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

Inductive current prediction control method for non-isolated charging Buck circuit

Technical Field

The invention belongs to the technical field of power electronic systems and electric automobiles, and particularly relates to an inductive current prediction control method for a non-isolated charging Buck circuit.

Background

The DC-DC converter has the advantages of high conversion efficiency, small volume, high control precision and the like, and is widely applied to various fields. In recent years, along with the rapid development of the electric automobile industry in various countries, the research and development of peripheral products have been receiving great attention. Particularly, how to effectively charge the battery of the electric vehicle becomes a problem of popular research. Moreover, in recent years, batteries of electric automobiles are continuously updated, and the requirements of novel efficient batteries on charging devices become stricter. The Buck circuit is simple to control, occupies a small space and is widely applied to a charging circuit.

At present, a Buck circuit is controlled by control methods such as PI control, repetitive control, fuzzy control and the like. However, most of the methods adopt PI control technology, and the method has the remarkable characteristic that the method does not depend on a model of a converter, and only needs to dynamically adjust the duty ratio of a switching tube according to the error of a control variable to realize the control of output voltage and other parameters. The PI control has the advantages that the control system is simple in design process and good in applicability; the method has the defects that the design of output feedback control is based on the control of target errors instead of model control, the dynamic response characteristic is slow, the control effect is poor, the optimization control cannot be realized, and the requirements of increasingly improved dynamic response and control precision of the switching power supply cannot be met.

Disclosure of Invention

The invention aims to provide an inductive current prediction control method for a non-isolated charging Buck circuit, which solves the problems of slow dynamic response characteristic and poor control precision in the prior art.

The technical scheme adopted by the invention is that the inductive current prediction control method for the non-isolated charging Buck circuit is implemented according to the following steps:

step 1, sampling the voltage value v of a low-voltage source in a Buck circuit_LVoltage value v of high voltage source_H、(n-1)T_SValue of the inductance current i at a time_L(n-1)、(n-1)T_SDuty ratio D of switch tube in period_bu(n-1)，

Wherein, T_SOne switching period of the switching tube;

step 2, judging nT_SCurrent on time of day inductor is given by i_Lref(n) whether the value is less than 0, if not, turning to the step 3; if less than 0, nT_SDuty ratio D of switch tube in period_x(n) is 0, go to step 9;

step 3, calculating nT through a formula (1)_SInstantaneous inductor current prediction value

Wherein,

l is an inductance value;

step 4, judgmentWhether it is true, if so, turn toGo to step 5; if not, nT_SDuty ratio D of switch tube in period_x(n) 1, go to step 9;

step 5, mixing nT_SGiven value of current i on time inductor_Lref(n) assigning a value to nT_SAverage value of inductor current in cycleNamely:

the predicted value of the inductive current obtained by the formula (1)Calculating nT_SDuty ratio D of switch tube in period_bu(n)：

Wherein D is_bt＝v_L/v_H；

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

judging whether w (n) is equal to or more than 0, if not, turning to the step 7; if yes, go to step 8;

step 7, obtaining an inductive current predicted value according to the formula (1)Calculating nT_SDuty ratio D of switch tube in period_bu(n)：

Step 8, calculating the duty ratio D after median processing according to a formula (7)_x(n)：

Wherein,is nT_SDuty ratio of the switching tube in steady state in the period;

step 9, generating duty ratio D_xAnd (n) controlling the switching tube by the PWM wave.

The present invention is also characterized in that,

the specific process for obtaining the formula (4) in the step 5 is as follows:

nT_Sincrement delta i of inductive current in switching-on process of switching tube in period_L+Comprises the following steps:

wherein i_Lmax(n) is nT_SThe maximum value of the inductor current during the period,

average value of current flowing in switching-on process of switch tubeComprises the following steps:

when the switch is on under ideal conditions, v_HRelease energy, energy E released by it_onComprises the following steps:

v_Hpart of the energy released is stored in the inductor and appears as the change of the inductor current in the period, and the part of the energy is expressed by delta E_LExpressed as:

another part appears as v for load consumption_LEnd-charging, energy consumed by load in a single cycle E_vLComprises the following steps:

under ideal conditions, and ignoring various losses, according to the conservation of energy:

E_on＝ΔE_L+E_vL(13)

obtaining the following components:

when the switch tube is turned off, the inductor supplies power to the load through the diode due to the continuity of the inductor current, so that the current in the inductor naturally drops. The attenuation value of the inductive current in this stage_L-Comprises the following steps:

at nT_SPeriod to (n +1) T_SIn the period, the inductor current is controlled by i_L(n) conversion to i_L(n +1), then (n +1) T is obtained by the formula (8) and the formula (15)_SInstantaneous inductor current i_L(n+1)：

Due to the reverse turn-off characteristic of the diode, the inductor current cannot continuously decay to a negative value, i_L(n +1) there is a discontinuity, expressed as:

converting equation (17) to:

when w (n) is more than or equal to 0, substituting the formula (16) into the formula (14) to obtain:

when it is satisfied with

Namely, it is

When, equation (19) has a solution, the solution is:

the specific process of obtaining the formula (6) in step 7 is as follows:

when w (n) < 0, i_LSubstituting (n +1) into 0 to obtain equation (14):

when it is satisfied with

Namely, it is

When, equation (22) has a solution, the solution is:

the Buck circuit in the step 1 comprises a low-voltage source v_LLow voltage source v_LRespectively connected with a high voltage source v_HIs connected with the anode of the diode D, and a high-voltage source v_HThe anode of the switch tube S is connected with the collector of the switch tube S, and the emitter of the switch tube S is respectively connected with the cathode of the diode D and the inductor L.

The switch tube S is a turn-off power switch device carrying an anti-parallel diode or having an anti-parallel diode characteristic.

The invention has the beneficial effects that:

the method includes the steps of summarizing specific states of the DCM, the CCM, the steady state, the dynamic state and the like, integrally classifying the specific states, obtaining the duty ratio according to energy conservation, converging a calculation result according to a steady expected value, and directly calculating the control duty ratio of a corresponding switching tube according to a predicted value and a steady predicted value so as to obtain the final duty ratio of the switching tube and realize the control of the inductive current.

Secondly, the duty ratio of the switching tube can be rapidly calculated according to the law of energy conservation. When convergence is not added, 1 switching period can track the given value; when convergence is applied, 2 switching cycles can track a given. When the sudden change is given, the given can be quickly tracked, and the dynamic response and the control precision are obviously improved.

Drawings

FIG. 1 is a schematic diagram of a Buck circuit in the present invention;

FIG. 2 is a dynamic waveform diagram of the inductor current of the Buck circuit of the present invention;

FIG. 3 is a diagram of seven operation modes of the Buck circuit inductive current in a single cycle in the invention;

FIG. 4 is a schematic diagram of the switching tube current waveform during a single switching cycle in accordance with the present invention;

FIG. 5 is a flow chart of a method of predictive control of inductor current in accordance with the present invention;

FIG. 6 is a graph of inductor current waveforms at different sample values according to the present invention;

fig. 7 is a waveform diagram of an inductor current in a steady state in the present invention.

Detailed Description

The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

FIG. 1 shows a Buck circuit of the present invention, which includes a low voltage source v_L(the low-voltage source is generally a battery or a super capacitor), and the low-voltage source v_LRespectively connected with a high voltage source v_H(generally, the voltage of a support capacitor connected in parallel with a direct current bus can be regarded as a voltage source in a short time because the voltage of the capacitor cannot be suddenly changed), and the cathode of a diode D are connected, and a high-voltage source v is connected_HThe anode of the switch tube S is connected with the collector of the switch tube S, and the emitter of the switch tube S is respectively connected with the cathode of the diode D and the inductor L.

The switching tube S is a turn-off power switch device carrying an anti-parallel diode or having an anti-parallel diode characteristic.

FIG. 2 shows the dynamic waveform of the inductor current in the Buck circuit, where i_L(n) is the moment nT of the switch tube opening action of the inductor_S(T_SOne switching cycle of the switching tube), T_sFor one switching cycle of the switching tube, D_buIs the duty cycle of the switch.

Buck generally describes the steady-state operation mode of a switching circuit in CCM and DCM, and dynamic operation processes of the circuit are omitted in the division, and as shown in FIG. 3, seven operation mode graphs of inductive current in a single period are shown, and the seven operation modes represent the operation modes of the Buck circuit.

During the switching-on process of the switching tube, the current flowing through the switching tube is as shown in fig. 4. Wherein Δ i_L+Is nT_SThe increment of the inductive current in the switching-on process of the switching tube in the period is expressed by a formula (8):

wherein i_Lmax(n) is nT_SThe maximum value of the inductor current during the period,

average value of current flowing in switching-on process of switch tubeComprises the following steps:

when the switch is on under ideal conditions, v_HRelease energy, energy E released by it_onComprises the following steps:

v_Hpart of the energy released is stored in the inductor and appears as the change of the inductor current in the period, and the part of the energy is expressed by delta E_LExpressed as:

another part appears as v for load consumption_LEnd-charging, energy consumed by load in a single cycle E_vLComprises the following steps:

under ideal conditions, and ignoring various losses, according to the conservation of energy:

E_on＝ΔE_L+E_vL(13)

obtaining the following components:

when the switch tube is turned off, the current is continuous due to the inductanceIn this way, the inductor will supply power to the load through the diode, so that the current in the inductor will naturally drop, and the attenuation value Δ i of the inductor current at this stage_L-Comprises the following steps:

at nT_SPeriod to (n +1) T_SIn the period, the inductor current is controlled by i_L(n) conversion to i_L(n +1), then (n +1) T is obtained by the formula (8) and the formula (15)_SInstantaneous inductor current i_L(n+1)：

Due to the reverse turn-off characteristic of the diode, the inductor current cannot continuously decay to a negative value, i_L(n +1) there is a discontinuity, expressed as:

converting equation (17) to:

when w (n) is more than or equal to 0, substituting the formula (16) into the formula (14) to obtain:

when it is satisfied with

Namely, it is

When, equation (19) has a solution, the solution is:

from equation (21), the equal sign in equation (21) holds when the duty ratio is 1, so equation (19) must have a solution under the condition that the limited duty ratio is less than 1; when the formula (21) is not satisfiedThe given current value can not be realized in a single period, multiple periods are needed to be completed, and the given duty ratio is directly set as an upper limit value.

When w (n) < 0, i_LSubstituting (n +1) into 0 to obtain equation (14):

when it is satisfied with

Namely, it is

When, equation (22) has a solution, the solution is:

since the average inductance current is constantIf the duty ratio is greater than or equal to 0, the formula (24) shows that the equation (22) has a certain solution, and the duty ratio can be calculated by the formula only if w (n) is less than 0.

Since the unit delay of the conventional Digital Signal Processing (DSP) cannot be avoided, the duty ratio must be calculated before the start of the cycle, and thus nT needs to be predicted_SInstantaneous inductor current

The invention relates to an inductive current prediction control method for a non-isolated charging Buck circuit, which is implemented according to the following steps, as shown in FIG. 5:

step 1, sampling the voltage value v of a low-voltage source in a Buck circuit_LVoltage value v of high voltage source_H、(n-1)T_SValue of the inductance current i at a time_L(n-1)、(n-1)T_SDuty ratio D of switch tube in period_bu(n-1)；

Step 2, judging nT_SCurrent on time of day inductor is given by i_Lref(n) whether the value is less than 0, if not, turning to the step 3; if less than 0, nT_SDuty ratio D of switch tube in period_x(n) 1, go to step 9;

step 3, calculating nT through a formula (1)_SInstantaneous inductor current prediction value

Wherein,

l is an inductance value, T_SOne switching period of the switching tube;

step 4, judgmentIf yes, turning to step 5; if not, nT_SDuty ratio D of switch tube in period_x(n) 1, go to step 9;

step 5, mixing nT_SGiven value of current i on time inductor_Lref(n) assigning a value to nT_SAverage value of inductor current in cycleNamely:

the predicted value of the inductive current obtained by the formula (1)Substituting into the solution obtained by equation (19) can obtain nT_SDuty ratio D of switch tube in period_bu(n)：

Wherein D is_bt＝v_L/v_H；

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

judging whether w (n) is equal to or more than 0, if not, turning to the step 7; if yes, go to step 8;

step 7, obtaining an inductive current predicted value according to the formula (1)Substituting into the solution obtained in equation (23), nT is calculated_SDuty ratio D of switch tube in period_bu(n)：

If the initial values of the inductor currents sampled are different, a situation may occur as shown in fig. 6, i.e., a problem of non-convergence of the inductor currents occurs.

Step 8, in order to solve the problem of non-convergence of the inductive current, only nT needs to be taken_SDuty ratio D of switch tube in period_bu(n) duty ratio D of switching tube at steady state moment_zAverage value D of (n)_x(n) calculating D according to equation (7)_x(n)：

When the switch tube reaches the steady state, the waveform of the inductive current is shown in fig. 7, namely

Δi_L+＝-Δi_L-，

The following can be obtained: nT_SDuty ratio D of switching tube in steady state in period_z(n) is:

step 9, generating dutyRatio of D_xAnd (n) controlling the switching tube by the PWM wave.

The invention obtains the duty ratio through energy conservation, can quickly calculate the duty ratio through the energy conservation, quickly tracks the given value, also can quickly track the given value when giving sudden change, and obviously improves the dynamic response and the control precision.

Claims (4)

1. The method for predicting and controlling the inductive current in the non-isolated charging Buck circuit is characterized by comprising the following steps of:

step 1, sampling a voltage value v of a low-voltage source in a non-isolated charging Buck circuit_LVoltage value v of high voltage source_H、(n-1)T_SValue of the inductance current i at a time_L(n-1)、(n-1)T_SDuty ratio D of switch tube in period_bu(n-1)，

Wherein, T_SOne switching period of the switching tube;

step 2, judging nT_SCurrent on time of day inductor is given by i_Lref(n) whether the value is less than 0, if not, turning to the step 3; if less than 0, nT_SDuty ratio D of switch tube in period_x(n) is 0, go to step 9;

step 3, calculating nT through a formula (1)_SInstantaneous inductor current prediction value

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

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 an inductance value;

step 4, judgmentIf yes, turning to step 5; if not, nT_SDuty ratio D of switch tube in period_x(n) 1, go to step 9;

step 5, mixing nT_SGiven value of current i on time inductor_Lref(n) assigning a value to nT_SAverage value of inductor current in cycleNamely:

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

the predicted value of the inductive current obtained by the formula (1)Calculating nT_SDuty ratio D of switch tube in period_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 is_bt＝v_L/v_H；

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

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

judging whether w (n) is equal to or more than 0, if not, turning to the step 7; if yes, go to step 8;

step 7, obtaining an inductive current predicted value according to the formula (1)Calculating nT_SDuty ratio D of switch tube in period_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, calculating the duty ratio D after median processing according to a formula (7)_x(n)：

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

Wherein,is nT_SDuty ratio of the switching tube in steady state in the period;

step 9, generating duty ratio D_x(n) controlling the switching tube by the PWM wave;

the Buck circuit in the step 1 comprises a low-voltage source v_LLow voltage source v_LRespectively connected with a high voltage source v_HIs connected with the anode of the diode D, and a high-voltage source v_HThe anode of the switch tube S is connected with the collector of the switch tube S, and the emitter of the switch tube S is respectively connected with the cathode of the diode D and the inductor L.

2. The method as claimed in claim 1, wherein the specific process of obtaining the formula (4) in the step 5 is as follows:

nT_Sincrement delta i of inductive current in switching-on process of switching tube in period_L+Comprises the following steps:

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

wherein i_Lmax(n) is nT_SThe maximum value of the inductor current during the period,

average value of current flowing in switching-on process of switch tubeComprises the following steps:

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

when the switch is on under ideal conditions, v_HRelease energy, energy E released by it_onComprises the following steps:

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

v_Hpart of the energy released is stored in the inductor and appears as the change of the inductor current in the period, and the part of the energy is expressed by delta E_LExpressed 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 appears as v for load consumption_LEnd-charging, energy consumed by load in a single cycle E_vLComprises the following steps:

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

under ideal conditions, and ignoring various losses, according to the conservation of energy:

E_on＝ΔE_L+E_vL(13)

obtaining the following components:

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

when the switch tube is turned off, the inductor supplies power to the load through the diode due to the continuity of the inductor current, so that the current in the inductor naturally drops, and the attenuation value delta i of the inductor current at the stage_L-Comprises the following steps:

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

at nT_SPeriod to (n +1) T_SIn the period, the inductor current is controlled by i_L(n) conversion to i_L(n +1), then (n +1) T is obtained by the formula (8) and the formula (15)_SInstantaneous inductor current i_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 the diode, the inductor current cannot continuously decay to a negative value, i_L(n +1) there is a discontinuity, expressed as:

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

converting equation (17) 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) is more than or equal to 0, substituting the formula (16) into the formula (14) to obtain:

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

when it is satisfied with

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

Namely, it is

When, equation (19) has a solution, the 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. the method as claimed in claim 2, wherein the specific process of obtaining the formula (6) in the step 7 is as follows:

when w (n) < 0, i_LSubstituting (n +1) into 0 to obtain equation (14):

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

when it is satisfied with

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

Namely, it is

When, equation (22) has a solution, the 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. the method as claimed in claim 3, wherein the switch tube S is a turn-off power switch device with an anti-parallel diode or an anti-parallel diode characteristic.