CN104753351B - It is a kind of to be used for inductive current forecast Control Algorithm in non-isolated charging Buck circuits - Google Patents

Abstract

The invention discloses it is a kind of for inductive current forecast Control Algorithm in non-isolated charging Buck circuits, it was (n 1) T by a upper moment_SThe inductor current value i at moment_L(n 1) predicts next moment i.e. nT_SThe inductor current value at moment and then according to power conservation, according to the nT of prediction_SThe inductor current value at moment calculates nT_SThe dutycycle of moment switching tube；Again according to stable state expected value, convergence process is carried out to result of calculation, the control dutycycle of respective switch pipe is directly calculated by predictive value and steady state predictions value, so as to obtain dutycycle D of final switching tube_xN (), generation dutycycle are D_xN the PWM ripples of () are realized to nT controlling the pipe that opens the light_SThe control of moment inductive current.The present invention obtains dutycycle by preservation of energy, and can quickly calculate dutycycle by preservation of energy, and rapid tracking is given, in given mutation, also can quickly follow the trail of given, and dynamic response, control accuracy are significantly improved.

Description

It is a kind of to be used for inductive current forecast Control Algorithm in non-isolated charging Buck circuits

Technical field

The invention belongs to power electronic system, electric vehicle engineering field, and in particular to a kind of to charge for non-isolated Inductive current forecast Control Algorithm in Buck circuits.

Background technology

DC-DC converter has the advantages that high conversion efficiency, small volume, control accuracy are high, is widely used in each neck Domain.And in recent years, as various countries are greatly developed to ev industry, the research and development to peripheral product thereupon are also gradually received To concern energetically.Specifically how charging batteries of electric automobile is effectively carried out, become the problem of the popular research of people. And, batteries of electric automobile constantly updates in recent years, and the requirement of new and effective battery to charging device becomes more It is strict.As the control of Buck circuits is simple, shared spatial volume is little, and is widely used in charging circuit.

Nowadays, Buck circuits control has the control methods such as PI controls, Repetitive controller, fuzzy control.But great majority are all Using PI control technologies, its distinguishing feature is the model which is independent of changer, but only need to according to the error of control variable, By the dutycycle of dynamic regulation switching tube, the control to output voltage and other parameters is realized.The advantage of PI controls is control System design process processed is simple, the suitability is preferable；The design for having the disadvantage output feedback ontrol be control based on target error and Model cootrol is not based on, dynamic response characteristic is poor compared with slow, control effect, it is impossible to realize optimal control, it is impossible to meet switch The requirement of dynamic response and control accuracy that power supply is increasingly improved.

The content of the invention

It is an object of the invention to provide a kind of for inductive current forecast Control Algorithm in non-isolated charging Buck circuits, solution Determine the problem that dynamic response characteristic present in prior art is slow, control accuracy is poor.

The technical solution adopted in the present invention is, a kind of for inductive current PREDICTIVE CONTROL in non-isolated charging Buck circuits Method, specifically implements according to following steps：

The magnitude of voltage v of the low tension potential source in step 1, sampling Buck circuits_L, high-tension electricity potential source magnitude of voltage v_H、(n-1) T_SThe inductor current value i at moment_L(n-1)、(n-1)T_SDutycycle D of switching tube in cycle_bu(n-1),

Wherein, T_SFor a switch periods of switching tube；

Step 2, judge nT_SGiven value of current i on moment inductance_LrefN whether () be less than 0, if being not less than 0, goes to step 3；If less than 0, then nT_SDutycycle D of switching tube in cycle_xN ()=0, goes to step 9；

Step 3, by formula (1) calculate nT_SThe inductive current predictive value at moment

Wherein,

L is inductance value；

Step 4, judgementWhether set up, if set up, go to step 5；If It is false, then nT_SDutycycle D of switching tube in cycle_xN ()=1, goes to step 9；

Step 5, by nT_SGiven value of current value i on moment inductance_LrefN () is assigned to nT_SCycle internal inductance electric current it is average ValueI.e.：

By the inductive current predictive value obtained in formula (1)Calculate nT_SDutycycle D of switching tube in cycle_bu (n)：

Wherein, D_bt=v_L/v_H；

Step 6, according to formula (5) calculate w (n)：

Judge whether w (n) >=0 sets up, if be false, go to step 7；If set up, step 8 is gone to；

Step 7, according to the inductive current predictive value obtained in formula (1)Calculate nT_SThe duty of switching tube in cycle Compare D_bu(n)：

Step 8, dutycycle D according to formula (7) calculating after intermediate value process_x(n)：

Wherein,For nT_SThe dutycycle of switching tube during cycle homeostasiss；

Step 9, generation dutycycle are D_xN the PWM ripples of () carry out controlling switch pipe.

The characteristics of of the invention, also resides in,

The detailed process for obtaining formula (4) in step 5 is：

nT_SIn cycle in switching tube opening process inductive current increment Delta i_L+For：

Wherein, i_LmaxN () is nT_SThe maximum of cycle internal inductance electric current,

The current average flow through in switching tube opening processFor：

In the ideal situation, when opening, v_HRelease energy, the ENERGY E discharged by it_onFor：

v_HThe energy part for releasing energy is stored in inductance, shows as the variable quantity of cycle internal inductance electric current, this Portion of energy Δ E_LIt is expressed as：

Another part is shown as to v for load consumption_LEnd is charged, the ENERGY E of load consumption in the monocycle_vLFor：

In the ideal situation, and ignore various losses, obtained according to preservation of energy：

E_on=Δ E_L+E_vL (13)

Obtain final product：

After switching tube is turned off, due to the seriality of inductive current, inductance will be powered to the load by diode, so electric Electric current in sense is by natural decline.In the pad value Δ i of this stage inductive current_L-For：

In nT_SCycle is to (n+1) T_SIn cycle, inductive current is by i_LN () is changed into i_L(n+1), then by formula (8) and Formula (15) obtains (n+1) T_SThe inductive current i at moment_L(n+1)：

Due to the reverse turn-off characteristic of diode, inductive current cannot continuously decay to negative value, then i_L(n+1) there is one Discontinuity point, expression formula is：

Formula (17) is converted to：

When w (n) >=0, formula (16) is substituted into into formula (14) and is obtained：

Work as satisfaction

I.e.

When, formula (19) has solution, and solution is：

The detailed process for obtaining formula (6) in step 7 is：

It is i as w (n) ＜ 0_L(n+1)=0 substitutes into formula (14) obtains：

Work as satisfaction

I.e.

When, formula (22) has solution, and solution is：

In step 1, Buck circuits include low tension potential source v_L, low tension potential source v_LNegative pole respectively with high-tension electricity potential source v_H's The positive pole connection of negative pole, diode D, high-tension electricity potential source v_HPositive pole connecting valve pipe S colelctor electrode, the emitter stage of switching tube S Connect negative pole, the inductance L of diode D respectively.

Switching tube S be carry anti-paralleled diode or with anti-paralleled diode characteristic can switch-off power switching device.

The invention has the beneficial effects as follows：

1. traditional modeling analysis are all based on two kinds of mode of operations of CCM and DCM, and the acquisition of dutycycle generally according to Small-signal analysis gets, it is of the invention then by summarizing the particular states such as DCM, CCM, stable state and dynamic, and carry out overall classification, according to Dutycycle is obtained according to preservation of energy, then according to stable state expected value, convergence process is carried out to result of calculation, by predictive value and surely State predictive value directly calculates the control dutycycle of respective switch pipe, so as to obtain the dutycycle of final switching tube, realizes to electricity The control of inducing current.

2. the present invention can quickly calculate the dutycycle of switching tube according to the rule of preservation of energy.When being not added with convergence, 1 Individual switch periods can just track given；Add when holding back, 2 switch periods can just be tracked and be given.In given mutation, also can be quick Tracking give, dynamic response, control accuracy are significantly improved.

Description of the drawings

Fig. 1 is Buck electrical schematic diagrams in the present invention；

Fig. 2 is the inductive current dynamic waveform figure of Buck circuits in the present invention；

Fig. 3 is seven kinds of working mode figures of Buck circuit inductance electric currents in the monocycle in the present invention；

Fig. 4 is switching tube current waveform schematic diagram in the Single switch cycle in the present invention；

Fig. 5 is the flow chart of inductive current forecast Control Algorithm of the present invention；

Fig. 6 is the asynchronous inductive current oscillogram of sampled value in the present invention；

Inductive current oscillogram when Fig. 7 is stable state in the present invention.

Specific embodiment

The present invention is described in detail with reference to the accompanying drawings and detailed description.

Buck circuit diagrams of the present invention are illustrated in figure 1, Buck circuits include low tension potential source v_L(low tension potential source is generally Accumulator or super capacitor), low tension potential source v_LNegative pole respectively with high-tension electricity potential source v_H(generally dc bus is in parallel props up Support electric capacity voltage, as capacitance voltage can not be mutated, so a voltage source can be regarded in the short time as) negative pole, two poles The positive pole connection of pipe D, high-tension electricity potential source v_HPositive pole connecting valve pipe S colelctor electrode, the emitter stage of switching tube S connects two respectively The negative pole of pole pipe D, inductance L.

Wherein switching tube S be carry anti-paralleled diode or with anti-paralleled diode characteristic can switch-off power derailing switch Part.

The dynamic waveform of inductive current in Buck circuits is illustrated in figure 2, wherein, i_LN () is open-minded in switching tube for inductance Action moment nT_S(T_SFor a switch periods of switching tube) electric current, T_sFor a switch periods of switching tube, D_buFor switch Dutycycle.

Buck generally describes the steady state operating mode of on-off circuit with CCM, DCM, and the dynamic of circuit is have ignored under this division The state course of work, is illustrated in figure 3 seven kinds of working mode figures of monocycle internal inductance electric current, and seven kinds of mode of operation sign Buck are electric The mode of operation on road.

In switching tube opening process, the electric current for flowing through switching tube is as shown in Figure 4.Wherein Δ i_L+For nT_SSwitch in cycle The increment of inductive current in pipe opening process, is expressed as by formula (8)：

Wherein, i_LmaxN () is nT_SThe maximum of cycle internal inductance electric current,

The current average flow through in switching tube opening processFor：

In the ideal situation, when opening, v_HRelease energy, the ENERGY E discharged by it_onFor：

v_HThe energy part for releasing energy is stored in inductance, shows as the variable quantity of cycle internal inductance electric current, this Portion of energy Δ E_LIt is expressed as：

Another part is shown as to v for load consumption_LEnd is charged, the ENERGY E of load consumption in the monocycle_vLFor：

In the ideal situation, and ignore various losses, obtained according to preservation of energy：

E_on=Δ E_L+E_vL (13)

Obtain final product：

After switching tube is turned off, due to the seriality of inductive current, inductance will be powered to the load by diode, so electric Electric current in sense by natural decline, in the pad value Δ i of this stage inductive current_L-For：

In nT_SCycle is to (n+1) T_SIn cycle, inductive current is by i_LN () is changed into i_L(n+1), then by formula (8) and Formula (15) obtains (n+1) T_SThe inductive current i at moment_L(n+1)：

Due to the reverse turn-off characteristic of diode, inductive current cannot continuously decay to negative value, then i_L(n+1) there is one Discontinuity point, expression formula is：

Formula (17) is converted to：

When w (n) >=0, formula (16) is substituted into into formula (14) and is obtained：

Work as satisfaction

I.e.

When, formula (19) has solution, and solution is：

Draw from formula (21), the equal sign when dutycycle is 1 in formula (21) is just set up, so limiting dutycycle Under conditions of 1, formula (19) necessarily has solution；When formula (21) is false i.e.Say Given current value cannot be realized in the bright monocycle, needs the multicycle to complete, given dutycycle is set to into higher limit directly.

It is i as w (n) ＜ 0_L(n+1)=0 substitutes into formula (14) obtains：

Work as satisfaction

I.e.

When, formula (22) has solution, and solution is：

Due to average inductor current perseveranceMore than or equal to 0, therefore understand that equation (22) necessarily has solution by formula (24), then only W (n) ＜ 0 need to be met, it is possible to dutycycle be calculated with above formula.

As existing Digital Signal Processing (DSP) unit delay cannot be avoided, so must calculate before the cycle starts Go out dutycycle, it is therefore desirable to predict nT_SThe inductive current at moment

The present invention is used for inductive current forecast Control Algorithm in non-isolated charging Buck circuits, specifically according to following steps reality Apply, as shown in Figure 5：

The magnitude of voltage v of the low tension potential source in step 1, sampling Buck circuits_L, high-tension electricity potential source magnitude of voltage v_H、(n-1) T_SThe inductor current value i at moment_L(n-1)、(n-1)T_SDutycycle D of switching tube in cycle_bu(n-1)；

Step 2, judge nT_SGiven value of current i on moment inductance_LrefN whether () be less than 0, if being not less than 0, goes to step 3；If less than 0, then nT_SDutycycle D of switching tube in cycle_xN ()=1, goes to step 9；

Step 3, by formula (1) calculate nT_SThe inductive current predictive value at moment

Wherein,

L is inductance value, T_SFor a switch periods of switching tube；

Step 4, judgementWhether set up, if set up, go to step 5；If It is false, then nT_SDutycycle D of switching tube in cycle_xN ()=1, goes to step 9；

Step 5, by nT_SGiven value of current value i on moment inductance_LrefN () is assigned to nT_SCycle internal inductance electric current it is average ValueI.e.：

By the inductive current predictive value obtained in formula (1)Substitute in the solution that formula (19) draws, can obtain nT_SDutycycle D of switching tube in cycle_bu(n)：

Wherein, D_bt=v_L/v_H；

Step 6, according to formula (5) calculate w (n)：

Judge whether w (n) >=0 sets up, if be false, go to step 7；If set up, step 8 is gone to；

Step 7, according to the inductive current predictive value obtained in formula (1)Substitute in the solution that formula (23) is obtained, meter Calculate nT_SDutycycle D of switching tube in cycle_bu(n)：

If the initial value of the inductive current of sampling is different, situation as shown in Figure 6 is likely to occur, that is, inductance electricity occur The problem that stream is not restrained.

Step 8, in order to solve the problems, such as that inductive current is not restrained, only need to take nT_SDutycycle D of switching tube in cycle_bu(n) With dutycycle D of stable state moment switching tube_zMeansigma methodss D of (n)_xN (), i.e., calculate D according to formula (7)_x(n)：

When switching tube reaches stable state, the waveform of inductive current is as shown in fig. 7, i.e.

Δi_L+=-Δ i_L-,

Can obtain：nT_SDutycycle D of switching tube during cycle homeostasiss_zN () is：

Step 9, generation dutycycle are D_xN the PWM ripples of () carry out controlling switch pipe.

The present invention obtains dutycycle by preservation of energy, and can quickly calculate dutycycle by preservation of energy, Rapid tracking is given, in given mutation, also can quickly follow the trail of given, and dynamic response, control accuracy are significantly improved.

Claims (4)

1. a kind of for inductive current forecast Control Algorithm in non-isolated charging Buck circuits, it is characterised in that specifically according to Lower step is implemented：

The magnitude of voltage v of the low tension potential source in step 1, sampling non-isolated charging Buck circuits_L, high-tension electricity potential source magnitude of voltage v_H、 (n-1)T_SThe inductor current value i at moment_L(n-1)、(n-1)T_SDutycycle D of switching tube in cycle_bu(n-1),

Wherein, T_SFor a switch periods of switching tube；

Step 2, judge nT_SGiven value of current i on moment inductance_LrefN whether () be less than 0, if being not less than 0, goes to step 3；Such as Fruit is less than 0, then nT_SDutycycle D of switching tube in cycle_xN ()=0, goes to step 9；

Step 3, by formula (1) calculate nT_SThe inductive current predictive value at moment

${\hat{i}}_L\left(n\right)=\left\{\begin{array}{cc}w(n-1),& w(n-1)\&GreaterEqual;0\\ 0,& w(n-1)<0\end{array}\right.---\left(1\right)$

Wherein,

$w(n-1)=i_L(n-1)+\frac{1}{L}\&CenterDot;T_S\&CenterDot;(v_H\&CenterDot;D_{bu}(n-1)-v_L)---\left(2\right)$

L is inductance value；

Step 4, judgementWhether set up, if set up, go to step 5；If not into Stand, then nT_SDutycycle D of switching tube in cycle_xN ()=1, goes to step 9；

Step 5, by nT_SGiven value of current value i on moment inductance_LrefN () is assigned to nT_SThe meansigma methodss of cycle internal inductance electric currentI.e.：

${\stackrel{\&OverBar;}{i}}_L\left(n\right)=i_{Lref}\left(n\right)---\left(3\right)$

By the inductive current predictive value obtained in formula (1)Calculate nT_SDutycycle D of switching tube in cycle_bu(n)：

$D_{bu}\left(n\right)=1-\sqrt{1-D_{bt}-\frac{2L\&CenterDot;\&lsqb;{\stackrel{\&OverBar;}{i}}_L\left(n\right)-{\hat{i}}_L\left(n\right)\&rsqb;}{v_H\&CenterDot;T_S}}---\left(4\right)$

Wherein, D_bt=v_L/v_H；

Step 6, according to formula (5) calculate w (n)：

$w\left(n\right)={\hat{i}}_L\left(n\right)+\frac{1}{L}\&CenterDot;T_S\&CenterDot;(v_H\&CenterDot;D_{bu}(n)-v_L)---\left(5\right)$

Judge whether w (n) >=0 sets up, if be false, go to step 7；If set up, step 8 is gone to；

Step 7, according to the inductive current predictive value obtained in formula (1)Calculate nT_SDutycycle D of switching tube in cycle_bu (n)：

$D_{bu}\left(n\right)=\frac{-L\&CenterDot;{\hat{i}}_L\left(n\right)}{(v_H-v_L)\&CenterDot;T_S}+\frac{\sqrt{D_{bt}\&CenterDot;\&lsqb;L^2\&CenterDot;{{\hat{i}}_L}^2\left(n\right)+2L\&CenterDot;T_S\&CenterDot;(v_H-v_L)\&CenterDot;{\stackrel{\&OverBar;}{i}}_L\left(n\right)\&rsqb;}}{(v_H-v_L)\&CenterDot;T_S}---\left(6\right)$

Step 8, dutycycle D according to formula (7) calculating after intermediate value process_x(n)：

$D_x\left(n\right)=\frac{1}{2}\left(D_{bu}\right(n)+D_z(n\left)\right)---\left(7\right)$

Wherein,For nT_SThe dutycycle of switching tube during cycle homeostasiss；

Step 9, generation dutycycle are D_xN the PWM ripples of () carry out controlling switch pipe；

In the step 1, Buck circuits include low tension potential source v_L, low tension potential source v_LNegative pole respectively with high-tension electricity potential source v_H's The positive pole connection of negative pole, diode D, high-tension electricity potential source v_HPositive pole connecting valve pipe S colelctor electrode, the emitter stage of switching tube S Connect negative pole, the inductance L of diode D respectively.

2. according to claim 1 a kind of for inductive current forecast Control Algorithm in non-isolated charging Buck circuits, its It is characterised by, the detailed process for obtaining formula (4) in the step 5 is：

nT_SIn cycle in switching tube opening process inductive current increment Delta i_L+For：

${\mathrm{\&Delta;i}}_{L+}=i_{Lmax}\left(n\right)-i_L\left(n\right)=\frac{1}{L}(v_H-v_L)\&CenterDot;D_{bu}\left(n\right)\&CenterDot;T_S---\left(8\right)$

Wherein, i_LmaxN () is nT_SThe maximum of cycle internal inductance electric current,

The current average flow through in switching tube opening processFor：

$\stackrel{\&OverBar;}{i_{on}}=i_L\left(n\right)+\frac{1}{2}{\mathrm{\&Delta;i}}_{L+}---\left(9\right)$

In the ideal situation, when opening, v_HRelease energy, the ENERGY E discharged by it_onFor：

$E_{on}=v_H\&CenterDot;\stackrel{\&OverBar;}{i_{on}}\&CenterDot;D_{bu}\left(n\right)\&CenterDot;T_S---\left(10\right)$

v_HThe energy part for releasing energy is stored in inductance, shows as the variable quantity of cycle internal inductance electric current, this part of energy Amount uses Δ E_LIt is expressed as：

${\mathrm{\&Delta;E}}_L=\frac{1}{2}L\&lsqb;{i_L}^2(n+1)-{i_L}^2\left(n\right)\&rsqb;---\left(11\right)$

Another part is shown as to v for load consumption_LEnd is charged, the ENERGY E of load consumption in the monocycle_vLFor：

$E_{v_L}=v_L\&CenterDot;{\stackrel{\&OverBar;}{i}}_L\left(n\right)\&CenterDot;T_S---\left(12\right)$

In the ideal situation, and ignore various losses, obtained according to preservation of energy：

E_on=Δ E_L+E_vL (13)

Obtain final product：

${\stackrel{\&OverBar;}{i}}_L\left(n\right)=\frac{L\&CenterDot;\&lsqb;{i_L}^2\left(n\right)-{i_L}^2(n+1)\&rsqb;}{2\&CenterDot;v_L\&CenterDot;T_S}+\frac{v_H}{v_L}\&CenterDot;D_{bu}\left(n\right)\&CenterDot;i_L\left(n\right)+\frac{1}{2L}\&CenterDot;\frac{v_H}{v_L}\&CenterDot;(v_H-v_L)\&CenterDot;{D^2}_{bu}\left(n\right)\&CenterDot;T_S---\left(14\right)$

After switching tube is turned off, due to the seriality of inductive current, inductance will be powered to the load by diode, so in inductance Electric current by natural decline, in the pad value Δ i of this stage inductive current_L-For：

${\mathrm{\&Delta;i}}_{L-}=\frac{1}{L}(-v_L)\&CenterDot;(1-D_{bu}(n\left)\right)\&CenterDot;T_S---\left(15\right)$

In nT_SCycle is to (n+1) T_SIn cycle, inductive current is by i_LN () is changed into i_L(n+1), then by formula (8) and formula (15) obtain (n+1) T_SThe inductive current i at moment_L(n+1)：

$i_L(n+1)=i_L\left(n\right)+{\mathrm{\&Delta;i}}_{L+}+{\mathrm{\&Delta;i}}_{L-}=i_L\left(n\right)+\frac{1}{L}\&CenterDot;T_S\&CenterDot;(v_H\&CenterDot;D_{bu}(n)-v_L)=w\left(n\right)---\left(16\right)$

Due to the reverse turn-off characteristic of diode, inductive current cannot continuously decay to negative value, then i_L(n+1) there is one not connect Continuous, expression formula is：

$i_L(n+1)=\left\{\begin{array}{cc}w\left(n\right),& w\left(n\right)\&GreaterEqual;0\\ 0,& w\left(n\right)<0\end{array}\right.---\left(17\right)$

Formula (17) is converted to：

$i_L(n+1)=\left\{\begin{array}{cc}w\left(n\right),& D_{bu}\left(n\right)\&GreaterEqual;D_{bt}-\frac{L\&CenterDot;i_L\left(n\right)}{v_H\&CenterDot;T_s}\\ 0,& D_{bu}\left(n\right)<D_{bt}-\frac{L\&CenterDot;i_L\left(n\right)}{v_H\&CenterDot;T_s}\end{array}\right.---\left(18\right)$

When w (n) >=0, formula (16) is substituted into into formula (14) and is obtained：

$v_H\&CenterDot;T_S\&CenterDot;{D^2}_{bu}\left(n\right)-2T_S\&CenterDot;v_H\&CenterDot;D_{bu}\left(n\right)+T_S\&CenterDot;v_L-2L\&lsqb;i_L\left(n\right)-{\stackrel{\&OverBar;}{i}}_L\left(n\right)\&rsqb;=0---\left(19\right)$

Work as satisfaction

$4\{\&lsqb;({v_H}^2-v_H\&CenterDot;v_L)\&CenterDot;T_S^2+2L\&CenterDot;v_H\&CenterDot;T_S\&lsqb;i_L\left(n\right)-{\stackrel{\&OverBar;}{i}}_L\left(n\right)\&rsqb;\&rsqb;\}\&GreaterEqual;0---\left(20\right)$

I.e.

When, formula (19) has solution, and solution is：

$D_{bu}\left(n\right)=1-\sqrt{1-D_{bt}-\frac{2L\&CenterDot;\&lsqb;{\stackrel{\&OverBar;}{i}}_L\left(n\right)-i_L\left(n\right)\&rsqb;}{v_H\&CenterDot;T_S}}.$

3. according to claim 2 a kind of for inductive current forecast Control Algorithm in non-isolated charging Buck circuits, its It is characterised by, the detailed process for obtaining formula (6) in the step 7 is：

It is i as w (n) ＜ 0_L(n+1)=0 substitutes into formula (14) obtains：

$v_H\&CenterDot;(v_H-v_L)\&CenterDot;T_S^2\&CenterDot;{D^2}_{bu}\left(n\right)+2L\&CenterDot;v_H\&CenterDot;T_S\&CenterDot;i_L\left(n\right)\&CenterDot;D_{bu}\left(n\right)+L^2\&CenterDot;{i_L}^2\left(n\right)-2L\&CenterDot;T_S\&CenterDot;v_L\&CenterDot;{\stackrel{\&OverBar;}{i}}_L\left(n\right)=0---\left(22\right)$

Work as satisfaction

$4\&CenterDot;v_H\&CenterDot;v_L\&CenterDot;T_S^2\&CenterDot;\&lsqb;L^2\&CenterDot;{i_L}^2\left(n\right)+2L\&CenterDot;T_S\&CenterDot;(v_H-v_L)\&CenterDot;{\stackrel{\&OverBar;}{i}}_L\left(n\right)\&rsqb;\&GreaterEqual;0---\left(23\right)$

I.e.

When, formula (22) has solution, and solution is：

$D_{bu}\left(n\right)=\frac{-L\&CenterDot;i_L\left(n\right)}{(v_H-v_L)\&CenterDot;T_S}+\frac{\sqrt{D_{bt}\&CenterDot;\&lsqb;L^2\&CenterDot;{i_L}^2\left(n\right)+2L\&CenterDot;T_S\&CenterDot;(v_H-v_L)\&CenterDot;{\stackrel{\&OverBar;}{i}}_L\left(n\right)\&rsqb;}}{(v_H-v_L)\&CenterDot;T_S}.$

4. according to claim 3 a kind of for inductive current forecast Control Algorithm in non-isolated charging Buck circuits, its Be characterised by, the switching tube S be carry anti-paralleled diode or with anti-paralleled diode characteristic can switch-off power switch Device.