CN201994846U - Special type harmonic wave repetitive controller - Google Patents

Abstract

The utility model discloses a special type harmonic wave repetitive controller, which comprises a repetitive control gain module, a positive and negative feedback gain module, an addition ring, two subtraction rings and two time delay modules. The special type harmonic wave repetitive controller has the advantages that the errorless tracking or elimination can be carried out on any nk+/-m harmonic waves, the error elimination speed is higher, fewer storage units are required for realizing digitalization, and in addition, universal expression forms are provided for various repetitive controllers. In order to improve the stability and the anti-jamming capability, the improved repetitive controller provided with a damping gain factor and low-pass filter is also provided for meeting the actual application requirements.

Description

A kind of certain kinds harmonic wave repetitive controller

Technical field

The utility model proposes a kind of certain kinds harmonic wave repetitive controller, be used for the error free tracking of nk ± m rd harmonic signal or elimination fully, belong to the repetitive controller field of Industry Control.

Background technology

For many years, " tracking of cyclical signal and Disturbance Rejection compensation problem " is the problem that numerous researchers pay close attention to always, and based on internal model principle to repeat control be exactly a kind of highly effective control device.It is T that general repetitive controller adopts delay time T _oDelay link to construct the primitive period be T _oThe internal mold of periodic signal, and with in it embedding control loop, thereby can implement static indifference tracking Control or disturbance elimination to this kind cyclical signal (comprising sinusoidal fundamental wave and each harmonic thereof), repetitive controller is many in the middle of actual realizes that with digital form the internal mold of this cyclical signal, its shared internal storage location number are at least N (N=T wherein _o/ T _sBe integer, T _sBe the sampling time).Yet in some practical applications, the harmonic wave that needs to follow the tracks of or eliminate is confined to certain specific quefrency, for example the three phase rectifier load concentrates on 6k ± 1 (k=1 for the harmonic pollution overwhelming majority that power-supply system caused, 2, ...) the subfrequency place, and the single-phase rectifier load give the harmonic pollution overwhelming majority that power-supply system caused concentrate on 4k ± 1 (k=1,2 ...) and subfrequency (being odd harmonic frequencies) locates.If can propose new repetitive controller only compensates at these frequencies, by transforming the internal mold of signal in the controller, its control lag time is shortened, and the speed of disturbance is eliminated by raising system greatly, and can significantly reduce the required memory space that takies of its Digital Implementation.Therefore be necessary still that the multiple control technology of counterweight does further research.

The utility model content

Technical problem: the purpose of this utility model is to propose a kind of certain kinds harmonic wave repetitive controller, this repetitive controller can be followed the tracks of fully or eliminate any nk ± m rd harmonic signal, time delay is much smaller than general repetitive controller, it is far away from general repetitive controller that the speed of its tracking or harmonic carcellation signal is wanted, and the shared memory space of Digital Implementation still less, and can unify existing multiple repetitive controller, its cost performance will promote greatly.

Technical scheme:

The utility model adopts following technical scheme for achieving the above object:

A kind of certain kinds harmonic wave of the utility model repetitive controller, comprise repetition ride gain module, the positive feedback gain module, the addition ring, two time delay modules that the subtraction ring is identical with two, wherein repeat the input of the output termination addition ring of ride gain module, the positive input terminal of the output termination first subtraction ring of addition ring and the input of very first time Postponement module, the input of the output termination second time delay module of very first time Postponement module and the input of positive feedback gain module, the negative input end of the output termination first subtraction ring of the second time delay module and the negative input end of the second subtraction ring, the positive input terminal of the output termination second subtraction ring of positive feedback gain module, the input of the output termination addition ring of the second subtraction ring.

Preferably, described two identical time delay modules have the damping gain coefficient, and the output of described two identical time delay modules is connected in series low pass filter respectively.

Preferably, described time delay module is an analog or digital time delay module.

Beneficial effect:

1, the nk that the utility model proposed ± m subharmonic repetitive controller carries out error free tracking at nk ± m rd harmonic signal specially or disturbance is eliminated, can customize different n and the numerical value of m according to the actual demand of harmonic carcellation disturbing signal or tracking reference signal.As at eliminating 6k ± 1 subharmonic in the three-phase inversion and following the tracks of the needs of first-harmonic reference signal, only need make n=6 and m=1 get final product; To eliminating odd harmonic in the single-phase inversion and following the tracks of the needs of first-harmonic reference signal, only need make n=4 and m=1 get final product.Compare with general repetitive controller, its time postpones to reduce greatly, and the speed of eliminating disturbance improves greatly.

2, the number of the required memory cell of Digital Implementation of nk ± m subharmonic repetitive controller also is significantly less than general repetition of figures controller.

3, nk ± m subharmonic repetitive controller has provided a kind of universal expression formula of repetitive controller, unified multiple repetitive controller, the patent documentation of being applied for as Gerardo Escobar Valderrama etc. " Repetitive Controller to Compensate for (6l ± 1) Harmonics ", US 2008/0167735A1, Jul.10, applied 6k in 2,008 one literary compositions ± 1 subharmonic repetitive controller are the utility model nk ± special case of m subharmonic repetitive controller when n=6 and m=1; The patent documentation " Repetitive Controller to Compensate for odd Harmonics " that JesusLeyva Ramos etc. is applied for, US 2007/0067051 A1, Mar.22, applied odd harmonic repetitive controller is the utility model nk ± special case of m subharmonic repetitive controller when n=4 and m=1 in 2,007 one literary compositions; And the patent documentation " Repetitive Controller for Compensation of Periodic Signals " that Jesus Leyva Ramos etc. are applied for, US 2007/0055721 A1, Mar.8, applied conventional repetitive controller is the utility model nk ± special case of m subharmonic repetitive controller when n=1 and m=0 in 2,007 one literary compositions.

4, nk ± m subharmonic repetitive controller ratio of being used for eliminating nk+m and these two kinds of frequencies of nk-m only needs a kind of time delay link to construct the disturbing signal internal mold during not for the disturbance of integral multiple relation, has therefore simplified the design of time delay link in the repetitive controller.

Description of drawings

Fig. 1 is that a kind of certain kinds harmonic wave repetitive controller that the utility model proposes is nk ± m subharmonic repetitive controller.

Fig. 2 is the Digital Implementation form of Fig. 1, is nk ± m subharmonic repetition of figures controller.

Fig. 3 is improved nk ± m subharmonic repetitive controller that the joining day postpones damping gain coefficient and low pass filter on Fig. 1 basis.

Fig. 4 is the Digital Implementation form of Fig. 3, is improved nk ± m subharmonic repetition of figures controller.

Embodiment

Be elaborated below in conjunction with the technical scheme of accompanying drawing to utility model:

The nk that the utility model proposed ± m subharmonic repetitive controller structured flowchart as shown in Figure 1, its transfer function is:

$G_{\mathrm{rc}}\left(s\right)=\frac{c\left(s\right)}{e\left(s\right)}=k_{\mathrm{rc}}\·\frac{1-e^{-\frac{2s{T}_o}{n}}}{1-2\cos \left(\frac{2\mathrm{\π}}{n}m\right)e^{-\frac{s{T}_o}{n}}{e}^{-\frac{2s{T}_o}{n}}}$

Wherein c (s) is the output variable of repetitive controller, and e (s) is the input variable of repetitive controller that is the departure amount of control system, k _RcFor repeating ride gain, s is Laplce (Laplace) variable of continuous time system, T _oBe the primitive period, T _o=2 π/ω _o=1/f _o, f _oBe fundamental frequency, ω _oBe the first-harmonic angular frequency, n, k and m are not less than zero integer and n ≠ 0, n＞m.Repeat the ride gain coefficient k by regulating _RcNumerical value, can change the convergence rate of system, k _RcBig more, the speed of system's convergence is fast more.Two time delay links among Fig. 1 are identical, and its delay time T all equals primitive period T _oN/one, long delay time path is made up of two above-mentioned delay links, so its total delay time is (2T _o/ n)＜T _o(when n＞2) therefore repeating ride gain k _RcUnder the identical situation, the response speed of this repetitive controller is more faster than general repetitive controller, and this is (the big advantage of subharmonic repetitive controller of nk ± m).

The transfer function of the repetitive controller that the utility model is shown in Figure 1 can be rewritten as follows:

$G_{\mathrm{rc}}\left(s\right)=\frac{c\left(s\right)}{e\left(s\right)}=k_{\mathrm{rc}}\·\frac{1-e^{-\frac{2s{T}_o}{n}}}{1-2\cos \left(\frac{2\mathrm{\π}}{n}m\right)e^{-\frac{{\mathrm{sT}}_o}{n}}+e^{-\frac{2s{T}_o}{n}}}=k_{\mathrm{rc}}\·\frac{e^{\frac{s{T}_o}{n}}-e^{-\frac{{\mathrm{sT}}_o}{n}}}{e^{\frac{{\mathrm{sT}}_o}{n}}+e^{-\frac{{\mathrm{sT}}_o}{n}}-2\cos \left(\frac{2\mathrm{\π}}{n}m\right)}$

$=k_{\mathrm{rc}}\·\frac{\sinh \left(\frac{{\mathrm{sT}}_o}{n}\right)}{\cosh \left(\frac{{\mathrm{sT}}_o}{n}\right)-\cos \left(\frac{2\mathrm{\π}}{n}m\right)}=k_{\mathrm{rc}}\·\frac{\frac{\mathrm{s\π}}{{\mathrm{n\ω}}_o}\·\underset{k=1}{\overset{\∞}{\mathrm{\Π}}}[1+\frac{s^2}{{\left(\frac{n}{2}k\right)}^2{\mathrm{\ω}}_o^2}]}{{\sin }^2\left(\frac{\mathrm{\π}}{n}m\right)\·\underset{k=-\∞}{\overset{\∞}{\mathrm{\Π}}}[1+\frac{s^2}{{(\mathrm{nk}+m)}^2{\mathrm{\ω}}_o^2}]}$

Following formula requires m ≠ 0; When m=0, the repetitive controller transfer function of eliminating nk ± m subharmonic can change into following form:

$G_{\mathrm{rc}}\left(s\right)=\frac{c\left(s\right)}{e\left(s\right)}=k_{\mathrm{rc}}\·\frac{1-e^{-\frac{2s{T}_o}{n}}}{1-2\cos \left(\frac{2\mathrm{\π}}{n}m\right)e^{-\frac{s{T}_o}{n}}+e^{-\frac{2s{T}_o}{n}}}{|}_{m=0}=k_{\mathrm{rc}}\·\frac{1-e^{-\frac{2s{T}_o}{n}}}{1-{2e}^{-\frac{{\mathrm{sT}}_o}{n}}+e^{-\frac{2s{T}_o}{n}}}$

$=k_{\mathrm{rc}}\·\frac{(1-e^{-\frac{{\mathrm{sT}}_o}{n}})(1+e^{-\frac{{\mathrm{sT}}_o}{n}})}{{(1-e^{-\frac{{\mathrm{sT}}_o}{n}})}^2}=k_{\mathrm{rc}}\·\frac{1+e^{-\frac{{\mathrm{sT}}_o}{n}}}{1-e^{-\frac{{\mathrm{sT}}_o}{n}}}=k_{\mathrm{rc}}\·\frac{e^{\frac{{\mathrm{sT}}_o}{2n}}+e^{-\frac{{\mathrm{sT}}_o}{2n}}}{e^{\frac{{\mathrm{sT}}_o}{2n}}-e^{-\frac{{\mathrm{sT}}_o}{2n}}}=k_{\mathrm{rc}}\·\frac{\cosh \left(\frac{{\mathrm{sT}}_o}{2n}\right)}{\sinh \left(\frac{{\mathrm{sT}}_o}{2n}\right)}$

$=k_{\mathrm{rc}}\·\frac{\underset{k=0}{\overset{\∞}{\mathrm{\Π}}}[1+\frac{s^2}{n^2{\left(\frac{2k+1}{2}\right)}^2{\mathrm{\ω}}_o^2}]}{\frac{\mathrm{s\π}}{n{\mathrm{\ω}}_o}\·\underset{k=1}{\overset{\∞}{\mathrm{\Π}}}[1+\frac{s^2}{n^2{k}^3{\mathrm{\ω}}_o^2}]}$

Comprehensive above-mentioned two formulas, the limit that can get repetitive controller shown in Figure 1 is the (ω of nk ± m) in frequency _oThe place, promptly pole frequency is m ω _o, (the ω of n ± m) _o, (the ω of 2n ± m) _o..., (the ω of in ± m) _o... (i=1 wherein, 2,3...), and be positioned at the midpoint frequency place of two adjacent extreme points zero point.Because this repetitive controller is the (ω of nk ± m) in frequency _oThe gain at place be infinitely great, therefore can thoroughly eliminate frequency among the departure e (s) and be (the ω of nk ± m) _oHarmonic component, thereby realize elimination fully or error free tracking to nk ± m subharmonic disturbance, so with this repetitive controller, the certain kinds harmonic wave repetitive controller that promptly the utility model proposes is called nk ± m subharmonic repetitive controller.In the middle of the practical application, can be at the demand of different occasions, give n and m with different numerical value, can realize error free tracking or Disturbance Rejection to specific nk ± m subharmonic.For example for the situation of three-phase inverter band three phase rectifier load, because its harmonic wave mainly concentrates on time (i.e. 5,7,11,13 grades) harmonics frequency component place, 6k ± 1, and often need follow the tracks of the first-harmonic reference signal, so only need make n=6 and m=1, just can realize to the error free tracking of first-harmonic reference signal with to the elimination fully of 6k ± 1 subharmonic; Situation for single-phase inverter band single-phase rectifier load, because its harmonic wave mainly concentrates on frequency component place, 4k ± 1 time (promptly 3,5,7,9 etc. odd), and often need follow the tracks of the first-harmonic reference signal, so only need make n=4 and m=1, just can realize to the error free tracking of first-harmonic reference signal with to the elimination fully of odd harmonic.

Repetitive controller is many in the middle of actual is realized and is used with digital form.The pairing Digital Implementation of repetitive controller shown in Figure 1 as shown in Figure 2, its transfer function is:

$G_{\mathrm{rc}}\left(z\right)=\frac{c\left(z\right)}{e\left(z\right)}=k_{\mathrm{rc}}\·\frac{1-z^{-2\frac{N}{n}}}{1-2\cos \left(\frac{2\mathrm{\π}}{n}m\right)z^{-\frac{N}{n}}+z^{-2\frac{N}{n}}}$

Wherein c (z) is the output variable of repetitive controller, and e (z) is the input variable of repetitive controller that is the departure amount of control system, k _RcFor repeating ride gain, z is the variable of the z conversion of discrete-time system, N=T _o/ T _sBe integer, T _oBe the primitive period, T _o=2 π/ω _o=1/f _o, f _oBe fundamental frequency, ω _oBe first-harmonic angular frequency, T _sBe the sampling period, n, k and m are not less than zero integer and n ≠ 0, n＞m.Two time delay links among Fig. 2 are identical, the internal storage location number that takies all is N/n, therefore its total internal storage location number is (2N/n)＜N (when n＞2), therefore the memory space that nk ± m subharmonic repetition of figures controller takies is wanted much less than general repetition of figures controller, and this is another big advantage of nk ± m subharmonic repetitive controller.

In actual applications, for improving the stability and the antijamming capability of control system, usually need be improved the nk among Fig. 1 or Fig. 2 ± m subharmonic repetitive controller, improved method is joining day delay damping gain coefficient K and low pass filter device Q (s) or Q (z) in repetitive controller, as shown in Figure 3 and Figure 4, wherein Fig. 4 is the Digital Implementation form of Fig. 3.The transfer function of improved nk shown in Figure 3 ± m subharmonic repetitive controller can be write as following form:

$G_{\mathrm{rc}}\left(s\right)=\frac{c\left(s\right)}{e\left(s\right)}=k_{\mathrm{rc}}\·\frac{1-K^2\·e^{-\frac{2s{T}_o}{n}}\·Q^2\left(s\right)}{1-2K\·\cos \left(\frac{2\mathrm{\π}}{n}m\right)e^{-\frac{{\mathrm{sT}}_o}{n}}\·Q\left(s\right)+K^2\·e^{-\frac{2s{T}_o}{n}}\·Q^2\left(s\right)}$

0＜K≤1 wherein.

The transfer function of improved nk shown in Figure 4 ± m subharmonic repetition of figures controller can be write as following form:

$G_{\mathrm{rc}}\left(z\right)=\frac{c\left(z\right)}{e\left(z\right)}=k_{\mathrm{rc}}\·\frac{1-K_2\·z^{-2\frac{N}{n}}\·Q^2\left(z\right)}{1-2K\·\cos \left(\frac{2\mathrm{\π}}{n}m\right)z^{-\frac{N}{n}}\·Q\left(z\right)+K^2\·z^{-2\frac{N}{n}}\·Q^2\left(z\right)}$

0＜K≤1 wherein.

Claims (3)

1. certain kinds harmonic wave repetitive controller, it is characterized in that comprising repetition ride gain module, the positive feedback gain module, the addition ring, two time delay modules that the subtraction ring is identical with two, wherein repeat the input of the output termination addition ring of ride gain module, the output of addition ring connects the positive input terminal of the first subtraction ring and the input of very first time Postponement module respectively, the output of very first time Postponement module connects the input of the second time delay module and the input of positive feedback gain module respectively, the output of the second time delay module connects the negative input end of the first subtraction ring and the negative input end of the second subtraction ring respectively, the positive input terminal of the output termination second subtraction ring of positive feedback gain module, the input of the output termination addition ring of the second subtraction ring.

2. a kind of certain kinds harmonic wave repetitive controller according to claim 1 is characterized in that described two identical time delay modules have the damping gain coefficient, and the output of described two identical time delay modules is connected in series low pass filter respectively.

3. a kind of certain kinds harmonic wave repetitive controller according to claim 1 and 2 is characterized in that described time delay module is an analog or digital time delay module.

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