CN107248822A - Inverter control method based on Fractional Order PID discrete sliding mode structure changes - Google Patents
Inverter control method based on Fractional Order PID discrete sliding mode structure changes Download PDFInfo
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- CN107248822A CN107248822A CN201710580984.9A CN201710580984A CN107248822A CN 107248822 A CN107248822 A CN 107248822A CN 201710580984 A CN201710580984 A CN 201710580984A CN 107248822 A CN107248822 A CN 107248822A
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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
- H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
- H02M7/42—Conversion of dc power input into ac power output without possibility of reversal
- H02M7/44—Conversion of dc power input into ac power output without possibility of reversal by static converters
- H02M7/48—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
- H02M7/53—Conversion of dc power input into ac power output without possibility of reversal 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
- H02M7/537—Conversion of dc power input into ac power output without possibility of reversal 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, e.g. single switched pulse inverters
- H02M7/5387—Conversion of dc power input into ac power output without possibility of reversal 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, e.g. single switched pulse inverters in a bridge configuration
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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
- H02M1/00—Details of apparatus for conversion
- H02M1/0003—Details of control, feedback or regulation circuits
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- Power Engineering (AREA)
- Feedback Control In General (AREA)
- Other Investigation Or Analysis Of Materials By Electrical Means (AREA)
Abstract
The invention discloses the inverter control method based on Fractional Order PID discrete sliding mode structure changes, applied to high plateau voltage type inverter system, a kind of new effective control strategy is provided for it.Under high plateau voltage type inverter system, with reference to Fractional Order PID control and sliding mode variable structure control method, the buffeting problem of sliding formwork control inherently is improved；Meanwhile, using glowworm swarm algorithm, optimization is carried out to control parameter and adjusted, ensures the excellent results of control method to a certain extent, and make system that there is intelligent feature.Control method of the present invention has the advantages that control accuracy is high, tracking velocity is fast, robustness is good, it is insensitive to disturb to external world, can guarantee that the dynamic property and steady-state behaviour of inverter system.
Description
Technical field
The present invention relates to the inverter control method based on Fractional Order PID discrete sliding mode structure changes, applied to high plateau voltage
Type inverter system, belongs to nonlinear control techniques field.
Background technology
New energy epoch, inversion transformation technique is represented as the core of Power Electronic Technique, has wide in actual production life
General application, such as：Uninterrupted power source, AC motor drive, automobile adapter etc..With the general of these inverters application
And, requirement of the people to its performance also more and more higher.
Conventional inverter control strategy is generally fed back using exporting, and is controlled in conjunction with linear control method, institute
Obtaining result, often wave distortion is obvious, and dynamic property is poor.Currently, widely used control strategy for inverter is main
Have：Track with zero error, Repetitive controller and the control of ratio resonance etc..These control methods respectively have advantage, but there is also some simultaneously
It is not enough.For example：Track with zero error dynamic property preferably, but requires higher to arithmetic speed and model accuracy；Repetitive controller master
It is used for the correction to periodic disturbance, it is poor to aperiodic disturbance control effect；The control of ratio resonance has to steady-state error
Certain elimination effect, but suffer from the restriction of bandwidth.
Traditional PID (proportional-integral-differential) controllers the characteristic such as are easy to adjust due to simple in construction, parameter, as work
Controller all the fashion in industry control field.Inverter system based on PID control method while extensive use but without
Method really solves the weakness that its tracking velocity is slow, control accuracy is poor.In recent ten years, numerous control systems or real thing are come from
Manage the differential equation of the more applicable arbitrary order of object or integral equation is represented and fractional order control device algorithm can be efficiently modified system
Control performance the reason for require, control object is focused in increasing research or controller is the situation of fractional order.Fraction
Rank PIλDμControl is exactly complied with the trend and proposed by international control field well-known professors Podlubny.Controlled compared to more traditional PID
System, fractional order PIλDμControl algolithm really can effectively improve the performance of control system because introducing extra free variable λ and μ
And obtained research and application in control field.
Sliding formwork control can change control knot as the special nonlinear control method of a class according to system real time execution situation
Structure, forces system mode to be slided along designed " mode " track in advance, i.e., so-called " sliding formwork motion ".Because sliding-mode surface can be with
It is designed according to actual control needs, and it is unrelated with control object model and external disturbance, so sliding formwork control has response
Rapidly, strong robustness, to Parameters variation and disturb it is insensitive, physics realization is simple the advantages of, be able in power system, ship system
The every field such as system, flight control system, Aero-Space, robot system, chaos system, photovoltaic system, networked system are obtained extensively
General application, is also more and more applied in the control of inverter system.
The engineer applieds such as fast development and industrial automation with digital computer technique, networking technology etc. are needed
Ask, control algolithm is realized frequently by digital computer, this directly results in Discrete-time Sliding Mode control in engineering practice
Increasingly play very important role.At present, there is not yet each excellent with reference to fractional order technology and Discrete-time Sliding Mode control
The control design case method of the inverter circuit system of gesture is delivered.
The content of the invention
The technical problems to be solved by the invention are：Inverter control based on Fractional Order PID discrete sliding mode structure changes is provided
Method processed, with reference to Fractional Order PID control and sliding mode variable structure control method, improves the buffeting problem of sliding formwork control inherently, carries
The high control performance of system.
The present invention uses following technical scheme to solve above-mentioned technical problem：
Based on the inverter control method of Fractional Order PID discrete sliding mode structure changes, comprise the following steps：
Step 1, the parameter of high plateau voltage type inverter system is initialized：DC bus voltage vDC, resistance R1、R2、RL, electricity
Feel L1、L2, and electric capacity C1、C2；The state space equation for setting up high plateau voltage type inverter system is：
Y=Cx
Wherein,For state vector x first derivative, u is control input, and A is state matrix, and B is input matrix, and C is defeated
Go out matrix, y exports for system；
State vector x is chosen, state matrix A and input matrix B is tried to achieve；Output variable is chosen, system output equation is tried to achieve；
Step 2, the sliding-mode surface function in Sliding mode variable structure control is designed with reference to Fractional Order PID, by sliding-mode surface function and step
Rapid 1 state space equation is combined, and tries to achieve control input；
Sliding-mode surface function is：
Wherein,For sliding-mode surface function s first derivative, kpFor ratio term coefficient, kiFor fractional order integration term coefficient, kdFor
Fractional order differential term coefficient, k0For constant term coefficient, D-λFor fractional order integration operator, DμFor fractional order differential operator, fractional order
Integral term integral number of times λ>0, fractional order differential differential times μ>0, sgn (s) represents sign function,
Trying to achieve control input is：
Wherein, etching system control input when u (k) is k, S represents switching vector,T is between the time
Every I is unit matrix, and s (k) is k moment sliding formwork functions, and sgn (s (k)) represents sign function, and s (k-j) is k-j moment sliding formworks
Function, TsFor time step, q0=1,d0=1,J=1 ..., k, x (k)
For k moment state vectors, xr(k+1) it is k+1 moment state vector reference values；
Step 3, control parameter is adjusted using glowworm swarm algorithm, control parameter includes：Proportional coefficient kp, fractional order integration
Term coefficient ki, fractional order differential term coefficient kd, constant term coefficient k0, fractional order integration integral number of times λ, fractional order differential Xiang Wei
Gradation number μ.
As a preferred embodiment of the present invention, the state vector x chosen described in step 1 is：
xT=[iC1 vC1 i2 vC2]
Subscript T represents transposition, and obtained state matrix A and input matrix B is respectively：
Wherein, iC1For capacitance current, vC1For capacitance voltage, i2For inductive current, vC2For capacitance voltage, vDCIt is total for direct current
Line voltage, R1、R2、RLIt is resistance, L1、L2It is inductance, C1、C2It is electric capacity.
As a preferred embodiment of the present invention, the output variable chosen described in step 1 is：Capacitance current iC1, inductance electricity
Flow i2, capacitance voltage vC2, obtained system output equation is：
Wherein, R1、R2、RLIt is resistance, L1、L2It is inductance, C1、C2It is electric capacity, iLFor resistor current, iC2For electric capacity
Electric current, vDCFor DC bus voltage, vC1For capacitance voltage, t is the time.
As a preferred embodiment of the present invention, time step T described in step 2sValue be 0.1.
As a preferred embodiment of the present invention, time interval T value described in step 2 is 0.001.
The present invention uses above technical scheme compared with prior art, with following technique effect：
1st, the present invention is under high plateau voltage type inverter system, with reference to Fractional Order PID control and Sliding mode variable structure control side
Method, improves the buffeting problem of sliding formwork control inherently, improves the control performance of system, with fast response time, strong robustness,
The good dynamic such as tracking accuracy height and steady-state characteristic.
2nd, control algolithm discretization is more suitable for the realization on digital computer by the present invention.Meanwhile, with firefly
Algorithm is adjusted to parameter, improves control algolithm, is improved control accuracy, has been fully demonstrated the intelligent of control method.
Brief description of the drawings
Fig. 1 is single-phase quadravalence voltage source inverter (VSI) circuit diagram.
Fig. 2 is system mode response diagram, wherein, (a) is electric current iC1Condition responsive figure, (b) is voltage vC1Condition responsive
Figure, (c) is electric current i2Condition responsive figure, (d) is voltage vC2Condition responsive figure.
Fig. 3 is iC1State error comparison diagram.
Fig. 4 is vC1State error comparison diagram.
Fig. 5 is i2State error comparison diagram.
Fig. 6 is vC2State error comparison diagram.
Fig. 7 is sliding formwork function s comparison diagrams.
Fig. 8 is controlled quentity controlled variable u comparison diagrams.
Embodiment
Embodiments of the present invention are described below in detail, the example of the embodiment is shown in the drawings.Below by
The embodiment being described with reference to the drawings is exemplary, is only used for explaining the present invention, and is not construed as limiting the claims.
It is an object of the invention to propose a kind of novel inverter control strategy, by Fractional Order PID and Discrete-time Sliding Mode
Variable-structure control combines, it is ensured that the dynamic property and steady-state behaviour of system.Using a single-phase quadravalence voltage source inverter as
Example, is comprised the following steps that：
1st, high plateau voltage type inverter system model is set up
As shown in figure 1, for single-phase quadravalence voltage source inverter circuit, its load end is provided with a LC network.vDCTo be straight
Flow bus voltage, vC2It is output voltage.
If the state space equation expression formula of system is
Y=Cx (2)
Wherein,For state vector x first derivative, u is control input, and A is state matrix, and B is input matrix, and C is defeated
Go out matrix, y exports for system；
Take state vector
xT=[iC1 vC1 i2 vC2] (3)
By Kirchhoff's second law (KVL) and current law (KCL), it can obtain
i1=iC1+i2 (5)
Therefore,
Again
On the one hand：
Therefore,
Again
It can obtain
By
On the other hand：
Therefore,
WillWith(8) formula of substitution, can be obtained
By v0=vDCU is substituted into
In addition, being easy to get by basic circuit principle and Kirchhoff's theorem
To sum up, sytem matrix and input matrix are as follows
Power taking capacitance current iC1, inductive current i2, and capacitance voltage vC2As output variable, then output equation can be write
Known according to system model
Therefore,
2nd, the sliding mode controller design based on Fractional Order PID
Because the SMC algorithms designed for continuous system are in direct perform, it is impossible to system is reached satisfied effect, very
To causing the unstable of system.Therefore we are first by system state equationIt is discrete to turn to
In formula, x (k) is the state vector at k-th of moment of system, and x (k+1) is the state vector at+1 moment of kth, u (k)
It is the controlled quentity controlled variable output vector at k-th of moment of system；A is state matrix, and B is input matrix；T is time interval.
OrderI is unit matrix.Then (30) formula can abbreviation be
Further to improve control performance, Fractional Order PID control is combined with classical sliding formwork control, sliding-mode surface letter is designed
Number is as follows：
In formula, s represents sliding-mode surface function, kpFor ratio term coefficient, kiFor fractional order integration term coefficient, kdIt is micro- for fractional order
Partial safety factor, k0For constant term coefficient, D-λFor fractional order integration operator, DμFor fractional order differential operator, λ>0, μ>0；sgn(s)
Represent sign function：
Fractional calculus algorithm is defined according to GL, discretization is obtained
Wherein,d0=1,J=1 ..., k.
To enable virtual condition amount to follow the trail of the change of state reference value, switching function is taken
S (k)=Sxe(k)
Wherein, s (k) represents sliding formwork function, and S represents switching vector, xe(k) state error is represented：xe(k)=xr(k)-x
(k), xr(k) it is k moment quantity of state reference values, x (k) is k moment quantity of state actual values.
Switching function is combined with (31) formula, is easy to get
(32) formula of substitution, is obtained
Control input u (k) can be obtained as follows：
Discrete-time Sliding Mode reaching condition is
[s(k+1)-s(k)]sgn(s(k))<0
[s(k+1)+s(k)]sgn(s(k))>0 (37)
Accordingly, sliding-mode surface function is combined with (33) formula, obtained
Meanwhile, when sampling period T is fully small, have
So, Fractional Order PID Sliding mode variable structure control Reaching Law meets above-mentioned accessibility condition, ensure that Reaching Law mould
State possesses good quality.
3rd, control parameter is adjusted with glowworm swarm algorithm
The mankind create a series of bionic intelligence algorithms by the behavior of biocenose in study, simulation nature.Wherein,
Glowworm swarm algorithm due to search strategy it is superior the advantages of, be widely used in dummy robot, sensor noise test, cluster point
In terms of analysis, multisignal source track and localization.
According to biologist it has been observed that firefly is exchanged by discharging fluorescein.Awing, fluorescein is dense
Degree is bigger, and the light of firefly borer population of attraction is more.
In glowworm swarm algorithm, all fireflies are being evenly distributed in search space at first.Every firefly
Fluorescein can be discharged, the decision domain of oneself, and higher than oneself by finding fluorescein concentration are determined according to fluorescein
Body, constitutes neighborhood collection.Concentrate, moved to the high firefly of fluorescein concentration in neighborhood.Therefore, the higher light of firefly of fluorescein concentration
Worm is bigger by the probability as mobile target.Fluorescein concentration is higher, and representative fitness function value is bigger, closer to most
Excellent solution.When population density is relatively low around firefly, the decision domain of oneself can be expanded, it is on the contrary then reduce the decision domain of oneself.
Concrete operations are as follows：
(1) initialization firefly position.In this example, the position coordinates of firefly is to be optimized in control algolithm to be
Number kp、ki、kd、k0、λ、μ。
(2) fitness function is changed into fluorescein value using formula (40).
li(t)=(1- ρ) li(t-1)+γJ(xi(t)) (40)
In formula, γ is fluorescein renewal frequency, and value is 0.6；ρ is fluorescein volatility coefficient, and value is 0.4；J(xi
(t)) it is fitness function value, li(t) it is fluorescein value.In this example, the opposite number of state error integral function is set to suitable
Response function.
(3) firefly is in dynamic decision domain radiusInterior and higher than oneself fluorescein value individual constitutes field together
Collect Ni(t), wherein For individual the perception radius.
(4) Probability p of firefly j movements of the firefly i into its field collection is calculated using formula (41)ij(t)。
(5) select after mobile target j, firefly i position is updated according to following formula.
In formula, st is step-length, and value is 0.03.
(6) finally, the decision domain of each firefly is updated according to formula (43).
In formula, β is that decision domain controls constant, and value is 0.08.
In order to verify the effect of the inventive method, comparison score rank PI sliding formwork controls (FOPISMC), fractional order PD sliding formwork controls
(FOPDSMC), the control performance of Fractional Order PID sliding formwork control (FOPIDSMC) are made, is emulated under quadravalence inverter model.
Control system parameter is as follows：DC terminal voltage vDC=355V；Resistance R1=R2=1 Ω, RL=2 Ω；Inductance L1=3.2mH, L2=
1.2mH；Electric capacity C1=C2=6000 μ F；Material calculation Ts=0.1；Sampling time T=0.001s.
Take state reference amount
x4ref=vC2ref=50sin12 π t (44)
x3ref=i2ref=3.6 π cos12 π t+25sin12 π t (45)
x2ref=vC1ref=0.288 π cos12 π t+ (17.5-0.05184 π2)sin12πt (46)
x1ref=iC1ref=-0.20736 π2sin12πt+(4.86π-0.00995π3)cos12πt (47)
Optimize through glowworm swarm algorithm, control algolithm parameter is：Proportional coefficient kp=6.44, fractional order integration term coefficient ki
=3.98, fractional order differential term coefficient kd=3.33, constant term coefficient k0=4.48；Fractional order integration λ=0.3, fractional order is micro-
Subitem μ=0.56.
As shown in Fig. 2 to Fig. 8, be the fractional order PI sliding formwork controls of single-phase quadravalence inverter, fractional order PD sliding formwork controls with
And the effect contrast figure of Fractional Order PID sliding formwork control.From top to bottom respectively to quantity of state x, tracking error xe, sliding formwork function s and
Controlled quentity controlled variable u is contrasted.
From Fig. 2 (a), (b), (c), (d), quantity of state iC1、vC1、i2And vC2Reason can be reached in very short time
Think state.
From Fig. 3 to Fig. 6, the error of four quantity of states can converge to 0 within the extremely short time.Wherein, fractional order
PID sliding formwork controls are fastest, and fractional order PD sliding formwork controls are taken second place, and fractional order PI sliding formwork controls are relatively.
As seen from Figure 7, the sliding-mode surface function of three kinds of methods can converge to 0 in very short time.Wherein, Fractional Order PID
Sliding formwork control needs to restrain for about 0.27 second, and fractional order PD sliding formwork controls need restrain for about 0.32 second, and fractional order PI sliding formwork controls are needed
Restrain within about 0.35 second.
As seen from Figure 8, the controlled quentity controlled variable u of three kinds of methods can reach perfect condition in very short time.
To sum up, three kinds of control methods can complete stability control within a short period of time.Wherein Fractional Order PID sliding formwork control
Fixture has optimal control effect, it is only necessary to can reach stable state within 0.27 second.State error restrains most fast, sliding formwork function s (x)
Convergence time is most short.Fractional order PD sliding formwork controls are taken second place, and fractional order PI sliding formwork controls are relatively poor.
The technological thought of above example only to illustrate the invention, it is impossible to which protection scope of the present invention is limited with this, it is every
According to technological thought proposed by the present invention, any change done on the basis of technical scheme each falls within the scope of the present invention
Within.
Claims (5)
1. the inverter control method based on Fractional Order PID discrete sliding mode structure changes, it is characterised in that comprise the following steps：
Step 1, the parameter of high plateau voltage type inverter system is initialized：DC bus voltage vDC, resistance R1、R2、RL, inductance L1、
L2, and electric capacity C1、C2；The state space equation for setting up high plateau voltage type inverter system is：
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State vector x is chosen, state matrix A and input matrix B is tried to achieve；Output variable is chosen, system output equation is tried to achieve；
Step 2, the sliding-mode surface function in Sliding mode variable structure control is designed with reference to Fractional Order PID, by sliding-mode surface function and step 1 shape
State space equation is combined, and tries to achieve control input；
Sliding-mode surface function is：
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Wherein,For sliding-mode surface function s first derivative, kpFor ratio term coefficient, kiFor fractional order integration term coefficient, kdFor fraction
Rank differential term coefficient, k0For constant term coefficient, D-λFor fractional order integration operator, DμFor fractional order differential operator, fractional order integration
Item integral number of times λ>0, fractional order differential differential times μ>0, sgn (s) represents sign function,
Trying to achieve control input is：
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Wherein, etching system control input when u (k) is k, S represents switching vector,T is time interval, I
For unit matrix, s (k) is k moment sliding formwork functions, and sgn (s (k)) represents sign function, and s (k-j) is k-j moment sliding formwork functions,
TsFor time step, q0=1,d0=1,When j=1 ..., k, x (k) are k
Carve state vector, xr(k+1) it is k+1 moment state vector reference values；
Step 3, control parameter is adjusted using glowworm swarm algorithm, control parameter includes：Proportional coefficient kp, fractional order integration term system
Number ki, fractional order differential term coefficient kd, constant term coefficient k0, fractional order integration integral number of times λ, fractional order differential differential
Number μ.
2. the inverter control method according to claim 1 based on Fractional Order PID discrete sliding mode structure changes, its feature exists
In the state vector x chosen described in step 1 is：
xT=[iC1 vC1 i2 vC2]
Subscript T represents transposition, and obtained state matrix A and input matrix B is respectively：
<mrow>
<mi>A</mi>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mfrac>
<msub>
<mi>R</mi>
<mn>1</mn>
</msub>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
</mfrac>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mfrac>
<mn>1</mn>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
</mfrac>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<msub>
<mi>L</mi>
<mn>2</mn>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<mfrac>
<msub>
<mi>R</mi>
<mn>1</mn>
</msub>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
</mfrac>
<mo>+</mo>
<mfrac>
<msub>
<mi>R</mi>
<mn>2</mn>
</msub>
<msub>
<mi>L</mi>
<mn>2</mn>
</msub>
</mfrac>
</mrow>
</mtd>
<mtd>
<mfrac>
<mn>1</mn>
<msub>
<mi>L</mi>
<mn>2</mn>
</msub>
</mfrac>
</mtd>
</mtr>
<mtr>
<mtd>
<mfrac>
<mn>1</mn>
<msub>
<mi>C</mi>
<mn>1</mn>
</msub>
</mfrac>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mfrac>
<mn>1</mn>
<msub>
<mi>L</mi>
<mn>2</mn>
</msub>
</mfrac>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<mfrac>
<msub>
<mi>R</mi>
<mn>2</mn>
</msub>
<msub>
<mi>L</mi>
<mn>2</mn>
</msub>
</mfrac>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<mfrac>
<mn>1</mn>
<msub>
<mi>L</mi>
<mn>2</mn>
</msub>
</mfrac>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mfrac>
<mn>1</mn>
<msub>
<mi>C</mi>
<mn>2</mn>
</msub>
</mfrac>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<mfrac>
<mn>1</mn>
<mrow>
<msub>
<mi>R</mi>
<mi>L</mi>
</msub>
<msub>
<mi>C</mi>
<mn>2</mn>
</msub>
</mrow>
</mfrac>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>,</mo>
<mi>B</mi>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mfrac>
<msub>
<mi>v</mi>
<mrow>
<mi>D</mi>
<mi>C</mi>
</mrow>
</msub>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
</mfrac>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>;</mo>
</mrow>
Wherein, iC1For capacitance current, vC1For capacitance voltage, i2For inductive current, vC2For capacitance voltage, vDCFor dc bus electricity
Pressure, R1、R2、RLIt is resistance, L1、L2It is inductance, C1、C2It is electric capacity.
3. the inverter control method according to claim 1 based on Fractional Order PID discrete sliding mode structure changes, its feature exists
In the output variable chosen described in step 1 is：Capacitance current iC1, inductive current i2, capacitance voltage vC2, obtained system output
Equation is：
<mrow>
<msub>
<mi>i</mi>
<mi>L</mi>
</msub>
<mo>=</mo>
<mfrac>
<msub>
<mi>v</mi>
<mrow>
<mi>C</mi>
<mn>2</mn>
</mrow>
</msub>
<msub>
<mi>R</mi>
<mi>L</mi>
</msub>
</mfrac>
</mrow>
<mrow>
<msub>
<mi>i</mi>
<mrow>
<mi>C</mi>
<mn>2</mn>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>C</mi>
<mn>2</mn>
</msub>
<mfrac>
<mrow>
<msub>
<mi>dv</mi>
<mrow>
<mi>C</mi>
<mn>2</mn>
</mrow>
</msub>
</mrow>
<mrow>
<mi>d</mi>
<mi>t</mi>
</mrow>
</mfrac>
</mrow>
<mrow>
<msub>
<mi>i</mi>
<mn>2</mn>
</msub>
<mo>=</mo>
<msub>
<mi>i</mi>
<mrow>
<mi>C</mi>
<mn>2</mn>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>i</mi>
<mi>L</mi>
</msub>
<mo>=</mo>
<msub>
<mi>C</mi>
<mn>2</mn>
</msub>
<mfrac>
<mrow>
<msub>
<mi>dv</mi>
<mrow>
<mi>C</mi>
<mn>2</mn>
</mrow>
</msub>
</mrow>
<mrow>
<mi>d</mi>
<mi>t</mi>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<msub>
<mi>v</mi>
<mrow>
<mi>C</mi>
<mn>2</mn>
</mrow>
</msub>
<msub>
<mi>R</mi>
<mi>L</mi>
</msub>
</mfrac>
</mrow>
<mrow>
<msub>
<mi>v</mi>
<mrow>
<mi>C</mi>
<mn>1</mn>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>L</mi>
<mn>2</mn>
</msub>
<msub>
<mi>C</mi>
<mn>2</mn>
</msub>
<mfrac>
<mrow>
<msup>
<mi>d</mi>
<mn>2</mn>
</msup>
<msub>
<mi>v</mi>
<mrow>
<mi>C</mi>
<mn>2</mn>
</mrow>
</msub>
</mrow>
<mrow>
<msup>
<mi>dt</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>+</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>R</mi>
<mn>2</mn>
</msub>
<msub>
<mi>C</mi>
<mn>2</mn>
</msub>
<mo>+</mo>
<mfrac>
<msub>
<mi>L</mi>
<mn>2</mn>
</msub>
<msub>
<mi>R</mi>
<mi>L</mi>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mfrac>
<mrow>
<msub>
<mi>dv</mi>
<mrow>
<mi>C</mi>
<mn>2</mn>
</mrow>
</msub>
</mrow>
<mrow>
<mi>d</mi>
<mi>t</mi>
</mrow>
</mfrac>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mfrac>
<msub>
<mi>R</mi>
<mn>2</mn>
</msub>
<msub>
<mi>R</mi>
<mi>L</mi>
</msub>
</mfrac>
<mo>+</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<msub>
<mi>v</mi>
<mrow>
<mi>C</mi>
<mn>2</mn>
</mrow>
</msub>
</mrow>
<mrow>
<msub>
<mi>i</mi>
<mrow>
<mi>C</mi>
<mn>1</mn>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>C</mi>
<mn>1</mn>
</msub>
<mo>&lsqb;</mo>
<msub>
<mi>L</mi>
<mn>2</mn>
</msub>
<msub>
<mi>C</mi>
<mn>2</mn>
</msub>
<mfrac>
<mrow>
<msup>
<mi>d</mi>
<mn>3</mn>
</msup>
<msub>
<mi>v</mi>
<mrow>
<mi>C</mi>
<mn>2</mn>
</mrow>
</msub>
</mrow>
<mrow>
<msup>
<mi>dt</mi>
<mn>3</mn>
</msup>
</mrow>
</mfrac>
<mo>+</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>R</mi>
<mn>2</mn>
</msub>
<msub>
<mi>C</mi>
<mn>2</mn>
</msub>
<mo>+</mo>
<mfrac>
<msub>
<mi>L</mi>
<mn>2</mn>
</msub>
<msub>
<mi>R</mi>
<mi>L</mi>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mfrac>
<mrow>
<msup>
<mi>d</mi>
<mn>2</mn>
</msup>
<msub>
<mi>v</mi>
<mrow>
<mi>C</mi>
<mn>2</mn>
</mrow>
</msub>
</mrow>
<mrow>
<msup>
<mi>dt</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mfrac>
<msub>
<mi>R</mi>
<mn>2</mn>
</msub>
<msub>
<mi>R</mi>
<mi>L</mi>
</msub>
</mfrac>
<mo>+</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mfrac>
<mrow>
<msub>
<mi>dv</mi>
<mrow>
<mi>C</mi>
<mn>2</mn>
</mrow>
</msub>
</mrow>
<mrow>
<mi>d</mi>
<mi>t</mi>
</mrow>
</mfrac>
<mo>&rsqb;</mo>
</mrow>
Wherein, R1、R2、RLIt is resistance, L1、L2It is inductance, C1、C2It is electric capacity, iLFor resistor current, iC2For capacitance current,
vDCFor DC bus voltage, vC1For capacitance voltage, t is the time.
4. the inverter control method according to claim 1 based on Fractional Order PID discrete sliding mode structure changes, its feature exists
In time step T described in step 2sValue be 0.1.
5. the inverter control method according to claim 1 based on Fractional Order PID discrete sliding mode structure changes, its feature exists
In time interval T value described in step 2 is 0.001.
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Cited By (10)
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| CN108233757A (en) * | 2017-12-18 | 2018-06-29 | 南京信息工程大学 | Inverter control method based on NEW TYPE OF COMPOSITE control algolithm |
| CN108539978A (en) * | 2018-04-13 | 2018-09-14 | 杭州电子科技大学 | A kind of adaptive control system of Boost type DC-DC converter |
| CN108925013A (en) * | 2018-10-12 | 2018-11-30 | 北京无线电计量测试研究所 | A kind of LED street lamp dimming controlling method and system based on interference observer |
| CN109167537A (en) * | 2018-10-11 | 2019-01-08 | 南京信息工程大学 | A kind of method for controlling number of revolution of brushless direct current motor |
| CN109245532A (en) * | 2018-09-29 | 2019-01-18 | 东北大学 | A kind of fractional order sliding-mode control of buck-boost converter |
| CN110083055A (en) * | 2019-05-15 | 2019-08-02 | 湘潭大学 | A kind of PID automatic setting method based on deep learning and LOGFA |
| CN111694276A (en) * | 2020-06-12 | 2020-09-22 | 常州工业职业技术学院 | Robust control research method for uncertain fractional order switching system |
| CN113078814A (en) * | 2021-05-20 | 2021-07-06 | 哈尔滨凯纳科技股份有限公司 | Sliding mode control method for buck converter |
| CN115173701A (en) * | 2022-07-22 | 2022-10-11 | 哈尔滨工业大学 | Power converter self-adaptive continuous sliding mode control method based on zero-crossing detection |
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| CN103269176A (en) * | 2013-05-17 | 2013-08-28 | 南京信息工程大学 | Inverter control method based on fractional order PI forecasting function |
| CN105932715A (en) * | 2016-06-28 | 2016-09-07 | 西南石油大学 | Method for determining position of suddenly-changed state of sliding mode controlled inverter |
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| CN103269176A (en) * | 2013-05-17 | 2013-08-28 | 南京信息工程大学 | Inverter control method based on fractional order PI forecasting function |
| CN105932715A (en) * | 2016-06-28 | 2016-09-07 | 西南石油大学 | Method for determining position of suddenly-changed state of sliding mode controlled inverter |
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| CN108233757A (en) * | 2017-12-18 | 2018-06-29 | 南京信息工程大学 | Inverter control method based on NEW TYPE OF COMPOSITE control algolithm |
| CN108539978A (en) * | 2018-04-13 | 2018-09-14 | 杭州电子科技大学 | A kind of adaptive control system of Boost type DC-DC converter |
| CN108539978B (en) * | 2018-04-13 | 2019-09-17 | 杭州电子科技大学 | A kind of adaptive control system of Boost type DC-DC converter |
| CN109245532A (en) * | 2018-09-29 | 2019-01-18 | 东北大学 | A kind of fractional order sliding-mode control of buck-boost converter |
| CN109245532B (en) * | 2018-09-29 | 2020-07-14 | 东北大学 | Fractional order sliding mode control method of buck-boost converter |
| CN109167537A (en) * | 2018-10-11 | 2019-01-08 | 南京信息工程大学 | A kind of method for controlling number of revolution of brushless direct current motor |
| CN108925013A (en) * | 2018-10-12 | 2018-11-30 | 北京无线电计量测试研究所 | A kind of LED street lamp dimming controlling method and system based on interference observer |
| CN110083055A (en) * | 2019-05-15 | 2019-08-02 | 湘潭大学 | A kind of PID automatic setting method based on deep learning and LOGFA |
| CN111694276A (en) * | 2020-06-12 | 2020-09-22 | 常州工业职业技术学院 | Robust control research method for uncertain fractional order switching system |
| CN113078814A (en) * | 2021-05-20 | 2021-07-06 | 哈尔滨凯纳科技股份有限公司 | Sliding mode control method for buck converter |
| CN115173701A (en) * | 2022-07-22 | 2022-10-11 | 哈尔滨工业大学 | Power converter self-adaptive continuous sliding mode control method based on zero-crossing detection |
| CN115981375A (en) * | 2023-03-17 | 2023-04-18 | 南京信息工程大学 | Multi-unmanned aerial vehicle time-varying formation controller design method based on event trigger mechanism |
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