CN112821756B - Method for realizing state track control and finite-state machine of switched capacitor resonant converter - Google Patents

Method for realizing state track control and finite-state machine of switched capacitor resonant converter Download PDF

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CN112821756B
CN112821756B CN202110166846.2A CN202110166846A CN112821756B CN 112821756 B CN112821756 B CN 112821756B CN 202110166846 A CN202110166846 A CN 202110166846A CN 112821756 B CN112821756 B CN 112821756B
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state
resonant
voltage
converter
state3
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CN112821756A (en
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凌睿
王攀
易琪淋
夏增豪
何欣驰
邓策亮
刘姝
张俊祎
吴浩
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Chongqing 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
    • H02M3/02—Conversion of dc power input into dc power output without intermediate conversion into ac
    • H02M3/04—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters
    • H02M3/10—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M3/145—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal
    • H02M3/155—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only
    • H02M3/156—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only with automatic control of output voltage or current, e.g. switching regulators
    • 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
    • H02M3/02—Conversion of dc power input into dc power output without intermediate conversion into ac
    • H02M3/04—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters
    • H02M3/10—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M3/145—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal
    • H02M3/155—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only
    • H02M3/156—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only with automatic control of output voltage or current, e.g. switching regulators
    • H02M3/158—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only with automatic control of output voltage or current, e.g. switching regulators including plural semiconductor devices as final control devices for a single load
    • 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

Abstract

The invention provides a method for realizing state trajectory control and a finite-state machine of a switched capacitor resonant converter, which is characterized by comprising the following steps of: the first switchPipe g1Drain connected to converter input voltage VinPositive electrode, first switching tube g1The source electrodes are respectively connected to the second switch tubes g2Drain and resonant inductance LrOne terminal, resonant inductor LrIs connected at the other end to a resonant capacitor CrOne end of (a), a second switching tube g2The source electrodes are respectively connected to a third switch tube g3Drain electrode, output capacitor CoutOne end of the load R, and a third switching tube g3The source electrodes are respectively connected to the fourth switching tubes g4Drain and resonant capacitance CrThe other end of (a); the fourth switch tube g4The sources are respectively connected to the converter input voltage VinNegative electrode, output capacitor CoutAnd the other end of the load R. The invention can ensure that the driving time sequence of the switching device has the phase-shifting characteristic while the output voltage thereof tracks the reference value; the state trajectory control method is utilized, and the dynamic response of the converter can be realized quickly without overshoot by detecting the resonant current, the output voltage and the resonant capacitor voltage, and the method has the characteristic of strong disturbance rejection.

Description

Method for realizing state trajectory control and finite-state machine of switch capacitor resonant converter
Technical Field
The invention relates to the field of automation control, in particular to a method for realizing state trajectory control and a finite-state machine of a switched capacitor resonant converter.
Background
A small inductor is added in a capacitor charging and discharging path of the switched capacitor converter to form a Switched Capacitor Resonant Converter (SCRC), soft switching can be realized by all switching devices, and peak current is eliminated by adding the resonant inductor. Therefore, the switch capacitor resonant converter effectively improves the power transmission efficiency on the basis of the switch capacitor converter, and has higher research and application values in high-frequency and high-power application occasions.
For the switched capacitor resonant converter, some feedback control methods such as frequency control, blanking time control, duty cycle control, etc. have been proposed, but there are the following disadvantages in these control methods:
(1) the switching device is switched on and off hard, so that the switching loss of the converter is increased;
(2) in the converter circuit, the peak values of the on-state current of the switching tube and the current of the resonant circuit are larger, and converter lines are added
Path loss and switching tube conduction loss;
both of the above disadvantages will eventually lead to a reduction in the power transfer efficiency of the converter. For a switched capacitor resonant converter structure formed by an upper half-bridge inverter and a lower half-bridge inverter, the phase-shifting control method not only realizes the continuous adjustment of output voltage, but also ensures the soft switching operation of the converter. However, the phase shift control research of the existing switched capacitor resonant converter mainly focuses on how to improve the power transmission efficiency of the converter in a wide load range, and the attention on the dynamic performance of the converter is not high. Traditional phase shift control mode, mostly based on output voltage construct simple closed loop feedback control system, its switched capacitor resonant converter's dynamic characteristic is influenced by controller parameter great, and has great promotion space, this needs the technical problem that technical personnel in this field solve corresponding.
Disclosure of Invention
The invention aims to at least solve the technical problems in the prior art, and particularly innovatively provides a method for controlling the state track of a switched capacitor resonant converter and realizing a finite-state machine.
In order to achieve the above object of the present invention, there is provided a switched capacitor resonant converter including: first switch tube g1Drain electrodeConnected to the converter input voltage VinPositive electrode, first switching tube g1The source electrodes are respectively connected to the second switch tubes g2Drain and resonant inductance LrOne terminal, resonant inductor LrIs connected at the other end to a resonant capacitor CrOne end of (1), a second switching tube g2The source electrodes are respectively connected to a third switch tube g3Drain electrode, output capacitor CoutOne end of the load R, and a third switching tube g3The source electrodes are respectively connected to the fourth switching tubes g4Drain and resonant capacitance CrThe other end of (a); the fourth switch tube g4Source electrodes connected to the converter input voltage VinNegative electrode, output capacitor CoutAnd the other end of the load R.
The invention also provides a method for controlling the state track of the switched capacitor resonant converter, which comprises the following steps:
s1, selecting control variables of the switched capacitor resonant converter according to equivalent circuits of the switched capacitor resonant converter in four states, constructing equations under different circuit structures according to the selected control variables, and establishing U related to the control variablesCrN-iLNAnd Uout-iLTwo state planes;
and S2, establishing a finite-state machine controller controlled by a state track, bringing the calculated critical switching condition into the finite-state machine controller, and adjusting the output voltage of the switched capacitor resonant converter to enable the output voltage to track the reference value.
The finite state machine controller comprises: the output of the state machine controller is essentially the driving signals of the four switching tubes, as shown in fig. 2.
The critical switching condition is determined by analyzing Uout-iLStatus plane and UCrN-iLNAnd standardizing a state plane trajectory equation to obtain another mathematical relation presented by an inequality, and completing state switching when the converter meets the inequality or an inequality group in the operation process.
Further, the air conditioner is provided with a fan,
the four states are State 1, State2, State3 and State 4;
the switching states of the equivalent circuit under the four states are as follows: in State 1 State, the switch tube g1And g4Conducting and switching tube g2And g3Turning off; in State2 State, the switch tube g1And g3Conducting, switching tube g2And g4Turning off; in State3 State, the switch tube g2And g3Conducting, switching tube g1And g4Turning off; in State4 State, the switch tube g2And g4Conducting, switching tube g1And g3And (6) turning off.
Further, the S1 includes:
s1-1, selecting a resonant current iLAnd resonant capacitor voltage UCrFor controlling variables, the four states State 1, State2, State3, State4 of the switched-capacitor resonant converter are in the standardized State plane UCrN-iLNThe trajectory equations above are respectively as follows:
State 1：(UCrN-1)2+iLN 2＝(UCrN0-1)2+iLN0 2 (1)
State 2：[UCrN-(1-M)]2+iLN 2＝[UCrN0-(1-M)]2+iLN0 2 (2)
State 3：UCrN 2+iLN 2＝UCrN0 2+iLN0 2 (3)
State 4：(UCrN-M)2+iLN 2＝(UCrN0-M)2+iLN0 2 (4)
wherein
Figure BDA0002935202400000031
UCrNTo standardize the resonant capacitor voltage, iLNTo normalize the resonant current, iLN0And UCrN0Are respectively iLNAnd UCrNAn initial value of (1); m represents a voltage conversion ratio, ZrRepresents a characteristic impedance, LrIs a resonant inductor, CrIs a resonant capacitor, VinIs the converter input voltage, UCrIs the resonant capacitor voltage iLIs a resonant current, UoutIs the converter output voltage;
s1-2, selecting the output voltage U of the converteroutAnd a resonant current iLFor controlling variables, according to the structural characteristics of the switch capacitance resonance converter in four states of State 1, State2, State3 and State4, dynamic equations of the converter in the four states are listed, and the dynamic equations of the converter in the four states of State 1, State2, State3 and State4 in U are deducedout-iLTrajectory equations on the state plane.
Further, the S1-2 includes:
the dynamic equations of the converter in the State 1 and State3 states are as follows:
Figure BDA0002935202400000041
wherein the content of the first and second substances,
Figure BDA0002935202400000042
representing the first derivative over time, iLIs a resonant current, LrIs a resonant inductor, UCrFor resonant capacitor voltage, m is a constant coefficient, VinIs the converter input voltage, CrIs a resonant capacitor, UoutIs the converter output voltage, R is the load, CoutIs an output capacitor;
solving the dynamic equation set (5) to obtain the following relation:
Figure BDA0002935202400000043
Figure BDA0002935202400000044
wherein iLIs a resonant current, LrIs a resonant inductor, CrIs a resonant capacitor, UCrFor resonant capacitor voltage, m is a constant coefficient, VinIs the converter input voltage, UoutIs the converter output voltage, R is the load, CoutFor the output capacitance, e is a natural base number, t is a time variable, iL0、UCr0And Uout0Are each iL、UCrAnd UoutAn initial value of (1);
when the system works in a State 1 State, the value of m is 1, as shown in an equation (8); when the system works in the State3 State, the value of m is 0, as in equation (9);
solving the system of equations (6) and (7) to obtain
Figure BDA0002935202400000045
Replacing the time variable t to obtain the State 1 State trajectory as follows:
Figure BDA0002935202400000046
wherein iLIs a resonant current, UoutIs the converter output voltage, CoutIs an output capacitor, R is a load, LrIs a resonant inductor, CrAs resonant capacitors, UCrTo the resonant capacitor voltage, VinIs the converter input voltage iL0、UCr0And Uout0Are each iL、UCrAnd UoutThe initial value of (1);
the State3 State trajectory is described as follows:
Figure BDA0002935202400000051
dynamic equation in State2 State:
Figure BDA0002935202400000052
wherein the content of the first and second substances,
Figure BDA0002935202400000053
representing the first derivative over time, iLIs a resonant current, LrIs a resonant inductor, UCrFor resonant capacitor voltage, UoutIs the converter output voltage, VinIs the converter input voltage, CrIs a resonant capacitor, R is a load, CoutIs an output capacitor;
to simplify the analysis, set to the no-load condition, R → ∞ i.e. the resistance goes to infinity, equation (10) reduces to:
Figure BDA0002935202400000054
to UoutObtaining a second derivative
Figure BDA0002935202400000055
The expression of (a) is as follows:
Figure BDA0002935202400000056
wherein the content of the first and second substances,
Figure BDA0002935202400000057
representing the second derivative, U, with respect to timeoutIs the converter output voltage, CoutTo output capacitance, iLIs a resonant current, LrIs a resonant inductor, UCrIs a resonant capacitor voltage, VinIs the converter input voltage, and further has the following relation according to the above formula:
Figure BDA0002935202400000058
equality both sides co-multiplying
Figure BDA0002935202400000059
And integrated over the time variable t to yield:
Figure BDA00029352024000000510
wherein, CoutTo output capacitance, LrIs a resonant inductor, UoutIs the output voltage of the converter and is,
Figure BDA0002935202400000061
the first derivative with respect to time is represented,
Figure BDA0002935202400000062
and Uout0Are respectively as
Figure BDA0002935202400000063
And UoutInitial value of (1), VinIs the converter input voltage, UCrIs the resonant capacitor voltage;
will be provided with
Figure BDA0002935202400000064
Substituting equation (14), the available State2 State trajectory is described as follows:
Figure BDA0002935202400000065
wherein, CoutTo output capacitance, LrIs a resonant inductor, iLIs a resonant current, UoutIs the converter output voltage, VinIs the converter input voltage, UCrIs the resonant capacitor voltage iL0Is iLInitial value of (1), Uout0Is UoutAn initial value of (1);
dynamic equation in State4 State:
Figure BDA0002935202400000066
wherein the content of the first and second substances,
Figure BDA0002935202400000067
representing the first derivative over time, iLIs a resonant current, LrIs a resonant inductor, UCrFor resonant capacitor voltage, UoutIs the converter output voltage, CrIs a resonant capacitor, R is a load, CoutIs an output capacitor;
to simplify the analysis, set to the no-load case, R → ∞ i.e., the resistance value tends to infinity, formula (10) is simplified as:
Figure BDA0002935202400000068
to UoutObtaining a second derivative
Figure BDA0002935202400000069
The expression of (a) is as follows:
Figure BDA00029352024000000610
wherein the content of the first and second substances,
Figure BDA00029352024000000611
representing the second derivative, U, with respect to timeoutIs the converter output voltage, CoutTo output capacitance, iLIs a resonant current, LrIs a resonant inductor, UCrFor the oscillating capacitor voltage, according to the above formula, there is further the following relation:
Figure BDA0002935202400000071
equality both sides co-multiplying
Figure BDA0002935202400000072
And integrated over the time variable t to yield:
Figure BDA0002935202400000073
wherein, CoutTo output capacitance, LrIn order to be a resonant inductor, the inductor,
Figure BDA0002935202400000074
representing the first derivative, U, with respect to timeoutIs the converter output voltage, UCrIs the voltage of the resonant capacitor(s),
Figure BDA0002935202400000075
and Uout0Are respectively as
Figure BDA0002935202400000076
And UoutAn initial value of (1);
will be provided with
Figure BDA0002935202400000077
Substituting equation (20), the available State4 State trajectory is described as follows:
Figure BDA0002935202400000078
wherein, CoutTo output capacitance, LrIs a resonant inductor, iLIs a resonant current, UoutIs the converter output voltage, UCrIs the resonant capacitor voltage iL0And Uout0Are each iLAnd UoutAn initial value of (1);
equations (8), (15), (9) and (21) are four states State 1, State2, State3, State4 of the switched capacitor resonant converter in the State plane Uout-iLThe trajectory equation above.
Further, the finite state machine controller for establishing state trajectory control comprises:
Uout≤Vrefstate trajectory control procedure and Uout＞VrefA state trajectory control process;
the U isout≤VrefThe state trajectory control process includes: an initialization stage, an output voltage rising regulation stage and an output voltage stabilization stage;
the initialization phase comprises: taking Rise State 1 as the first activated State after initialization State;
the output voltage rise regulation phase comprises four state drives: rise State 1, Rise State2, Rise State3, Rise State 4;
the U isout＞VrefThe state trajectory control process includes: the method comprises an initialization stage, an output voltage drop regulation stage, an output voltage stability regulation stage and an initial stage;
the initialization phase comprises: taking Fall State 1 as the first activation State after initialization State;
the output voltage droop regulation phase includes four state drives: fall State 1, Fall State2, Fall State3, Fall State 4;
the output voltage stabilization regulation phase comprises four state drives: steady State 1, Steady State2, Steady State3, Steady State 4;
wherein, UoutIs the converter output voltage, VrefIs the output voltage reference value; state 1, State2, State3 and State4 respectively correspond to four states of the converter;
the State prefix Steady represents the stable regulation of the output voltage, and the State track is circularly driven according to the sequence of Steady State 1 → Steady State2 → Steady State3 → Steady State 4;
the State prefix Rise represents the rising regulation of the output voltage, and the State track is circularly driven according to the sequence of Rise State 1 → Rise State2 → Rise State3 → Rise State 4;
the State prefix Fall represents output voltage drop regulation, and the State trajectory is cyclically driven in the order Fall State 1 → Fall State4 → Fall State3 → Fall State 2.
Further, the output voltage rise regulation phase comprises:
setting d asState 1 maximum forward resonant current, 1-UCrNSIs the minimum resonant capacitor voltage, and-d is the State3 maximum negative resonant current, UCrNSIs the maximum resonant capacitor voltage;
thus, the switching condition from Rise State 1 to Rise State2 is iLD, the switching condition from Rise State3 to Rise State4 is iL≤-d；
In the standardized state plane UCrN-iLNAbove, the known State 1 and State3 trajectory equations are:
(UCrN-1)2+iLN 2＝(UCrN0-1)2+iLN0 2 (1)
UCrN 2+iLN 2＝UCrN0 2+iLN0 2 (3)
wherein, UCrNTo standardize the resonant capacitor voltage, iLNTo normalize the resonant current, iLN0And UCrN0Are respectively iLNAnd UCrNAn initial value of (1);
under the circuit structure of the State 1 converter, the State track takes (1, 0) as the center of a circle,
Figure BDA0002935202400000081
a circular trajectory of radius; the minimum resonant capacitance voltage of Rise State 1 is 1-UCrNSThat is, the movement locus of Rise State 1 will pass through the point (1-U)CrNS0), the switching condition from Rise State4 to Rise State 1 is as follows:
(UCrN-1)2+iLN 2≥R1 2＝UCrNS 2or iL≥0；
Wherein, UCrNTo standardize the resonant capacitor voltage, iLNFor normalizing the resonant current, UCrNSIs the maximum resonant capacitor voltage, R1Radius of circular track, i, of State 1LIs a resonant current;
under the circuit structure of the Rise State3 converter, the State track takes (0,0) as the center of a circle,
Figure BDA0002935202400000091
the maximum resonant capacitance voltage of Rise State3 is U in the form of a circular locus of radiusCrNSThat is, the movement trace of Rise State3 will pass through the point (U)CrNS0), the switching condition from Rise State2 to Rise State3 is as follows:
UCrN 2+iLN 2≥R3 2＝UCrNS 2or iL≤0；
Wherein, UCrNTo standardize the resonant capacitor voltage, iLNFor normalizing the resonance current, R3Radius of circular orbit, U, of State3CrNSIs the maximum resonant capacitor voltage, iLIs a resonant current.
Further, the output voltage droop regulation stage comprises:
at UCrN-iLNOn the State plane, d is set as State 1 maximum forward resonant current, 1-UCrNSIs the minimum resonant capacitance voltage, and-d is the State3 maximum negative resonant current, UCrNSIs the maximum resonant capacitor voltage; the same analysis method is adopted as the output voltage rising stage, and the switching condition from Fall State 1 to Fall State4 is iLD, the switching condition from the Fall State4 to the Fall State3 is as follows:
UCrN 2+iLN 2≥R3 2＝UCrNS 2or iL≤0；
Wherein, UCrNTo standardize the resonant capacitor voltage, iLNFor normalizing the resonance current, R3Radius of circular orbit, U, of State3CrNSIs the maximum resonant capacitor voltage, iLIs a resonant current;
the switching condition from Fall State3 to Fall State2 is iLD is less than or equal to, and the switching condition from State2 to State 1 is as follows:
(UCrN-1)2+iLN 2≥R1 2＝UCrNS 2or iL≥0；
Wherein, UCrNTo standardise the resonant capacitor voltage, iLNFor normalizing the resonance current, R1Radius of circular orbit of State 1, UCrNSIs the maximum resonant capacitor voltage, iLIs a resonant current;
u in the states of Fall State2 and Fall State4out＜VrefAnd regulating the State of the descending stage by the output voltage, and respectively jumping to the states Steady State4 and Steady State2 of the stable stage of the output voltage.
Further, the output voltage stabilization regulation phase comprises:
at this time, the output voltage UoutAt a reference value VrefFluctuating up and down, and increasing the Steady State2 State output voltage to be equal to the Steady State3 State output voltage drop; steady State4 State voltage rise equals the Steady State 1 State voltage drop;
in the State of the Steady State3,
Figure BDA0002935202400000101
wherein iLIs a resonant current, LrIs a resonant inductor, CrIs a resonant capacitor, UCrFor resonant capacitor voltage, m is a constant coefficient, VinIs the converter input voltage, t is a time variable, iL0、UCr0And Uout0Are each iL、UCrAnd UoutAn initial value of (1);
can be rewritten as:
Figure BDA0002935202400000102
wherein iLNFor normalizing the resonant current, UCrNTo standardize the resonant capacitor voltage, iLN0And UCrN0Are respectively iLNAnd UCrNIs set to the initial value of (a),
Figure BDA0002935202400000103
the included angle of the connecting line of the initial position of the State and the circle center (0,0) relative to the horizontal axis on the State3 State track is represented as wrIs the resonance angular frequency, t is the time variable;
let theta be wrt，
Figure BDA0002935202400000104
Wherein wrIs at a resonant angular frequency, and
Figure BDA0002935202400000105
then is at UCrN-iLNOn the plane, theta represents the central angle of the current position relative to the initial position of the State on the State3 State track, alpha represents the included angle of the connecting line of the current position and the circle center (0,0) relative to the horizontal axis on the State3 State track,
Figure BDA0002935202400000106
on the State3 State track, the angle of the connecting line of the initial position of the State and the circle center (0,0) relative to the horizontal axis is as follows:
Figure BDA0002935202400000107
Figure BDA0002935202400000108
Figure BDA0002935202400000111
wherein iLNFor normalizing the resonant current, UCrNTo standardize the resonant capacitor voltage, iLN0And UCrN0Are respectively iLNAnd UCrNAn initial value of (1);
by
Figure BDA0002935202400000112
Obtaining:
Figure BDA0002935202400000113
where θ represents the central angle of the current position relative to the initial position of the State on the State3 State trajectory, wrFor the resonant angular frequency, t is the time variable, UoutIs the converter output voltage, Uout0Is UoutInitial value of (1), CoutIs an output capacitor, R is a load, LrIs a resonant inductor, CrIs a resonant capacitor;
by calculating the equations (25), (26):
Figure BDA0002935202400000114
wherein iLNFor normalizing the resonant current, UCrNTo standardize the resonant capacitor voltage, iLN0And UCrN0Are respectively iLNAnd UCrNAn initial value of (1); u shapeoutIs the converter output voltage, Uout0Is UoutInitial value of (1), CoutIs an output capacitor, R is a load, LrIs a resonant inductor, CrIs a resonant capacitor;
at Uout-iLOn the plane, ideally, Steady State3 trajectory passes through (V)ref0), i.e. (V)ref0) satisfies equation (27), taken available:
Figure BDA0002935202400000115
wherein iLN0And UCrN0Respectively, a normalized resonance current iLNAnd normalized resonant capacitor voltage UCrNAn initial value of (1); vrefFor outputting a voltage reference value, Uout0For outputting voltage to the converterUoutInitial value of (1), CoutIs an output capacitor, R is a load, LrIs a resonant inductor, CrIs a resonant capacitor;
in the Steady State2 State, when iLWhen greater than 0, UoutAnd increasing, wherein the switching condition from Steady State2 to Steady State3 in the output voltage stable regulation phase after the deformation of the (28) is as follows:
Figure BDA0002935202400000121
wherein, UoutIs the converter output voltage, VrefFor outputting a voltage reference value, iLNFor normalizing the resonant current, UCrNTo normalize the resonant capacitor voltage, LrIs a resonant inductor, CrIs a resonant capacitor, CoutIs an output capacitor, R is a load, and e is a natural base number;
by adopting the same analysis method, the switching condition from Steady State4 to Steady State 1 in the stable output voltage regulation stage is as follows:
Figure BDA0002935202400000122
wherein, UoutIs the converter output voltage, VrefFor outputting a voltage reference value, iLNFor normalizing the resonant current, UCrNFor normalizing the resonant capacitor voltage, LrIs a resonant inductor, CrIs a resonant capacitor, CoutIs the output capacitance, R is the load, and e is the natural base number.
Further, in the Steady State 1 State of the output voltage, if U is in the Steady Stateout≤VrefAnd i isLD or more, jumping to Steady State2 State in stable regulation stage, and if U is greater than dout＞VrefAnd i isLD or more, jumping to a Fall State4 State in a voltage reduction stage;
in the Steady regulation phase Steady State2 State of the output voltage, if U is in the Steady regulation phaseout<VrefThen the State jumps to Rise State2 in the voltage rising regulation stage;
in the Steady regulation stage Steady State3 State of the output voltage, if U is in the Steady regulation stageout≤VrefAnd i isLIf the State is less than or equal to-d, the State jumps to the Steady State4 State of the stable regulation stage, if U is less than or equal to dout＞VrefAnd i isLThe State jumps to a Fall State2 State of a voltage reduction stage when the voltage is less than or equal to-d;
if U is in the Steady State4 State in the stable regulation phase of the output voltageout<VrefThen the State jumps to Rise State4 in the voltage rising regulation stage;
wherein, UoutIs the converter output voltage, VrefFor the output voltage reference, d is the State 1 maximum positive resonant current, and d is the State3 maximum negative resonant current.
In summary, due to the adoption of the technical scheme, the controller provided by the invention can adjust the output voltage of the converter, so that the output voltage of the converter tracks the reference value and the driving time sequence of the switching device is ensured to have the phase-shifting characteristic; the state trajectory control method is used, and the resonant current, the output voltage and the resonant capacitor voltage are detected, so that the converter can realize quick and overshoot-free dynamic response, and has the characteristic of strong disturbance resistance.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
Drawings
The above and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 is a schematic diagram of a switched capacitor resonant converter of the present invention;
FIG. 2 is a waveform diagram illustrating the operation of the switched capacitor resonant converter of the present invention;
FIG. 3 is a finite state machine controller of the novel state trajectory control method of the present invention;
FIG. 4 shows the output voltage of the converter of the present inventionStable regulation phase, UCrN-iLNThe normalized state of the alpha on the plane of the state,
Figure BDA0002935202400000131
a geometric relationship diagram of θ;
FIG. 5 shows a U of the present inventionCrN-iLNU on planeout≤VrefRegulating Process and Uout＞VrefA state trajectory motion map of the adjustment process;
FIG. 6 shows a U-shaped section of the present inventionout-iLU on planeout≤VrefRegulating Process and Uout＞VrefA state trajectory motion map of the adjustment process;
FIG. 7 shows the output voltage U of the present inventionoutAt Uout≤VrefRegulating Process and Uout＞VrefThe adjustment process is plotted against time.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
FIG. 1 shows a circuit configuration of a switched capacitor resonant converter according to the present invention, the first switching transistor g1Drain connected to converter input voltage VinPositive electrode, first switching tube g1The source electrodes are respectively connected to the second switch tubes g2Drain and resonant inductance LrOne terminal, resonant inductor LrIs connected at the other end to a resonant capacitor CrOne end of (a), a second switching tube g2The source electrodes are respectively connected to a third switch tube g3Drain electrode, output capacitor CoutOne end of the load R, and a third switching tube g3The source electrodes are respectively connected to the fourth switching tubes g4Drain and resonant capacitance CrThe other end of (a); the fourth switch tube g4The sources are respectively connected to the converter input voltage VinNegative electrodeOutput capacitor CoutAnd the other end of the load R.
In fig. 1, the positive direction of the resonance current is defined, and the positive direction is the same as the predetermined current direction, and the negative direction is opposite to the predetermined current direction.
The converter has four states of State 1, State2, State3 and State4, and in the State 1 State, the switch tube g1And g4Conducting, switching tube g2And g3Turning off; in State2 State, the switch tube g1And g3Conducting, switching tube g2And g4Turning off; in State3 State, the switch tube g2And g3Conducting, switching tube g1And g4Turning off; in State4 State, switch tube g2And g4Conducting, switching tube g1And g3And (6) turning off.
Wherein, for the switch tube g1、g2、g3、g4U is a control quantity, u-1 indicates that the switching tube is on, and u-0 indicates that the switching tube is off.
According to the converter output voltage UoutAnd an output voltage reference value VrefThe relationship between magnitude and state trajectory is divided into Uout≤VrefAnd Uout＞VrefTwo control processes. U shapeout≤VrefThe ideal State track of the control process is driven by 9 states of Rise State 1, Rise State2, Rise State3, Rise State4, Steady State 1, Steady State2, Steady State3, Steady State4 and Initial State. U shapeout＞VrefThe ideal State track of the control process is driven by 9 states including Fall State 1, Fall State2, Fall State3, Fall State4, Steady State 1, Steady State2, Steady State3, Steady State4 and Initial State;
in the output voltage rising regulation stage, the operation timing of the switching tube is as shown in fig. 2(a), and the converter is circularly driven in the sequence of the State Rise State 1 → Rise State2 → Rise State3 → Rise State 4. After the system is started, the controller is initialized firstly, the Rise State 1 is used as the first activation State after the initialization State initialization State, and according to the circuit parametersSetting d as State 1 maximum forward resonant current, 1-UCrNSIs the minimum resonant capacitor voltage, and-d is the State3 maximum negative resonant current, UCrNSIs the maximum resonant capacitor voltage. Thus, the switching condition from Rise State 1 to Rise State2 is iLD, the switching condition from Rise State3 to Rise State4 is iL≤-d。
In the standardized state plane UCrN-iLNAbove, the known State 1 and State3 trajectory equations are:
(UCrN-1)2+iLN 2＝(UCrN0-1)2+iLN0 2 (1)
UCrN 2+iLN 2＝UCrN0 2+iLN0 2 (3)
wherein, UCrNTo standardize the resonant capacitor voltage, iLNTo normalize the resonant current, iLN0And UCrN0Are respectively iLNAnd UCrNThe initial value of (1);
therefore, under the State 1 converter circuit structure, the State track takes (1, 0) as the center of a circle,
Figure BDA0002935202400000151
the minimum resonant capacitance voltage of Rise State 1 is 1-U in a circular track with radiusCrNSThat is, the movement locus of Rise State 1 will pass through the point (1-U)CrNS0), the switching condition from Rise State4 to Rise State 1 is as follows:
(UCrN-1)2+iLN 2≥R1 2＝UCrNS 2；
wherein, UCrNTo standardize the resonant capacitor voltage, iLNFor normalizing the resonant current, UCrNSIs the maximum resonant capacitor voltage, R1Radius of circular track, i, of State 1LIs a resonant current;
under the circuit structure of Rise State3 converterThe state track takes (0,0) as the center of a circle,
Figure BDA0002935202400000152
the maximum resonant capacitance voltage of Rise State3 is U in the form of a circular locus of radiusCrNSI.e. the motion trajectory of Rise State3 will pass through the point (U)CrNS0), the switching condition from Rise State2 to Rise State3 is as follows:
UCrN 2+iLN 2≥R3 2＝UCrNS 2；
wherein, UCrNTo standardize the resonant capacitor voltage, iLNFor normalizing the resonance current, R3Radius of circular orbit, U, of State3CrNSIs the maximum resonant capacitor voltage, iLIs a resonant current;
in addition, under the circuit structure of the Rise State2 and Rise State4 converters, the State tracks are respectively circular tracks with (1-M,0) and (M,0) as the circle centers, as the output voltage rises, the circle center of the Rise State2 track moves left, and the circle center of the Rise State4 track moves right, so that the converter can not meet the switching conditions under the State operation of the Rise State2 and Rise State4, the converter normally jumps to the next State, and finally the State track of the whole control process is converged under the condition of a non-target track, and in order to avoid the situation, the phase-shifting characteristic of the switching time sequence of the switching device is ensured. Consider the additional increase of the Rise State2 to Rise State3 switching condition iL≦ 0, and Rise State4 to Rise State 1 switching condition iLIs more than or equal to 0. At Uout-iLQualitative analysis on State plane, and output capacitance C in Rise State 1 StateoutDischarging the load individually, UoutDecrease; in the Rise State2 State, if the resonant current iL＞0，UoutIncrease if iL＜0，UoutDecrease; in the Rise State3 State, the output capacitor CoutDischarging the load individually, UoutDecrease, in the Rise State4 State, if the resonant current iL＜0，UoutIncrease if iL＞0，UoutAnd decreases. When Rise State2 or Rise StU at ate4 stateout≥VrefAnd regulating the state of the rising stage by the output voltage, and jumping to the corresponding state of the stable stage of the output voltage.
In the output voltage drop regulation phase, the working sequence of the switch tube is shown in fig. 2(b), and the converter is circularly driven in the sequence of states Fall State 1 → Fall State4 → Fall State3 → Fall State 2. After the system is started, the controller is initialized firstly, the Fall State 1 is used as the first activation State after the initialization State, and according to the circuit parameters, the State is in UCrN-iLNOn the State plane, d is set as State 1 maximum forward resonant current, 1-UCrNSIs the minimum resonant capacitor voltage, and-d is the State3 maximum negative resonant current, UCrNSIs the maximum resonant capacitor voltage. The same analysis method is adopted as the output voltage rising stage, and the switching condition from Fall State 1 to Fall State4 is iLD, the switching condition from the Fall State4 to the Fall State3 is as follows:
UCrN 2+iLN 2≥R3 2＝UCrNS 2or iL≤0；
UCrNTo standardize the resonant capacitor voltage, iLNFor normalizing the resonance current, R3Radius of circular orbit, U, of State3CrNSIs the maximum resonant capacitor voltage, iLIs a resonant current;
the switching condition from Fall State3 to Fall State2 is iLD is less than or equal to the value-d, and the switching condition from Fall State2 to Fall State 1 is as follows:
(UCrN-1)2+iLN 2≥R1 2＝UCrNS 2or iL≥0；
Wherein, UCrNTo standardize the resonant capacitor voltage, iLNFor normalizing the resonance current, R1Radius of circular orbit, U, of State 1CrNSIs the maximum resonant capacitor voltage, iLIs a resonant current;
u in the states of Fall State2 and Fall State4out＜VrefThe falling stage state is regulated by the output voltageAnd respectively jumping to the Steady State4 and Steady State2 states of the output voltage stabilization stage.
In the output voltage stabilization regulation phase, the operation timing of the switching tube is as shown in fig. 2(c), and the inverter is cyclically driven in the order of State ready State 1 → ready State2 → ready State3 → ready State 4. At this time, the output voltage UoutAt a reference value VrefFluctuating up and down, and increasing the Steady State2 State output voltage to be equal to the Steady State3 State output voltage drop; the Steady State4 State voltage rise is equal to the Steady State 1 State voltage drop.
In Steady State3 State, equation
Figure BDA0002935202400000171
Rewritable as follows:
Figure BDA0002935202400000172
wherein iLNFor normalizing the resonant current, UCrNTo standardize the resonant capacitor voltage, iLN0And UCrN0Are respectively iLNAnd UCrNIs set to the initial value of (a),
Figure BDA0002935202400000173
the included angle of the connecting line of the initial position of the State and the circle center (0,0) relative to the horizontal axis on the State3 State track is represented as wrIs the resonance angular frequency, t is the time variable;
let theta be wrt，
Figure BDA0002935202400000174
Wherein wrIs at a resonant angular frequency, and
Figure BDA0002935202400000175
then is at UCrN-iLNOn the plane, theta represents the central angle of the current position relative to the initial position of the State on the State3 State track, alpha represents the connecting line of the current position and the center (0,0) relative to the horizontal axis on the State3 State trackThe angle of,
Figure BDA0002935202400000176
on the State3 State track, the angle of the connecting line of the initial position of the State and the circle center (0,0) relative to the horizontal axis is as follows:
Figure BDA0002935202400000181
Figure BDA0002935202400000182
Figure BDA0002935202400000183
wherein iLNFor normalizing the resonant current, UCrNTo standardize the resonant capacitor voltage, iLN0And UCrN0Are respectively iLNAnd UCrNAn initial value of (1);
further described by the State trajectory of State3, equation (9):
Figure BDA0002935202400000184
where θ represents the central angle of the current position relative to the initial position of the State on the State3 State trajectory, wrFor the resonant angular frequency, t is the time variable, UoutIs the converter output voltage, Uout0Is UoutThe initial value of (1); coutIs a filter capacitor, R is a load, LrIs a resonant inductance, CrIs a resonant capacitor;
by calculating the equations (25), (26):
Figure BDA0002935202400000185
at Uout-iLPlane surfaceIdeally, the Steady State3 trajectory passes through (V)ref0), i.e. (V)ref0) satisfies trajectory equation (27), taken to be available:
Figure BDA0002935202400000186
iLN0and UCrN0Respectively, a normalized resonance current iLNAnd normalized resonant capacitor voltage UCrNInitial value of (1), VrefFor outputting a voltage reference value, Uout0For converter output voltage UoutInitial value of (1), CoutIs a filter capacitor, R is a load, LrIs a resonant inductor, CrIs a resonant capacitor;
in the Steady State2 State, when iLWhen greater than 0, UoutAnd increasing, wherein the switching condition from Steady State2 to Steady State3 in the output voltage stable regulation phase after the deformation of the (28) is as follows:
Figure BDA0002935202400000191
wherein, UoutIs the converter output voltage, VrefFor outputting a voltage reference value, iLNFor normalizing the resonant current, UCrNFor normalizing the resonant capacitor voltage, LrIs a resonant inductor, CrIs a resonant capacitor, CoutIs a filter capacitor, R is a load, and e is a natural base number;
by adopting the same analysis method, the switching condition from Steady State4 to Steady State 1 in the stable output voltage regulation stage is obtained as follows:
Figure BDA0002935202400000192
wherein, UoutIs the converter output voltage, VrefFor outputting a voltage reference value, iLNFor normalizing the resonant current, UCrNFor normalizing the resonant capacitor voltage, LrIs harmonic toVibration inductance, CrIs a resonant capacitor, CoutIs the output capacitance, R is the load, and e is the natural base number.
In addition, in order to make the output voltage quickly follow the reference value, in the Steady State 1 State of the stable regulation phase of the output voltage, if U is in the Stateout≤VrefAnd i isLD or more, jumping to Steady State2 State in stable regulation stage, and if U is greater than dout＞VrefAnd i isLD or more, jumping to a Fall State4 State in a voltage reduction stage; in the Steady regulation phase Steady State2 State of the output voltage, if U is in the Steady regulation phaseout<VrefThen the State jumps to Rise State2 for the voltage ramp up regulation phase; in the Steady regulation stage Steady State3 State of the output voltage, if U is in the Steady regulation stageout≤VrefAnd i isLIf the State is less than or equal to-d, the State jumps to the Steady State4 State of the stable regulation stage, if U is less than or equal to dout＞VrefAnd i isLThe State jumps to a Fall State2 State of a voltage reduction stage when the voltage is less than or equal to-d; if U is in the Steady State4 State in the stable regulation phase of the output voltageout<VrefThen the State jumps to Rise State4 in the voltage rising regulation stage; wherein, UoutIs the converter output voltage, VrefFor the output voltage reference, d is the State 1 maximum positive resonant current, and d is the State3 maximum negative resonant current.
FIG. 3 shows a finite state machine controller for a state trajectory control method based on the converter output voltage UoutAnd an output voltage reference value VrefSize relationship, the state machine controller is divided into Uout≤VrefAnd Uout＞VrefTwo control processes. U shapeout≤VrefThe ideal State track of the control process is driven by 9 states of Rise State 1, Rise State2, Rise State3, Rise State4, Steady State 1, Steady State2, Steady State3, Steady State4 and Initial State. U shapeout＞VrefThe ideal State track of the control process is driven by 9 states including Fall State 1, Fall State2, Fall State3, Fall State4, Steady State 1, Steady State2, Steady State3, Steady State4 and Initial State; it is composed ofIn the method, State 1, State2, State3 and State4 respectively correspond to four states of a converter, a State prefix Steady represents stable regulation of output voltage, and the State track is circularly driven according to the sequence of Steady State 1 → Steady State2 → Steady State3 → Steady State 4; the State prefix Rise represents the rising regulation of the output voltage, and the State track is circularly driven according to the sequence of Rise State 1 → Rise State2 → Rise State3 → Rise State 4; the State prefix Fall represents output voltage drop regulation, and the State trajectory is cyclically driven in the order Fall State → Fall State4 → Fall State3 → Fall State 2.
The designed state critical switching condition is brought into a finite state controller, and the input voltage V is input into a switched capacitor resonant converter circuit parameter converterin30V, resonant inductance Lr27 muH, resonant capacitance Cr9.4 μ F, output capacitance CoutAt 150 μ F, the output voltage reference is set to VrefThe output voltage is initially set to U at 16Vout00V, yielding U as shown in fig. 5(a), 6(a) and 7(a)CrN-iLNMotion trajectory in planar state, Uout-iLPlanar motion trajectory and output voltage UoutA step response curve; the reference value of the output voltage is set to VrefThe initial value of the output voltage is set to U at 14Vout030V, yielding U as shown in fig. 5(b), 6(b), and 7(b)CrN-iLNMotion trajectory in planar state, Uout-iLPlanar state motion trajectory and output voltage UoutStep response curve.
FIG. 4 shows the converter of the present invention during the output voltage regulation phase, UCrN-iLNThe normalized state of the alpha on the plane of the state,
Figure BDA0002935202400000201
geometric relationship of θ:
let theta be wrt，
Figure BDA0002935202400000202
Wherein wrIs at a resonant angular frequency, and
Figure BDA0002935202400000203
then is at UCrN-iLNOn the plane, theta represents the central angle of the current position relative to the initial position of the State on the State3 State track, alpha represents the included angle of the connecting line of the current position and the circle center (0,0) relative to the horizontal axis on the State3 State track,
Figure BDA0002935202400000211
on the State3 State track, the angle of the connecting line of the initial position of the State and the circle center (0,0) relative to the horizontal axis is as follows:
Figure BDA0002935202400000212
Figure BDA0002935202400000213
Figure BDA0002935202400000214
wherein iLNFor normalizing the resonant current, UCrNTo standardize the resonant capacitor voltage, iLN0And UCrN0Are respectively iLNAnd UCrNOf (4) is calculated.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the invention have been shown and described, it will be understood by those of ordinary skill in the art that: various changes, modifications, substitutions and alterations can be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims (10)

1. A method for controlling a state track of a switched capacitor resonant converter is characterized by comprising the following steps:
s1, selecting control variables of the switched capacitor resonant converter according to equivalent circuits of the switched capacitor resonant converter in four states, constructing equations under different circuit structures according to the selected control variables, and establishing U related to the control variablesCrN-iLNAnd Uout-iLTwo state planes, wherein UCrNTo standardize the resonant capacitor voltage, iLNFor normalizing the resonant current, UoutIs the converter output voltage iLIs a resonant current;
and S2, establishing a finite-state machine controller controlled by a state track, bringing the calculated critical switching condition into the finite-state machine controller, and adjusting the output voltage of the switched capacitor resonant converter to enable the output voltage to track the reference value.
2. The method for controlling the state trajectory of the switched capacitor resonant converter according to claim 1, comprising:
the four states are State 1, State2, State3 and State 4;
the switching states of the equivalent circuit under the four states are as follows: in State 1 State, the switch tube g1And g4Conducting, switching tube g2And g3Turning off; in State2 State, the switch tube g1And g3Conducting, switching tube g2And g4Turning off; in State3 State, the switch tube g2And g3Conducting, switching tube g1And g4Turning off; in State4 State, the switch tube g2And g4Conducting, switching tube g1And g3And (6) turning off.
3. The method according to claim 1, wherein the step S1 includes:
s1-1, selecting a resonant current iLAnd resonant capacitor voltage UCrFor controlling variables, the four states State 1, State2, State3, State4 of the switched-capacitor resonant converter are in the standardized State plane UCrN-iLNThe trajectory equations above are respectively as follows:
State 1：(UCrN-1)2+iLN 2＝(UCrN0-1)2+iLN0 2 (1)
State 2：[UCrN-(1-M)]2+iLN 2＝[UCrN0-(1-M)]2+iLN0 2 (2)
State 3：UCrN 2+iLN 2＝UCrN0 2+iLN0 2 (3)
State 4：(UCrN-M)2+iLN 2＝(UCrN0-M)2+iLN0 2 (4)
wherein
Figure FDA0003438261220000021
UCrNTo standardize the resonant capacitor voltage, iLNTo normalize the resonant current, iLN0And UCrN0Are respectively iLNAnd UCrNAn initial value of (1); m represents a voltage conversion ratio, ZrRepresents a characteristic impedance, LrIs a resonant inductor, CrIs a resonant capacitor, VinIs the converter input voltage, UCrIs the resonant capacitor voltage, iLIs a resonant current, UoutIs the converter output voltage;
s1-2, selecting the output voltage U of the converteroutAnd a resonant current iLFor controlling variables, according to switching powerThe structure characteristics of the capacitance resonance converter in four states of State 1, State2, State3 and State4 are respectively listed, the dynamic equations of the converter in the four states are listed, and the U states of State 1, State2, State3 and State4 of the converter are deducedout-iLTrajectory equations on the state plane.
4. The switched capacitor resonant converter state trajectory control method of claim 3, wherein the S1-2 comprises:
the dynamic equations of the converter in the State 1 and State3 states are as follows:
Figure FDA0003438261220000022
where "·" denotes the first derivative with respect to time, iLIs a resonant current, LrIs a resonant inductor, UCrFor resonant capacitor voltage, m is a constant coefficient, VinIs the converter input voltage, CrIs a resonant capacitor, UoutIs the converter output voltage, R is the load, CoutIs an output capacitor;
solving the dynamic equation set (5) to obtain the following relation:
Figure FDA0003438261220000023
Figure FDA0003438261220000024
wherein iLIs a resonant current, LrIs a resonant inductor, CrIs a resonant capacitor, UCrFor resonant capacitor voltage, m is a constant coefficient, VinIs the converter input voltage, UoutIs the converter output voltage, R is the load, CoutFor the output capacitance, e is a natural base number, t is a time variable, iL0、UCr0And Uout0Are each iL、UCrAnd UoutAn initial value of (1);
when the system works in a State 1 State, the value of m is 1, as shown in an equation (8); when the system works in the State3 State, the value of m is 0, as in equation (9);
solving the system of equations (6) and (7) to obtain
Figure FDA0003438261220000031
Replacing the time variable t to obtain the State 1 State trajectory as follows:
Figure FDA0003438261220000032
wherein iLIs a resonant current, UoutIs the converter output voltage, CoutIs an output capacitor, R is a load, LrIs a resonant inductor, CrIs a resonant capacitor, UCrIs a resonant capacitor voltage, VinIs the converter input voltage iL0、UCr0And Uout0Are each iL、UCrAnd UoutAn initial value of (1);
the State3 State trajectory is described as follows:
Figure FDA0003438261220000033
dynamic equation in State2 State:
Figure FDA0003438261220000034
where "·" denotes the first derivative with respect to time, iLIs a resonant current, LrIs a resonant inductor, UCrFor resonant capacitor voltage, UoutIs the converter output voltage, VinIs the converter input voltage, CrIs a resonant capacitor, R is a load, CoutFor transfusionDischarging a capacitor;
to simplify the analysis, set to the no-load case, R → ∞ i.e., the resistance value tends to infinity, formula (10) is simplified as:
Figure FDA0003438261220000041
to UoutObtaining a second derivative
Figure FDA0003438261220000042
The expression of (a) is as follows:
Figure FDA0003438261220000043
where "· denotes the second derivative with respect to time, UoutIs the converter output voltage, CoutTo output capacitance, iLIs a resonant current, LrIs a resonant inductor, UCrIs a resonant capacitor voltage, VinIs the converter input voltage, and further has the following relation according to the above formula:
Figure FDA0003438261220000044
equality both sides co-multiplying
Figure FDA0003438261220000045
And integrated over the time variable t to yield:
Figure FDA0003438261220000046
wherein, CoutTo output capacitance, LrIs a resonant inductor, UoutIs the converter output voltage, "·" denotes the first derivative with respect to time,
Figure FDA0003438261220000047
and Uout0Are respectively as
Figure FDA0003438261220000048
And UoutInitial value of (1), VinIs the converter input voltage, UCrIs the resonant capacitor voltage;
will be provided with
Figure FDA0003438261220000049
Substituting (14), the available State2 State trajectory is described as follows:
Figure FDA00034382612200000410
wherein, CoutTo output capacitance, LrIs a resonant inductor, iLIs a resonant current, UoutIs the converter output voltage, VinIs the converter input voltage, UCrIs the resonant capacitor voltage iL0Is iLInitial value of (1), Uout0Is UoutAn initial value of (1);
dynamic equation in State4 State:
Figure FDA0003438261220000051
where "·" denotes the first derivative with respect to time, iLIs a resonant current, LrIs a resonant inductor, UCrFor resonant capacitor voltage, UoutIs the converter output voltage, CrIs a resonant capacitor, R is a load, CoutIs an output capacitor;
to simplify the analysis, set to the no-load case, R → ∞ i.e., the resistance value tends to infinity, formula (10) is simplified as:
Figure FDA0003438261220000052
to UoutObtaining a second derivative
Figure FDA0003438261220000053
The expression of (a) is as follows:
Figure FDA0003438261220000054
where "· denotes the second derivative with respect to time, UoutIs the converter output voltage, CoutTo output capacitance, iLIs a resonant current, LrIs a resonant inductor, UCrFor the oscillating capacitor voltage, according to the above formula, there is further the following relation:
Figure FDA0003438261220000055
equality both sides co-multiplying
Figure FDA0003438261220000056
And integrated over the time variable t to yield:
Figure FDA0003438261220000057
wherein, CoutTo output capacitance, LrFor resonant inductance, ". denotes the first derivative with respect to time, UoutIs the converter output voltage, UCrIs the voltage of the resonant capacitor(s),
Figure FDA0003438261220000058
and Uout0Are respectively as
Figure FDA0003438261220000059
And UoutAn initial value of (1);
will be provided with
Figure FDA00034382612200000510
Substituting equation (20), the available State4 State trajectory is described as follows:
Figure FDA00034382612200000511
wherein, CoutTo output capacitance, LrIs a resonant inductor, iLIs a resonant current, UoutIs the converter output voltage, UCrIs the resonant capacitor voltage iL0And Uout0Are each iLAnd UoutThe initial value of (1);
equations (8), (15), (9) and (21) are the four states State 1, State2, State3 and State4 of the switched capacitor resonant converter in the State plane Uout-iLThe trajectory equation above.
5. The switched capacitor resonant converter state-trajectory control method of claim 1, wherein the finite-state-machine controller establishing state-trajectory control comprises:
Uout≤Vrefstate trajectory control procedure and Uout＞VrefA state trajectory control process;
the U isout≤VrefThe state trajectory control process comprises the following steps: an initialization stage, an output voltage rising regulation stage and an output voltage stabilization stage;
the initialization phase comprises: taking Rise State 1 as the first activated State after initialization State;
the output voltage rise regulation phase comprises four state drives: rise State 1, Rise State2, Rise State3, Rise State 4;
the U isout＞VrefThe state trajectory control process comprises the following steps: the method comprises an initialization stage, an output voltage drop regulation stage, an output voltage stability regulation stage and an initial stage;
the initialization phase comprises: taking Fall State 1 as the first activation State after initialization State;
the output voltage droop regulation phase includes four state drives: fall State 1, Fall State2, Fall State3, Fall State 4;
the output voltage stabilization regulation phase comprises four state drives: steady State 1, Steady State2, Steady State3, Steady State 4;
wherein, UoutIs the converter output voltage, VrefIs the output voltage reference value; state 1, State2, State3 and State4 respectively correspond to four states of the converter;
the State prefix Steady represents the stable regulation of the output voltage, and the State track is circularly driven according to the sequence of Steady State 1 → Steady State2 → Steady State3 → Steady State 4;
the State prefix Rise represents the rising regulation of the output voltage, and the State track is circularly driven according to the sequence of Rise State 1 → Rise State2 → Rise State3 → Rise State 4;
the State prefix Fall represents output voltage drop adjustment, and the State trajectory is circularly driven in the order Fall State 1 → Fall State4 → Fall State3 → Fall State 2.
6. The switched capacitor resonant converter state trajectory control method of claim 5, wherein the output voltage rise regulation phase comprises:
according to the circuit parameters, d is set as State 1 maximum forward resonant current 1-UCrNSIs the minimum resonant capacitor voltage, and-d is the State3 maximum negative resonant current, UCrNSIs the maximum resonant capacitor voltage;
thus, the switching condition from Rise State 1 to Rise State2 is iLD, the switching condition from Rise State3 to Rise State4 is iL≤-d；
In the standardized state plane UCrN-iLNAbove, the known State 1 and State3 trajectory equations are:
(UCrN-1)2+iLN 2＝(UCrN0-1)2+iLN0 2 (1)
UCrN 2+iLN 2＝UCrN0 2+iLN0 2 (3)
wherein, UCrNTo standardize the resonant capacitor voltage, iLNTo normalize the resonant current, iLN0And UCrN0Are respectively iLNAnd UCrNAn initial value of (1);
under the circuit structure of the State 1 converter, the State track takes (1, 0) as the center of a circle,
Figure FDA0003438261220000071
a circular trajectory of radius; the minimum resonant capacitor voltage of Rise State 1 is 1-UCrNSThat is, the movement locus of Rise State 1 will pass through the point (1-U)CrNS0), the switching condition from Rise State4 to Rise State 1 is as follows:
(UCrN-1)2+iLN 2≥R1 2＝UCrNS 2or iL≥0；
Wherein, UCrNTo standardize the resonant capacitor voltage, iLNFor normalizing the resonant current, UCrNSIs the maximum resonant capacitor voltage, R1Radius of circular track, i, of State 1LIs a resonant current;
under the circuit structure of the Rise State3 converter, the State track takes (0,0) as the center of a circle,
Figure FDA0003438261220000072
the maximum resonant capacitance voltage of Rise State3 is U in the form of a circular locus of radiusCrNSI.e. the motion trajectory of Rise State3 will pass through the point (U)CrNS0), the switching condition from Rise State2 to Rise State3 is as follows:
UCrN 2+iLN 2≥R3 2＝UCrNS 2or iL≤0；
Wherein, UCrNTo standardize the resonant capacitor voltage, iLNFor normalizing the resonance current, R3Radius of circular orbit, U, of State3CrNSIs the maximum resonant capacitor voltage, iLIs a resonant current.
7. The switched capacitor resonant converter state trajectory control method of claim 5, wherein the output voltage droop regulation stage comprises:
at UCrN-iLNOn the State plane, d is set as State 1 maximum forward resonant current, 1-UCrNSIs the minimum resonant capacitor voltage, and-d is the State3 maximum negative resonant current, UCrNSIs the maximum resonant capacitor voltage; the same analysis method is adopted as the output voltage rising stage, and the switching condition from Fall State 1 to Fall State4 is iLD, the switching condition from the Fall State4 to the Fall State3 is as follows:
UCrN 2+iLN 2≥R3 2＝UCrNS 2or iL≤0；
Wherein, UCrNTo standardize the resonant capacitor voltage, iLNFor normalizing the resonance current, R3Radius of circular orbit, U, of State3CrNSIs the maximum resonant capacitor voltage, iLIs a resonant current;
the switching condition from Fall State3 to Fall State2 is iLD is less than or equal to, and the switching condition from State2 to State 1 is as follows:
(UCrN-1)2+iLN 2≥R1 2＝UCrNS 2or iL≥0；
Wherein, UCrNTo standardize the resonant capacitor voltage, iLNFor normalizing the resonance current, R1Radius of circular orbit, U, of State 1CrNSIs the maximum resonant capacitor voltage, iLIs a resonant current;
u in Fall State2 and Fall State4 statesout＜VrefThen is passed byAnd (4) outputting the voltage regulation descending stage State, and jumping to the Steady State4 State and the Steady State2 State of the output voltage stabilization stage respectively.
8. The switched capacitor resonant converter state trajectory control method of claim 5, wherein the output voltage stabilization regulation phase comprises:
at this time, the output voltage UoutAt a reference value VrefFluctuating up and down, and increasing the Steady State2 State output voltage to be equal to the Steady State3 State output voltage drop; steady State4 State voltage rise equals the Steady State 1 State voltage drop;
in the State of the Steady State3,
Figure FDA0003438261220000091
wherein iLIs a resonant current, LrIs a resonant inductor, CrIs a resonant capacitor, UCrFor resonant capacitor voltage, m is a constant coefficient, VinIs the converter input voltage, t is a time variable, iL0、UCr0And Uout0Are each iL、UCrAnd UoutAn initial value of (1);
can be rewritten as:
Figure FDA0003438261220000092
wherein iLNFor normalizing the resonant current, UCrNTo standardize the resonant capacitor voltage, iLN0And UCrN0Are respectively iLNAnd UCrNIs set to the initial value of (a),
Figure FDA0003438261220000093
the included angle of the connecting line of the initial position of the State and the circle center (0,0) relative to the horizontal axis on the State3 State track is represented as wrIs the resonance angular frequency, t is the time variable;
let theta be wrt，
Figure FDA0003438261220000094
Wherein wrIs at a resonant angular frequency, and
Figure FDA0003438261220000095
then is at UCrN-iLNOn the plane, theta represents the central angle of the current position relative to the initial position of the State on the State3 State track, alpha represents the included angle of the connecting line of the current position and the circle center (0,0) relative to the horizontal axis on the State3 State track,
Figure FDA0003438261220000096
on the State3 State track, the angle of the connecting line of the initial position of the State and the circle center (0,0) relative to the horizontal axis is as follows:
Figure FDA0003438261220000097
Figure FDA0003438261220000098
Figure FDA0003438261220000099
wherein iLNFor normalizing the resonant current, UCrNTo standardize the resonant capacitor voltage, iLN0And UCrN0Are respectively iLNAnd UCrNAn initial value of (1);
by
Figure FDA00034382612200000910
Obtaining:
Figure FDA0003438261220000101
where θ represents the central angle of the current position relative to the initial position of the State on the State3 State trajectory, wrFor the resonant angular frequency, t is the time variable, UoutIs the converter output voltage, Uout0Is UoutInitial value of (1), CoutIs an output capacitor, R is a load, LrIs a resonant inductor, CrIs a resonant capacitor;
by calculating the equations (25), (26):
Figure FDA0003438261220000102
wherein iLNFor normalizing the resonant current, UCrNTo standardize the resonant capacitor voltage, iLN0And UCrN0Are respectively iLNAnd UCrNAn initial value of (1); u shapeoutIs the converter output voltage, Uout0Is UoutInitial value of (A), CoutIs an output capacitor, R is a load, LrIs a resonant inductor, CrIs a resonant capacitor;
at Uout-iLOn the plane, ideally, Steady State3 trajectory passes through (V)ref0), i.e. (V)ref0) satisfies equation (27), taken available:
Figure FDA0003438261220000103
wherein iLN0And UCrN0Respectively, a normalized resonance current iLNAnd normalized resonant capacitor voltage UCrNAn initial value of (1); vrefTo output a voltage reference value, Uout0For converter output voltage UoutInitial value of (1), CoutIs an output capacitor, R is a load, LrIs a resonant inductor, CrIs a resonant capacitor;
in Steady State2 State, when iLWhen greater than 0, UoutAnd increasing, wherein the switching condition from Steady State2 to Steady State3 in the output voltage stable regulation phase after the deformation of the (28) is as follows:
Figure FDA0003438261220000104
wherein, UoutIs the converter output voltage, VrefFor outputting a voltage reference value, iLNFor normalizing the resonant current, UCrNFor normalizing the resonant capacitor voltage, LrIs a resonant inductor, CrIs a resonant capacitor, CoutIs an output capacitor, R is a load, and e is a natural base number;
by adopting the same analysis method, the switching condition from Steady State4 to Steady State 1 in the stable output voltage regulation stage is as follows:
Figure FDA0003438261220000111
wherein, UoutIs the converter output voltage, VrefTo output a voltage reference value, iLNFor normalizing the resonant current, UCrNFor normalizing the resonant capacitor voltage, LrIs a resonant inductor, CrIs a resonant capacitor, CoutIs the output capacitance, R is the load, and e is the natural base number.
9. The method for controlling the state trajectory of the switched capacitor resonant converter according to claim 5, comprising:
in the Steady regulation stage Steady State 1 State of the output voltage, if U is in the Steady regulation stageout≤VrefAnd i isLD or more, jumping to Steady State2 State in stable regulation stage, and if U is greater than dout＞VrefAnd i isLD or more, jumping to a Fall State4 State in a voltage reduction stage;
regulating stage for output voltage stabilizationIn the State of Steady State2, if U isout<VrefThen the State jumps to Rise State2 in the voltage rising regulation stage;
if U is in the Steady State3 State in the stable regulation phase of the output voltageout≤VrefAnd i isLIf the State is less than or equal to-d, the State jumps to the Steady State4 State of the stable regulation stage, if U is less than or equal to dout＞VrefAnd i isLThe State jumps to a Fall State2 State of a voltage reduction stage when the voltage is less than or equal to-d;
if U is in the Steady State4 State in the stable regulation phase of the output voltageout<VrefThen the State jumps to Rise State4 in the voltage rising regulation stage;
wherein, UoutIs the converter output voltage, VrefFor the output voltage reference, d is the State 1 maximum positive resonant current, and d is the State3 maximum negative resonant current.
10. The method according to claim 1, wherein the switch-capacitor resonant converter comprises: the first switch tube g1Drain connected to converter input voltage VinPositive electrode, first switching tube g1The source electrodes are respectively connected to the second switch tubes g2Drain and resonant inductance LrOne terminal, resonant inductor LrIs connected at the other end to a resonant capacitor CrOne end of (a), a second switching tube g2The source electrodes are respectively connected to a third switch tube g3Drain electrode, output capacitor CoutOne end of the load R, and a third switching tube g3The source electrodes are respectively connected to the fourth switching tubes g4Drain and resonant capacitance CrThe other end of (a); the fourth switch tube g4The sources are respectively connected to the converter input voltage VinNegative electrode, output capacitor CoutAnd the other end of the load R.
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