CN106301052A - A kind of sliding moding structure Delta modulator approach of improvement - Google Patents

Abstract

The present invention relates to the sliding moding structure Delta modulator approach of a kind of improvement, its technical characterstic is: comprise the following steps: the series resonant inverter discrete time dynamic model that step 1, foundation control based on conventional current adjustable Delta controller, and step 2, introducing integrator improve the output performance of current adjustment Delta controller；Step 3, on off state based on sliding mode control theory analysis series resonant inverter, choose suitable integrator integral gain value Ki；Step 4, introducing integral reset link, choose suitable error bandwidth, expand the higher limit of integrator integral gain value Ki further.The present invention, by adding the integrator with reset function in traditional current adjustment Delta controller, further reduces the steady state bias value of output electric current, keeps ripple current content a relatively low level simultaneously.

Description

A kind of sliding moding structure Delta modulator approach of improvement

Technical field

The invention belongs to power electronics and control technical field, relate to the big merit such as induction heating power, uninterrupted power source (UPS) Rate Switching Power Supply, the sliding moding structure Delta modulator approach of a kind of improvement.

Background technology

Along with power semiconductor switching device speed and the raising of rated capacity, at inducing melting, uninterruptedly electricity The field voltage-source type series resonant inverters such as source are of increased attention.Voltage source series resonant inverter generally by Direct voltage source, high-frequency inverter, load matched transformator and induction coil are constituted, corresponding control load output electric current or The method of person's output is to utilize silicon con trolled rectifier device and the constant inverter of switching frequency to realize this process.To the greatest extent Manage this method the most easily to realize, but the switching device in commutator is usually operated at hard switching state, further Add the volume and weight of power attenuation and equipment.

For the problems referred to above, have employed a kind of high-performance electric flow control technology at present.Inverter is uncontrollable whole by diode Current circuit provides unidirectional current, and it is close to obtain higher output that the device for power switching in inverter circuit is operated in resonant condition Degree.Another is current adjustment Delta controller (CRDM) to be applied to series resonant inverter control the product of pulse train Raw, this method uses the actuator of high-gain, thus has stronger robustness and the speed of response.But CRDM controls output Electric current is frequently accompanied by non-zero steady-state error and biasing, causes output penalty.

Summary of the invention

It is an object of the invention to overcome the deficiencies in the prior art, it is provided that a kind of stable state reasonable in design, output electric current is inclined Put the sliding moding structure Delta modulator approach of the improvement that value is little and ripple current content is low.

The present invention solves it and technical problem is that and take techniques below scheme to realize:

The sliding moding structure Delta modulator approach of a kind of improvement, comprises the following steps:

The series resonant inverter discrete time that step 1, foundation control based on conventional current adjustable Delta controller is dynamic Model, and by the equivalent analysis of the series resonant inverter controlled based on conventional current adjustable Delta controller is drawn In one sampling period, when using conventional current adjustable Delta controller to control, the output loading electricity of series resonant inverter Relational expression between stream and current ripples amplitude；

Step 2, pass according to the output load current variable quantity of the series resonant inverter of step 1 with current ripples amplitude It is expression formula, draws out under different equivalent controls input, load output electric current and the corresponding relation figure of current ripples amplitude；And In order to reduce the outlet side current offset value of current adjustment Delta controller, introduce integrator and improve current adjustment Delta control The output performance of device；

Step 3, on off state based on sliding mode control theory analysis series resonant inverter, choose the most long-pending Divide device integral gain value Ki；

Step 4, in order to expand the higher limit of described integrator integral gain value Ki further, in the introducing of described step 2 Introduce integral reset link in the feedforward path of the current adjustment Delta controller of integrator, choose suitable error bandwidth η, When outlet side current error value is more than error bandwidth η preset, integrator is forced to reset, by this control method, enters One step expands the higher limit of integrator integral gain value Ki.

And, the relation between output load current and the current ripples amplitude of the series resonant inverter of described step 1 Expression formula is:

$\begin{array}{c}\mathrm{\Δ}I(k+1)=I_o(k+1)-I_o\left(k\right)\\ =\frac{\mathrm{\π}}{2Q}\{I_{\max }{u}^{*}(k+1)-I_o\left(k\right)\}\end{array}$

Wherein, u* (k+1) is equivalent control input, and corresponding expression formula is:

$u^{*}(k+1)=\frac{M\left(k\right)+M(k+1)}{2}$

Wherein, M (k) is used for describing the operational mode of inverter, can be expressed as follows:

In above formula, Q is loaded quality factor；Δ I is current ripples amplitude；I_maxFor output current maxima；I_oFor output Electric current.

And, the integrator that introduces of described step 2 improves the output performance concrete grammar of current adjustment Delta controller For: in the feedforward path of conventional current adjustable Delta controller, add an integrator, in every half harmonic period, Gather series resonant inverter output current value to compare with reference current value, produce error signal, then through integrator Regulation produces the switch controlling signal of subsequent time inverter, and then determines the operational mode of subsequent time inverter.

And, described step 3 method particularly includes: in order to choose suitable integrator gain Ki, introduce sliding moding structure Control theory, sets up on off state expression formula based on Sliding mode variable structure control, by setting up opening under Sliding mode variable structure control Off status and the relation of equivalent control input, draw the corresponding expression formula of storage gain Ki and equivalent control input u* (k+1), enter And input by choosing different equivalent control, determine that the higher limit of storage gain Ki is:

$0<K_i<\frac{\mathrm{\&pi;}}{2QT}$

In above formula, T is half harmonic period；

And, described step 4 choose suitable error bandwidth η method particularly includes: the described series connection of integrating step 1 is humorous Shake the relational expression between output load current and the current ripples amplitude of inverter, and mapping obtains at different reference current values Under equivalent control input and the homologous thread of current error value, and then the expression formula having analyzed error bandwidth η is:

${\mathrm{\&eta;}}_{min}=max\left\{\right|{\mathrm{\&Delta;I}}_{(u^{*}=0.5)}|+|{\mathrm{\&Delta;I}}_{(u^{*}=1)}|,|{\mathrm{\&Delta;I}}_{(u^{*}=0.5)}|+|{\mathrm{\&Delta;I}}_{(u^{*}=0)}\left|\right\}=\frac{1.5\mathrm{\&pi;}}{2Q}{I}_{max}$

Advantages of the present invention and good effect be:

1, the present invention proposes the sliding moding structure Delta modulator approach of a kind of improvement, by traditional current adjustment Delta controller (CRDM) adds the integrator with reset function, further reduces the steady state bias value of output electric current, Keep ripple current content almost can ignore in a relatively low level, transient response overshoot simultaneously.And tested by experiment The regulation performance of current controller, when applying the present invention to the system such as induction heating power, uninterrupted power source, output work are demonstrate,proved Rate density is high, controls to adjust wide ranges.

2, the present invention is based on the analysis carrying out the series resonant inverter dynamic current model of Zero Current Switch state, carries Go out the sliding moding structure Delta modulator approach of a kind of improvement.For integrator gain and error bandwidth setting use based on from Dissipate the sliding mode variable structure theory of time domain, further increase the stability of resonance inverter output electric current, improve series connection humorous Shake the output of inverter.

Accompanying drawing explanation

Fig. 1 is the inventive method flow chart；

Fig. 2 is the series resonant circuit schematic diagram of the present invention；

Fig. 3 is that different equivalent controls under input, load output electric current and the corresponding relation schematic diagram of current ripples amplitude；

Fig. 4 is the conventional current adjustable Delta controller principle figure of the present invention；

Fig. 5 is the current adjustment Delta controller principle figure adding integral reset of the present invention；

Fig. 6 be the present invention work as I_ref<0.5I_maxTime corresponding current error and control input value schematic diagram；

Fig. 7 be the present invention work as I_ref>0.5I_maxTime corresponding current error and control input value schematic diagram.

Detailed description of the invention

Below in conjunction with accompanying drawing, the embodiment of the present invention is described in further detail:

A kind of sliding moding structure Delta modulator approach of improvement, as it is shown in figure 1, comprise the following steps:

The series resonant inverter discrete time that step 1, foundation control based on conventional current adjustable Delta controller is dynamic Model, by drawing one the equivalent analysis of the series resonant inverter controlled based on conventional current adjustable Delta controller In the individual sampling period, when using conventional current adjustable Delta controller to control, the output load current of series resonant inverter And the relational expression between current ripples amplitude:

$\begin{array}{c}\mathrm{\&Delta;}I(k+1)=I_o(k+1)-I_o\left(k\right)\\ =\frac{\mathrm{\&pi;}}{2Q}\{I_{\max }{u}^{*}(k+1)-I_o\left(k\right)\}\end{array}$

Wherein, u* (k+1) is equivalent control input, and corresponding expression formula is:

$u^{*}(k+1)=\frac{M\left(k\right)+M(k+1)}{2}$

Wherein, M (k) is used for describing the operational mode of inverter, can be expressed as follows:

In above formula, Q is loaded quality factor；Δ I is current ripples amplitude；I_maxFor output current maxima；I_oFor output Electric current；

Step 2, pass according to the output load current variable quantity of the series resonant inverter of step 1 with current ripples amplitude Be expression formula, draw out as shown in Figure 3 under different equivalent controls input, load output electric current and current ripples amplitude right Schematic diagram should be related to；From the figure 3, it may be seen that when equivalent control input is for negative value, corresponding invertor operation is at regenerating condition, load electricity Flow valuve is gradually reduced, and current ripples amplitude increases.In this case, control input value and only have 0 and 1 two state, output State switch speed or current change rate can not be properly adjusted, and cause outlet side current ripples content high, and electric current is inclined Put big.Therefore, in order to reduce the outlet side current offset value of current adjustment Delta controller, in conventional current as shown in Figure 4 Add an integrator in the feedforward path of adjustable Delta controller, in every half harmonic period, gather series-resonant inverting Device output current value I_oWith reference current value I_refCompare, produce error signal I_e, then produce through the regulation of integrator The switch controlling signal of subsequent time inverter, so determine subsequent time inverter operational mode, thus improve electric current can Adjust the output performance of Delta controller.

Step 3, on off state based on sliding mode control theory analysis series resonant inverter, choose the most long-pending Divide device integral gain value Ki；

Described step 3 method particularly includes: in order to choose suitable integrator gain Ki, introduce Sliding mode variable structure control reason Opinion, sets up on off state expression formula based on Sliding mode variable structure control, by setting up the on off state under Sliding mode variable structure control With the relation of equivalent control input, draw the corresponding expression formula of storage gain Ki and equivalent control input u* (k+1), and then pass through Choose different equivalent control inputs, determine that the higher limit of storage gain Ki is:

$0<K_i<\frac{\mathrm{\&pi;}}{2QT}$

In above formula, T is half harmonic period；

Step 4, in order to expand the higher limit of described integrator integral gain value Ki further, in the introducing of described step 2 Integral reset link is introduced, it is then determined that error bandwidth η is in the feedforward path of the current adjustment Delta controller of integrator Little value, in order to reduce overshoot, needs to choose a less η value, meets maximum current error amount under steady state conditions simultaneously Time do not make integrator reset；Choose suitable error bandwidth η, when outlet side current error value is more than error bandwidth η preset, Integrator is forced to reset, and by this control method, expands the higher limit of integrator integral gain value Ki further.

The current adjustment Delta controller principle figure adding integral reset of the present invention, as shown in Figure 5；

Described step 4 choose suitable error bandwidth η method particularly includes: the described series resonance of integrating step 1 is inverse Becoming the relational expression between output load current and the current ripples amplitude of device, mapping obtains under different reference current values Equivalent control inputs and the homologous thread of current error value, and then the expression formula having analyzed error bandwidth η is:

${\mathrm{\&eta;}}_{min}=max\left\{\right|{\mathrm{\&Delta;I}}_{(u^{*}=0.5)}|+|{\mathrm{\&Delta;I}}_{(u^{*}=1)}|,|{\mathrm{\&Delta;I}}_{(u^{*}=0.5)}|+|{\mathrm{\&Delta;I}}_{(u^{*}=0)}\left|\right\}=\frac{1.5\mathrm{\&pi;}}{2Q}{I}_{max}$

Below the determination process of the higher limit of the storage gain Ki of integrator in the present embodiment is described in detail:

Known matching transformer secondary side output voltage initial value is V_s, corresponding moment t=0, then output electric current i_oAnd the tank circuit Capacitance voltage v_cSimplified expression can be expressed as:

$i_o\left(t\right)=-e^{\mathrm{\&alpha;}t}\frac{v_c\left(0\right)-V_s}{{\mathrm{\&omega;}}_d{L}_{eq}}sin\left({\mathrm{\&omega;}}_{d}t\right)---\left(1\right)$

$v_c\left(t\right)=V_s+e^{-\mathrm{\&alpha;}t}\left(v_c\right(0)-V_s)\frac{{\mathrm{\&omega;}}_r}{{\mathrm{\&omega;}}_d}cos({\mathrm{\&omega;}}_{d}t-\mathrm{\&phi;})---\left(2\right)$

Wherein,

$\mathrm{\&alpha;}=\frac{R_{eq}}{2L_{eq}},{\mathrm{\&omega;}}_d={\mathrm{\&omega;}}_r\sqrt{1-{\left(\frac{1}{2Q}\right)}^2},\mathrm{\&phi;}={\sin }^{-1}\left(\frac{1}{2Q}\right),Q=\frac{{\mathrm{\&omega;}}_r{L}_{eq}}{R_{eq}}$

In above formula, L_eqFor load equivalent inductance value；R_eqFor load equivalent resistance value；

Due to each device for power switching always at its on off state of current zero-crossing point time changing, thus switching device Switching frequency always equal to load resonant frequency.Value V of the input terminal voltage of series resonant circuit as shown in Figure 2_dcBy inverse Become device on off state and determine as follows:

$v_s=\left\{\begin{array}{ccc}{V}_{dc}& if& (Q_1,Q_2)areON\\ 0& if& (Q_1,Q_2)or(Q_3,Q_4)areON\\ -V_{dc}& if& (Q_3,Q_4)areON\end{array}\right\}---\left(3\right)$

In above formula, Q₁、Q₂、Q₃、Q₄Device for power switching state in the most corresponding series resonant inverter；

Define discrete variable M (k) and describe the operational mode of inverter, can be expressed as follows:

Convolution (4), formula (3) can be write as:

v_s(t)=V_dcM(k)sign(i_o(t)) for kT ＜ t ＜ (k+1) T (5)

In above formula, T=π/ω_dIt it is half harmonic period；

Assuming that load exports the absolute value of current peak is I_o, in half harmonic period, switch instantaneous capacitance voltage For V_c, with above-mentioned two discrete variable as quantity of state, formula (1), (2) and (5) can obtain:

$I_o\left(k\right)=\left|i_o(kT+\frac{T}{2})\right|=\frac{V_{dc}M\left(k\right)+V_c\left(k\right)}{{\mathrm{\&omega;}}_d{L}_{eq}}\exp \left(\frac{-\mathrm{\&pi;}}{4Q}\right)---\left(6\right)$

$\begin{array}{c}{V}_c(k+1)=\left|v_c(kT+T)\right|\\ =V_c\left(k\right)\exp \left(\frac{-\mathrm{\&pi;}}{2Q}\right)+(1+\exp (\frac{-\mathrm{\&pi;}}{2Q}\left)\right)V_{dc}M\left(k\right)\end{array}---\left(7\right)$

In above formula, loaded quality factor Q > > 1；

Formula (7) is substituted into (6), it can be deduced that the electric current I under discrete time_o(k+1):

I_o(k+1)=Φ I_o(k)+Γu^*(k+1) (8)

Equivalent control input u* (k+1) span is that { 1,0.5,0 ,-0.5 ,-1}, then the output flowing through loading coil is electric Stream maximum can be drawn by formula (8):

$I_{max}=\frac{\mathrm{\&Gamma;}}{(1-\mathrm{\&Phi;})}=\frac{4V_{dc}}{{\mathrm{\&pi;R}}_{eq}}---\left(9\right)$

Within a sampling period, the change of load current determines the amplitude of current ripples, and relational expression is:

$\begin{array}{c}\mathrm{\&Delta;}I(k+1)=I_o(k+1)-I_o\left(k\right)\\ =(\mathrm{\&Phi;}-1)I_o\left(k\right)+{\mathrm{\&Gamma;u}}^{*}(k+1)\\ =\frac{\mathrm{\&pi;}}{2Q}\{I_{\max }{u}^{*}(k+1)-I_o\left(k\right)\}\end{array}---\left(10\right)$

Wherein,

$\mathrm{\&Phi;}=\exp \left(\frac{-\mathrm{\&pi;}}{2Q}\right)=1-\frac{\mathrm{\&pi;}}{2Q},\mathrm{\&Gamma;}=\exp \left(\frac{-\mathrm{\&pi;}}{4Q}\right)\frac{2V_{dc}}{R_{eq}Q}=(1-\frac{\mathrm{\&pi;}}{4Q})\frac{2V_{dc}}{R_{eq}Q},u^{*}(k+1)=\frac{M\left(k\right)+M(k+1)}{2}$

On off state S (k) based on Sliding mode variable structure control can be expressed as:

S (k)=I_e(k)+K_iz(k) (11)

Z (k+1)=z (k)+TI_e(k) (12)

In above formula, I_eFor current error value；Z (k) is integration gain factor；

S (k) can be drawn with simultaneous formula (8), (11) and (12)；

$\begin{array}{c}S(k+1)-S\left(k\right)=(1-\mathrm{\&Phi;})I_o\left(k\right)-{\mathrm{\&Gamma;u}}^{*}(k+1)+K_i{\mathrm{TI}}_e\left(k\right)\\ =-\mathrm{\&Delta;}I(k+1)+K_i{\mathrm{TI}}_e\left(k\right)\end{array}---\left(13\right)$

When S (k+1)-S (k)=0, solve K_i；

$K_i=\frac{\mathrm{\&Delta;}I(k+1)}{{\mathrm{TI}}_e\left(k\right)}=\frac{\mathrm{\&pi;}}{2QT}\{1+\frac{I_{max}{u}^{*}(k+1)-I_{ref}}{i_e\left(k\right)}\}---\left(14\right)$

When controlling input signal values M (k+1)=1, value possible for u* (k+1) is { 1,0.5}；

As u* (k+1)=1, K_iMeet:

0 ＜ K_i＜ K₁ (15)

Wherein, K₁For at u* (k+1)=1 and I_e(k) > 0 time correspondence K_iValue；

When controlling input signal values M (k+1)=0, value possible for u* (k+1) is { 0,0.5}；

As u* (k+1)=0, K_iMeet:

0 ＜ K_i＜ K_o (16)

Wherein, K_oFor at u* (k+1)=0 and I_e(k) < K that 0 up-to-date style (12) is corresponding_iValue.

As u* (k+1)=0 or 1, formula (14), (15) K can be obtained_iMeet:

$0<K_i<\frac{\mathrm{\&pi;}}{2QT}\&lsqb;1+min\{\frac{I_{max}-I_{ref}}{\left|I_e\left(k\right)\right|},\frac{I_{ref}}{\left|I_e\left(k\right)\right|}\}\&rsqb;---\left(17\right)$

But, as u* (k+1)=0.5, K_iCannot solve, now corresponding S (k) < 0, I_o(k)<0.5 or S (k)>0, I_o (k) > 0.5 two kinds of situations, in order to reduce current ripples in this case, the value of subsequent time S (k+2) should meet:

S (k) { S (k+2)-S (k+1) } ＜ 0 (18)

Now, u^*(k+2) possible value is { 1,0}, and meet M (k+2)=M (k+1) simultaneously；

By above-mentioned formula (17), when meeting I_ref=I_maxOr I_refWhen=0, it can be deduced that:

$0<K_i<\frac{\mathrm{\&pi;}}{2QT}---\left(19\right)$

In the present embodiment, Fig. 6 and Fig. 7 be respectively the present invention work as I_ref<0.5I_maxTime and work as I_ref>0.5I_maxTime corresponding Current error and control input value schematic diagram.Wherein, I_refFor reference current value, I_maxFor output current maxima, Jin Erfen The expression formula separating out error bandwidth η is:

${\mathrm{\&eta;}}_{min}=max\left\{\right|{\mathrm{\&Delta;I}}_{(u^{*}=0.5)}|+|{\mathrm{\&Delta;I}}_{(u^{*}=1)}|,|{\mathrm{\&Delta;I}}_{(u^{*}=0.5)}|+|{\mathrm{\&Delta;I}}_{(u^{*}=0)}\left|\right\}=\frac{1.5\mathrm{\&pi;}}{2Q}{I}_{max}---\left(20\right)$

The operation principle of the present invention is:

The present invention is applicable to the high power switching power supply such as induction heating power, uninterrupted power source (UPS), first of all for electricity Flow adjustable Delta controller (CRDM) to carry out simplifying and effectively analyzing, it is proposed that one based on series resonant inverter from Dissipate Time Dynamic Model.Analysis has drawn under different on off states, the corresponding situation of change of resonance inverter output current value With output current ripple Producing reason.

Then when adding the current adjustment Delta controller with integral reset and controlling resonance inverter, the most defeated Do well switch speed or the response time of current change rate shortens the most further, and outlet side current ripples content is the most corresponding Reducing, current offset reduces.

Analyze inverter switching states in conjunction with Sliding mode variable structure control, choose suitable integral gain value and error bandwidth Value, compares the inverter circuit outlet side current value collected in every half harmonic period with reference current value, generation The error signal output by PI controller, then the regulation through actuator, and then determine the operation mould of subsequent time inverter Formula.

It is emphasized that embodiment of the present invention is illustrative rather than determinate, bag the most of the present invention Include the embodiment being not limited to described in detailed description of the invention, every by those skilled in the art according to technical scheme Other embodiments drawn, also belong to the scope of protection of the invention.

Claims (5)

1. the sliding moding structure Delta modulator approach improved, it is characterised in that: comprise the following steps:

The series resonant inverter discrete time dynamic analog that step 1, foundation control based on conventional current adjustable Delta controller Type, and by the equivalent analysis of the series resonant inverter controlled based on conventional current adjustable Delta controller is drawn one In the individual sampling period, when using conventional current adjustable Delta controller to control, the output load current of series resonant inverter And the relational expression between current ripples amplitude；

Step 2, relation table according to the output load current variable quantity of the series resonant inverter of step 1 with current ripples amplitude Reach formula, draw out under different equivalent controls input, load output electric current and the corresponding relation figure of current ripples amplitude；And in order to Reduce the outlet side current offset value of current adjustment Delta controller, introduce integrator and improve current adjustment Delta controller Output performance；

Step 3, on off state based on sliding mode control theory analysis series resonant inverter, choose suitable integrator Integral gain value Ki；

Step 4, in order to expand the higher limit of described integrator integral gain value Ki further, at the introducing integration of described step 2 Introduce integral reset link in the feedforward path of the current adjustment Delta controller of device, choose suitable error bandwidth η, when defeated When going out side current error value more than error bandwidth η preset, integrator is forced to reset, by this control method, further Expand the higher limit of integrator integral gain value Ki.

The sliding moding structure Delta modulator approach of a kind of improvement the most according to claim 1, it is characterised in that: described step Relational expression between output load current and the current ripples amplitude of the series resonant inverter of rapid 1 is:

$\begin{array}{c}\mathrm{\&Delta;}I(k+1)=I_o(k+1)-I_o\left(k\right)\\ =\frac{\mathrm{\&pi;}}{2Q}\{I_{\max }{u}^{*}(k+1)-I_o\left(k\right)\}\end{array}$

Wherein, u* (k+1) is equivalent control input, and corresponding expression formula is:

$u^{*}(k+1)=\frac{M\left(k\right)+M(k+1)}{2}$

Wherein, M (k) is used for describing the operational mode of inverter, can be expressed as follows:

In above formula, Q is loaded quality factor；Δ I is current ripples amplitude；I_maxFor output current maxima；I_oFor output electric current.

The sliding moding structure Delta modulator approach of a kind of improvement the most according to claim 1 and 2, it is characterised in that: described The integrator that introduces of step 2 improves the output performance of current adjustment Delta controller method particularly includes: adjustable in conventional current Add an integrator in the feedforward path of Delta controller, in every half harmonic period, gather series resonant inverter Output current value compares with reference current value, produces error signal, then produces subsequent time through the regulation of integrator The switch controlling signal of inverter, and then determine the operational mode of subsequent time inverter.

The sliding moding structure Delta modulator approach of a kind of improvement the most according to claim 1 and 2, it is characterised in that: described Step 3 method particularly includes: in order to choose suitable integrator gain Ki, introduce sliding mode control theory, set up based on The on off state expression formula of Sliding mode variable structure control, defeated with equivalent control by setting up the on off state under Sliding mode variable structure control The relation entered, draws the corresponding expression formula of storage gain Ki and equivalent control input u* (k+1), and then different etc. by choosing Effect controls input, determines that the higher limit of storage gain Ki is:

$0<K_i<\frac{\mathrm{\&pi;}}{2QT}$

In above formula, T is half harmonic period.

The sliding moding structure Delta modulator approach of a kind of improvement the most according to claim 1 and 2, it is characterised in that: described Step 4 choose suitable error bandwidth η method particularly includes: the output of the described series resonant inverter of integrating step 1 is born Carrying the relational expression between electric current and current ripples amplitude, mapping obtains the equivalent control input under different reference current values With the homologous thread of current error value, and then the expression formula having analyzed error bandwidth η is:

${\mathrm{\&eta;}}_{min}=max\{\left|{\mathrm{\&Delta;I}}_{(u^{*}=0.5)}\right|+\left|{\mathrm{\&Delta;I}}_{(u^{*}=1)}\right|,\left|{\mathrm{\&Delta;I}}_{(u^{*}=0.5)}\right|+\left|{\mathrm{\&Delta;I}}_{(u^{*}=0)}\right|\}=\frac{1.5\mathrm{\&pi;}}{2Q}{I}_{max}.$