CN103441499B - The Linearization Feedback neural network sliding mode control method of Three Phase Shunt Active Filter - Google Patents

Abstract

The invention discloses a kind of Linearization Feedback neural network sliding mode control method of Three Phase Shunt Active Filter, RBF neural is adopted to approach and the method for adaptive control, utilize Linearization Feedback technology, devise a kind of adaptive neural network sliding mode controller, with the linearization feedback neural sliding formwork control law of controller, approach the switch function of Three Phase Shunt Active Filter, thus control the break-make of active filter main circuit switch, the present invention combines Linearization Feedback method, sliding formwork controls, the advantage of adaptive algorithm and RBF neural, can detection constantly harmonic wave in tracking power supply electric current, by producing equal and opposite in direction, the offset current that direction is contrary, reach harmonic carcellation, improve the object of the quality of power supply, and the present invention is based on lyapunov function design adaptive law, the weights of adjustment neural net that can be online, make system possess 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 control technique 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 a series of harm such as apparatus overheat, loss increase, electric current can be caused excessive, must be suppressed.Relative to passive power filter, Active Power Filter-APF (APF) more can involve power factor by the humorous of processing variation load effectively, it has the work characteristics of real-time and accuracy, is acknowledged as the comprehensive regulation " electric network pollution " the most effective means.

The control technology of APF is one of key technology of APF, the control effects of APF depends on the performance of its controller to a great extent, and along with the development of industrial technology, the designing requirement of control system is improved day by day, in order to improve the quality of power supply better, there are great theory and realistic meaning to the research of the control strategy of APF.Due to real system exist complexity, non-linear, time distortion, the factor such as uncertain, cannot 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 the new branch of of Based Intelligent Control, opens new way for solving complicated control problem that is non-linear, uncertain, that be uncertain of system.

Local directed complete set in RBF (RBF) neuron network simulation human brain, mutually cover the neural network structure of acceptance region, it has three layers of feedforward network of single hidden layer, hidden layer action function adopts Gaussian bases, RBF network is the neural net of partial approximation, as long as neuron abundant in theory, RBF neural can approach arbitrary continuation function with arbitrary accuracy.RBF network is nonlinear by the mapping being input to output, and hidden layer space is linear to the mapping of output region, therefore adopts RBF network greatly can accelerate pace of learning and avoid 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.The fundamental difference of this control strategy and conventional control is the discontinuity controlled, and namely one makes system " structure " time dependent switching characteristic.This control characteristic can force system to do by a small margin along the state trajectory of regulation, high-frequencyly to move up and down under certain characteristic, i.e. so-called " sliding formwork motion ".The motion of this sliding formwork can design, and has nothing to do with the parameter of system and disturb.Like this, the system being in sliding formwork motion just has good robustness.

Linearization Feedback neural network sliding mode control is Linearization Feedback technology, sliding formwork controls, RBF neural controls and the combination of adaptive control, combine the advantage of various control, be a kind of Novel Control solving uncertain parameters systems control problem, improve the combination property of system.In recent years, Linearization Feedback neural network control theory achieves a series of impressive progress, and because the method has good accuracy, robustness and adaptivity, engineering has good application prospect.

Summary of the invention

The present invention approaches and the method for adaptive control by adopting neural net, utilize Linearization Feedback technology, devise a kind of adaptive neural network sliding mode controller, the method that Linearization Feedback method, adaptive sliding-mode observer combine with RBF neural is controlled APF system, can the impact of uncertain factor and external interference in 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) Mathematical Modeling of controlled device Three Phase Shunt Active Filter is set up;

2) Linearization Feedback method, sliding formwork control, adaptive algorithm and RBF neural are combined, design linearisation feedback adaptive RBF neural network sliding mode control device, Linearization Feedback neural network sliding mode control rule is acted on the switch function of Three Phase Shunt Active Filter, be specially

2-1) utilize Linearization Feedback method, design sliding mode controller, obtains sliding formwork control law, is specially,

Definition sliding formwork function s is: s (t)=ce

Wherein, c is sliding formwork coefficient, and e is tracking error

The mathematical modulo pattern of active filter is:

According to Linearization Feedback technology, design sliding formwork control law u ₁for:

Wherein, R=ξ (x)-ρ sgn (s)

x _mfor Setting signal, ρ is 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 Three Phase Shunt Active Filter switch function, thus control the break-make of active filter main circuit switch, produce the offset current contrary with harmonic current equal and opposite in direction, direction, offset harmonic wave, be specially

First, suppose to there is neural network weight w, make the output of neural net approach time-varying function f (x), its approximation accuracy is ε, that is:

$\max \left|\right|\hat{f}\left(x\right)-f\left(x\right)\left|\right|\≤\mathrm{\ϵ}$

Definition w _tfor neural network weight w is in the estimated value of t

With the output of neural net replace time-varying function f (x), obtaining Linearization Feedback neural network sliding mode control rule u is, $u=\frac{R-\hat{f}\left(x\right)}{b}$

Wherein, x is the input of RBF neural, and h (x) is Gaussian function, exports for the estimated value of unknown nonlinear function f (x);

3) according to lyapunov function design adaptive law, the stability of Linearization Feedback self_adaptive RBF neural network sliding mode control device is guaranteed,

Described lyapunov function V is chosen for,

Described adaptive law be designed to,

Wherein, for neural network weight is in the error of t, w _t ^*for neural network weight is in the optimal value of t, p is auto-adaptive parameter.

Aforesaid step 1) set up the Mathematical Modeling of controlled device Three Phase Shunt Active Filter, be specially

1-1) according to Circuit theory and Kirchhoff's theorem, the Mathematical Modeling of active filter is expressed as

${\stackrel{\·}{i}}_c=-\frac{r}{L}{i}_c+\frac{V_s}{L}+\frac{V_{\mathrm{dc}}}{L}\mathrm{\β}---\left(4\right)$

Wherein, i _cfor active filter offset current, V _dcfor DC capacitor voltage, V _sfor active filter terminal voltage, r is resistance, and L is inductance, and β is switch function;

1-2) define parameter x, parameter u, time-varying function f (x), constant term b,

Make x=i _c, $f\left(x\right)=-\frac{r}{L}x+\frac{V_s}{L},b=\frac{V_{\mathrm{dc}}}{L},$ u=β

Then the mathematical modulo pattern (4) of active filter becomes: (5)

In this, as the basis of Linearization Feedback neural network sliding mode control.

Aforesaid step foretells 1) in, the operating state of switch function instruction IGBT, is defined as $\mathrm{\β}=\left\{\begin{array}{cc}1& Q_N=1\\ 0& Q_N=0\end{array}\right.,$ Conducting is 1, and shutoff is 0.

Compared with the prior art, beneficial effect of the present invention is embodied in:

First, the distinguishing feature of neural net is without the need to carrying out system modelling, make full use of neuronic association search and learning ability to realize controlling object, the present invention is made not rely on accurate APF model, can compensate preferably harmonic wave, effective stability and dynamic property improving APF system, improves power transmission and distribution, power grid security guarantee and the quality of power supply.

Secondly, present invention incorporates Linearization Feedback technology, sliding formwork controls, RBF neural controls and adaptive control advantage separately, APF system is made to have higher accuracy, robustness and adaptivity, effectively can reduce the impact of error and external interference, thus ensure that APF can work normally in actual environment, relative to Traditional control, there is range of application widely.

Accompanying drawing explanation

Fig. 1 is the schematic diagram of Linearization Feedback neural network sliding mode control of the present invention;

Fig. 2 is the offset current trace command current waveform figure that in the embodiment of the present invention, APF exports;

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:

See Fig. 1, controlled device of the present invention is Three-Phase Parallel Active Power Filter-APF, and the Linearization Feedback neural network sliding mode control method of Three Phase Shunt Active Filter, comprises the following steps

One, the Mathematical Modeling of Three Phase Shunt Active Filter is set up

According to Circuit theory and Kirchhoff's theorem, the Mathematical Modeling of active filter is expressed as:

${\stackrel{.}{i}}_{\mathrm{ca}}=-\frac{{\mathrm{ri}}_{\mathrm{ca}}+V_{\mathrm{sa}}}{L}+\frac{V_{\mathrm{dc}}}{L}\mathrm{\β}---\left(1\right)$

${\stackrel{.}{i}}_{\mathrm{cb}}=-\frac{{\mathrm{ri}}_{\mathrm{cb}}+V_{\mathrm{sb}}}{L}+\frac{V_{\mathrm{dc}}}{L}\mathrm{\β}---\left(2\right)$

${\stackrel{.}{i}}_{\mathrm{cc}}=-\frac{{\mathrm{ri}}_{\mathrm{cc}}+V_{\mathrm{sc}}}{L}+\frac{V_{\mathrm{dc}}}{L}\mathrm{\β}---\left(3\right)$

Wherein, β is switch function, and the operating state of instruction IGBT, is defined as $\mathrm{\β}=\left\{\begin{array}{cc}1& Q_N=1\\ 0& Q_N=0\end{array}\right.,$ 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 power filter terminal voltage, V _dcfor DC capacitor voltage, r is resistance, and L is inductance,

Can by above-mentioned component equation with being write as following form:

${\stackrel{\·}{i}}_c=-\frac{r}{L}{i}_c+\frac{V_s}{L}+\frac{V_{\mathrm{dc}}}{L}\mathrm{\β}---\left(4\right)$

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

$\stackrel{\·}{x}=f\left(x\right)+\mathrm{bu}---\left(5\right)$

Wherein, x=i _c, $f\left(x\right)=-\frac{r}{L}x+\frac{V_s}{L},b=\frac{V_{\mathrm{dc}}}{L},u=\mathrm{\β}$

In this, as the basis of the neural sliding formwork of Linearization Feedback.

Two, Linearization Feedback method, sliding formwork control, white adaptive algorithm and RBF neural are combined, design Linearization Feedback adapts to RBF neural network sliding mode control device in vain, linearization feedback neural sliding formwork control law is acted on the switch function of Three Phase Shunt Active Filter, realize described controller approaching Three Phase Shunt Active Filter switch function, thus control the break-make of active filter main circuit switch, produce the offset current contrary with harmonic current equal and opposite in direction, direction, offset harmonic wave, be specially

1, Linearization Feedback theory is:

Consider following SISO system:

$\left\{\begin{array}{c}\stackrel{\·}{x}=f_0\left(x\right)+g_0\left(x\right)\mathrm{\τ}\\ y=h\left(x\right)\end{array}\right.---\left(6\right)$

Wherein, x ∈ R ⁿfor state variable, function f ₀(x), g ₀x () meets: R ⁿ→ R ⁿ(be input as n and tie up constant, so exporting also is that n ties up constant), function h (x) meets: R ⁿ→ R ⁿ, and f ₀(0)=0, h ₀(0)=0

Then $\stackrel{.}{y}=\frac{\∂h}{\∂x}\stackrel{\·}{x}=\frac{\∂h}{\∂x}{f}_0\left(x\right)+\frac{\∂h}{\∂x}{g}_0\left(x\right)\mathrm{\τ}---\left(7\right)$

Will be defined as f ₁(x), be defined as g ₁(x),

$\stackrel{\·}{y}=f_1\left(x\right)+g_1\left(x\right)\mathrm{\τ}$

Suppose g ₁(x) ≠ 0, design linearisation Feedback Control Laws τ is:

$\mathrm{\τ}=\frac{R-f_1\left(x\right)}{g_1\left(x\right)}---\left(8\right)$

Then formula (7) becomes linear system

If position command is y _d, getting R is

$R={\stackrel{\·}{y}}_d-\mathrm{\α}(y-y_d)---\left(9\right)$

Wherein, α >0 is proportionality coefficient, then formula (9) becomes

$\stackrel{\·}{e}+\mathrm{\αe}=0---\left(10\right)$

Wherein e is error function, e=y-y _d.

Obvious formula (10) is error dynamics equation, and e (t) levels off to zero with exponential form, if then e (t) free (t>=0) be all zero.

2, utilize Linearization Feedback theoretical, design sliding mode controller, obtains sliding formwork control law

Know that the Mathematical Modeling of APF can be write as the target controlled makes x follow the tracks of a Setting signal x exactly _m,

Definition tracking error function e is, e=x-x _m,

Definition sliding formwork function s is s (t)=ce (11)

Wherein, c is sliding formwork coefficient,

According to Linearization Feedback technology, by sliding formwork control law u ₁be designed to

$u_1=\frac{R-f\left(x\right)}{b}---\left(12\right)$

Wherein, R=ξ (x)-ρ sgn (s) (13)

$\mathrm{\ξ}\left(x\right)={\stackrel{\·}{x}}_m---\left(14\right)$

ρ is Linearization Feedback parameter, ρ >0

Stability proves:

Definition Lyapunov function V ₁

$V_1=\frac{1}{2}{s}^2---\left(15\right)$

To its differentiate, obtain

${\stackrel{\·}{V}}_1=s\stackrel{\·}{s}=\mathrm{sc}\stackrel{\·}{e}=\mathrm{sc}(\stackrel{\·}{x}-{\stackrel{\·}{x}}_m)---\left(16\right)$

$=\mathrm{sc}(f\left(x\right)+\mathrm{bu}-{\stackrel{\·}{x}}_m)$

By sliding formwork control law u ₁substitute into formula (16) as switch function u to obtain

${\stackrel{\·}{V}}_1=-\mathrm{sc\ρsgn}\left(s\right)---\left(17\right)$

Namely

${\stackrel{\·}{V}}_1=-\mathrm{c\ρ}\left|s\right|---\left(18\right)$

So ${\stackrel{\·}{V}}_1\≤0$

The stability of APF system can be proved thus according to Lyapunov Theory of Stability.

3, design self_adaptive RBF neural network sliding mode control device, obtain Linearization Feedback neural network sliding mode control rule u,

Because time-varying function f (x) is unknown, sliding formwork control law formula (12) is difficult to realize, utilize RBF neural with the function of arbitrary accuracy Approximation of Arbitrary Nonlinear Function, can to approach nonlinear function f (x) of the unknown, with the output of RBF neural replace f (x), realize adaptive neural network sliding formwork and control, concrete grammar is:

Suppose to there is neural network weight w, make approach f (x), its approximation accuracy is ε, that is:

$\max \left|\right|\hat{f}\left(x\right)-f\left(x\right)\left|\right|\≤\mathrm{\ϵ}$

Definition w _tfor weight w is in the estimated value of t,

Then obtaining Linearization Feedback neural network sliding mode control rule u is,

$u=\frac{R-\hat{f}\left(x\right)}{b}---\left(19\right)$

Wherein,

$\hat{f}\left(x\right)=w_{t}h\left(x\right)---\left(20\right)$

X is the input of RBF neural, and h (x) is Gaussian function, exports for the estimated value of unknown nonlinear function f (x).

4, according to lyapunov function design adaptive law, the stability of Linearization Feedback self_adaptive RBF neural network sliding mode control device is guaranteed,

Design adaptive law for

${\stackrel{\·}{w}}_t=\mathrm{pcsh}\left(x\right)---\left(20\right)$

P is auto-adaptive parameter.

If neural network weight in the optimal value of t is

$w_t^{*}=\arg \underset{w_t\∈{\mathrm{\Ω}}_t}{\min }\left[\sup \right|\hat{f}\left(x\right|\underset{x\∈R^n}{w_t})-f\left(x\right)\left|\right]---\left(21\right)$

Wherein, Ω _tbe respectively w _tset.

Definition minimum approximation error m is

$m=f\left(x\right)-\hat{f}\left(x\right|w_t^{*})---\left(22\right)$

|m|≤m _max(23)

M _maxfor the upper bound of minimum approximation error

Then sliding formwork function derivative

$\begin{array}{c}\stackrel{\·}{s}=c\stackrel{\·}{e}=c(\stackrel{\·}{x}-{\stackrel{\·}{x}}_m)=c[f\left(x\right)+\mathrm{bu}-{\stackrel{\·}{x}}_m]\\ =c[f\left(x\right)+R-\hat{f}\left(x\right)-{\stackrel{\·}{x}}_m]\\ =c[\hat{f}\left(x{{/w}^{*}}_t\right)+m+\mathrm{\ξ}\left(x\right)-\mathrm{\ρsgn}\left(s\right)-\hat{f}\left(x\right){{\stackrel{\·}{x}}_m}_{}]\\ =c[\hat{f}(x/{w^{*}}_t)-\hat{f}\left(x\right)+m-\mathrm{\ρsgn}\left(s\right)]\\ =c[{w_t}^{*}h\left(x\right)-w_{t}h\left(x\right)+m-\mathrm{\ρsgn}\left(s\right)]\\ =c[\tilde{w}h\left(x\right)+m-\mathrm{\ρsgn}\left(s\right)]\end{array}---\left(24\right)$

Wherein, for neural network weight is in the error of t.

Choosing lyapunov function V is

$V=\frac{1}{2}(s^2+\frac{1}{p}{\tilde{w}}^T\tilde{w})---\left(25\right)$

Wherein, p is auto-adaptive parameter.

Lyapunov function V differentiate is obtained

$\stackrel{\·}{V}=s\stackrel{\·}{s}+\frac{1}{p}{\tilde{w}}^T\stackrel{\·}{\tilde{w}}$

$=\mathrm{sc}[{\tilde{w}}^{T}h\left(x\right)+m-\mathrm{\ρsgn}\left(s\right)]+\frac{1}{p}{\tilde{w}}^T\stackrel{\·}{\tilde{w}}---\left(26\right)$

$=\mathrm{sc}{\tilde{w}}^{T}h\left(x\right)+\frac{1}{p}{\tilde{w}}^T\stackrel{\·}{\tilde{w}}+\mathrm{sc}(m-\mathrm{\ρsgn}\left(s\right))$

$=\frac{1}{p}{\tilde{w}}^T(\mathrm{pcsh}\left(x\right)+\stackrel{\·}{\tilde{w}})+\mathrm{sc}(m-\mathrm{\ρsgn}\left(s\right))$

Wherein, because w _t ^*for constant, therefore

Adaptive law formula (20) is substituted into formula (26) obtain

$\stackrel{\·}{V}=\mathrm{sc}(m-\mathrm{\ρsgn}\left(s\right))---\left(27\right)$

When minimum approximation error m is substantially equal to 0, formula (27) can be write as

$\stackrel{\·}{V}=-\mathrm{sc\ρsgn}\left(s\right)=-\mathrm{c\ρ}\left|s\right|---\left(28\right)$

So we just can obtain

$\stackrel{\·}{V}\≤0.$

Now meet Lyapunov stability condition, can prove that Linearization Feedback self_adaptive RBF neural network sliding mode control device is stable thus.

Through above-mentioned steps, achieve RBF neural network sliding mode control device based on Linearization Feedback to the control constantly of Three-Phase Shunt Active Power electric-power filter, thus realize the compensation to harmonic wave, reduce current distortion rate, improve grid supply quality.

Finally by emulation experiment, checking the inventive method

In the present embodiment, self_adaptive RBF neural network sliding mode control device played a role from 0.05 second, and emulation in 0.16 second terminates.Parameter designing is as follows:

Parameter in RBF neural: 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;

PI controller controls 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 offset current trace command electric current that APF exports, what Fig. 3 described is the oscillogram of offset current and instruction current deviation, as can be seen from the figure, white adaptation RBF neural network sliding mode control device is introduced when 0.05 second, the switch function of APF is controlled, within 0.06 second, precompensation electric current can trace into instruction current, both deviations level off to 0, tracking effect is better, be effectively eliminated harmonic wave like this, adopt white adaptive algorithm to adjust the weights of RBF neural simultaneously, significantly reduce percent harmonic distortion, make source current close to sinusoidal wave, greatly reduce percent harmonic distortion.Show that Active Power Filter-APF has good compensation effect to harmonic current thus, demonstrating 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, comprise the following steps:

1) Mathematical Modeling of controlled device Three Phase Shunt Active Filter is set up;

2) Linearization Feedback method, sliding formwork control, adaptive algorithm and RBF neural are combined, design linearisation feedback adaptive RBF neural network sliding mode control device, its linearization feedback neural sliding formwork control law is acted on the switch function of Three Phase Shunt Active Filter, is specially:

2-1) utilize Linearization Feedback method, design sliding mode controller, obtains sliding formwork control law, is specially,

Definition sliding formwork function s is: s (t)=ce

Wherein, c is sliding formwork coefficient, and e is tracking error

The mathematical modulo pattern of active filter is:

According to Linearization Feedback technology, design sliding formwork control law u ₁for:

Wherein, R=ξ (x)-ρ sgn (s)

x _mfor Setting signal, ρ is Linearization Feedback parameter, ρ > 0

2-2) 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 Three Phase Shunt Active Filter switch function, thus control the break-make of active filter main circuit switch, produce the offset current contrary with harmonic current equal and opposite in direction, direction, offset harmonic wave, be specially

First, suppose to there is neural network weight w, make the output of neural net approach time-varying function f (x), its approximation accuracy is ε, that is:

$max||\hat{f}\left(x\right)-f\left(x\right)||\≤\mathrm{\ϵ}$

Definition w _tfor neural network weight w is in the estimated value of t

With the output of neural net replace time-varying function f (x), obtaining Linearization Feedback neural network sliding mode control rule u is, $u=\frac{R-\hat{f}\left(x\right)}{b}$

Wherein, x is the input of RBF neural, and h (x) is Gaussian function, exports for the estimated value of unknown nonlinear function f (x);

3) according to lyapunov function design adaptive law, the stability of Linearization Feedback self_adaptive RBF neural network sliding mode control device is guaranteed,

Described lyapunov function V is chosen for,

Described adaptive law be designed to,

Wherein, for neural network weight is in the error of t, w _t ^*for neural network weight is in the optimal value of t, 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) set up the Mathematical Modeling of controlled device Three Phase Shunt Active Filter, be specially

1-1) according to Circuit theory and Kirchhoff's theorem, the Mathematical Modeling of active filter is expressed as

$\stackrel{\·}{i}{c}_{}=-\frac{r}{L}{i}_c+\frac{V_s}{L}+\frac{V_{dc}}{L}\mathrm{\β}---\left(4\right)$

Wherein, i _cfor active filter offset current, V _dcfor DC capacitor voltage, V _sfor active filter terminal voltage, r is resistance, and L is inductance, and β is switch function;

1-2) define parameter x, parameter u, time-varying function f (x), constant term b,

Make x=i _c, $f\left(x\right)=-\frac{r}{L}x+\frac{V_s}{L},$ $b=\frac{V_{dc}}{L},$ u＝β

Then the mathematical modulo pattern (4) of active filter becomes:

$\stackrel{\·}{x}=f\left(x\right)+bu---\left(5\right)$

In this, as the basis of 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 instruction IGBT, is defined as $\mathrm{\β}=\{\begin{array}{cc}1& Q_N=1\\ 0& Q_N=0\end{array},$ Q _nrepresent the operating state of IGBT, conducting is 1, and shutoff is 0.