CN103812368A - Quarter period repeated controller for converter - Google Patents

Abstract

The invention discloses a kind of a quarter period repetitive controllers for inverter. Existing Repetitive Control Technique can realize perfect tracking or inhibition to periodical external drive signal, need to save the control and output signal of previous whole cycle. The present invention include given link, Periodic feedback link, Signal conversion module and subtract/addition ring. Given link generates The reference signal of periodic symmetry; Construction Periodic feedback link; According to rule method is attracted, construct Signal conversion module, output signal are used for the correction amount of repetitive controller; Then input of the output signal as controlled device of repetitive controller is calculated. Specific attitude conirol work can be carried out according to characterization system convergence performance indicator, and provide monotone decreasing region, absolute attractable layer and the steady-state error band boundary of characterization tracking error convergence process. The present invention be it is a kind of can effectively inhibit Symmtry Signals interference, mention high control precision and greatly reduce 1/4 period repetitive controller of EMS memory occupation.

Description

For 1/4th cycle repetitive controllers of inverter

Technical field

The invention belongs to Repetitive Control Technique field, especially a kind of 1/4th cycle repetitive controllers for inverter.

Background technology

Repeat to control is a kind of control method based on internal model principle.The essence of internal model principle is that system external signal dynamic model (being internal mold) is implanted in control system, forms high-precision feedback control system with this, makes system can follow to floating input signal.According to internal model principle design repetitive controller, the generation multinomial of periodic signal need be inserted in closed-loop system, form one-period Delay Feedback link.Regardless of waveform input signal, as long as repeating with the primitive period, controller output is cumulative to input signal Cycle by Cycle, plays the effect that suppresses PERIODIC INTERFERENCE completely.Current Repetitive Control Technique concentrates on the Domain Design based on internal model principle.For realizing the tracking/inhibition completely along the whole cycle about external cycles signal, the realization mechanism that internal model principle requires internal system to comprise same period signal.Implementation has two kinds: one is that dead time link is positioned at preceding paragraph passage; Another kind is to be positioned at feedback path.Can produce any period signal containing the reponse system of dead time link, the cycle of signal determined by lag time constant, and the closed-loop system of formation is Infinite-dimensional, and it has infinite multiple limit in the imaginary axis.The system that is zero for relative rank (it is true that object passes letter), repeats control and can make closed-loop system Exponential Stability, but for strict true system, closed-loop system can not be accomplished Exponential Stability.Like this, wish realizes controlled system and follows the tracks of any period signal (following the tracks of any radio-frequency component), need to propose very strict requirement to system configuration.Conventionally abandon the tracking to reference input radio-frequency component, only guarantee the demand of steady state error in low frequency frequency range.A kind of way is, before dead time link, low pass filter is set, and clips radio-frequency component more than shearing frequency.

In the time adopting Discrete-Delay internal mold, closed-loop system is finite dimension.Conventionally, the feedforward compensation design that stable minimum phase system can adopt zero utmost point to offset, stable non minimum phase system can adopt zero phase compensation.Follow the tracks of (ZPETC) method of control design repetitive controller with null phase error, its stability easily judges, only depends on choosing of repetitive controller gain.Zero phase compensation can offset the phase shift of introducing unstable zero point, is 1 but can not make to offset rear gain.The tracking performance that affect high fdrequency component is understood in not exclusively offseting of gain, need further take measures to eliminate its impact.

Discretely repeat to control that to need the structure cycle be any period signal internal mold of N.Cycle is that the generation mechanism of the symmetric signal of N is

$x\left(t\right)=\frac{q^{-N}}{1-q^{-N}}{x}_0\left(t\right)---\left(1\right)$

Here q, ^-1be a step backward shift operator,, for signal f (t), have q ^-1f (t)=f (t-1); The periodic signal that x (t) produces for this mechanism, x ₀(t) be the initial value of signal, i.e. the value in periodic signal x (t) first cycle.We claim 1-q ^-Nfor producing multinomial.The represented periodic signal generation mechanism of formula (1) as shown in Figure 1.According to the producing method of above periodic signal, we can construct periodic feedback link

$u\left(t\right)=\frac{q^{-N}}{1-q^{-N}}v\left(t\right)---\left(2\right)$

Here, v (t), u (t) is respectively the input and output signal of controller, and u (t) is called again control signal.Repetitive controller comprises periodic feedback link and e/v signal transform part two parts, and e/v signal transform part can be written as v (t)=f (e (t)).The represented periodic feedback link of formula (2) as shown in Figure 2.Like this, formula (2) can be write as again

u(t)＝u(t-N)+v(e(t-N)) (3)

Can be found out by formula (3), while realizing repetitive controller, need the data in storage u (t-N) and e (t-N) whole cycle.

What cause people's interest is the approximate or limited rank internal molds in the limited rank of time lag internal mold.For example, the finite dimension of internal mold is approximate continuously, plan feed forward method (PFF) is limit with limited rank Polynomial modeling band and disturbed, comb filter is used as Discrete-Delay internal mold.Simpler situation is, for tracking/inhibition problem of sinusoidal signal, only to construct sinusoidal internal mold and just can reach object.The memory requirements that reduces controller is the major issue that real-time control will solve.The odd harmonic repetitive controller of the designs such as Ramon effectively utilizes the half period symmetry of signal, derives the generator of half period symmetric signal in frequency domain.Adopt this generator to make EMS memory occupation amount reduce half.Because it only considers frequency domain factor, and signal symmetry is often portrayed with time domain, therefore, can not effectively process for more complicated Symmtry Signals, causes existing still larger technological deficiency of EMS memory occupation amount.

Summary of the invention

For overcome existing complete cycle repetitive controller and half period repetitive controller can not effectively process more complicated Symmtry Signals, deficiency that EMS memory occupation amount is larger, the invention provides a kind of 1/4th cycle repetitive controllers for inverter, to effectively process more complicated symmetric signal, significantly reduce EMS memory occupation space.

The technical solution used in the present invention is:

For 1/4th cycle repetitive controllers of inverter, set the reference signal r (t) with 1/4 cyclic symmetry, there are following two kinds of symmetric case

p1. $r\left(t\right)=\left\{\begin{array}{c}\&PlusMinus;r(t-N/4)+r_0\left(t\right),0<\mathrm{mod}(t,N)\&le;N/4\\ \&PlusMinus;r(t-N/4)+r_0\left(t\right),N/4<\mathrm{mod}(t,N)\&le;N/2\\ \&PlusMinus;r(t-N/4)+r_0\left(t\right),N/2<\mathrm{mod}(t,N)\&le;3N/4\\ \&PlusMinus;r(t-N/4)+r_0\left(t\right),3N/4<\mathrm{mod}(t,N)<\mathrm{Nor}\mathrm{mod}(t,N)=0\end{array}\right.---\left(4\right)$

And t >=N/4; Or

p2. $r\left(t\right)=\left\{\begin{array}{c}\&PlusMinus;r(t-t^{\&prime;})+r_0\left(t\right),0<\mathrm{mod}(t,N)\&le;N/4\\ \&PlusMinus;r(t-t^{\&prime;})+r_0\left(t\right),N/4<\mathrm{mod}(t,N)\&le;N/2\\ \&PlusMinus;r(t-t^{\&prime;})+r_0\left(t\right),N/2<\mathrm{mod}(t,N)\&le;3N/4\\ \&PlusMinus;r(t-t^{\&prime;})+r_0\left(t\right),3N/4<\mathrm{mod}(t,N)<\mathrm{Nor}\mathrm{mod}(t,N)=0\end{array}\right.---\left(5\right)$

And t > N/4, wherein,

$t^{\&prime;}=\left\{\begin{array}{cc}2(t\mathrm{mod}N/4)& t\mathrm{mod}N/4\&NotEqual;0\\ N/2& t\mathrm{mod}N/4=0\end{array}\right.$

N is cycle reference signal; r ₀(t) be the initial value of signal, i.e. the value in first 1/4 cycle of periodic signal, on interval t > N/4, perseverance is got null value.Here, need judge as the case may be that current time is in the particular location in one-period, then according to 1/4 periodic symmetry characteristic, judgement " ± " here gets "+" still to get "-".

Set 1/4 periodic feedback link, for different situations, the general structure of repetitive controller can be expressed as respectively: for situation p1,

$u\left(t\right)=\left\{\begin{array}{c}\&PlusMinus;u(t-N/4)+v\left(t\right),0<\mathrm{mod}(t,N)\&le;N/4\\ \&PlusMinus;u(t-N/4)+v\left(t\right),N/4<\mathrm{mod}(t,N)\&le;N/2\\ \&PlusMinus;u(t-N/4)+v\left(t\right),N/2<\mathrm{mod}(t,N)\&le;3N/4\\ \&PlusMinus;u(t-N/4)+v\left(t\right),3N/4<\mathrm{mod}(t,N)<\mathrm{Nor}\mathrm{mod}(t,N)=0\end{array}\right.---\left(6\right)$

And t >=N/4; For situation p2,

$u\left(t\right)=\left\{\begin{array}{c}\&PlusMinus;u(t-t^{\&prime;})+v\left(t\right),0<\mathrm{mod}(t,N)\&le;N/4\\ \&PlusMinus;u(t-t^{\&prime;})+v\left(t\right),N/4<\mathrm{mod}(t,N)\&le;N/2\\ \&PlusMinus;u(t-t^{\&prime;})+v\left(t\right),N/2<\mathrm{mod}(t,N)\&le;3N/4\\ \&PlusMinus;u(t-t^{\&prime;})+v\left(t\right),3N/4<\mathrm{mod}(t,N)<\mathrm{Nor}\mathrm{mod}(t,N)=0\end{array}\right.---\left(7\right)$

And t > N/4, wherein, u (t) is the output signal of repetitive controller, v (t) is the input signal of periodic feedback link, obtains through e/v signal conversion links.For system concrete model, according to attracting rule method, can obtain the conversion regime of e/v signal.

Further, described reference signal is sinusoidal signal, and as t >=N/4, its 1/4 periodic symmetry characteristic is

$r\left(t\right)=\left\{\begin{array}{c}-r(t-N/4)+r_0\left(t\right),0<\mathrm{mod}(t,N)\&le;N/4\\ r(t-N/4)+r_0\left(t\right),N/4<\mathrm{mod}(t,N)\&le;N/2\\ -r(t-N/4)+r_0\left(t\right),N/2<\mathrm{mod}(t,N)\&le;3N/4\\ r(t-N/4)+r_0\left(t\right),3N/4<\mathrm{mod}(t,N)<\mathrm{Nor}\mathrm{mod}(t,N)=0\end{array}\right.---\left(8\right)$

According to the symmetry characteristic of sinusoidal signal, as t >=N/4, the periodic feedback link of repetitive controller is

$u\left(t\right)=\left\{\begin{array}{c}-u(t-N/4)+v\left(t\right),0<\mathrm{mod}(t,N)\&le;N/4\\ u(t-N/4)+v\left(t\right),N/4<\mathrm{mod}(t,N)\&le;N/2\\ -u(t-N/4)+v\left(t\right),N/2<\mathrm{mod}(t,N)\&le;3N/4\\ u(t-N/4)+v\left(t\right),3N/4<\mathrm{mod}(t,N)<\mathrm{Nor}\mathrm{mod}(t,N)=0\end{array}\right.---\left(9\right)$

Construct following continuous attraction rule

$\stackrel{.}{e}\left(t\right)=-\mathrm{\&rho;e}\left(t\right)-\mathrm{\&epsiv;}\sqrt{\frac{\left|e\left(t\right)\right|}{\frac{1}{\mathrm{\&delta;}}+\left|e\left(t\right)\right|}}\mathrm{sgn}\left(e\left(t\right)\right)---\left(10\right)$

Wherein, 1 > ρ > 0, ε > 0,0 < δ < 1; E (t) is tracking error signal.Formula (10) is that finite time attracts rule, and be its time of advent

${\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="HDA0000445204730000014.png,HDA0000445204730000033.png"\; state="\{\{state\}\}">t</figure-callout>}}_1<\frac{1}{\mathrm{\&epsiv;\&delta;}}[\frac{{(1+\frac{1}{\mathrm{\&delta;e}\left(0\right)})}^{\frac{3}{2}}}{\frac{1}{\mathrm{\&delta;e}\left(0\right)}}-\frac{1}{2}(2\sqrt{1+\frac{1}{\mathrm{\&delta;e}\left(0\right)}}+\ln |\frac{\sqrt{1+\frac{1}{\mathrm{\&delta;e}\left(0\right)}}-1}{\sqrt{1+\frac{1}{\mathrm{\&delta;e}\left(0\right)}}+1}\left|\right)]---\left(11\right)$

Attract continuously the discrete form of rule (10) to be

$e(t+1)=(1-\mathrm{\&rho;})e\left(t\right)-\mathrm{\&epsiv;}\sqrt{\frac{\left|e\left(t\right)\right|}{\frac{1}{\mathrm{\&delta;}}+\left|e\left(t\right)\right|}}\mathrm{sgne}\left(t\right)---\left(12\right)$

Wherein, 0 < ρ < 1, ε > 0,0 < δ < 1.For the ability of the anti-periodic disturbances of raising system, discrete attraction rule (12) can be modified to

$e(t+1)=(1-\mathrm{\&rho;})e\left(t\right)-\mathrm{\&epsiv;}\sqrt{\frac{\left|e\left(t\right)\right|}{\frac{1}{\mathrm{\&delta;}}+\left|e\left(t\right)\right|}}\mathrm{sgne}\left(t\right)+d^{*}(t+1)-d(t+1)---\left(13\right)$

Wherein, for situation p1,

; For situation p2,

d (t+1) is equivalent disturbance, d ^*(t+1) be the compensating signal of equivalent disturbance; W (t+1) is system disturbance item.

Inverter dynamic performance model can be expressed as following form (being also suitable for other periodic duty process that this model is expressed):

y(t+1)+a ₁y(t)+a ₂y(t-1)＝b ₁u(t)+b ₂u(t-1)+w(t+1) (14)

Wherein, y (t) the expression t moment exports, and u (t) represents t moment controlled quentity controlled variable, and w (t+1) is the disturbing signal in t+1 moment.The expression that accordingly, can provide e/v transform part is:

For situation p1,

For situation p2,

Be sinusoidal signal for the reference signal of inverter

Wherein, z (t)=r (t+1)+a ₁y (t)+a ₂y (t-1)-b ₂u (t-1), e (t)=r (t)-y (t).

After repetitive controller has designed, the index that the performance of 1/4 cycle repetitive controller can be levied convergence process by following table is weighed, and these indexs are monotone decreasing zone boundary Δs _mDR, definitely attractable layer border Δ _aAL, steady-state error band border Δ _sSE, its expression is

1) monotone decreasing region (Δ _mDR)

Δ _MDR＝max{Δ _MDR1,Δ _MDR2} (18)

In formula, Δ _mDR1, Δ _mDR2for arithmetic number, meet

$\left\{\begin{array}{c}{\mathrm{\&rho;\&Delta;}}_{\mathrm{MDR}1}+\mathrm{\&epsiv;}\sqrt{\frac{{\mathrm{\&Delta;}}_{\mathrm{MDR}1}}{\frac{1}{\mathrm{\&delta;}}+{\mathrm{\&Delta;}}_{\mathrm{MDR}1}}}-\mathrm{\&Delta;}=0\\ (1-\mathrm{\&rho;}){\mathrm{\&Delta;}}_{\mathrm{MDR}2}-\mathrm{\&epsiv;}\sqrt{\frac{{\mathrm{\&Delta;}}_{\mathrm{MDR}1}}{\frac{1}{\mathrm{\&delta;}}+{\mathrm{\&Delta;}}_{\mathrm{MDR}1}}}-\mathrm{\&Delta;}=0\end{array}\right.---\left(19\right)$

2) absolute attractable layer (Δ _aAL)

Δ _AAL＝max{Δ _AAL1,Δ _AAL2} (20)

In formula, Δ _aAL1, Δ _aAL2for arithmetic number, can be determined by following formula

$\left\{\begin{array}{c}{\mathrm{\&rho;\&Delta;}}_{\mathrm{AAL}1}+\mathrm{\&epsiv;}\sqrt{\frac{{\mathrm{\&Delta;}}_{\mathrm{AAL}1}}{\frac{1}{\mathrm{\&delta;}}+{\mathrm{\&Delta;}}_{\mathrm{AAL}1}}}-\mathrm{\&Delta;}=0\\ (2-\mathrm{\&rho;}){\mathrm{\&Delta;}}_{\mathrm{AAL}2}-\mathrm{\&epsiv;}\sqrt{\frac{{\mathrm{\&Delta;}}_{\mathrm{AAL}2}}{\frac{1}{\mathrm{\&delta;}}+{\mathrm{\&Delta;}}_{\mathrm{AAL}2}}}-\mathrm{\&Delta;}=0\end{array}\right.---\left(21\right)$

3) steady-state error band (Δ _sSE)

A. work as Δ _sSEwhen>=ξ

Δ _SSE＝max{Δ _SSE1,Δ} (22)

Wherein Δ _sSE1it is equation ${\mathrm{\&rho;\&Delta;}}_{\mathrm{SSE}}+\mathrm{\&epsiv;}\sqrt{\frac{{\mathrm{\&Delta;}}_{\mathrm{SSE}}}{\frac{1}{\mathrm{\&delta;}}+{\mathrm{\&Delta;}}_{\mathrm{SSE}}}}-\mathrm{\&Delta;}=0$ Maximum arithmetic number solution

B. when 0 < Δ _sSEwhen < ξ

Δ _SSE＝max{Δ _SSE2,Δ _SSE3} (23)

Wherein Δ _sSE2Δ _sSE3respectively, $\left(\begin{array}{c}{\mathrm{\&rho;\&Delta;}}_{\mathrm{<figure-callout\; id="2"\; label="SSE"\; filenames="HDA0000445204730000021.png,HDA0000445204730000031.png"\; state="\{\{state\}\}">SSE</figure-callout>}2}+\mathrm{\&epsiv;}\sqrt{\frac{{\mathrm{\&Delta;}}_{\mathrm{<figure-callout\; id="2"\; label="SSE"\; filenames="HDA0000445204730000021.png,HDA0000445204730000031.png"\; state="\{\{state\}\}">SSE</figure-callout>}2}}{\frac{1}{\mathrm{\&delta;}}+{\mathrm{\&Delta;}}_{\mathrm{SSE}2}}}-\mathrm{\&Delta;}=0\\ -(1-\mathrm{\&rho;})\mathrm{\&xi;}+\mathrm{\&epsiv;}\sqrt{\frac{\mathrm{\&xi;}}{\frac{1}{\mathrm{\&delta;}}+\mathrm{\&xi;}}}+\mathrm{\&Delta;}={\mathrm{\&Delta;}}_{\mathrm{<figure-callout\; id="3"\; label="SSE"\; filenames="HDA0000445204730000021.png"\; state="\{\{state\}\}">SSE</figure-callout>}3}\end{array}\right.$ Maximum real solution.

ξ is $(1-\mathrm{\&rho;})-\frac{\mathrm{\&epsiv;}}{2\mathrm{\&delta;}\sqrt{\mathrm{\&xi;}}\sqrt{{(\frac{1}{\mathrm{\&delta;}}+\mathrm{\&xi;})}^3}}=0$ Equation real solution.

The adjustable parameters of 1/4 cycle repetitive controller comprises ρ, ε, and δ, parameter tuning can carry out according to above-mentioned characterization system constringency performance index.

The attraction rule method that the present invention provides is also applicable to repeat control complete cycle.In the time of t >=N, its reference signal symmetry characteristic is

r(t)＝r(t-N)+r ₀(t) (24)

Wherein, r ₀(t) be the initial value of signal, i.e. the value in first cycle of periodic signal, on interval t > N, perseverance is got null value; Its controller expression formula is

$\begin{array}{c}u\left(t\right)=u(t-N)+\frac{1}{b_1}[-(1-\mathrm{\&rho;})e\left(t\right)+\mathrm{\&epsiv;}\sqrt{\frac{\left|e\left(t\right)\right|}{\frac{1}{\mathrm{\&delta;}}+\left|e\left(t\right)\right|}}\mathrm{sgne}\left(t\right)\\ -d^{*}(t+1)+z\left(t\right)-z(t-N)+e(t-N+1)]\end{array}---\left(25\right)$

Wherein, z (t)=r (t+1)+a ₁y (t)+a ₂y (t-1)-b ₂u (t-1); It is identical that its boundary condition and 1/4 cycle repeat to control boundary condition, do not repeating at this.

The attraction rule method that the present invention provides is also applicable to FEEDBACK CONTROL.In the time of t >=1, its reference signal meets

r(t)＝r(t-1)+r ₀(t) (26)

Wherein, r ₀(t) be the initial value of signal, i.e. the value in first cycle of periodic signal, on interval t > 1, perseverance is got null value; Its controller is

$\begin{array}{c}u\left(t\right)=u(t-1)+\frac{1}{b_1}[-(1-\mathrm{\&rho;})e\left(t\right)+\mathrm{\&epsiv;}\sqrt{\frac{\left|e\left(t\right)\right|}{\frac{1}{\mathrm{\&delta;}}+\left|e\left(t\right)\right|}}\mathrm{sgne}\left(t\right)\\ -d^{*}(t+1)+z\left(t\right)-z(t-1)+e\left(t\right)]\end{array}---\left(27\right)$

Wherein, z (t)=r (t+1)+a ₁y (t)+a ₂y (t-1)-b ₂u (t-1).

Technical conceive of the present invention is, current repetitive controller method design focuses mostly in Domain Design, and signal symmetry characteristic shows in time domain.Therefore, time domain method for designing is more direct and have a distinctive feature when repetitive controller in design, and the controller of designing is more succinct, intuitively.

The present invention is directed to the reference signal with 1/4 periodic symmetry characteristic, provide the time domain design of 1/4 cycle repetitive controller.1/4 cycle repetitive controller can further significantly reduce taking up room of internal memory, its memory requirements be complete cycle repetitive controller 1/4th; The method for designing basis signal providing is at the different symmetry characteristic design repetitive controllers in different time interval, and every 1/4 cycle is revised control signal, realizes the inhibition completely for same period characteristic interference signal.And compared with complete cycle repetitive controller, the response time is faster, is of value to acceleraton disturbance and eliminates.

The present invention can effectively process more complicated symmetric reference signal, and greatly reduces EMS memory occupation space, has Fast Convergent performance concurrently, accelerates to disturb and suppress and high control precision.

Accompanying drawing explanation

Fig. 1 is periodic signal generator block diagram.

Fig. 2 is periodic feedback link block diagram.

Fig. 3 is for the invention provides 1/4 periodic signal generator block diagram, and wherein Fig. 3 a is for p1 situation, and Fig. 3 b is for p2 situation.

Fig. 4 is the reference signal all kinds exemplary graph that the present invention provides, and wherein Fig. 4 a is that the reference signal all kinds with 1/4 cyclic symmetry that the present invention provides are given an example, and adds up to 60 kinds of situations; Fig. 4 b, for can be equivalent to 1/2nd symmetry characteristic reference signal types, adds up to 4 kinds.

Fig. 5 is for the invention provides 1/4 periodic feedback link block diagram, and wherein Fig. 5 a is for p1 situation, and Fig. 5 b is for p2 situation.

Fig. 6 is 1/4 cycle repeated controlling system block diagram provided by the invention, and wherein Fig. 6 a is for p1 situation, and Fig. 6 b is for p2 situation.

Fig. 7 is inverter control system block diagram in the embodiment of the present invention.

Fig. 8 is inverter theory diagram in the embodiment of the present invention.

Fig. 9 is the error signal while adopting FEEDBACK CONTROL in the embodiment of the present invention.

Figure 10 adopts in the embodiment of the present invention to repeat to control time error signal complete cycle.

Figure 11 is the control signal producing while adopting repeat to control complete cycle in the embodiment of the present invention.

Figure 12 adopted for 1/4 cycle repeated to control time error signal in the embodiment of the present invention.

Figure 13 is the control signal producing while adopting for 1/4 cycle repeated to control in the embodiment of the present invention.

Embodiment

Below in conjunction with accompanying drawing, the specific embodiment of the invention is described further.

With reference to Fig. 3～Fig. 8, for 1/4th cycle repetitive controllers of inverter.

The first step. determine 1/4 periodic reference signal

The generation with the periodic reference signal of 1/4 cyclic symmetry can adopt following mechanism to be

For situation p1

$r\left(t\right)=\left\{\begin{array}{c}\frac{1}{1\&PlusMinus;q^{-N/4}}{r}_0\left(t\right),0<\mathrm{mod}(t,N)\&le;N/4\\ \frac{1}{1\&PlusMinus;q^{-N/4}}{r}_0\left(t\right),N/4<\mathrm{mod}(t,N)\&le;N/2\\ \frac{1}{1\&PlusMinus;q^{-N/4}}{r}_0\left(t\right),N/2<\mathrm{mod}(t,N)\&le;3N/4\\ \frac{1}{1\&PlusMinus;q^{-N/4}}{r}_0\left(t\right),3N/4<\mathrm{mod}(t,N)<\mathrm{Nor}\mathrm{mod}(t,N)=0\end{array}\right.---\left(1\right)$

And t >=N/4;

For situation p2

$r\left(t\right)=\left\{\begin{array}{c}\frac{1}{1\&PlusMinus;q^{-t^{\&prime;}}}{r}_0\left(t\right),0<\mathrm{mod}(t,N)\&le;N/4\\ \frac{1}{1\&PlusMinus;q^{-t^{\&prime;}}}{r}_0\left(t\right),N/4<\mathrm{mod}(t,N)\&le;N/2\\ \frac{1}{1\&PlusMinus;q^{-t^{\&prime;}}}{r}_0\left(t\right),N/2<\mathrm{mod}(t,N)\&le;3N/4\\ \frac{1}{1\&PlusMinus;q^{-t^{\&prime;}}}{r}_0\left(t\right),3N/4<\mathrm{mod}(t,N)<\mathrm{Nor}\mathrm{mod}(t,N)=0\end{array}\right.---\left(2\right)$

And t > N/4.

The generation mechanism of 1/4 periodic reference signal as shown in Figure 3.1/4 periodic reference signal producing under this mechanism as shown in Figure 4, here, r ₀(t) be the initial value of signal, i.e. the value in first 1/4 cycle of periodic signal, on interval t > N/4, perseverance is got null value; / 4th cyclic symmetries of reference signal, have 64 kinds of situations, wherein possess the 60 kinds of situations that have of 1/4th symmetry characteristics, as Fig. 4 a; What can be equivalent to satisfied 1/2nd symmetry characteristics has 4 kinds, as Fig. 4 b.

For sinusoidal reference signal, as t >=N/4, the concrete generation mechanism of its 1/4 cyclic symmetry can be expressed as

$r\left(t\right)=\left\{\begin{array}{c}\frac{1}{1-q^{-N/4}}{r}_0\left(t\right),0<\mathrm{mod}(t,N)\&le;N/4\\ \frac{1}{1+q^{-N/4}}{r}_0\left(t\right),N/4<\mathrm{mod}(t,N)\&le;N/2\\ \frac{1}{1-q^{-N/4}}{r}_0\left(t\right),N/2<\mathrm{mod}(t,N)\&le;3N/4\\ \frac{1}{1+q^{-N/4}}{r}_0\left(t\right),3N/4<\mathrm{mod}(t,N)<\mathrm{Nor}\mathrm{mod}(t,N)=0\end{array}\right.---\left(3\right)$

Second step. design 1/4 cycle repetitive controller

Utilize this generation mechanism, the corresponding general type of 1/4 cycle repetitive controller of design is respectively: for situation p1

$u\left(t\right)=\left\{\begin{array}{c}\frac{1}{1\&PlusMinus;q^{-N/4}}v\left(t\right),0<\mathrm{mod}(t,N)\&le;N/4\\ \frac{1}{1\&PlusMinus;q^{-N/4}}v\left(t\right),N/4<\mathrm{mod}(t,N)\&le;N/2\\ \frac{1}{1\&PlusMinus;q^{-N/4}}v\left(t\right),N/2<\mathrm{mod}(t,N)\&le;3N/4\\ \frac{1}{1\&PlusMinus;q^{-N/4}}v\left(t\right),3N/4<\mathrm{mod}(t,N)<\mathrm{Nor}\mathrm{mod}(t,N)=0\end{array}\right.---\left(4\right)$

And t >=N/4; For situation p2

$u\left(t\right)=\left\{\begin{array}{c}\frac{1}{1\&PlusMinus;q^{-t^{\&prime;}}}v\left(t\right),0<\mathrm{mod}(t,N)\&le;N/4\\ \frac{1}{1\&PlusMinus;q^{-t^{\&prime;}}}v\left(t\right),N/4<\mathrm{mod}(t,N)\&le;N/2\\ \frac{1}{1\&PlusMinus;q^{-t^{\&prime;}}}v\left(t\right),N/2<\mathrm{mod}(t,N)\&le;3N/4\\ \frac{1}{1\&PlusMinus;q^{-t^{\&prime;}}}v\left(t\right),3N/4<\mathrm{mod}(t,N)<\mathrm{Nor}\mathrm{mod}(t,N)=0\end{array}\right.---\left(5\right)$

And t > N/4.Its represented periodic feedback link as shown in Figure 5.

For sinusoidal reference signal, as t >=N/4, the feedback element of its 1/4 cycle repetitive controller is

$u\left(t\right)=\left\{\begin{array}{c}\frac{1}{1-q^{-N/4}}v\left(t\right),0<\mathrm{mod}(t,N)\&le;N/4\\ \frac{1}{1+q^{-N/4}}v\left(t\right),N/4<\mathrm{mod}(t,N)\&le;N/2\\ \frac{1}{1-q^{-N/4}}v\left(t\right),N/2<\mathrm{mod}(t,N)\&le;3N/4\\ \frac{1}{1+q^{-N/4}}v\left(t\right),3N/4<\mathrm{mod}(t,N)<\mathrm{Nor}\mathrm{mod}(t,N)=0\end{array}\right.---\left(6\right)$

The 3rd step. determine plant model

In order to provide the v (t) in controller, take following inverter control system model as example:

y(t+1)+a ₁y(t)+a ₂y(t-1)＝b ₁u(t)+b ₂u(t-1)+w(t+1) (7)

Wherein, parameter a ₁, a ₂, b ₁, b ₂can obtain by modelling by mechanism or Experimental modeling; Disturbing signal w (t) has 1/4 cyclic symmetry; Given reference signal r (t), output signal y (t), tracking error e (t)=r (t)-y (t).

The 4th step. structure discrete system tracking error attracts rule equation

$e(t+1)=(1-\mathrm{\&rho;})e\left(t\right)-\mathrm{\&epsiv;}\sqrt{\frac{\left|e\left(t\right)\right|}{\frac{1}{\mathrm{\&delta;}}+\left|e\left(t\right)\right|}}\mathrm{sgne}\left(t\right)+d^{*}(t+1)-d(t+1)---\left(8\right)$

Wherein, for p1 situation

, for p2 situation ; Need to judge that current time is in the particular location in one-period, then according to 1/4 periodic symmetry characteristic, judgement " ± " here gets "+" still to get "-".

The 5th step. provide concrete v (t) expression formula of e/v transform part: for situation p1

For situation p2

Be sinusoidal signal for the reference signal of inverter

Wherein, z (t)=r (t+1)+a ₁y (t)+a ₂y (t-1)-b ₂u (t-1), tracking error e (t)=r (t)-y (t).

Adopt the control system block diagram of this repetitive controller as shown in Figure 6.Comprise the function f (e (t)) that is converted into control signal v (t) by error signal e (t), 1/4 cycle repetitive controller module 101 and controlled system module 102.

The 6th step. controller parameter is adjusted

After repetitive controller has designed, its controller parameter of need to adjusting.Its adjustable parameters comprises ρ, ε, and δ, concrete parameter tuning work can be carried out according to the constringent index of following characterization system.For characterizing tracking error convergence process, the present invention introduces monotone decreasing region, and definitely attractable layer and steady-state error band concept, is defined as follows:

Monotone decreasing region Δ _mDR

$\left\{\begin{array}{c}0<e(t+1)<e\left(t\right),e\left(t\right)>{\mathrm{\&Delta;}}_{\mathrm{MDR}}\\ e\left(t\right)<e(t+1)<0,e\left(t\right)<-{\mathrm{\&Delta;}}_{\mathrm{MDR}}\end{array}\right.---\left(12\right)$

Definitely attractable layer Δ _aAL

$\left|e\left(t\right)\right|>{\mathrm{\&Delta;}}_{\mathrm{AAL}}\&DoubleRightArrow;\left|e(t+1)\right|<\left|e\left(t\right)\right|---\left(13\right)$

Steady-state error band Δ _sSE

$\left|e\left(t\right)\right|\&le;{\mathrm{\&Delta;}}_{\mathrm{SSE}}\&DoubleRightArrow;\left|e(t+1)\right|{\&le;\mathrm{\&Delta;}}_{\mathrm{SSE}}---\left(14\right)$

1) monotone decreasing region (Δ _mDR)

Δ _MDR＝max{Δ _MDR1,Δ _MDR2} (15)

In formula, Δ _mDR1, Δ _mDR2for arithmetic number, and meet

$\left\{\begin{array}{c}{\mathrm{\&rho;\&Delta;}}_{\mathrm{<figure-callout\; id="1"\; label="MDR"\; filenames="HDA0000445204730000014.png,HDA0000445204730000033.png"\; state="\{\{state\}\}">MDR</figure-callout>}1}+\mathrm{\&epsiv;}\sqrt{\frac{{\mathrm{\&Delta;}}_{\mathrm{<figure-callout\; id="1"\; label="MDR"\; filenames="HDA0000445204730000014.png,HDA0000445204730000033.png"\; state="\{\{state\}\}">MDR</figure-callout>}1}}{\frac{1}{\mathrm{\&delta;}}+{\mathrm{\&Delta;}}_{\mathrm{MDR}1}}}-\mathrm{\&Delta;}=0\\ (1-\mathrm{\&rho;}){\mathrm{\&Delta;}}_{\mathrm{MDR}2}-\mathrm{\&epsiv;}\sqrt{\frac{{\mathrm{\&Delta;}}_{\mathrm{<figure-callout\; id="1"\; label="MDR"\; filenames="HDA0000445204730000014.png,HDA0000445204730000033.png"\; state="\{\{state\}\}">MDR</figure-callout>}1}}{\frac{1}{\mathrm{\&delta;}}+{\mathrm{\&Delta;}}_{\mathrm{MDR}1}}}-\mathrm{\&Delta;}=0\end{array}\right.---\left(16\right)$

2) absolute attractable layer (Δ _aAL)

Δ _AAL＝max{Δ _AAL1,Δ _AAL2} (17)

In formula, Δ _aAL1, Δ _aAL2for arithmetic number, can be determined by following formula,

$\left\{\begin{array}{c}{\mathrm{\&rho;\&Delta;}}_{\mathrm{<figure-callout\; id="1"\; label="AAL"\; filenames="HDA0000445204730000014.png,HDA0000445204730000033.png"\; state="\{\{state\}\}">AAL</figure-callout>}1}+\mathrm{\&epsiv;}\sqrt{\frac{{\mathrm{\&Delta;}}_{\mathrm{<figure-callout\; id="1"\; label="AAL"\; filenames="HDA0000445204730000014.png,HDA0000445204730000033.png"\; state="\{\{state\}\}">AAL</figure-callout>}1}}{\frac{1}{\mathrm{\&delta;}}+{\mathrm{\&Delta;}}_{\mathrm{AAL}1}}}-\mathrm{\&Delta;}=0\\ (2-\mathrm{\&rho;}){\mathrm{\&Delta;}}_{\mathrm{AAL}2}-\mathrm{\&epsiv;}\sqrt{\frac{{\mathrm{\&Delta;}}_{\mathrm{<figure-callout\; id="2"\; label="AAL"\; filenames="HDA0000445204730000021.png,HDA0000445204730000031.png"\; state="\{\{state\}\}">AAL</figure-callout>}2}}{\frac{1}{\mathrm{\&delta;}}+{\mathrm{\&Delta;}}_{\mathrm{AAL}2}}}-\mathrm{\&Delta;}=0\end{array}\right.---\left(18\right)$

3) steady-state error band (Δ _sSE)

A. work as Δ _sSEwhen>=ξ

Δ _SSE＝max{Δ _SSE1,Δ} (19)

Wherein Δ _sSE1it is equation ${\mathrm{\&rho;\&Delta;}}_{\mathrm{SSE}}+\mathrm{\&epsiv;}\sqrt{\frac{{\mathrm{\&Delta;}}_{\mathrm{<figure-callout\; id="1"\; label="SSE"\; filenames="HDA0000445204730000014.png,HDA0000445204730000033.png"\; state="\{\{state\}\}">SSE</figure-callout>}}}{\frac{1}{\mathrm{\&delta;}}+{\mathrm{\&Delta;}}_{\mathrm{SSE}}}}-\mathrm{\&Delta;}=0$ Maximum arithmetic number solution

B. when 0 < Δ _sSEwhen < ξ

Δ _SSE＝max{Δ _SSE2,Δ _SSE3} (20)

Wherein Δ _sSE2, Δ _sSE3, respectively $\left(\begin{array}{c}{\mathrm{\&rho;\&Delta;}}_{\mathrm{<figure-callout\; id="2"\; label="SSE"\; filenames="HDA0000445204730000021.png,HDA0000445204730000031.png"\; state="\{\{state\}\}">SSE</figure-callout>}2}+\mathrm{\&epsiv;}\sqrt{\frac{{\mathrm{\&Delta;}}_{\mathrm{<figure-callout\; id="2"\; label="SSE"\; filenames="HDA0000445204730000021.png,HDA0000445204730000031.png"\; state="\{\{state\}\}">SSE</figure-callout>}2}}{\frac{1}{\mathrm{\&delta;}}+{\mathrm{\&Delta;}}_{\mathrm{SSE}2}}}-\mathrm{\&Delta;}=0\\ -(1-\mathrm{\&rho;})\mathrm{\&xi;}+\mathrm{\&epsiv;}\sqrt{\frac{\mathrm{\&xi;}}{\frac{1}{\mathrm{\&delta;}}+\mathrm{\&xi;}}}+\mathrm{\&Delta;}={\mathrm{\&Delta;}}_{\mathrm{<figure-callout\; id="3"\; label="SSE"\; filenames="HDA0000445204730000021.png"\; state="\{\{state\}\}">SSE</figure-callout>}3}\end{array}\right.$ Maximum real solution.

ξ is $(1-\mathrm{\&rho;})-\frac{\mathrm{\&epsiv;}}{2\mathrm{\&delta;}\sqrt{\mathrm{\&xi;}}\sqrt{{(\frac{1}{\mathrm{\&delta;}}+\mathrm{\&xi;})}^3}}=0$ Equation real solution

Do following explanation for above-mentioned 14 cycles repetitive controller design:

1) attract to introduce d in rule ^*(t+1) braking measure for the disturbing signal of period demand pattern, d have been reflected ^*(t+1) be the offset of d (t+1), for compensating aperiodic disturbance.

A kind of directly offset determines that method is d ^*(t+1)=d (t).

Here the offset while providing a kind of d (t) boundary known, is determined method.If the upper and lower boundary of equivalent disturbance d (t) is respectively d _u, d _l, d (t+1) meets inequality

d _l≤d(t)≤d _u

Note $\stackrel{\&OverBar;}{d}=\frac{d_u+{\mathrm{<figure-callout\; id="2"\; label="d\; l"\; filenames="HDA0000445204730000021.png,HDA0000445204730000031.png"\; state="\{\{state\}\}">d</figure-callout>}}_l}{2},\mathrm{\&Delta;}=\frac{d_u-d_{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA0000445204730000021.png,HDA0000445204730000031.png"\; state="\{\{state\}\}">l</figure-callout>}}}{2},$ ,

$|d\left(t\right)-\stackrel{\&OverBar;}{d}|\&le;\mathrm{\&Delta;}$

Desirable

$d^{*}(t+1)=\stackrel{\&OverBar;}{d}=\frac{d_u+{\mathrm{<figure-callout\; id="2"\; label="d\; l"\; filenames="HDA0000445204730000021.png,HDA0000445204730000031.png"\; state="\{\{state\}\}">d</figure-callout>}}_l}{2}$

2) formula (8), (9), in (10) and (11), e (t), y (t), y (t-1), y (t-N/4+1), y (t-N/4), y (t-N/4-1), all can be by measuring, u (t-1), u (t-N/4), the storing value that u (t-N/4-1) is control signal can read from internal memory.

3), for FEEDBACK CONTROL, its reference signal symmetry characteristic is r (t)=r (t-1).Therefore, the 14 cycle repetitive controllers that propose in the present invention are also applicable to often be worth adjusting problem, and now equivalent disturbance is d (t)=w (t)-w (t-1).

4) repeat complete cycle to control, its reference signal symmetry characteristic is r (t)=r (t-N).Equivalent disturbance is d (t)=w (t)-w (t-N), and the present invention is equally also applicable to repeat control complete cycle.

5) method proposed by the invention is also applicable to five-parameter model (inverter model adopts five-parameter model conventionally).Five-parameter model is as follows

y(t+1)+a ₁y(t)+a ₂y(t-1)＝b ₁u(t)+b ₂u(t-1)+c ₁+w(t+1) (21)

In formula, c ₁for normal value.Get

by its substitution formula (21),

$y(t+1)=-a_{1}y\left(t\right)-a_{2}y(t-1)+b_1{u}_c\left(t\right)+b_2{u}_c(t-1)+{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA0000445204730000014.png,HDA0000445204730000033.png"\; state="\{\{state\}\}">c</figure-callout>}}_1+b_1\stackrel{\&OverBar;}{u}+b_2\stackrel{\&OverBar;}{u}+d(t+1)---\left(22\right)$

Get

$\stackrel{\&OverBar;}{u}=-\frac{c_1}{{\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="HDA0000445204730000014.png,HDA0000445204730000033.png"\; state="\{\{state\}\}">b</figure-callout>}}_1+b_2}---\left(23\right)$

$u\left(t\right)=u_c\left(t\right)-\frac{c_1}{{\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="HDA0000445204730000014.png,HDA0000445204730000033.png"\; state="\{\{state\}\}">b</figure-callout>}}_1+b_2}---\left(24\right)$

Be that formula (22) can turn to

y(t+1)＝-a ₁y(t)-a ₂y(t-1)+b ₁u _c(t)+b ₂u _c(t-1)+d(t+1) (25)

Utilize formula (25), five-parameter model can be transformed to four parameter model.Like this, can carry out with reference to four parameter model about the repetitive controller design of five-parameter model.

6) above-mentioned 14 cycle repetitive controllers provide for second-order system (7), can provide equally the design result of high order system according to identical method.

Embodiment

Reference signal is the repetitive controller design of sinusoidal signal, and shown in Fig. 2,1/4 periodic symmetry characteristic of sinusoidal signal is formula (3), and according to the symmetry characteristic of this signal, repetitive controller can be designed to formula (6).

The present embodiment is controlled for inverter output waveforms.The inverter system adopting is by given signal section, 1/4 cycle repetitive controller, and PWM modulating part, converter main circuit (the LC filter circuit that comprises rear class etc.) and testing circuit form.Wherein given signal, three parts of repetitive controller and PWM modulation module realize by DSP, and remainder is realized by hardware circuit.Whole system is by the given desired signal that needs output of DSP, and this part is equivalent to the input signal of whole closed-loop system.After PWM modulation, become the high low pulse signal that can drive inverter bridge-type contactor pipe, inverter output is reduced into sinusoidal signal through LC filter circuit, be back to DSP by testing circuit sampling, repeat to revise input signal after control action through 1/4 cycle, thereby realize the control of inverter waveform tracking.

Provide the design process of 1/4 cycle of inverter repetitive controller below and realize result, and with conventional FEEDBACK CONTROL and repeat to control effect complete cycle and contrast.

Model system mathematic model.The inverter control system that the present embodiment uses is as Fig. 7.Comprise e/v transform part f (e (t)), periodic feedback link, periodic signal PWM modulation module 201, converter main circuit 202, testing circuit 203.Wherein, the above two form 1/4 cycle repetitive controller 301, and rear three forms inverter system 302.

Converter main circuit and rear class LC filter circuit, sample circuit are carried out to modeling as object, obtain following second-order difference equation model

y(t+1)+a ₁y(t)+a ₂y(t-1)＝b ₁u(t)+b ₂u(t-1)+w(t+1) (29)

Wherein y (t) represents t moment inverter output voltage, and u (t) represents the controlled quentity controlled variable of t moment inverter, and the uncertain characteristic of w (t+1) expression system, is made up of external disturbance, measurement noise and not modeling characteristic.Parameter a in model ₁, a ₂, b ₁, b ₂obtained by modelling by mechanism, its concrete value is

a ₁＝-0.5385,a ₂＝0.2504,b ₁＝0.3606,b ₂＝0.2358

FEEDBACK CONTROL: formula (6), get d (t+1)=w (t+1)-w (t),

$e(t+1)=(1-\mathrm{\&rho;})e\left(t\right)-\mathrm{\&epsiv;}\sqrt{\frac{\left|e\left(t\right)\right|}{\frac{1}{\mathrm{\&delta;}}+\left|e\left(t\right)\right|}}\mathrm{sgne}\left(t\right)+d^{*}(t+1)-w(t+1)+w\left(t\right)---\left(30\right)$

1/4 cycle repeated to control: given reference signal r (t), system tracking error dynamical equation is

$e(t+1)=(1-\mathrm{\&rho;})e\left(t\right)-\mathrm{\&epsiv;}\sqrt{\frac{\left|e\left(t\right)\right|}{\frac{1}{\mathrm{\&delta;}}+\left|e\left(t\right)\right|}}\mathrm{sgne}\left(t\right)+d^{*}(t+1)-d(t+1)---\left(8\right)$

The design of e/v signal conversion links in 1/4 cycle repetitive controller as shown in the formula

In embodiment, the reference signal r of inverter (k)=20sin (2 π fkT _s), unit is volt (V), signal frequency f=50Hz, sampling time T _s=0.0001s, in formula (15), gets ρ=0.3, δ=0.01, ε=0.5.Putting disturbing signal is

$w\left(k\right)=0.1[\mathrm{rand}\left(1\right)-0.5]+\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{c}_i\sin (2\mathrm{\&pi;}50*(2i-1)\frac{{\mathrm{kT}}_s}{N}),c_i=1/(2i-1)---\left(31\right)$

Wherein, preceding paragraph is random perturbation signal, consequent for simulating inverter odd harmonic disturbing signal.Now, d (t+1) bound numerical value is equal, and symbol is contrary.Therefore, desirable d ^*(t+1)=0, it is Δ that error e (t) will converge to radius _sSEformer vertex neighborhood in.In reality, the bound of d (t+1) can be closer to zero, and error will converge in the more small neighbourhood of initial point.

Get said system parameter and control parameter and carry out emulation, the result of implementation of check 1/4 cycle Repetitive Control on inversion system, and contrast with the result of implementation that repeats FEEDBACK CONTROL and complete cycle to control:

1) error signal under feedback controller effect as shown in Figure 9.Can see, although error signal convergence, its error signal amplitude is large and present obvious cyclophysis, and this is because the cycle harmonic disturbance signal of this control is not eliminated.Therefore known feedback controller does not have circular error inhibition ability.

2) as shown in figure 10, control signal as shown in figure 11 for the error signal under repetitive controller effect complete cycle.Controller parameter is got ρ=0.3, δ=0.01, and the valuation (getting Δ=0.05 after removing odd harmonic disturbance) of ε=0.5 and Δ, can provide the dividing value of characterization system constringency performance: monotone decreasing region Δ _mDR=0.1111V, definitely attractable layer Δ _aAL=0.2797V, steady-state error band Δ _sSE=0.2994V.The descending monotone decreasing region (Δ that is respectively of dividing value in Figure 10 _mDR), steady-state error band (Δ _sSE) and absolute attractable layer (Δ _aAL).As shown in Figure 10, adopt that to repeat to be controlled in the situation of disturbance error convergence complete cycle rapider, error signal and adopt FEEDBACK CONTROL effect identical within first complete cycle, after 0.02 second, error signal converges to rapidly characterization system and restrains in boundary.

3) as shown in figure 12, control signal as shown in figure 13 for the error signal under the repetitive controller effect of 1/4 cycle.With reference to complete cycle repetitive controller parameter get ρ=0.3, δ=0.01, the valuation (getting Δ=0.05 after removing odd harmonic disturbance) of ε=0.5 and Δ, can provide the dividing value of characterization system constringency performance: monotone decreasing region Δ _mDR=0.1111V, definitely attractable layer Δ _aAL=0.2797V, steady-state error band Δ _sSE=0.2994V.The descending steady-state error band (Δ that is respectively of dividing value in Figure 12 _sSE), definitely attractable layer (Δ _aAL) and monotone decreasing region (Δ _mDR).As shown in Figure 12, adopted for 1/4 cycle repeated to be controlled under the impact of disturbance error convergence rapider compared with repeating complete cycle to control, first 1/4th circular error with adopt that to control effect when FEEDBACK CONTROL identical, after 0.005 second, error signal converges to rapidly in characterization system convergence circle.Odd harmonic disturbing signal is eliminated, and has only been left the very little fluctuating error that random perturbation signal causes.Visible, this 1/4 cycle repetitive controller can be eliminated cycle harmonic disturbance signal effectively fast, and greatly reduces memory headroom and take.

Claims (5)

1. for 1/4th cycle repetitive controllers of inverter, be particularly useful for inverter, and periodic duty process in industrial occasions, it is characterized in that:

(1) given reference signal r (t), this reference signal has 1/4 periodic symmetry characteristic

p1. $r\left(t\right)=\left\{\begin{array}{c}\&PlusMinus;r(t-N/4)+r_0\left(t\right),0<\mathrm{mod}(t,N)\&le;N/4\\ \&PlusMinus;r(t-N/4)+r_0\left(t\right),N/4<\mathrm{mod}(t,N)\&le;N/2\\ \&PlusMinus;r(t-N/4)+r_0\left(t\right),N/2<\mathrm{mod}(t,N)\&le;3N/4\\ \&PlusMinus;r(t-N/4)+r_0\left(t\right),3N/4<\mathrm{mod}(t,N)<\mathrm{Nor}\mathrm{mod}(t,N)=0\end{array}\right.---\left(1\right)$

And t >=N/4;

p2. $r\left(t\right)=\left\{\begin{array}{c}\&PlusMinus;r(t-t^{\&prime;})+r_0\left(t\right),0<\mathrm{mod}(t,N)\&le;N/4\\ \&PlusMinus;r(t-t^{\&prime;})+r_0\left(t\right),N/4<\mathrm{mod}(t,N)\&le;N/2\\ \&PlusMinus;r(t-t^{\&prime;})+r_0\left(t\right),N/2<\mathrm{mod}(t,N)\&le;3N/4\\ \&PlusMinus;r(t-t^{\&prime;})+r_0\left(t\right),3N/4<\mathrm{mod}(t,N)<\mathrm{Nor}\mathrm{mod}(t,N)=0\end{array}\right.---\left(2\right)$

And t > N/4; Wherein,

$t^{\&prime;}=\left\{\begin{array}{cc}2(t\mathrm{mod}N/4)& t\mathrm{mod}N/4\&NotEqual;0\\ N/2& t\mathrm{mod}N/4=0\end{array}\right.$

N is cycle reference signal; r ₀(t) be the initial value of signal, i.e. the value in first 1/4 cycle of periodic signal, on interval t > N/4, perseverance is got null value; Judge that as the case may be current time is in the particular location in one-period, then according to 1/4 periodic symmetry characteristic, judgement " ± " here gets "+" still to get "-";

The reference signal of described inverter is sinusoidal signal, and as t >=N/4, its 1/4 periodic symmetry characteristic is

$r\left(t\right)=\left\{\begin{array}{c}-r(t-N/4)+r_0\left(t\right),0<\mathrm{mod}(t,N)\&le;N/4\\ r(t-N/4)+r_0\left(t\right),N/4<\mathrm{mod}(t,N)\&le;N/2\\ -r(t-N/4)+r_0\left(t\right),N/2<\mathrm{mod}(t,N)\&le;3N/4\\ r(t-N/4)+r_0\left(t\right),3N/4=\mathrm{mod}(t,N)<\mathrm{Nor}\mathrm{mod}(t,N)=0\end{array}\right.---\left(3\right)$

(2) structure attracts rule continuously

$\stackrel{.}{e}\left(t\right)=-\mathrm{\&rho;e}\left(t\right)-\mathrm{\&epsiv;}\sqrt{\frac{\left|e\left(t\right)\right|}{\frac{1}{\mathrm{\&delta;}}+\left|e\left(t\right)\right|}}\mathrm{sgn}\left(s\right)---\left(4\right)$

Wherein, e (t)=r (t)-y (t) represents tracking error, ρ > 0, ε > 0,0 < δ < 1; Formula (4) is that finite time attracts rule, and be its time of advent

$t_1<\frac{1}{\mathrm{\&epsiv;\&delta;}}[\frac{{(1+\frac{1}{\mathrm{\&delta;e}\left(0\right)})}^{\frac{3}{2}}}{\frac{1}{\mathrm{\&delta;e}\left(0\right)}}-\frac{1}{2}(2\sqrt{1+\frac{1}{\mathrm{\&delta;e}\left(0\right)}}+\ln |\frac{\sqrt{1+\frac{1}{\mathrm{\&delta;e}\left(0\right)}}-1}{\sqrt{1+\frac{1}{\mathrm{\&delta;e}\left(0\right)}}+1}\left|\right)]---\left(5\right)$

Attract the discrete form of rule (4) to be

$e(t+1)=(1-\mathrm{\&rho;})e\left(t\right)-\mathrm{\&epsiv;}\sqrt{\frac{\left|e\left(t\right)\right|}{\frac{1}{\mathrm{\&delta;}}+\left|e\left(t\right)\right|}}\mathrm{sgne}\left(t\right)---\left(6\right)$

Wherein, 0 < ρ < 1, ε > 0,0 < δ < 1;

(3) add and disturb inhibition, set up discrete attraction rule

$e(t+1)=(1-\mathrm{\&rho;})e\left(t\right)-\mathrm{\&epsiv;}\sqrt{\frac{\left|e\left(t\right)\right|}{\frac{1}{\mathrm{\&delta;}}+\left|e\left(t\right)\right|}}\mathrm{sgne}\left(t\right)+d^{*}(t+1)-d(t+1)---\left(7\right)$

Wherein, equivalent disturbance w (t+1) is system disturbance item, d ^*(t+1) be the compensation of equivalent disturbance, for suppressing the impact of interference signal d (t+1);

(4) according to the symmetric 1/4 cycle repetitive controller of cycle reference signal

(a) the periodic feedback link of 1/4 cycle repetitive controller: for situation p1

$u\left(t\right)=\left\{\begin{array}{c}\&PlusMinus;u(t-N/4)+v\left(t\right),0<\mathrm{mod}(t,N)\&le;N/4\\ \&PlusMinus;u(t-N/4)+v\left(t\right),N/4<\mathrm{mod}(t,N)\&le;N/2\\ \&PlusMinus;u(t-N/4)+v\left(t\right),N/2<\mathrm{mod}(t,N)\&le;3N/4\\ \&PlusMinus;u(t-N/4)+v\left(t\right),3N/4<\mathrm{mod}(t,N)<\mathrm{Nor}\mathrm{mod}(t,N)=0\end{array}\right.---\left(8\right)$

And t >=N/4; For situation p2

$u\left(t\right)=\left\{\begin{array}{c}\&PlusMinus;u(t-t^{\&prime;})+v\left(t\right),0<\mathrm{mod}(t,N)\&le;N/4\\ \&PlusMinus;u(t-t^{\&prime;})+v\left(t\right),N/4<\mathrm{mod}(t,N)\&le;N/2\\ \&PlusMinus;u(t-t^{\&prime;})+v\left(t\right),N/2<\mathrm{mod}(t,N)\&le;3N/4\\ \&PlusMinus;u(t-t^{\&prime;})+v\left(t\right),3N/4<\mathrm{mod}(t,N)<\mathrm{Nor}\mathrm{mod}(t,N)=0\end{array}\right.---\left(9\right)$

And t > N/4; Wherein, u (t) is the output signal of repetitive controller, and v (t) is the input signal of periodic feedback link, obtains through e/v signal conversion links; For system concrete model, according to attracting rule method, can obtain the conversion regime of e/v signal;

(b) inverter by the periodic feedback link of repetitive controller is

$u\left(t\right)=\left\{\begin{array}{c}-u(t-N/4)+v\left(t\right),0<\mathrm{mod}(t,N)\&le;N/4\\ u(t-N/4)+v\left(t\right),N/4<\mathrm{mod}(t,N)\&le;N/2\\ -u(t-N/4)+v\left(t\right),N/2<\mathrm{mod}(t,N)\&le;3N/4\\ u(t-N/4)+v\left(t\right),3N/4=\mathrm{mod}(t,N)<\mathrm{Nor}\mathrm{mod}(t,N)=0\end{array}\right.---\left(10\right)$

(5) concrete v (t) expression formula that provides e/v transform part is: for situation p1

For situation p2

Be sinusoidal signal for the reference signal of inverter

Wherein, z (t)=r (t+1)+a ₁y (t)+a ₂y (t-1)-b ₂u (t-1), the z (t) here provides for inverter dynamic performance model:

y(t+1)+a ₁y(t)+a ₂y(t-1)＝b ₁u(t)+b ₂u(t-1)+w(t+1) (14)

Y (t) the expression t moment exports, and u (t) represents t moment controlled quentity controlled variable; a ₁, a ₂, b ₁, b ₂for system parameters; W (t+1) represents disturbance.

2. controller as claimed in claim 1, is characterized in that: the index that the performance of this controller is levied convergence process by following table is weighed, and comprises monotone decreasing region, and definitely attractable layer and steady-state error band, is defined as follows:

Monotone decreasing region Δ _mDR

$\left\{\begin{array}{c}0<e(t+1)<e\left(t\right),e\left(t\right)>{\mathrm{\&Delta;}}_{\mathrm{MDR}}\\ e\left(t\right)<e(t+1)<0,e\left(t\right)<-{\mathrm{\&Delta;}}_{\mathrm{MDR}}\end{array}\right.---\left(15\right)$

Definitely attractable layer Δ _aAL

$\left|e\left(t\right)\right|>{\mathrm{\&Delta;}}_{\mathrm{AAL}}\&DoubleRightArrow;\left|e(t+1)\right|<\left|e\left(t\right)\right|---\left(16\right)$

Steady-state error band Δ _sSE

$\left|e\left(t\right)\right|\&le;{\mathrm{\&Delta;}}_{\mathrm{SSE}}\&DoubleRightArrow;\left|e(t+1)\right|{\&le;\mathrm{\&Delta;}}_{\mathrm{SSE}}---\left(17\right)$

Restrained by described discrete attraction, determine the monotone decreasing zone boundary Δ of 1/4 cycle repetitive controller _mDR, definitely attractable layer border Δ _aAL, steady-state error band border Δ _sSE, its expression is as follows:

(1) monotone decreasing region

Δ _MDR＝max{Δ _MDR1,Δ _MDR2} (18)

In formula, Δ _mDR1, Δ _mDR2for arithmetic number, and meet

$\left\{\begin{array}{c}{\mathrm{\&rho;\&Delta;}}_{\mathrm{MDR}1}+\mathrm{\&epsiv;}\sqrt{\frac{{\mathrm{\&Delta;}}_{\mathrm{MDR}1}}{\frac{1}{\mathrm{\&delta;}}+{\mathrm{\&Delta;}}_{\mathrm{MDR}1}}}-\mathrm{\&Delta;}=0\\ (1-\mathrm{\&rho;}){\mathrm{\&Delta;}}_{\mathrm{MDR}2}-\mathrm{\&epsiv;}\sqrt{\frac{{\mathrm{\&Delta;}}_{\mathrm{MDR}1}}{\frac{1}{\mathrm{\&delta;}}+{\mathrm{\&Delta;}}_{\mathrm{MDR}1}}}-\mathrm{\&Delta;}=0\end{array}\right.---\left(19\right)$

(2) absolute attractable layer

Δ _AAL＝max{Δ _AAL1,Δ _AAL2} (20)

In formula, Δ _aAL1, Δ _aAL2for arithmetic number, can be determined by following formula

$\left\{\begin{array}{c}{\mathrm{\&rho;\&Delta;}}_{\mathrm{AAL}1}+\mathrm{\&epsiv;}\sqrt{\frac{{\mathrm{\&Delta;}}_{\mathrm{AAL}1}}{\frac{1}{\mathrm{\&delta;}}+{\mathrm{\&Delta;}}_{\mathrm{AAL}1}}}-\mathrm{\&Delta;}=0\\ (2-\mathrm{\&rho;}){\mathrm{\&Delta;}}_{\mathrm{AAL}2}-\mathrm{\&epsiv;}\sqrt{\frac{{\mathrm{\&Delta;}}_{\mathrm{AAL}2}}{\frac{1}{\mathrm{\&delta;}}+{\mathrm{\&Delta;}}_{\mathrm{AAL}2}}}-\mathrm{\&Delta;}=0\end{array}\right.---\left(21\right)$

(3) steady-state error band

Δ _sSEconcrete value can be according to Δ _aALdetermine

A. work as Δ _aALwhen>=ξ

Δ _SSE＝max{Δ _SSE1,Δ} (22)

Wherein Δ _sSE1it is equation ${\mathrm{\&rho;\&Delta;}}_{\mathrm{SSE}}+\mathrm{\&epsiv;}\sqrt{\frac{{\mathrm{\&Delta;}}_{\mathrm{SSE}}}{\frac{1}{\mathrm{\&delta;}}+{\mathrm{\&Delta;}}_{\mathrm{SSE}}}}-\mathrm{\&Delta;}=0$ Maximum arithmetic number solution

B. when 0 < Δ _aALwhen < ξ

Δ _SSE＝max{Δ _SSE2,Δ _SSE3} (23)

Wherein Δ _sSE2, Δ _sSE3, respectively $\left(\begin{array}{c}{\mathrm{\&rho;\&Delta;}}_{\mathrm{SSE}2}+\mathrm{\&epsiv;}\sqrt{\frac{{\mathrm{\&Delta;}}_{\mathrm{SSE}2}}{\frac{1}{\mathrm{\&delta;}}+{\mathrm{\&Delta;}}_{\mathrm{SSE}2}}}-\mathrm{\&Delta;}=0\\ -(1-\mathrm{\&rho;})\mathrm{\&xi;}+\mathrm{\&epsiv;}\sqrt{\frac{\mathrm{\&xi;}}{\frac{1}{\mathrm{\&delta;}}+\mathrm{\&xi;}}}+\mathrm{\&Delta;}={\mathrm{\&Delta;}}_{\mathrm{SSE}3}\end{array}\right.$ Maximum real solution;

ξ is $(1-\mathrm{\&rho;})-\frac{\mathrm{\&epsiv;}}{2\mathrm{\&delta;}\sqrt{\mathrm{\&xi;}}\sqrt{{(\frac{1}{\mathrm{\&delta;}}+\mathrm{\&xi;})}^3}}=0$ Equation real solution.

3. controller as claimed in claim 1, is characterized in that: the adjustable parameters of this controller comprises ρ, ε, δ; Parameter tuning can carry out according to the index that characterizes convergence process.

4. controller as claimed in claim 1 or 2, is characterized in that: reference signal meets r (t)=r (t-N)+r ₀(t), there is symmetry characteristic complete cycle; This repetitive controller is also applicable to repeat control complete cycle, and equivalent disturbance is at this moment d (t+1)=w (t+1)-w (t+1-N); Complete cycle, repetitive controller was

$\begin{array}{c}u\left(t\right)=u(t-N)+\frac{1}{b_1}[-(1-\mathrm{\&rho;})e\left(t\right)+\mathrm{\&epsiv;}\sqrt{\frac{\left|e\left(t\right)\right|}{\frac{1}{\mathrm{\&delta;}}+\left|e\left(t\right)\right|}}\mathrm{sgne}\left(t\right)\\ -d^{*}(t+1)+z\left(t\right)-z(t-N)+e(t-N+1)]\end{array},---\left(24\right).$

5. controller as claimed in claim 1 or 2, is characterized in that: reference signal meets r (t)=r (t-1)+r ₀(t); This repetitive controller is also applicable to often be worth adjusting problem, and equivalent disturbance is at this moment d (t)=w (t)-w (t-1); Normal value conditioning controller is

$\begin{array}{c}u\left(t\right)=u(t-1)+\frac{1}{b_1}[-(1-\mathrm{\&rho;})e\left(t\right)+\mathrm{\&epsiv;}\sqrt{\frac{\left|e\left(t\right)\right|}{\frac{1}{\mathrm{\&delta;}}+\left|e\left(t\right)\right|}}\mathrm{sgne}\left(t\right)\\ -d^{*}(t+1)+z\left(t\right)-z(t-1)+e\left(t\right)]\end{array}---\left(25\right).$

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