CN110456645B - Discrete repetitive control method for inverter - Google Patents

Discrete repetitive control method for inverter Download PDF

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CN110456645B
CN110456645B CN201910761405.XA CN201910761405A CN110456645B CN 110456645 B CN110456645 B CN 110456645B CN 201910761405 A CN201910761405 A CN 201910761405A CN 110456645 B CN110456645 B CN 110456645B
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inverter
tracking error
interference
attraction
discrete
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林志明
邬玲伟
陈�光
梅盼
朱莺莺
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Taizhou University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
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    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
    • 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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Abstract

The invention discloses a discrete repetitive control method for an inverter. Constructing an attraction law with interference suppression effect by adopting an equivalent interference second-order difference compensation technology; according to the attraction law, an e/v signal conversion module is constructed, and an output signal of the e/v signal conversion module is used for repeating the correction quantity of the controller. The specific controller parameter setting can be based on a specific expression representing the maximum number of steps required by an absolute attraction layer, a steady-state error band and a tracking error in the convergence process of the system to enter the steady-state error band for the first time. The invention is a discrete repetitive controller which can completely eliminate the homogeneous harmonic and the even harmonic, effectively restrain the fractional harmonic and improve the control precision.

Description

Discrete repetitive control method for inverter
Technical Field
The invention relates to a discrete repetitive control method for an inverter, which is suitable for an inverter power supply and is also suitable for a periodic operation process in industrial control.
Background
Repetitive controllers are a control technique with a "periodic learning" feature. The control technique adopts a positive feedback form 1/(1-e) of a delay link with the delay time of T-Ts) A periodic signal internal model with the period of T is constructed and embedded into a stable closed loop system, the output of the internal model can accumulate input signals cycle by cycle to form a control effect, and the problem of periodic tracking of reference signals or suppression of periodic interference signals is solved. It is widely used in motor servo system, power electronic inverter, hard disk/optical disk servo system and other repeated operation process.
In actual engineering, a computer control technology is adopted, and a control system is mostly realized in a discrete time mode. There are two main approaches to discrete repetitive controller design: one is obtained by discretizing a continuous repetitive controller; the other is to design the controller directly for a discrete time system. Taking a sampling period TsMaking the period of the reference signal an integer multiple of the sampling period, recording eachThe number of sampling points in a cycle being N, i.e. T ═ NTs. Thus, the discrete periodic signal internal model is 1/(1-Z)-N). The discrete repetitive controller frequency domain design employs such a discrete internal model.
In practice, an inverter control technology under a periodic reference signal is adopted, and most systems are realized in a discrete mode, so that the problem of buffeting exists, and periodic interference signals cannot be completely inhibited. For the buffeting problem caused by the intermittent characteristic, a continuous processing method is commonly used, for example, a saturation function, a hyperbolic tangent function, a unit vector continuous function and the like replace a sign function, but the convergence speed and the robustness of the system are reduced by the processing. In addition, while periodic interference is eliminated, signals such as non-periodic interference or fractional inter-harmonics are further suppressed, and the problem of effectively reducing a steady-state error bound is a difficult problem to be solved urgently.
Disclosure of Invention
The invention provides a discrete repetitive control method for an inverter. In order to inhibit the influence of the inverter homogeneous/even harmonic and the inter-fractional harmonic on the system performance and improve the tracking control precision, an equivalent interference second-order differential compensation technology is adopted and embedded into a novel hyperbolic tangent attraction law, and a discrete repetitive controller is designed according to the technology, so that a closed-loop system has the characteristics described by the hyperbolic tangent attraction law, and the inverter homogeneous/even harmonic and the fractional harmonic are inhibited. The invention specifically provides specific expressions of 3 indexes such as an absolute attraction layer, a steady-state error band and the maximum step number required for a tracking error to enter the steady-state error band for the first time, and the specific expressions are used for guiding the parameter setting of the controller.
The technical scheme adopted by the invention for solving the technical problems is as follows:
in order to suppress the homogeneous/even harmonic and the fractional interharmonic of an inverter and enable the system output to approach a given reference signal within a limited time, the invention constructs the following discrete novel hyperbolic tangent attraction law:
Figure BDA0002170446390000021
wherein rho is more than 0 and less than 1, epsilon is more than or equal to 0, and delta is more than 0 and is a parameter for adjusting the suction speed;
Figure BDA0002170446390000022
ek+1,ekis divided into k +1, the tracking error at time k, and ek＝rk-yk；
In the attraction law (1), tracking error ekThe dynamic behavior of (c) is as follows: 1) when in use
Figure BDA0002170446390000023
When epsilon is more than 0, the tracking error will be strictly and monotonously converged, without buffeting, and without alternately converging positive and negative
Figure BDA0002170446390000024
Within a neighborhood of (c); 2) when in use
Figure BDA0002170446390000025
When epsilon is more than 0, the tracking error is strictly and absolutely converged, and the positive and negative alternate convergence is at the origin; 3) when e iskWhen not equal to 0 and epsilon is 0, the tracking error is strictly and monotonously converged, and the tracking error is converged to the origin without buffeting and positive and negative alternation; 4) when e iskNot equal to 0 and epsilon > 0, the tracking error is from an arbitrary initial value e0Begin to pass through
Figure BDA00021704463900000210
The step passes through the origin for the first time; wherein the content of the first and second substances,
Figure BDA00021704463900000211
is the smallest integer not less than;
Figure BDA0002170446390000026
Figure BDA0002170446390000027
in order to improve the inhibiting capability of the system on the even order, the even order and the fractional harmonic interference, an equivalent interference second order difference compensation technology is adopted to modify the discrete attraction law (1) into a discrete attraction law
Figure BDA0002170446390000028
Wherein d isk+1＝wk+1-wk+1-NThe equivalent interference at the k +1 moment is expressed, and the suppression of the homogeneous harmonic and the even harmonic can be realized;
Figure BDA0002170446390000029
for compensating inter (fractional) harmonics and other non-periodic disturbances of the inverter;
the discrete repetitive controller is designed according to the attraction law (4)
Figure BDA0002170446390000031
Wherein u isk，uk-1，uk-N，uk-1-NRespectively are control input signals at the k, k-1, k-N, k-1-N moments; y isk,yk-1,yk-1-N,yk-N,yk+1-NRespectively are output signals at the k, k-1, k-1-N, k-N, k +1-N moments; r isk+1A given reference signal at time k + 1; n is the period of a given reference signal; a in formula (5)1,a2,b1,b2For the system parameters of the inverter, the mathematical model of the inverter is as follows:
yk+1+a1yk+a2yk-1＝b1uk+b2uk-1+wk+1 (6)
wherein, yk+1,yk,yk-1Is the output signal at the moment k +1, k, k-1 of the inverter, uk,uk-1Control input signal representing the time of inverter k, k-1, a1,a2,b1,b2Is a system parameter; w is ak+1System interference signal at time k +1, including homogeneous harmonicsWaves, even harmonics, and other inter-harmonics and parametric perturbations;
will ukAs control input signal of inverter, output signal y of inverter system can be measuredkFollows the reference signal rkThe dynamic behavior of the system tracking error is characterized by equation (4);
further, in order to represent the attraction process of the attraction law, the invention provides a specific expression of 3 indexes, namely an absolute attraction layer, a steady-state error band and the maximum step number required for the tracking error to enter the steady-state error band for the first time; these 3 indicators can be used to guide controller parameter tuning, where the absolute attraction layer and steady state error band are defined as follows:
1) absolute attraction layer ΔAAL
|ek+1|＜|ekI, when ek|＞ΔAAL (7)
2) Steady state error band ΔSSE
|ek+1|≤ΔSSEWhen | ek|≤ΔSSE (8)
Here,. DELTA.AALTo absolute attraction layer boundary, ΔSSEIs a steady state error band boundary.
Under the action of the discrete repetitive controller (5), the second order differential compensation error of the equivalent interference is satisfied
Figure BDA0002170446390000032
The expression of each index is as follows:
1) absolute attraction layer ΔAALExpressed as:
ΔAAL＝max{ΔAAL1,ΔAAL2} (10)
in the formula,. DELTA.AAL1，ΔAAL2Is positive and real, and satisfies
Figure BDA0002170446390000041
Wherein, delta is the supremum of the equivalent interference compensation error;
2) steady state error band ΔSSEExpressed as:
ΔSSE＝max{ΔSSE1,ΔSSE2,Δ}
(12)
in the formula,. DELTA.SSE1，ΔSSE2Is positive and real, is determined by
Figure BDA0002170446390000042
Where ξ is a positive real number and is determined by the following equation
Figure BDA0002170446390000043
Where sech (-) is a hyperbolic secant function,
Figure BDA0002170446390000044
3) convergence step number | k**|
Figure BDA0002170446390000045
Wherein e is0As initial value of tracking error, eiTracking error at the ith moment; psi satisfies
Figure BDA0002170446390000046
The technical conception of the invention is as follows: a discrete repetitive controller for an inverter is proposed, which is a time domain design method, different from the commonly adopted frequency domain method. The time domain design of the controller is easy to incorporate existing interference suppression means. According to the invention, the equivalent interference second-order differential compensation term is embedded into the attraction law, so that the steady-state error bound of the tracking error of the system is smaller while the effective inhibition of the interference of alignment subharmonic, even subharmonic and fractional harmonic is realized.
The control effect of the invention is mainly shown in that: the method has the advantages of equivalent interference second order difference compensation, complete elimination of homogeneous harmonics and even harmonics, effective suppression of fractional harmonics, quick convergence performance and high tracking precision.
Drawings
FIG. 1 is a flow chart of control system design based on the attraction law method.
Fig. 2 is a graph comparing error convergence rates of the attraction law proposed by the present invention, the exponential attraction law, and the conventional hyperbolic tangent attraction law.
Fig. 3 is a block diagram of a discrete repetitive controller.
FIG. 4 is an internal module block diagram of the discrete repetitive control system.
Fig. 5 is a block diagram of an inverter control system in an embodiment of the present invention.
FIG. 6 is a graph of the interference compensation term taken into account in the controller (9) (only homogeneous/even harmonics are present)
Figure BDA0002170446390000051
A given reference signal, an output signal and a tracking error signal under influence;
FIG. 7 is a graph of the interference compensation term taken into account in the controller (9) (only homogeneous/even harmonics are present)
Figure BDA0002170446390000052
) A given reference signal, an output signal and a tracking error signal under influence;
FIG. 8 is a graph of the interference compensation term taken into account in the controller (9) (only homogeneous/even harmonics are present and the interference compensation term is taken into account
Figure BDA0002170446390000053
) A given reference signal, an output signal and a tracking error signal under influence;
FIG. 9 is a graph of the interference compensation term taken into account in the controller (9) (presence of homogeneous/even/fractional harmonics)
Figure BDA0002170446390000054
) A given reference signal, an output signal and a tracking error signal under influence;
FIG. 10 is a graph of the interference compensation term taken into account in the controller (9) (only homogeneous/even/fractional harmonics are present)
Figure BDA0002170446390000055
) A given reference signal, an output signal and a tracking error signal under influence;
FIG. 11 is a graph of the interference compensation term taken into account in the controller (9) (only homogeneous/even/fractional harmonics are present)
Figure BDA0002170446390000056
) A given reference signal, an output signal and a tracking error signal under influence;
Detailed Description
The following further describes embodiments of the present invention with reference to the accompanying drawings.
Referring to fig. 1-11, a method for discrete repetitive control of an inverter, a control system design flow chart is shown in fig. 1, wherein a mathematical model of the inverter control system is as follows:
yk+1+a1yk+a2yk-1＝b1uk+b2uk-1+wk+1 (1)
wherein, yk+1,yk,yk-1Is the output signal at the moment k +1, k, k-1 of the inverter, uk,uk-1Control input signal representing the time of inverter k, k-1, a1,a2,b1,b2Is a system parameter; w is ak+1System interference signals at the time k +1, including homogeneous harmonics, even harmonics, and other inter (fractional) harmonics and parameter perturbations;
given reference signal rkIs a sine signal with the period of N, and satisfies
rk＝Asin(2πk/N)，rk＝rk-N (2)
Wherein r isk,rk-NGiven reference signals at times k, k-N, respectively, A being a given reference signal rkThe amplitude of (d);
the invention constructs the following discrete novel hyperbolic tangent attraction law:
Figure BDA0002170446390000061
wherein rho is more than 0 and less than 1, epsilon is more than or equal to 0, and delta is more than 0 and is a parameter for adjusting the suction speed;
Figure BDA0002170446390000062
ek+1,ekis divided into k +1, the tracking error at time k, and ek＝rk-yk(ii) a FIG. 2 shows the law of attraction (solid line) and the law of conventional hyperbolic tangent attraction proposed by the present invention
Figure BDA0002170446390000063
(dot-dash line) and the exponential attraction law ek+1＝(1-ρ)ek-εsgn(ek) (dotted line) comparative graph; fig. 2 shows that the suction law proposed by the present invention achieves faster error convergence while reducing system chatter;
in the attraction law (1), tracking error ekThe dynamic behavior of (c) is as follows: 1) when in use
Figure BDA0002170446390000064
When epsilon is more than 0, the tracking error will be strictly and monotonously converged, without buffeting, and without alternately converging positive and negative
Figure BDA0002170446390000065
Within a neighborhood of (c); 2) when in use
Figure BDA0002170446390000066
When epsilon is more than 0, the tracking error is strictly and absolutely converged, and the positive and negative are alternately converged in the neighborhood of the origin; 3) when e iskWhen not equal to 0 and epsilon is 0, the tracking error is strictly monotonously converged, and the tracking error is converged to the origin without buffeting and alternation of positive and negative; 4) when e iskNot equal to 0 and epsilon > 0, the tracking error is from an arbitrary initial value e0Begin to pass through
Figure BDA00021704463900000610
The step passes through the origin for the first time; wherein the content of the first and second substances,
Figure BDA00021704463900000611
is the smallest integer not less than;
Figure BDA0002170446390000067
Figure BDA0002170446390000068
in order to improve the suppression capability of the system for the order of alignment, even order and fractional harmonic interference, the discrete attraction law (3) can be modified into
Figure BDA0002170446390000069
Wherein d isk+1＝wk+1-wk+1-NThe equivalent interference at the k +1 moment is expressed, and the suppression of the homogeneous harmonic and the even harmonic can be realized;
Figure BDA0002170446390000075
for compensating inter (fractional) harmonics and other non-periodic disturbances of the inverter;
by tracking error ek＝rk-ykAnd the system (1) is characterized in that,
Figure BDA0002170446390000071
will dk+1＝wk+1-wk+1-NIs expressed as
Figure BDA0002170446390000072
When the formula (8) is substituted into the formula (6), the expression of the discrete repetitive controller (see fig. 3) is
Figure BDA0002170446390000073
As shown in fig. 4, the repetitive controller (9) can also be expressed as
uk＝uk-N+vk (10)
Wherein the content of the first and second substances,
Figure BDA0002170446390000074
will ukAs control input signal of inverter, output signal y of inverter system can be measuredkFollows the reference signal rkChanges and the dynamic behavior of the system tracking error is characterized by equation (6);
further, in order to represent the attraction process of the attraction law, the invention provides a specific expression of 3 indexes, namely an absolute attraction layer, a steady-state error band and the maximum step number required for the tracking error to enter the steady-state error band for the first time; these 3 indicators can be used to guide controller parameter tuning, where the absolute attraction layer and steady state error band are defined as follows:
1) absolute attraction layer ΔAAL
|ek+1|＜|ekI, when ek|＞ΔAAL (12)
2) Steady state error band ΔSSE
|ek+1|≤ΔSSEWhen | ek|≤ΔSSE (13)
Here,. DELTA.AALTo absolute attraction layer boundary, ΔSSEIs a steady state error band boundary.
Under the action of a discrete repetitive controller (9), the second order differential compensation error of the equivalent interference is satisfied
Figure BDA0002170446390000081
The expression of each index is as follows:
1) absolute attraction layer ΔAALExpressed as:
ΔAAL＝max{ΔAAL1,ΔAAL2} (15)
in the formula,. DELTA.AAL1，ΔAAL2Is positive and real, and satisfies
Figure BDA0002170446390000082
Wherein, delta is the supremum of the equivalent interference second order difference compensation error;
2) steady state error band ΔSSEExpressed as:
ΔSSE＝max{ΔSSE1,ΔSSE2,Δ}
(17)
in the formula,. DELTA.SSE1，ΔSSE2Is positive and real, is determined by
Figure BDA0002170446390000083
Where ξ is a positive real number and is determined by the following equation
Figure BDA0002170446390000084
Where sech (-) is a hyperbolic secant function,
Figure BDA0002170446390000085
3) convergence step number | k**|
Figure BDA0002170446390000086
Wherein e is0For initial values of tracking errors，eiTracking error at the ith moment; psi satisfies
Figure BDA0002170446390000091
And furthermore, after the design of the discrete repetitive controller is finished, the parameters of the controller in the discrete repetitive controller need to be set. The adjustable parameters rho, epsilon and delta can be set according to 3 indexes representing the attraction process of the attraction law.
The following description is made for the above repetitive controller design:
1) the attraction law provided by the invention adopts a hyperbolic tangent function to design a novel attraction law; compared with the exponential attraction law and the conventional hyperbolic tangent attraction law, the attraction law provided by the invention has remarkable advantages in the aspects of convergence speed and reduction of system buffeting (see fig. 2);
2) introduction of d into the law of attractionk+1Reflects suppression measures for periodic disturbance signals of known period, such as homogeneous and even harmonic disturbances in the inverter;
Figure BDA0002170446390000092
is dk+1For compensating fractional harmonics and other non-periodic disturbances. Two methods of interference compensation are commonly used: (1) a simple method of determining the compensation value is a one-step delay method, i.e.
Figure BDA0002170446390000093
(2) Dk+1And (3) determining a compensation value when the boundary is known. Setting the equivalent interference dk+1Are respectively d at the upper and lower boundariesu、dlThen d isk+1Satisfy inequality dl≤dk+1≤du(ii) a Note the book
Figure BDA0002170446390000094
Then
Figure BDA0002170446390000095
Is convenient to use
Figure BDA0002170446390000096
The invention adopts equivalent interference second order difference compensation technology and uses
Figure BDA0002170446390000097
The method is used for compensating inter (fractional) harmonic and other non-periodic interference of the inverter, and can enable the steady-state error bound of the system tracking error to reach dk+1-2dk+dk-1＝O(T3) A smaller steady state error bound is obtained.
3) In the formula (9), yk-1，yk+1-N，yk，yk-N，yk-N-1All can be obtained by measurement; u. ofk-N，uk，uk-1，uk-1-NThe stored value of the control signal may be read from memory.
4) The attraction law method provided by the invention is also suitable for feedback control under a constant reference signal. Equivalent interference is dk+1＝wk+1-wk(ii) a The controller is as follows:
Figure BDA0002170446390000098
examples
And carrying out closed-loop control on the output waveform of the inverter. As shown in fig. 5, the inverter system used is composed of a given sinusoidal signal section, a repetitive controller, a PWM modulation section, an inverter main control circuit, and a sampling circuit. The given sine signal, the repetitive controller and the PWM module are all realized by a DSP control board, and the rest parts are realized by an inverter hardware circuit. In the whole inverter control system, an expected signal required to be output is given by the DSP, and the high-low pulse signal of a power switch tube of the inverter is driven after PWM modulation, so that the on-off is realized. The output signal of the inverter is reduced into a sine signal through an LC filter, signal data such as required voltage and current are sampled by a voltage sensor and a current sensor and returned to the DSP, and then the input signal is corrected after the action of a repetitive controller, so that the waveform tracking control of the inverter is realized, and the THD value of the output waveform of the inverter is reduced.
The following gives the design process of the discrete repetitive controller of the inverter.
First, a system mathematical model is established. Modeling by taking a main control circuit, an LC filter circuit and a sampling circuit of the inverter as objects to obtain a second-order difference equation model
yk+1+a1yk+a2yk-1＝b1uk+b2uk-1+wk+1 (23)
Wherein, yk+1,yk,yk-1Respectively representing the inverter output voltage at the time k +1, k, k-1, uk,uk-1Represents the control quantity of the inverter at the time of k and k-1, wk+1The inverter system is an uncertain characteristic of the inverter system and is composed of external interference, unmodeled characteristics and the like. System parameter a in model1,a2,b1,b2The method is obtained by mechanism modeling, and the specific values are as follows:
a1＝-0.5775,a2＝0.2804,b1＝0.4102,b2＝0.2589 (24)
in an embodiment, a given reference signal r of the inverterk+1＝220sin(2πfkTs) Unit is V, signal frequency is 50Hz, sampling period is TsThe reference signal period is 0.02s, 0.0001 s. Disturbance signal of inverter system is
Figure BDA0002170446390000101
The first term is used for simulating inverter homogeneous harmonic interference signals, the second term is used for simulating inverter even harmonic interference signals, the third term is used for simulating inter-inverter (fractional) harmonic interference signals, and the fourth term is random disturbance signals.
And carrying out numerical simulation on the system parameters to check the implementation result of the discrete repetitive controller on the inverter system.
1) Adopts a controller (9) andtaking into account interference compensation terms
Figure BDA0002170446390000102
During simulation, the interference of the inverter system only considers the interference of the homogeneous harmonic and the even harmonic, and then h1＝10,h2＝5,h3＝0,h 40; the controller parameters were chosen to be ρ 0.5, ε 0.2, δ 0.5, and the simulation results are shown in FIG. 6.
2) Using a controller (9) and taking into account the interference compensation term
Figure BDA0002170446390000103
During simulation, the interference of the inverter system only considers the interference of the homogeneous harmonic and the even harmonic, and then h1＝10,h2＝5,h3＝0,h 40; the controller parameters were chosen to be ρ 0.5, ε 0.2, δ 0.5, and the simulation results are shown in FIG. 7.
3) Using a controller (9) and taking into account the interference compensation term
Figure BDA0002170446390000104
During simulation, the interference of the inverter system only considers the interference of the homogeneous harmonic and the even harmonic, and then h1＝10,h2＝5,h3＝0,h 40; the controller parameters were chosen to be ρ 0.5, ε 0.2, δ 0.5, and the simulation results are shown in FIG. 8.
4) Using a controller (9) and taking into account the interference compensation term
Figure BDA0002170446390000105
In simulation, the interference of the inverter system is considered to be homogeneous harmonic interference, even harmonic interference, fractional harmonic interference and random interference, and then h1＝10,h2＝5,h3＝2,h40.05, Δ 2.6341 is obtained; the controller parameters are selected as rho is 0.5, epsilon is 0.2, delta is 0.5, and delta can be obtainedAAL＝ΔSSE3.6483; the simulation results are shown in fig. 9.
5) Using a controller (9) and taking into account the interference compensation term
Figure BDA0002170446390000111
Simulation (Emulation)When the inverter system interference considers homogeneous harmonic, even harmonic interference, fractional harmonic interference and random interference, then h1＝10,h2＝5,h3＝2,h4Δ ═ 0.762 can be obtained when 0.05 is obtained; the controller parameters are selected as rho is 0.5, epsilon is 0.2, delta is 0.5, and delta can be obtainedAAL＝ΔSSE0.7929; the simulation results are shown in fig. 10.
6) Using a controller (9) and taking into account the interference compensation term
Figure BDA0002170446390000112
In simulation, the interference of the inverter system is considered to be homogeneous harmonic interference, even harmonic interference, fractional harmonic interference and random interference, and then h1＝10,h2＝5,h3＝2,h40.05, Δ 0.2989 is obtained; the controller parameters are selected as rho is 0.5, epsilon is 0.2, delta is 0.5, and delta can be obtainedAAL＝0.331，ΔSSE0.3327; the simulation results are shown in fig. 11.
The above numerical simulation results verify that the discrete repetitive controller provided by the patent of the present invention functions in 0.02s, and as shown in fig. 6-8, the repetitive control can well eliminate periodic interference (homogeneous harmonic interference and even harmonic interference). As shown in fig. 9-11, the repetitive controller using the equivalent interference second order difference compensation technique has a greater advantage in suppressing the fractional harmonic signals and a smaller steady state error margin.

Claims (2)

1. A discrete repetitive control method for an inverter, characterized by:
1) constructing a discrete hyperbolic tangent attraction law:
Figure FDA0003421619460000011
wherein rho is more than 0 and less than 1, epsilon is more than or equal to 0, and delta is more than 0 and is a parameter for adjusting the suction speed;
Figure FDA0003421619460000012
ek+1,ektracking divided into k +1, k momentsError, and ek＝rk-yk；
In the attraction law (1), tracking error ekThe dynamic behavior of (c) is as follows: 1) when in use
Figure FDA0003421619460000013
When epsilon is more than 0, the tracking error will be strictly and monotonously converged, and no buffeting and no positive and negative alternation are converged at
Figure FDA0003421619460000014
Within a neighborhood of (c); 2) when in use
Figure FDA0003421619460000015
When epsilon is more than 0, the tracking error is strictly and absolutely converged, and the positive and negative alternate convergence is at the origin; 3) when e iskWhen not equal to 0 and epsilon is 0, the tracking error is strictly and monotonously converged, and the tracking error is converged to the origin without buffeting and positive and negative alternation; 4) when e iskNot equal to 0 and epsilon > 0, the tracking error is from an arbitrary initial value e0Begin to pass through
Figure FDA0003421619460000016
The step passes through the origin for the first time; wherein the content of the first and second substances,
Figure FDA0003421619460000017
is the smallest integer not less than;
Figure FDA0003421619460000018
Figure FDA0003421619460000019
2) in order to improve the inhibiting capability of the system on the even order, the even order and the fractional harmonic interference, an equivalent interference second order difference compensation technology is adopted to modify the discrete attraction law (1) into a discrete attraction law
Figure FDA00034216194600000110
Wherein d isk+1＝wk+1-wk+1-NThe equivalent interference at the k +1 moment is expressed, and the suppression of the homogeneous harmonic and the even harmonic can be realized;
Figure FDA00034216194600000111
for compensating inter-fractional sub-harmonics and other non-periodic disturbances of the inverter;
3) the discrete repetitive controller is designed according to the attraction law (4)
Figure FDA0003421619460000021
Wherein u isk，uk-1，uk-N，uk-1-NRespectively are control input signals at the k, k-1, k-N, k-1-N moments; y isk,yk-1,yk-1-N,yk-N,yk+1-NRespectively are output signals at the k, k-1, k-1-N, k-N, k +1-N moments; r isk+1A given reference signal at time k + 1; n is the period of a given reference signal; a in formula (5)1,a2,b1,b2For the system parameters of the inverter, the mathematical model of the inverter is as follows:
yk+1+a1yk+a2yk-1＝b1uk+b2uk-1+wk+1 (6)
wherein, yk+1,yk,yk-1Is the output signal at the moment k +1, k, k-1 of the inverter, uk,uk-1Control input signal representing the time of inverter k, k-1, a1,a2,b1,b2Is a system parameter; w is ak+1System interference signals at the moment k +1 comprise homogeneous harmonics, even harmonics and other inter-harmonics and parameter perturbations;
4) will ukAs control input signal for inverterAnd the output signal y of the inverter system can be measured and obtainedkFollows the reference signal rkThe dynamic behavior of the system tracking error is characterized by equation (4);
5) and a repetitive controller (5) is adopted, the attraction process of the tracking error of the system is represented by an absolute attraction layer, a steady-state error band and at most 3 indexes of the steps required by the tracking error entering the steady-state error band for the first time, and the 3 indexes can be used for guiding the parameter setting of the controller.
2. A discrete repetitive control method for an inverter as set forth in claim 1, characterized in that: under the action of the repetitive controller (5), the equivalent interference second order differential compensation error meets the requirement
Figure FDA0003421619460000022
The expression of the 3 indices is as follows:
1) absolute attraction layer ΔAALExpressed as:
ΔAAL＝max{ΔAAL1,ΔAAL2} (8)
in the formula,. DELTA.AAL1，ΔAAL2Is positive and real, and satisfies
Figure FDA0003421619460000023
Wherein, delta is the supremum of the equivalent interference second order difference compensation error;
2) steady state error band ΔSSEExpressed as:
ΔSSE＝max{ΔSSE1,ΔSSE2,Δ} (10)
in the formula,. DELTA.SSE1，ΔSSE2Is positive and real, is determined by
Figure FDA0003421619460000031
Where ξ is a positive real number and is determined by the following equation
Figure FDA0003421619460000032
Where sech (-) is a hyperbolic secant function,
Figure FDA0003421619460000033
3) convergence step number | k**|
Figure FDA0003421619460000034
Wherein e is0As initial value of tracking error, eiTracking error at the ith moment; psi satisfies
Figure FDA0003421619460000035
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