CN110380615B - Segmented control system design method of LLC resonant converter - Google Patents

Segmented control system design method of LLC resonant converter Download PDF

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CN110380615B
CN110380615B CN201910577253.8A CN201910577253A CN110380615B CN 110380615 B CN110380615 B CN 110380615B CN 201910577253 A CN201910577253 A CN 201910577253A CN 110380615 B CN110380615 B CN 110380615B
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陆益民
刘�东
黄险峰
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Guangxi University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M3/00—Conversion of dc power input into dc power output
    • H02M3/22—Conversion of dc power input into dc power output with intermediate conversion into ac
    • H02M3/24—Conversion of dc power input into dc power output with intermediate conversion into ac by static converters
    • H02M3/28—Conversion of dc power input into dc power output with intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode to produce the intermediate ac
    • H02M3/325—Conversion of dc power input into dc power output with intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode to produce the intermediate ac using devices of a triode or a transistor type requiring continuous application of a control signal
    • H02M3/335—Conversion of dc power input into dc power output with intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode to produce the intermediate ac using devices of a triode or a transistor type requiring continuous application of a control signal using semiconductor devices only
    • H02M3/33569—Conversion of dc power input into dc power output with intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode to produce the intermediate ac using devices of a triode or a transistor type requiring continuous application of a control signal using semiconductor devices only having several active switching elements
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02B—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO BUILDINGS, e.g. HOUSING, HOUSE APPLIANCES OR RELATED END-USER APPLICATIONS
    • Y02B70/00—Technologies for an efficient end-user side electric power management and consumption
    • Y02B70/10—Technologies improving the efficiency by using switched-mode power supplies [SMPS], i.e. efficient power electronics conversion e.g. power factor correction or reduction of losses in power supplies or efficient standby modes

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Abstract

The invention relates to the technical field of electronic converter control, and particularly discloses a sectional type control system design method of an LLC resonant converter, which comprises the following steps: establishing a small signal model according to circuit parameters of the LLC resonant converter; dividing a small signal model of the LLC resonant converter into two parts by taking the resonant frequency as a boundary, and respectively obtaining corresponding transfer function analytic expressions of the two parts; determining two working intervals of the LLC resonant converter according to the resonant frequency ranges of the two parts and the direct current gain curves corresponding to the full load and minimum load conditions respectively; substituting the state variables corresponding to the boundary points of each working interval into the corresponding transfer function analytical expressions to obtain the stability margin of the system open loop under the corresponding state; and comparing the stability margins of all boundary points in the working interval to obtain the boundary point with the worst open-loop stability margin and designing a corresponding compensator. Therefore, a sectional type control system of the converter is designed, and the stability of the controller is improved.

Description

Segmented control system design method of LLC resonant converter
Technical Field
The invention relates to the technical field of power electronic converter control, in particular to a sectional type control system design method of an LLC resonant converter.
Background
In order to improve the stability of the LLC resonant converter, an optimal design of the control system of the LLC resonant converter is therefore required, which is premised on modeling, whereas small-signal modeling is very challenging for the resonant converter. The averaging concept commonly used in converters using Pulse Width Modulation (PWM) is no longer applicable because the ac component is large in some of the state variables. For LLC resonant converters, the equivalent circuit model proposed based on the extended description function concept is the most successful model. This modeling method uses a fundamental approximation, i.e. only the fundamental component of the resonant network variables is considered. During operation of the resonant converter, the fundamental component accounts for a large proportion of the ac signal, so it is reasonable to use the fundamental approximation. The small-signal model established using the fundamental component method is sufficiently accurate for the description of the LLC resonant converter. However, in the current LLC resonant converter control system design process, because of lack of simple and systematic design flow guidance, the currently commonly adopted design approach is to first measure the bode diagram of the object to be controlled by the relevant test equipment, fit out the corresponding transfer function, and then design the control system for the LLC resonant converter device, the order of the equivalent circuit model adopted by the method is too high, and the transfer function is still derived based on the numerical solution rather than the analytic solution, which brings difficulty to the design of the LLC resonant converter control system, thereby resulting in that the stability of the LLC resonant converter cannot be enhanced.
The information disclosed in this background section is only for enhancement of understanding of the general background of the invention and should not be taken as an acknowledgement or any form of suggestion that this information forms the prior art already known to a person skilled in the art.
Disclosure of Invention
The invention aims to provide a control system design method of an LLC resonant converter, so as to solve the problem that the stability of the LLC resonant converter cannot be improved due to the difficulty in design of the control system.
In order to achieve the above object, the present invention discloses a method for designing a segmented control system of an LLC resonant converter, comprising:
s1, establishing a small signal model according to the circuit parameters of the LLC resonant converter;
s2, dividing a small signal model of the LLC resonant converter into two parts by taking the resonant frequency as a boundary, and respectively obtaining corresponding transfer function analytic expressions of the two parts;
s3, acquiring direct current gain curves of the LLC resonant converter under the conditions of full load and minimum load, acquiring a working interval of the LLC resonant converter by combining a switching frequency range, and dividing the working interval into two parts by taking resonant frequency as a boundary;
s4, substituting state variables corresponding to the boundary working points of each working interval into a sectional type transfer function analytic expression to obtain open loop transfer functions of the boundary working points in the working interval, and obtaining the open loop stability margin of each boundary working point through the open loop transfer functions of the boundary working points;
and S5, comparing the stability margins of each boundary point in the two working intervals, and respectively acquiring the boundary working point with the worst open-loop stability margin in the two working intervals to design a corresponding compensator.
Preferably, in the above technical solution, the LLC resonant converter includes a half-bridge circuit, a transformer, a rectifying and filtering module, and two power switching tubes Q1、Q2The series connection forms a half-bridge circuit, the half-bridge circuit is connected with an input power supply in parallel, the output of the half-bridge circuit is connected with a resonance circuit, and the resonance circuit is composed of a resonance inductor LrResonant capacitor CrResonant inductor LmThe resonant circuit is connected to a rectifying and filtering module and a load through a transformer, wherein the rectifying and filtering module is composed of a rectifying diode D1、D2And output filter capacitor CoAnd (4) forming.
Preferably, in the above technical solution, the working range of the LLC resonant converter is at the resonant frequency frFor the boundary to be divided into two parts, there are two resonance frequencies in the LLC resonant converter:
first, a resonant inductor LrAnd a resonance capacitor CrResonance frequency f at which resonance occursr
Figure BDA0002112351930000031
Second, resonant inductor LrResonant capacitor CrAnd a resonant inductor LmResonance frequency f at which resonance occursm
Figure BDA0002112351930000032
Preferably, in the above technical solution, a power switch Q is provided1、Q2Has a switching frequency of fsWhen f ism≤fs＜frThe transfer function analytic expression of the LLC resonant converter at the time is shown in (3):
Figure BDA0002112351930000033
when f iss≥frThe transfer function of the LLC resonant converter is analyzed as shown in (4)
Figure BDA0002112351930000034
Preferably, in the above technical solution, the designed compensator is used to compensate the transfer function corresponding to the screened boundary operating point of each frequency band, so as to realize the stability adjustment of the LLC resonant converter.
Compared with the prior art, the invention has the following beneficial effects:
the method for designing the control system of the LLC resonant converter is based on the existing LLC resonant converter simplified segmented equivalent three-order circuit model, combines a corresponding transfer function expression and segmented control, and designs a set of LLC resonant converter control system design method.
Drawings
Fig. 1 is a schematic design flow diagram of an LLC resonant converter control system proposed by the present invention.
Fig. 2 is a block diagram of a control system of the LLC resonant converter proposed by the present invention.
Fig. 3 is a topology diagram of the LLC resonant converter proposed by the present invention.
FIG. 4a shows the invention fm≤fs＜frSmall signal model of LLC resonant converter.
FIG. 4b is a drawing of the invention fs≥frSmall signal model of time LLC resonant converter。
Fig. 5a is a gain curve of an LLC resonant converter.
FIG. 5b is fm≤fs＜frThe working interval of the LLC resonant converter.
FIG. 5c is fs≥frThe working interval of the LLC resonant converter.
FIG. 6a shows an LLC resonant converter with a control system designed according to the invention at fm≤fs＜frThe input voltage of the time disturbs the simulation oscillogram.
FIG. 6b shows the LLC resonant converter at f using the control system designed by the inventionm≤fs＜frThe load disturbance of time simulates a waveform diagram.
FIG. 6c shows the LLC resonant converter at f using the control system designed by the inventions≥frThe input voltage of the time disturbs the simulation oscillogram.
FIG. 6d shows the LLC resonant converter at f using the control system designed by the inventions≥frThe load disturbance of time simulates a waveform diagram.
FIG. 7 is an experimental waveform of input voltage disturbance of the LLC resonant converter.
FIG. 8 is an experimental waveform of a disturbance of an LLC resonant converter load current increase.
FIG. 9 is an experimental waveform of the LLC resonant converter load current reduction disturbance.
Detailed Description
The following detailed description of the present invention is provided in conjunction with the accompanying drawings, but it should be understood that the scope of the present invention is not limited to the specific embodiments.
Throughout the specification and claims, unless explicitly stated otherwise, the word "comprise", or variations such as "comprises" or "comprising", will be understood to imply the inclusion of stated elements but not the exclusion of any other elements.
Fig. 1 shows a schematic design flow diagram of an LLC resonant converter control system proposed by the present invention. The design process specifically comprises the following steps:
s1, establishing a small signal model according to the circuit parameters of the LLC resonant converter;
s2, dividing a small signal model of the LLC resonant converter into two parts by taking the resonant frequency as a boundary, and respectively obtaining corresponding transfer function analytic expressions of the two parts;
s3, acquiring direct current gain curves of the LLC resonant converter under the conditions of full load and minimum load, acquiring a working interval of the LLC resonant converter by combining a switching frequency range, and dividing the working interval into two parts by taking resonant frequency as a boundary;
s4, substituting state variables corresponding to the boundary working points of each working interval into a sectional type transfer function analytic expression to obtain open loop transfer functions of the boundary working points in the working interval, and obtaining the open loop stability margin of each boundary working point through the open loop transfer functions of the boundary working points;
and S5, comparing the stability margins of each boundary point in the two working intervals, respectively obtaining the boundary working point with the worst open-loop stability margin in the two working intervals, designing a corresponding compensator, and substituting the corresponding compensator into a transfer function in each resonant frequency range to realize the stability adjustment of the LLC resonant converter.
Fig. 2 shows a block diagram of a control system of the LLC resonant converter proposed by the invention. In FIG. 2H(s) is the sample transfer function, Gc(s) is the controller transfer function, Gvco(s) is the transfer function of the voltage-to-frequency converter, Gvω(s) is a transfer function of the LLC resonant converter output voltage and switching frequency. By switching frequency fsValue of (3) adjusting the controller transfer function GcPID parameter in(s), at fm≤fs＜frWhen is about to be Gc1(s) into Gc(s) at fs≥frWhen is about to be Gc2(s) into GcAnd(s) the stability regulation of the LLC resonant converter can be realized.
Fig. 3 is a diagram of an LLC resonant converter topology, wherein: v. ofinIs an input power supply; q1、Q2Is a power switch tube; from LrIs a resonant inductor; crIs a resonant capacitor; l ismIs a resonant inductor; d1、D2Is a rectifier diode, CoIs an output filter capacitor; rLIs a load. Two power switch transistors Q1、Q2The series connection forms a half-bridge circuit, the half-bridge circuit is connected with an input power supply in parallel, the output of the half-bridge circuit is connected with a resonance circuit, and the resonance circuit is composed of a resonance inductor LrResonant capacitor CrResonant inductor LmThe resonant circuit is connected to the rectifying and filtering module and the load via the transformer, wherein the resonant inductor LmThe transformer excitation inductor is used for replacing the transformer excitation inductor, and the rectifying and filtering module is composed of a rectifying diode D1、D2And output filter capacitor CoAnd (4) forming. Wherein iLrIs a resonant current; v. ofCrIs the resonant capacitor voltage; i.e. ioIs an output current; v. ofoIs the output voltage; the turn ratio of the transformer is n:1: 1. By means of a functional description, a small-signal circuit model of the LLC resonant converter as shown in fig. 4a-4b is obtained.
There are two resonant frequencies in an LLC resonant converter:
(1) series resonant inductor LrAnd a resonance capacitor CrFrequency at which resonance occurs
Figure BDA0002112351930000061
(2) Series resonant inductor LrResonant capacitor CrAnd a resonant inductor LmFrequency of resonance occurring in parallel
Figure BDA0002112351930000071
In FIG. 4a is fm≤fs＜frSmall signal model of LLC resonant converter at time, fig. 4b is fs≥frSmall signal model of LLC resonant converter. Transfer function analytic expressions of the LLC resonant converter are obtained through a series of derivation according to the small signal circuit models in FIGS. 4a-4 b:
fm≤fs＜frLLC resonant conversion of timeThe small signal model of the device is shown in the formula (3)
Figure BDA0002112351930000072
Wherein the content of the first and second substances,
direct current gain:
Figure BDA0002112351930000073
resonant tank quality factor:
Figure BDA0002112351930000074
equivalent quality factor:
Figure BDA0002112351930000075
equivalent resonance angular frequency
Figure BDA0002112351930000076
Equivalent inductance:
Figure BDA0002112351930000081
per unit value of switching frequency:
Figure BDA0002112351930000082
inductance coefficient:
Figure BDA0002112351930000083
resonance angular frequency: omegar＝2πfr
fs≥frThe small signal model of the LLC resonant converter is shown in (4)
Figure BDA0002112351930000084
Wherein the content of the first and second substances,
direct current gain:
Figure BDA0002112351930000085
equivalent inductance:
Figure BDA0002112351930000086
equivalent load:
Figure BDA0002112351930000087
resonant tank impedance:
Figure BDA0002112351930000088
carrier angular frequency: omegas＝ωs＝2πfs
Fig. 5a shows an operating region of the LLC resonant converter, which can be obtained by combining the calculated frequency range of the LLC resonant converter and the dc gain curves under full load and minimum load conditions.
FIG. 5a is a diagram of the operation region of the LLC resonant converter, FIGS. 5b and 5c are partial expansions of FIG. 5a, and the ordinate values in FIGS. 5a-5c represent the DC gain M of the LLC resonant converterdcThe abscissa value represents the switching frequency fsPer unit value ofnWherein f is2Is the per unit value f of the lowest switching frequency7Is the per unit value, f, of the highest switching frequency4Is the per unit value of the resonance frequency, f4＝fr＝1。
Direct current gain:
Figure BDA0002112351930000091
in fig. 5a-5c the dashed line is the dc gain curve at minimum load condition and the solid line is the dc gain curve at full load condition. From fig. 5a-5c, it is known that in the operating region, the higher the switching frequency of the LLC resonant converter, the lower the dc gain, i.e. in the case of a fixed load, the lower the input voltage, the lower the switching frequency, and the higher the input voltage, the higher the switching frequency. A is a low-voltage (input voltage) light-load working point, B is a low-voltage heavy-load working point, E is a resonant frequency working point, C is a high-voltage light-load working point, and D is a high-voltage heavy-load working point.
Due to the adoption of a segmented LLC resonant converter small signal model and a transfer function, the design of a control system also needs to be designed respectively for working intervals of different frequency bands.
First, refer to f in FIG. 5bm≤fs＜frThe frequency band working interval is designed, and the slope of the curve of the AE segment can be known from FIG. 5b>The BE section curve slope is used as a reference for designing a controller. Respectively substituting each state quantity corresponding to the working point A, E into the formula (3), respectively obtaining a system open loop transfer function at the working point A, E, drawing a baud chart corresponding to the obtained transfer function, and knowing that the stability margin of the working point A is smaller than that of the working point E through the baud chart, namely the worst working point is a low-voltage light load point. Therefore, the designed control system can ensure that the converter is at f as long as the LLC resonant converter can be ensured to be stable at the working point Am≤fs＜frStability of this region. For fm≤fs＜frTransfer function design compensator G for time operating point Ac1(s)。
Next, refer to f in FIG. 5cs≥frThe working interval of the frequency band is designed, and the slope of the curve of the DE band can be known from FIG. 5c>The slope of the curve in the CE section should be designed based on the curve in the DE section. Respectively substituting each state quantity corresponding to the working point D, E into the formula (4), respectively obtaining a system open loop transfer function at the working point D, E, drawing a baud chart corresponding to the obtained transfer function, and knowing that the stability margin of the working point D is larger than that of the working point E through the baud chart, namely the worst working point is a low-voltage load point. Therefore, the designed control system can ensure that the converter is at f as long as the LLC resonant converter can be ensured to be stable at the working point Es≥frStability of this region. For fs≥frTransfer function design compensator G for time operating point Ec2(s)。
In summary, only f is requiredm≤fs＜frWhen is about to be Gc1(s) into G in FIG. 2c(s)，fs≥frWhen is about to be Gc2(s) into G in FIG. 2cAnd(s), designing the LLC resonant converter control system.
Simulation verification:
based on the design method of the LLC resonant converter control system, a Simulink simulation model is set up in MATLAB software for simulation verification. The design parameters of the converter are as follows: DC input voltage vinThe range is 140-280V, and the rated input voltage Vin(nom)200V, DC output voltage Vo12V, full load output power Po120W, resonant frequency fr＝100kHz，fm50kHz, 20:2:2 transformer turn ratio n, and resonant inductance Lr57.6 muH, excitation inductance Lm172.8 muH, resonant capacitance Cr44nF, output filter capacitance Co＝1000μF。
FIG. 6a is fm≤fs＜frThe input voltage disturbs a simulation oscillogram, the input voltage jumps according to the sequence of 200V to 170V to 200V to 230V, and the output voltage can be kept stable; FIG. 6b is fm≤fs＜frThe time load disturbance simulates a waveform diagram, the output load current jumps according to the sequence of 10A to 1A to 10A, and the output voltage can be kept stable; FIG. 6c is fs≥frThe input voltage disturbs a simulation oscillogram, the input voltage jumps according to the sequence of 270V to 260V to 270V to 280V, and the output voltage can be kept stable; FIG. 6d is fs≥frThe time load disturbance simulates a waveform diagram, the output load current jumps according to the sequence of 10A to 1A to 10A, and the output voltage can be kept stable. From the waveforms, it can be seen that the controller exhibits good dynamic and static characteristics, demonstrating the effectiveness of the designed control system.
Fig. 7 is an experimental waveform diagram of the influence of the input voltage disturbance of the LLC resonant converter on the output voltage, where the input voltage changes from 270V to 140V, and it can be seen from fig. 7 that the output voltage can be recovered to be stable in a short time.
Fig. 8 is an experimental waveform diagram of the effect of the increase of the load current of the LLC resonant converter on the output voltage, where the load current changes from 3A to 8A, and it can be seen from fig. 8 that the output voltage can be recovered to be stable in a short time.
Fig. 9 is a waveform diagram of an experiment of the effect of the reduction of the load current of the LLC resonant converter on the output voltage, the load current is changed from 8A to 3A, and it can be seen from fig. 9 that the output voltage can be recovered to be stable in a short time.
Therefore, as can be seen from the experimental results in fig. 7 to 9, the stability of the control system of the LLC resonant converter is significantly improved after the control system is designed by the method provided by the present invention.
The invention provides a complete set of complete theoretical system comprising modeling, analysis and control system design for an LLC resonant converter, comprising: a method for simplifying a segmented equivalent circuit model is selected to model the LLC resonant converter, designed circuit parameters of the LLC resonant converter and state parameters of boundary working points of a working area are substituted into a transfer function analytic expression corresponding to the segmented model, the stability margin of each boundary working point can be calculated, a boundary working point with the lowest stability margin is selected for the upper working area and the lower working area of a resonant frequency to carry out controller design, a segmented control system can be designed to control the LLC resonant converter, and the stability of the LLC resonant converter is greatly enhanced by the design.
The foregoing descriptions of specific exemplary embodiments of the present invention have been presented for purposes of illustration and description. It is not intended to limit the invention to the precise form disclosed, and obviously many modifications and variations are possible in light of the above teaching. The exemplary embodiments were chosen and described in order to explain certain principles of the invention and its practical application to enable one skilled in the art to make and use various exemplary embodiments of the invention and various alternatives and modifications as are suited to the particular use contemplated. It is intended that the scope of the invention be defined by the claims and their equivalents.

Claims (1)

1. A method for designing a segmented control system of an LLC resonant converter is characterized by comprising the following steps:
s1, establishing a small signal model according to the circuit parameters of the LLC resonant converter;
s2, dividing a small signal model of the LLC resonant converter into two parts by taking the resonant frequency as a boundary, and respectively obtaining corresponding transfer function analytic expressions of the two parts;
s3, acquiring direct current gain curves of the LLC resonant converter under the conditions of full load and minimum load, acquiring a working interval of the LLC resonant converter by combining a switching frequency range, and dividing the working interval into two parts by taking resonant frequency as a boundary;
s4, respectively substituting state variables corresponding to the boundary working points of each working interval into a sectional type transfer function analytic expression to obtain open loop transfer functions of the boundary working points in the working interval, and obtaining the open loop stability margin of each boundary working point through the open loop transfer functions of the boundary working points;
s5, comparing the stability margins of each boundary point in the two working intervals, and respectively obtaining the boundary working point with the worst open loop stability margin in the two working intervals to design a corresponding compensator;
the LLC resonant converter comprises a half-bridge circuit, a transformer, a rectification filter module and two power switching tubes Q1、Q2The series connection forms a half-bridge circuit, the half-bridge circuit is connected with an input power supply in parallel, the output of the half-bridge circuit is connected with a resonance circuit, and the resonance circuit is composed of a resonance inductor LrResonant capacitor CrResonant inductor LmThe resonant circuit is connected to the rectifying and filtering module and the load R through the transformerLWherein the rectifying and filtering module is composed of a rectifying diode D1、D2And output filter capacitor CoComposition is carried out;
LLC resonant converter operating range at resonant frequency frFor the boundary to be divided into two parts, there are two resonance frequencies in the LLC resonant converter:
first, a resonant inductor LrAnd a resonance capacitor CrResonance frequency f at which resonance occursr
Figure FDA0002957051560000011
Second, resonant inductor LrResonant capacitor CrAnd a resonant inductor LmResonance frequency f at which resonance occursm
Figure FDA0002957051560000021
With power switch Q1、Q2Has a switching frequency of fsWhen f ism≤fs＜frThe transfer function analytic expression of the LLC resonant converter at the time is shown in (3):
Figure FDA0002957051560000022
in the formula (3), QpIs an equivalent quality factor, omegapTo an equivalent resonant angular frequency, GDCIs a direct current gain;
when f iss≥frThe transfer function of the LLC resonant converter is analyzed as shown in (4)
Figure FDA0002957051560000023
Wherein L ise2Is an equivalent inductance, ReqFor equivalent load, XeqIs the resonant tank impedance, RLTo be a load, CoIn order to output the filter capacitance,
Figure FDA0002957051560000024
is a small signal model function of the LLC resonant converter;
and compensating the transfer function corresponding to the screened boundary working point of each frequency band by using the designed compensator so as to realize the stability regulation of the LLC resonant converter.
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