neural net simultaneously, effectively reduced percent harmonic distortion, source current is approached sinusoidal wave, greatly reduce percent harmonic distortion.Show that thus Active Power Filter-APF has good compensation effect to harmonic current, verified that Linearization Feedback neural network sliding mode control utensil has good control ability.

Claims (3)

1. the Linearization Feedback neural network sliding mode control method of Three Phase Shunt Active Filter, is characterized in that, comprises the following steps:
1) set up the Mathematical Modeling of controlled device Three Phase Shunt Active Filter;
2) Linearization Feedback method, sliding formwork control, adaptive algorithm and RBF neural net are combined, design linearisation feedback adaptive RBF neural network sliding mode control device, its linearization feedback neural sliding formwork control law is acted on to the switch function of Three Phase Shunt Active Filter, is specially:
2-1) utilize the Linearization Feedback method, the design sliding mode controller, obtain the sliding formwork control law, be specially,
Definition sliding formwork function s is: s (t)=ce
Wherein, c is the sliding formwork coefficient, and e is tracking error
The mathematical modulo pattern of active filter is:
Figure FDA00003559579800011
According to the Linearization Feedback technology, design sliding formwork control law u 1for:
Figure FDA00003559579800012
Wherein, R=ξ (x)-ρ sgn (s)
Figure FDA00003559579800013
x mfor given signal, ρ is the Linearization Feedback parameter, ρ>0
2-3) design self_adaptive RBF neural network sliding mode control device, with the output of neural net
Figure FDA00003559579800014
replace f (x), obtain Linearization Feedback neural network sliding mode control rule u, realize described controller approaching the Three Phase Shunt Active Filter switch function, thereby control the break-make of active filter main circuit switch, produce the offset current with harmonic current equal and opposite in direction, opposite direction, offset harmonic wave, be specially
At first, suppose to exist neural network weight w, make the output of neural net
Figure FDA00003559579800015
approach time-varying function f (x), its approximation accuracy is ε, that is:
max | | f ^ ( x ) - f ( x ) | | ≤ ϵ
Definition w tfor neural network weight w at t estimated value constantly
Output by neural net
Figure FDA00003559579800017
replace time-varying function f (x), obtain Linearization Feedback neural network sliding mode control rule u and be, u = R - f ^ ( x ) b
Wherein, the input that x is the RBF neural net, h (x) is Gaussian function, output
Figure FDA000035595798000110
estimated value for unknown nonlinear function f (x);
3) according to lyapunov function design adaptive law, guarantee the stability of Linearization Feedback self_adaptive RBF neural network sliding mode control device,
Described lyapunov function V is chosen for,
Figure FDA00003559579800021
Described adaptive law
Figure FDA00003559579800022
be designed to,
Wherein,
Figure FDA00003559579800024
for neural network weight at t error constantly, w t *for neural network weight, in the t optimal value in the moment, p is auto-adaptive parameter.
2. the Linearization Feedback neural network sliding mode control method of Three Phase Shunt Active Filter according to claim 1, is characterized in that, described step 1) is set up the Mathematical Modeling of controlled device Three Phase Shunt Active Filter, is specially
1-1) according to Circuit theory and Kirchhoff's theorem, the Mathematical Modeling of active filter is expressed as
i . c = - r L i c + V s L + V dc L β - - - ( 4 )
Wherein, i cfor active filter offset current, V dcfor DC capacitor voltage, V sfor the active filter terminal voltage, r is resistance, and L is inductance, and β is switch function;
1-2) definition parameter x, parameter u, time-varying function f (x), constant term b,
Make x=i c, f ( x ) = - r L x + V s L , b = V dc L , u=β
The mathematical modulo pattern (4) of active filter becomes:
x . = f ( x ) + bu - - - ( 5 )
Using this basis as the Linearization Feedback neural network sliding mode control.
3. the Linearization Feedback neural network sliding mode control method of Three Phase Shunt Active Filter according to claim 2, is characterized in that described step 1-1) in, the operating state of switch function indication IGBT, be defined as β = 1 Q N = 1 0 Q N = 0 , Conducting is 1, and shutoff is 0.
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CN105305446A (en) * 2015-10-22 2016-02-03 南京亚派科技股份有限公司 Harmonic current tracking method based on intelligent control
CN106015951A (en) * 2016-07-07 2016-10-12 北京信息科技大学 Gas transmission pipeline leakage detection system and method suitable for multiple state changes
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CN105140924A (en) * 2015-09-24 2015-12-09 上海电力学院 Nonlinear controller design method of mixed type active power filter
CN105305446A (en) * 2015-10-22 2016-02-03 南京亚派科技股份有限公司 Harmonic current tracking method based on intelligent control
CN106015951A (en) * 2016-07-07 2016-10-12 北京信息科技大学 Gas transmission pipeline leakage detection system and method suitable for multiple state changes
CN106015951B (en) * 2016-07-07 2018-11-09 北京信息科技大学 A kind of gas pipeline leak detection system and method adapting to various states variation
CN108110761A (en) * 2018-01-24 2018-06-01 河海大学常州校区 Fuzzy High-Order Sliding Mode Control Method of Active Power Filter based on Linearization Feedback
CN108667326A (en) * 2018-04-11 2018-10-16 天津大学 A kind of multi-level converter selective harmonic elimination pulsewidth modulation Fast implementation
CN109546660A (en) * 2018-11-22 2019-03-29 中国航空综合技术研究所 Active power filter circuit and control method based on neural network sliding mode control strategy
CN109546660B (en) * 2018-11-22 2021-03-02 中国航空综合技术研究所 Active power filter circuit based on neural sliding mode control strategy and control method

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