CN110098733B - Method for eliminating influence of ESL in DC-DC buck second-order sliding mode control - Google Patents

Method for eliminating influence of ESL in DC-DC buck second-order sliding mode control Download PDF

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CN110098733B
CN110098733B CN201910463048.9A CN201910463048A CN110098733B CN 110098733 B CN110098733 B CN 110098733B CN 201910463048 A CN201910463048 A CN 201910463048A CN 110098733 B CN110098733 B CN 110098733B
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state
controller
sliding mode
delta
esl
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CN110098733A (en
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凌睿
王殿
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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
    • 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
    • H02M1/00—Details of apparatus for conversion
    • H02M1/0003—Details of control, feedback or regulation circuits

Abstract

The invention provides a method for eliminating the influence of ESL in DC-DC buck second-order sliding mode control, which comprises the following steps: step 1, establishing a second-order sliding mode controller of a finite-state machine for an ideal buck converter (without considering parasitic parameters); and 2, introducing the value of output voltage jump caused by the parasitic parameter ESL into a judgment condition controlled by the state machine, and correcting the actual output voltage overshoot caused by the ESL.

Description

Method for eliminating influence of ESL in DC-DC buck second-order sliding mode control
Technical Field
The invention relates to the field of automatic control, in particular to a method for eliminating the influence of ESL in DC-DC buck second-order sliding mode control.
Background
DC-DC converters are widely used in power systems, electric vehicles, and various applications to accommodate various voltage and current levels between a power source and a load. When the parasitic parameters are not considered, the ideal DC-DC buck converter second-order sliding mode control method is based on a controller with a state machine structure, does not need any current measuring circuit, only adopts voltage feedback, can enable the buck converter to have good dynamic performance, and has good robustness to parameter uncertainty and load disturbance. In practical applications, however, parasitic parameters in the circuit are unavoidable, and the parasitic parameters may reduce the control performance of the second-order sliding mode controller.
Disclosure of Invention
The invention aims to solve the problems that in DC-DC buck second-order sliding mode control, output voltage overshoot is caused by ESL, and the control performance of a controller is reduced.
The invention provides a control method for eliminating the influence of series parasitic inductance (ESL) in a DC-DC buck circuit in second-order sliding mode control. On the basis of a state machine controller of an ideal buck converter, the method introduces a jump value delta h of output voltage jump caused by series parasitic inductance into a state switching judgment condition for compensation, avoids error judgment on delta, and eliminates output voltage overshoot possibly caused by switch misoperation.
In order to achieve the above object, the present invention provides a control method for eliminating the influence of series parasitic inductance (ESL) in a DC-DC buck circuit in second-order sliding mode control, which is characterized by comprising:
step 1, establishing a second-order sliding mode controller of a finite-state machine for an ideal buck converter (without considering parasitic parameters), defining sliding mode variables, establishing a sliding mode surface, and setting an effective state and an initial state to enable the effective state to correspond to the output quantity of the controller;
and 2, introducing a value of output voltage jump caused by the ESL into the judgment condition of the state machine controller on the delta in the step 1, and correcting the output voltage overshoot caused by the ESL.
In the control method for eliminating the influence of series parasitic inductance (ESL) in the DC-DC buck circuit in second-order sliding mode control, preferably, the step 1 includes:
and step 1-1, establishing an ideal buck circuit finite state machine second-order sliding mode controller without considering the influence of parasitic parameters. Defining a sliding mode variable s, and under the conditions of uncertain controller parameters and load disturbance, enabling the controller track to reach a second-order sliding mode surface within limited time
Figure BDA0002078626830000021
It comprises 4 active states OFF+,OFF-,ON+,ON-And 1 initial state (initial). State OFF+And ON+Corresponding to a sliding mode quantity s ≧ 0 and a state OFF-And ON-Corresponding to a sliding mode quantity s < 0, and a state OFF+And OFF-Corresponding to the first derivative of the sliding mode quantity
Figure BDA0002078626830000022
Reduced system motion trajectory, and state ON+And ON-Corresponding to the first derivative of the sliding mode quantity
Figure BDA0002078626830000023
In each active state, u-1 or u-0 is the output of the controller. (ii) a
Step 1-2, the controller adopts two variables smAnd sM，smSaving sliding mode variables s in active states ON+And ON-Minimum of, and sMSaving s in State OFF+And OFF-By a variable s, the switching condition of the controller being defined bymAnd sMDetermining the variable smAnd sMWill alternate with the switching of state in the controller;
step 1-3, when the state track is ON from the effective state-After departure, variable smThe minimum value of s will be saved when triggering condition β smAfter the condition is satisfied, wherein 0 is less than β and less than 1, the effective state is OFF-Will be activated, since 0 < β < 1, the coordinate point β smRatio smCloser to the origin, OFF in the active state-In the middle, the motion track of the system gradually approaches to the transverse axis, and the variable sMWill be continuously updated until the trajectory reaches the horizontal axis, and after traversing the horizontal axis, the trajectory will be far from the horizontal axis until the condition s-s is satisfiedmDelta, where delta is a determined time lag value for limiting the switching frequency of the controller output, followed by state ON-Will be activated again in state ON-In (1), when the system track crosses the transverse axis, the variable smWill be replaced by the minimum value of the sliding mode variable s and then, following the same convergence process, if δ is small enough, the controller will take the trajectory to
Figure BDA0002078626830000031
Near the origin of the phase plane, when the controller trajectory is from
Figure BDA0002078626830000032
Starting from the right side of the phase plane, there will be a similar convergence trajectory.
In the control method for eliminating the influence of series parasitic inductance (ESL) in the DC-DC buck circuit in second-order sliding mode control, preferably, the step 2 includes:
and 2-1, considering the influence of a parasitic parameter ESL, adopting the finite state machine second-order sliding mode controller in the step 1, wherein when the switching state is switched every time, the ESL in the buck circuit causes a jump of delta h on the output voltage, so that the switching state switching condition misjudges delta, and the output voltage is over-regulated.
And 2-2, introducing the delta h into a state machine switching judgment condition, compensating jump caused by ESL, and eliminating overshoot of output voltage.
In the control method for eliminating the influence of series parasitic inductance (ESL) in the DC-DC buck circuit in second-order sliding mode control, preferably, the step 2-1 includes:
when the switching state is u equals 1, the output voltage is
Figure BDA0002078626830000033
Wherein VcIn order to output the voltage across the capacitor C,
Figure BDA0002078626830000034
is the voltage across the series parasitic resistance (ESR),
Figure BDA0002078626830000035
is the absolute value of the voltage across the ESL. When the switch state is u-0, the output voltage is
Figure BDA0002078626830000036
Jump value of output voltage
Figure BDA0002078626830000037
Namely, the jump value deltah is determined by the jump value of the voltage at two ends of the ESL at the switching moment of the switch.
In the control method for eliminating the influence of series parasitic inductance (ESL) in the DC-DC buck circuit in second-order sliding mode control, preferably, the step 2-2 includes:
in the running process of the finite-state machine missed sliding mode controller introducing the jump value delta h, the following steps are carried out
Figure BDA0002078626830000038
To
Figure BDA0002078626830000041
Is changed from s in the ideal stateMS.gtoreq.delta to sM- (s + Δ h) Δ or more; from
Figure BDA0002078626830000042
To
Figure BDA0002078626830000043
S is not less than s in the ideal stateβNsm+ delta is changed into s-delta h not less than βNsm+ δ; from
Figure BDA0002078626830000044
To
Figure BDA0002078626830000045
S is less than or equal to β in an ideal statePsM-delta becomes s + delta h ≦ βPsM- δ; from
Figure BDA0002078626830000046
To
Figure BDA0002078626830000047
The switching condition of (A) is determined by s-s in an ideal statemChange from ≥ delta to (s-delta h) -smIs not less than delta, wherein the parameter βNAnd βPBy
Figure BDA0002078626830000048
And
Figure BDA0002078626830000049
and (6) dynamically adjusting.
In summary, due to the adoption of the technical scheme, the invention has the beneficial effects that:
1. the output power is not overshot;
2. the dynamic response speed is high;
3. no current needs to be detected;
4. the method has good robustness to the uncertainty of circuit parameters;
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 circuit diagram of a DC-DC buck converter according to a control method of the present invention for eliminating the effect of ESL in a DC-DC buck circuit in a second-order sliding mode control;
FIG. 2 is a diagram of a second-order sliding mode controller track motion in a state plane of an ideal buck circuit finite state machine of the control method for eliminating the influence of ESL in the second-order sliding mode control in the DC-DC buck circuit
Figure BDA00020786268300000410
Left side of (2);
FIG. 3 is a second-order sliding mode controller of a finite-state machine for an ideal buck circuit in a control method for eliminating the influence of ESL in a DC-DC buck circuit in second-order sliding mode control according to the invention;
FIG. 4 is a steady-state limit loop track of a second-order sliding mode controller of a finite-state machine of an ideal buck circuit in the control method for eliminating the influence of ESL in the DC-DC buck circuit in the second-order sliding mode control;
FIG. 5 shows the output voltages in three cases of the control method for eliminating the influence of ESL in the DC-DC buck circuit in the second-order sliding mode control according to the present invention;
FIGS. 6A to 6B are two switch states when parasitic parameters are considered in a control method for eliminating the influence of ESL in a DC-DC buck circuit in second-order sliding mode control according to the present invention;
FIG. 7 shows an output voltage jump caused by ESL in a control method for eliminating the influence of ESL in a DC-DC buck circuit in second-order sliding mode control according to the invention.
FIG. 8 is a second-order sliding mode controller of a finite-state machine according to a control method for eliminating the influence of ESL in a DC-DC buck circuit in second-order sliding mode control;
FIG. 9 is a flow chart of the present invention;
FIG. 10 is a diagram of the effect of the simulation of the circuit of the present invention;
FIG. 11 is a dynamic response diagram of the circuit of the present invention.
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 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 drawings are illustrative only and should not be construed as limiting the invention.
In the description of the present invention, it is to be understood that the terms "longitudinal", "lateral", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", and the like, indicate orientations or positional relationships based on those shown in the drawings, and are used merely for convenience of description and for simplicity of description, and do not indicate or imply that the referenced devices or elements must have a particular orientation, be constructed and operated in a particular orientation, and thus, are not to be construed as limiting the present invention.
The invention discloses a method for eliminating the influence of ESL in DC-DC buck second-order sliding mode control,
fig. 1 shows a circuit diagram of a DC-DC buck converter. In the figure, VgIs an input voltage, VoIs the output voltage iLIs the inductive current, RloadIs a load resistance, L is an inductance, RcIs ESR, LcIs ESL, the sliding mode quantity selected is as follows:
s＝Vo-Vref(1)
the first order differential is:
Figure BDA0002078626830000061
the second order differential is:
Figure BDA0002078626830000062
if the converter is unloaded, use
Figure BDA0002078626830000063
Standardizing (3) to
Figure BDA0002078626830000064
As shown in fig. 2
Figure BDA0002078626830000065
Is selected as the slip form surface. When the control trajectory crosses the horizontal axis, smKeeping the minimum value of s. sMKeeping s at its maximum value, δ being a hysteresis parameter; theoretically, as δ approaches 0, the switching frequency approaches infinity, and in practice the control trajectory will enter a limit loop near the equilibrium point under δ.
FIG. 3 is a state machine controller for an ideal buck circuit, during start-up phase, entering ON if s < 0-When s ≧ β is satisfiednsmIs switched to OFF at + delta-(ii) a Then, when s-s is satisfiedM< delta > will turn ON again-And simultaneously updating βNAnd smThe value of (c). When s ≧ 0, the case is similar.
The ideal switching value is
Figure BDA0002078626830000066
Figure BDA0002078626830000067
When near the equilibrium point, the root trajectory enters a limit cycle, as shown in FIG. 4. In fact, parasitic parameters may degrade the performance of the controller, as shown in fig. 5, the green yellow and purple lines represent the output voltage of the original controller of the ideal buck circuit, the output voltage of the buck circuit considering the parasitic parameters being overshot under the control of the original controller, and the output voltage of the buck circuit considering the parasitic parameters under the control of the improved controller, respectively.
Calculating the parameter Δ h
The two states of the converter are shown in fig. 6A and 6B, and the following equations are satisfied:
Figure BDA0002078626830000071
Figure BDA0002078626830000078
Figure BDA0002078626830000072
at circuit start-up, when u equals 1, VgCharging L and C with current icIncrease, LcA voltage across the terminals of
Figure BDA0002078626830000073
At this time
Figure BDA0002078626830000074
When u is 0, inductances L and LcReleasing energy to continue charging C, current icDecrease, LcThe voltage across is reversed, is
Figure BDA0002078626830000075
At this time
Figure BDA0002078626830000076
So when the switch is switched from on to off, VoA jump Δ h occurs in
Figure BDA0002078626830000077
When the switch is switched from off to on, V is shown in FIG. 7oAlso, a jump occurs, s lags behind VoTime tcon，tconThe time it takes for the analog signal to be converted to a digital signal by the time a/D converter. This means that V is used to calculate soIs tconThe previous value, the jump Δ h caused by each switch switching, makes s at tconFollowed by a sudden change.
When Δ h > δ, there are two cases of switch malfunction:
misconduction:
when the switch is switched from on to off, s is delayed by tconThe latter decrease Δ h, which leads to the following decisionThe broken condition meets the following conditions:
sM-s＝Δh≥δ (11)
the controller switches the error to u-1.
False turn-off:
when the switch is switched from on-off to switching, s is delayed by tconThe latter increase Δ h, which causes the following decision condition to be satisfied:
s-sm＝Δh≥δ (12)
the controller switches the error to u-0
Second-order sliding mode state machine controller corrected by delta h
To eliminate the effect of voltage jumps across the ESL on the output voltage, Δ h can be used to compensate the state machine controller. The corrected state machine determination conditions are as follows:
from OFF-To ON-:
s-Δh≥βNsm+δ (13)
From ON-To OFF-:
sM-(s+Δh)≥δ (14)
From OFF+To ON+:
s+Δh≤βPsM-δ (15)
From ON+To OFF+:
(s-Δh)-sm≥δ (16)
Using Δ h, which can be measured in real time, the jump in s can be compensated to avoid overshoot of the output voltage caused by ESL, and the improved state machine controller is shown in fig. 8.
As shown in fig. 9, the present invention provides an improved DC-DC buck converter second-order sliding-mode control method, which is characterized by comprising:
step 1, establishing a second-order sliding mode controller of a finite-state machine for an ideal buck converter (without considering parasitic parameters), defining sliding mode variables, establishing a sliding mode surface, and setting an effective state and an initial state to enable the effective state to correspond to the output quantity of the controller;
and 2, introducing a value of output voltage jump caused by the ESL into the judgment condition of the state machine controller on the delta in the step 1, and correcting the output voltage overshoot caused by the ESL.
In which matlab/simulink simulations were used to verify the method of the invention. Parameters as shown in Table 1 parameters of the synchronous BuckDC-DC converter of Table 1
Vg 5V
Vref 1.25V
δ 0.006
L 1uH
C 270uf
R 0.5-5Ω
The circuit simulation effect is shown in FIG. 10, V1Is the output voltage waveform, V, of the state controller without introducing Δ h2The improved state machine controller output voltage waveform after introducing Δ h.
When the load is switched, the dynamic response of the circuit is as shown in FIG. 11, the switched load is Rload0.5 Ω and R load5 Ω, L of the circuitC＝2nH,RC＝0.006Ω。
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 (3)

1. A method for eliminating the influence of ESL in DC-DC buck second-order sliding mode control, which is characterized by comprising the following steps:
step 1, establishing a second-order sliding mode controller of a finite-state machine for an ideal buck converter, defining a sliding mode variable, establishing a sliding mode surface, and setting an effective state and an initial state to enable the effective state to correspond to the output quantity of the controller;
step 2, introducing a value of output voltage jump caused by the ESL into a judgment condition of the state machine controller for delta in the step 1, and correcting output voltage overshoot caused by the ESL; delta is a determined time lag value;
the step 2 further comprises:
step 2-1, considering the influence of a parasitic parameter ESL, adopting the finite state machine second-order sliding mode controller in the step 1, wherein when the switch state is switched every time, the ESL in the buck circuit causes a jump of delta h on the output voltage, so that the switch state switching condition misjudges delta, and the output voltage is over-regulated;
the step 2-1 comprises the following steps:
when the switching state is u equals 1, the output voltage is
Figure FDA0002352944110000011
Wherein VcIn order to output the voltage across the capacitor C,
Figure FDA0002352944110000012
is the voltage across the series parasitic resistance (ESR),
Figure FDA0002352944110000013
the absolute value of the voltage at two ends of the ESL; when the switch state is u-0, the output voltage is
Figure FDA0002352944110000014
Jump value of output voltage
Figure FDA0002352944110000015
Namely, the jump value delta h is determined by the jump value of the voltage at two ends of the ESL at the switching moment of the switch;
and 2-2, introducing the delta h into a state machine switching judgment condition, compensating jump caused by ESL, and eliminating overshoot of output voltage.
2. The method for eliminating the influence of ESL in DC-DC buck second-order sliding-mode control according to claim 1, wherein the step 1 comprises:
step 1-1, establishing an ideal buck circuit finite-state machine second-order sliding mode controller without considering the influence of parasitic parameters; defining a sliding mode variable s, and under the conditions of uncertain controller parameters and load disturbance, enabling the controller track to reach a second-order sliding mode surface within limited time
Figure FDA0002352944110000021
Comprising 4 active states OFF+,OFF-,ON+,ON-And 1 initial state, active state OFF+And ON+Corresponding to the sliding mode quantity s being more than or equal to 0 and the effective state OFF-And ON-Corresponding to the sliding mode quantity s less than 0 and the effective state OFF+And OFF-Corresponding to the first derivative of the sliding mode quantity
Figure FDA0002352944110000022
Reduced system motion trajectory, and active state ON+And ON-Corresponding to the first derivative of the sliding mode quantity
Figure FDA0002352944110000023
Increased system motion trajectory of U in each of said active states+Or U-Is the output of the controller;
step 1-2, the controller adopts two variables smAnd sM，smSaving sliding mode variable s in valid state
Figure FDA0002352944110000024
And
Figure FDA0002352944110000025
minimum of, and sMSaving s in state
Figure FDA0002352944110000026
And
Figure FDA0002352944110000027
by a variable s, the switching condition of the controller being defined bymAnd sMDetermining the variable smAnd sMWill alternate with the switching of states in the controller;
step 1-3, when the state track is from the effective state
Figure FDA0002352944110000028
After departure, variable smThe minimum value of s will be saved when triggering condition β smAfter the condition is satisfied, wherein 0 is less than β and less than 1, the effective state
Figure FDA0002352944110000029
Will be activated, since 0 < β < 1, coordinate point β smRatio smCloser to the origin, in the active state
Figure FDA00023529441100000210
In the middle, the system motion track is gradually close to the horizontal axis, and the variable sMWill be continuously updated until the trajectory reaches the horizontal axis, and after traversing the horizontal axis, the trajectory will be far from the horizontal axis until the condition s-s is satisfiedmDelta, where delta is a determined time lag value for limiting the switching frequency of the controller output, followed by a state
Figure FDA00023529441100000211
Will be activated again in the state
Figure FDA00023529441100000212
In (1), when the system track crosses the horizontal axis, the variable smWill be replaced by the minimum value of the sliding mode variable s and then, following the same convergence process, if δ is small enough, the controller will take the trajectory to
Figure FDA00023529441100000213
Near the origin of the phase plane, when the controller trajectory is from
Figure FDA00023529441100000214
Starting from the right side of the phase plane, there will be a similar convergence trajectory.
3. The method for eliminating the influence of ESL in DC-DC buck second-order sliding-mode control according to claim 1, wherein the step 2-2 comprises:
in the running process of the finite-state machine missed sliding mode controller introducing the jump value delta h, the following steps are carried out
Figure FDA0002352944110000039
To
Figure FDA0002352944110000033
Is changed from s in the ideal stateMS.gtoreq.delta to sM- (s + Δ h) Δ or more; from
Figure FDA00023529441100000310
To
Figure FDA0002352944110000034
The switching condition of (b) is set to s ≧ β in the ideal stateNsm+ delta is changed into s-delta h not less than βNsm+ δ; from
Figure FDA0002352944110000035
To
Figure FDA0002352944110000036
S is less than or equal to β in an ideal statePsM-delta becomes s + delta h ≦ βPsM- δ; from
Figure FDA0002352944110000037
To
Figure FDA0002352944110000038
The switching condition of (A) is determined by s-s in an ideal statemChange from ≥ delta to (s-delta h) -smNot less than delta, wherein the primary side parameter β of the controllerNAnd secondary parameters β of transformerPFrom the minimum value of the primary parameter of the controller
Figure FDA0002352944110000031
And controller secondary parameter minimum
Figure FDA0002352944110000032
And (6) dynamically adjusting.
CN201910463048.9A 2019-05-30 2019-05-30 Method for eliminating influence of ESL in DC-DC buck second-order sliding mode control Expired - Fee Related CN110098733B (en)

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CN104901538A (en) * 2015-05-29 2015-09-09 重庆大学 Second-order sliding mode controller and flying capacitor voltage balance method of three-level DC-DC buck converter

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CN104901538A (en) * 2015-05-29 2015-09-09 重庆大学 Second-order sliding mode controller and flying capacitor voltage balance method of three-level DC-DC buck converter

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固定频率BUCK直流变换器的二阶滑模控制;刘金平;《中国优秀硕士学位论文全文数据库信息科技辑》;20190415(第04期);第三章第3.4.1-3.4.12节、第3.5节及附图3.1-3.2 *
电压型滞环控制的同步Buck变换器;李丹青等;《电源技术应用》;20041031;第7卷(第10期);第3.2小节 *

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