CN112821758A - Fractional order sliding mode control method of Buck type power converter aiming at unmatched interference - Google Patents

Fractional order sliding mode control method of Buck type power converter aiming at unmatched interference Download PDF

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CN112821758A
CN112821758A CN202011628216.4A CN202011628216A CN112821758A CN 112821758 A CN112821758 A CN 112821758A CN 202011628216 A CN202011628216 A CN 202011628216A CN 112821758 A CN112821758 A CN 112821758A
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power converter
sliding mode
buck
type power
order sliding
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CN112821758B (en
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刘发刚
吴立刚
林欣魄
房淑贤
刘健行
孙玉君
孙光辉
郑贵
刘壮
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Suihua Power Supply Co Of State Grid Heilongjiang Electric Power Co ltd
Harbin Institute of Technology
State Grid Corp of China SGCC
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Suihua Power Supply Co Of State Grid Heilongjiang Electric Power Co ltd
Harbin Institute of Technology
State Grid Corp of China SGCC
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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
    • 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
    • H02M3/1582—Buck-boost converters
    • 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
    • H02M1/36—Means for starting or stopping converters
    • 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
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E10/00—Energy generation through renewable energy sources
    • Y02E10/50—Photovoltaic [PV] energy
    • Y02E10/56—Power conversion systems, e.g. maximum power point trackers

Abstract

A fractional order sliding mode control method for a Buck type power converter aiming at unmatched interference belongs to the technical field of power electronic control and aims to solve the problems that the Buck type power converter is poor in stability and low in robustness when the Buck type power converter faces unmatched interference. According to the method, a Buck-type power converter model is built, a high-order sliding mode observer is designed, a fractional order sliding mode controller is designed, matched and unmatched interference of the Buck-type power converter model is observed and built by the designed high-order sliding mode observer, the unmatched interference observed by the high-order sliding mode observer is introduced into the designed fractional order sliding mode controller, and the unmatched interference is compensated. The method has the beneficial effects that the stability and the robustness of the Buck type power converter in the face of unmatched disturbance are improved.

Description

Fractional order sliding mode control method of Buck type power converter aiming at unmatched interference
Technical Field
The invention belongs to the technical field of power electronic control.
Background
Thanks to the rapid development of the micro-grid technology, the occupation ratio of the distributed renewable energy in the power system is steadily improved; the DC-DC Buck type power converter is an important component in a micro-grid system and is widely applied to a photovoltaic system, a direct current motor driving system and an energy storage system; the Buck-type power converter functions to convert an input dc voltage into another fixed or adjustable desired dc voltage, thereby achieving a stable flow of energy throughout the system.
Generally, the control target of a Buck-type power converter is to regulate the output voltage to a reference value; however, the Buck power converter contains different kinds of interference, such as load disturbance and parameter uncertainty, etc., wherein the load disturbance and the uncertainty of the capacitance parameter are non-matching interference for the control of the Buck power converter; the existence of non-matching interference easily has very serious influence on the control of the Buck type power converter; in addition, some special working conditions put higher requirements on the performance of the Buck type power converter; therefore, a good control strategy is needed to enable the Buck power converter to maintain good dynamic and steady-state performance under the condition of containing non-matching interference.
As is well known, an effective control strategy that can obtain a desired dc voltage and also make the controller simple in structure and easy to implement is difficult to obtain; because the linear PI controller is simple and the parameters are easy to set, the method is generally used in industrial application, but the PI controller cannot well cope with the condition that the parameters are uncertain; in recent years, a nonlinear controller is applied to control of a Buck-type power converter, such as sliding mode control, model predictive control, H-infinity control, fuzzy control, and the like, and the control problem of the Buck-type power converter has been greatly developed; sliding mode control is receiving more and more attention due to the advantages of high control precision and robustness to matching interference; however, when the system contains mismatched interference, the robustness of the existing sliding mode control will be greatly affected; as shown above, the Buck-type power converter is a typical system with non-matching interference, and the existing sliding mode control method fails.
Most of the existing sliding mode control is based on integer-order sliding mode control; in fact, fractional calculus has the same long history of development as integer calculus; fractional calculus has been used in recent years for PID control and has been applied to 2-degree-of-freedom direct drive robotic arms; however, the development of fractional order sliding mode control is still in the infancy stage.
Disclosure of Invention
The invention aims to solve the problems of poor stability and low robustness of a Buck-type power converter in the face of unmatched disturbance, and provides a fractional order sliding mode control method of the Buck-type power converter aiming at unmatched disturbance.
The invention discloses a fractional order sliding mode control method of a Buck type power converter aiming at unmatched interference, which comprises the following steps:
step one, building a Buck type power converter model;
designing a high-order sliding mode observer;
step three, designing a fractional order sliding mode controller according to the Buck type power converter model established in the step one;
and step four, establishing matched and unmatched interference of the Buck type power converter model by utilizing the high-order sliding mode observer observation step one designed in the step two, introducing the unmatched interference observed by the high-order sliding mode observer into the fractional order sliding mode controller designed in the step three, and compensating the unmatched interference.
The invention has the beneficial effect of improving the stability and robustness of the Buck type power converter in the face of unmatched disturbance. The control of the invention consists of a high-order sliding mode observer and a fractional order sliding mode controller; the high-order sliding mode observer is used for observing matching and non-matching interference in a system, an estimated value of the interference is introduced into a sliding mode surface, the output voltage of the system can be better adjusted, and the output voltage of the system can quickly follow a reference value; meanwhile, the fractional order integrator is adopted in the sliding mode surface, and practice proves that the fractional order sliding mode surface has greater advantage in the aspect of improving the convergence speed of the system compared with the integer order sliding mode surface, and the system is more flexible to control due to the fact that one more adjustable degree of freedom is provided; the experimental result shows that the regulation performance and the steady-state performance of the output voltage of the system are improved under the control of the method
Drawings
FIG. 1 is a circuit diagram of a Buck power converter according to one embodiment;
FIG. 2 is a schematic diagram of a fractional order sliding mode controller with a high order sliding mode observer according to a first embodiment;
FIG. 3 is a diagram illustrating the variation of the output voltage of the Buck-type power converter during startup according to an embodiment;
FIG. 4 is a diagram illustrating the variation of the output voltage of the Buck-type power converter when the reference value is changed according to the first embodiment;
FIG. 5 is a diagram illustrating the output voltage variation of a Buck-type power converter during a load dump in accordance with an embodiment;
FIG. 6 is a diagram illustrating the output voltage variation of a Buck-type power converter during a load surge in accordance with an embodiment;
fig. 7 is a diagram of the output voltage variation of the Buck-type power converter in consideration of the load surge under the uncertainty of the parameters according to the first embodiment.
Detailed Description
The first embodiment is as follows: the present embodiment is described with reference to fig. 1 to 7, and the fractional order sliding mode control method for a mismatch interference Buck power converter according to the present embodiment includes the following steps:
step one, building a Buck type power converter model;
designing a high-order sliding mode observer;
step three, designing a fractional order sliding mode controller according to the Buck type power converter model established in the step one;
and step four, establishing matched and unmatched interference of the Buck type power converter model by utilizing the high-order sliding mode observer observation step one designed in the step two, introducing the unmatched interference observed by the high-order sliding mode observer into the fractional order sliding mode controller designed in the step three, and compensating the unmatched interference.
In the present embodiment, a Buck power converter model is shown in fig. 1, where the power supply voltage is VinThe system chops the power supply voltage through a power switch tube Q, then obtains the output voltage through an LC filter, R is an equivalent load resistor, and the actual value of the R is unknown; according to the control method, unknown load and parameter uncertainty are regarded as unknown disturbance, a fractional order sliding mode controller with a high-order sliding mode observer is used for processing the unknown disturbance of the Buck type power converter, and the output voltage of the Buck type power converter is enabled to track a reference value.
The specific method for establishing the Buck type power converter model in the first step comprises the following steps:
the Buck-type power converter is represented by a state space method as follows:
Figure BDA0002873470610000031
let x1＝vo-vd，
Figure BDA0002873470610000032
The Buck-type power converter model can be rewritten as:
Figure BDA0002873470610000033
wherein the content of the first and second substances,
Figure BDA0002873470610000034
for mismatched interference in a Buck-type power converter model,
Figure BDA0002873470610000035
for matching disturbances in a Buck-type power converter model,
Figure BDA0002873470610000036
vofor the output voltage of a Buck-type power converter model,
Figure BDA0002873470610000037
is v isoFirst derivative of vinInput voltage, v, for a Buck-type power converter modelin0Nominal value of input voltage of Buck-type power converter model for input voltage, u ∈ [0,1 ]]For controlling the input, i.e. duty cycle, v, of Buck-type power convertersdAs a reference voltage, the voltage of the reference voltage,
Figure BDA0002873470610000038
is v isdThe first derivative of (a) is,
Figure BDA0002873470610000039
is v isdSecond derivative of (i)LIn order to be the current of the inductor,
Figure BDA00028734706100000310
is iLThe first derivative of (a);
Figure BDA00028734706100000311
is x1The first derivative of (a) is,
Figure BDA00028734706100000312
is x2R is the actual load resistance value, R0Is a nominal load resistance value, C is an actual capacitance value, C0Is a nominal capacitance value, L is an actual inductance value, L0Is the nominal inductance value.
In the present embodiment, the following is assumed for the disturbance:
Figure BDA0002873470610000041
wherein L is a normal number.
The specific form of the high-order sliding mode observer designed in the step two is as follows:
Figure BDA0002873470610000042
wherein i ∈ {1,2}, sgnκ(·)＝|·|κsign (·), sign () is a sign function in mathematics, κ is an arbitrary real number,
Figure BDA0002873470610000043
and
Figure BDA0002873470610000044
all the components are intermediate in weight percentage,
Figure BDA0002873470610000045
and
Figure BDA0002873470610000046
are also all intermediate quantities, and,
Figure BDA0002873470610000047
Figure BDA0002873470610000048
is xiIs determined by the estimated value of (c),
Figure BDA0002873470610000049
is composed of
Figure BDA00028734706100000410
The first derivative of (a) is,
Figure BDA00028734706100000411
Figure BDA00028734706100000412
is diIs determined by the estimated value of (c),
Figure BDA00028734706100000413
is composed of
Figure BDA00028734706100000414
The first derivative of (a) is,
Figure BDA00028734706100000415
Figure BDA00028734706100000416
is diAn estimate of the first derivative;
Figure BDA00028734706100000417
Liis the normal number to be designed;
Figure BDA00028734706100000418
and
Figure BDA00028734706100000419
are all constant, and
Figure BDA00028734706100000420
in the present embodiment, the normal number L is only required to be designediThe observed value of the high-order sliding mode observer adopted by the control method can be converged into an interval shown in the specification within a limited time; i.e. there is a TsSuch that when T > TsThe method comprises the following steps:
Figure BDA00028734706100000421
Figure BDA00028734706100000422
Figure BDA00028734706100000423
Figure BDA00028734706100000424
wherein, deltai(i is 1,2,3,4) is a normal number.
The specific steps of designing the fractional order sliding mode controller in the third step are as follows:
step three, determining a control target: enabling the output voltage v of the system to be in the condition that the Buck type power converter model contains unmatched interferenceoTracking to a given value vd；
Namely: v. ofo→vd(4)；
Step three, designing a slip form surface;
and step three, determining the specific form of the fractional order sliding mode controller.
The concrete method of the slip form surface designed in the third step and the second step comprises the following steps:
Figure BDA0002873470610000051
wherein theta is more than 0 and less than 1, chi is more than 0 and less than 1, c1＞0，c2> 0 is four normal numbers to be designed;
Figure BDA0002873470610000052
for the fractional operator, the following is defined:
Figure BDA0002873470610000053
wherein mu is an arbitrary real number, and when mu is less than 0, the fractional order integral is defined as follows:
Figure BDA0002873470610000054
wherein
Figure BDA0002873470610000055
Is a Gamma function;
when μ > 0, the fractional order differential is defined as follows:
Figure BDA0002873470610000056
wherein m is the largest integer less than μ.
In this embodiment, equation (5) reduces the effect of mismatch interference, and a sliding mode surface is used as shown in equation (5), which introduces mismatch disturbance d1And the observed value of (2) and the associated x1The fractional order integral of the method can greatly reduce the influence caused by unmatched disturbance and accelerate the speed of convergence to a far point after the system state reaches; the Gamma function is a Gamma function;
the specific form of the fractional order sliding mode controller in the third step is as follows:
u＝ueq+usw
Figure BDA0002873470610000057
Figure BDA0002873470610000058
γ1and gamma2The selection method comprises the following steps:
γ1＞0
Figure BDA0002873470610000059
wherein u iseqAs an equivalent control term, uswFor switching control items, γ1γ2Are all designed control parameters, δ4Behind a high-order sliding-mode observer for adoption
Figure BDA0002873470610000061
The final convergence interval of (a) to (b),
Figure BDA0002873470610000062
is d2The first derivative of (a) is,
Figure BDA0002873470610000063
is d2An estimate of the first derivative.
In the present embodiment, the formula shown in formula (9) is used as the approach rate,
equation (9) is as follows:
Figure BDA0002873470610000064
wherein, γ1> 0 and gamma2> 0 are the control parameters that are designed.
The effectiveness of the invention is demonstrated by experimental results, the system parameters are shown in table 1, in order to prove the effectiveness of the invention, the performance indexes of the system under a fractional order sliding mode surface (formula one) without disturbance estimation values, PI double-loop control and an integer order sliding mode surface (formula two) with disturbance estimation values are compared and analyzed, and the specific control parameters are shown in table 2.
Figure BDA0002873470610000065
Figure BDA0002873470610000066
TABLE 1
Figure BDA0002873470610000067
TABLE 2
Figure BDA0002873470610000068
A. Starting performance
Fig. 3 shows the performance of four methods at start-up, where (a) is a start-up waveform under a fractional-order sliding mode surface without a disturbance estimation value, (b) is a start-up waveform under PI control, (c) is a start-up waveform under an integer-order sliding mode surface with a disturbance estimation value, and (d) is a start-up waveform under a fractional-order sliding mode surface with a disturbance estimation value, which is proposed by the present invention. It can be seen that the output voltage of the system under the fractional order sliding mode surface without the disturbance estimated value can not track the given value, the output voltage of the other three control methods can track the given value, wherein the tracking speed is fastest and the overshoot is minimum by the method provided by the invention. Specific indices are shown in Table 3
TABLE 3
Figure BDA0002873470610000071
B. Changing tracking performance of a reference system
Fig. 4 shows the performance of four methods when the reference value is changed from 20V to 10V, where (a) is the start waveform under the fractional-order sliding mode surface without disturbance estimation value, (b) is the start waveform under PI control, (c) is the start waveform under the integer-order sliding mode surface with disturbance estimation value of the start waveform, and (d) is the start waveform under the fractional-order sliding mode surface with disturbance estimation value proposed by the present invention. It can be seen that the system under the fractional order sliding mode surface without the disturbance estimation value can not track the given value at two moments, and the other three methods can track the given value, wherein the adjustment time is fastest and the undershoot is minimum by the method provided by the invention. Specific indexes are shown in table 4:
TABLE 4
Figure BDA0002873470610000072
C. Recovery performance of system during sudden load drop
Figure 5 shows the performance of the system when the system load is ramped from 10 ohms to 20 ohms. The starting waveform under the integral-order sliding mode surface is (a) free of disturbance estimation value, (b) under PI control, (c) containing disturbance estimation value, and (d) provided by the invention. It can be seen that the system under the fractional order sliding mode surface without the disturbance estimation value can not track the given value at two moments, and the other three methods can track the given value, wherein the overshoot is minimum by the method provided by the invention, and the method has a faster recovery time similar to that of the integer order sliding mode surface. Specific indices are shown in Table 5
TABLE 5
Figure BDA0002873470610000081
D. Recovery performance of system during sudden load drop
Figure 6 shows the performance of the system when the system load is ramped from 20 ohms to 10 ohms. The starting waveform under the integral-order sliding mode surface is (a) free of disturbance estimation value, (b) under PI control, (c) containing disturbance estimation value, and (d) provided by the invention. It can be seen that the system under the fractional order sliding mode surface without the disturbance estimation value can not track the given value at two moments, and the other three methods can track the given value, wherein the undershoot is minimum by the method provided by the invention, and the method has a faster recovery time similar to that of the integer order sliding mode surface. Specific indices are shown in Table 6
TABLE 6
Figure BDA0002873470610000082
E. Effect of parameter uncertainty on System
Figure 7 shows the performance of the system when there is a ± 10% deviation from the given capacitance parameter of the system, with the system load suddenly increasing from 20 ohms to 10 ohms. It can be seen that the system still maintains the equivalent adjustment capability as shown in fig. 6, which illustrates the better adaptability of the controller designed by the present invention to the system with parameter uncertainty.

Claims (6)

1. A fractional order sliding mode control method for a mismatch interference Buck power converter, the control method comprising the steps of:
step one, building a Buck type power converter model;
designing a high-order sliding mode observer;
step three, designing a fractional order sliding mode controller according to the Buck type power converter model established in the step one;
and step four, establishing matched and unmatched interference of the Buck type power converter model by utilizing the high-order sliding mode observer observation step one designed in the step two, introducing the unmatched interference observed by the high-order sliding mode observer into the fractional order sliding mode controller designed in the step three, and compensating the unmatched interference.
2. The fractional order sliding mode control method for the mismatch interference Buck power converter as claimed in claim 1, wherein the specific method for building the Buck power converter model in the first step is:
the Buck-type power converter is represented by a state space method as follows:
Figure FDA0002873470600000011
let x1＝vo-vd，
Figure FDA0002873470600000012
The Buck-type power converter model can be rewritten as:
Figure FDA0002873470600000013
wherein the content of the first and second substances,
Figure FDA0002873470600000014
for mismatched interference in a Buck-type power converter model,
Figure FDA0002873470600000015
for matching disturbances in a Buck-type power converter model,
Figure FDA0002873470600000016
vofor the output voltage of a Buck-type power converter model,
Figure FDA0002873470600000017
is v isoFirst derivative of vinIs the actual value, v, of the input voltage of a Buck-type power converter modelin0Nominal value of input voltage of Buck-type power converter model for input voltage, u ∈ [0,1 ]]For controlling the input, i.e. duty cycle, v, of Buck-type power convertersdAs a reference voltage, the voltage of the reference voltage,
Figure FDA0002873470600000018
is v isdThe first derivative of (a) is,
Figure FDA0002873470600000019
is v isdSecond derivative of (i)LIn order to be the current of the inductor,
Figure FDA00028734706000000110
is iLThe first derivative of (a);
Figure FDA00028734706000000111
is x1The first derivative of (a) is,
Figure FDA00028734706000000112
is x2R is the actual load resistance value, R0Is a nominal load resistance value, C is an actual capacitance value, C0Is a nominal capacitance value, L is an actual inductance value, L0Is the nominal inductance value.
3. The fractional order sliding mode control method for the mismatch interference Buck-type power converter according to claim 2, wherein the specific form of the high-order sliding mode observer designed in the second step is:
Figure FDA0002873470600000021
wherein i ∈ {1,2}, sgnκ(·)＝|·|κsign (·), sign () is a sign function in mathematics, κ is an arbitrary real number;
Figure FDA0002873470600000022
and
Figure FDA0002873470600000023
all the components are intermediate in weight percentage,
Figure FDA0002873470600000024
and
Figure FDA0002873470600000025
are also all intermediate quantities, and,
Figure FDA0002873470600000026
Figure FDA0002873470600000027
is xiIs determined by the estimated value of (c),
Figure FDA0002873470600000028
is composed of
Figure FDA0002873470600000029
The first derivative of (a) is,
Figure FDA00028734706000000210
Figure FDA00028734706000000211
is diIs determined by the estimated value of (c),
Figure FDA00028734706000000212
is composed of
Figure FDA00028734706000000213
The first derivative of (a) is,
Figure FDA00028734706000000214
Figure FDA00028734706000000215
is diAn estimate of the first derivative;
Figure FDA00028734706000000216
Liis the normal number to be designed;
Figure FDA00028734706000000217
and
Figure FDA00028734706000000218
are all constant, and
Figure FDA00028734706000000219
4. the fractional order sliding mode control method for the mismatch interference Buck-type power converter according to claim 3, wherein the step three of designing the fractional order sliding mode controller comprises the following specific steps:
step three, determining a control target: enabling the output voltage v of the system to be in the condition that the Buck type power converter model contains unmatched interferenceoTracking to a given value vd；
Namely: v. ofo→vd(4)；
Step three, designing a slip form surface;
and step three, determining the specific form of the fractional order sliding mode controller.
5. The fractional order sliding mode control method for the mismatch interference Buck-type power converter according to claim 4, wherein the specific method of the sliding mode surface designed in the third step and the second step is as follows:
Figure FDA00028734706000000220
wherein theta is more than 0 and less than 1, chi is more than 0 and less than 1, c1＞0，c2> 0 is four normal numbers to be designed;
Figure FDA00028734706000000221
for the fractional operator, the following is defined:
Figure FDA0002873470600000031
wherein mu is an arbitrary real number, and when mu is less than 0, the fractional order integral is defined as follows:
Figure FDA0002873470600000032
wherein
Figure FDA0002873470600000033
Is a Gamma function;
when μ > 0, the fractional order differential is defined as follows:
Figure FDA0002873470600000034
wherein m is the largest integer less than μ.
6. The fractional order sliding mode control method for the mismatch interference Buck power converter according to claim 4, wherein the fractional order sliding mode controller in step three is in the specific form:
u＝ueq+usw
Figure FDA0002873470600000035
Figure FDA0002873470600000036
γ1and gamma2The selection method comprises the following steps:
γ1＞0
Figure FDA0002873470600000037
wherein u iseqAs an equivalent control term, uswFor switching control items, γ1γ2Are all designed control parameters, δ4Behind a high-order sliding-mode observer for adoption
Figure FDA0002873470600000038
The final convergence interval of (a) to (b),
Figure FDA0002873470600000039
is d2The first derivative of (a) is,
Figure FDA00028734706000000310
is d2An estimate of the first derivative.
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CN114865916A (en) * 2022-07-06 2022-08-05 佛山仙湖实验室 Sliding mode control method of DC-DC converter applied to hydrogen fuel automobile
CN117639483A (en) * 2023-11-15 2024-03-01 燕山大学 New energy hydrogen production converter optimal control method

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