CN102176115B - Specific-class harmonic repetitive controller and control method - Google Patents

Abstract

The invention discloses a specific-class harmonic repetitive controller and a control method. The controller comprises a repetitive control gain module, a positive feedback gain module, an addition ring, two subtraction rings and two time delay modules. In the method, the error-free tracking or elimination of nk+/-m harmonic is realized by combining a forward path, a positive feedback path, a negative feedback path and a negative feedforward path, specific parameters in the positive feedback gain module are determined according to the frequency order of the harmonic to be tracked or eliminated, and the error elimination speed is regulated by the repetitive control gain module. The specific-class harmonic repetitive controller and the control method have the advantages that: the error-free tracking or elimination of the nk+/-m harmonic can be realized, the error elimination speed is higher, fewer memory cells are required by digital realization, and a universal expression form is provided for a plurality of repetitive controllers; and the improved repetitive controller with a damping gain coefficient and a low-pass filter also can achieve improvements in stability and anti-jamming capability, and meet the requirements of actual application.

Description

A kind of certain kinds harmonic wave repetitive controller and control method

Technical field

The present invention proposes a kind of certain kinds harmonic wave repetitive controller and control method, 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 researchists 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 molds 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, and for example the three phase rectifier load concentrates on 6k ± 1 (k=1,2 for the harmonic pollution overwhelming majority that power-supply system caused;) 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 ...) subfrequency (being odd harmonic frequencies) locates.If can propose new repetitive controller only compensates to these frequencies; Through 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 storage space that takies of its Digital Implementation.Therefore be necessary still that the multiple control technology of counterweight does further research.

Summary of the invention

Technical matters: the objective of the invention is to propose a kind of certain kinds harmonic wave repetitive controller and control method; This repetitive controller can be followed the tracks of or eliminate any nk ± m rd harmonic signal fully; Time delay is much smaller than general repetitive controller, and it is far away from general repetitive controller that the speed of its tracking or harmonic carcellation signal is wanted, and the shared storage space of Digital Implementation still less; And can unify existing multiple repetitive controller, its cost performance will promote greatly.

Technical scheme:

The present invention adopts following technical scheme for realizing above-mentioned purpose:

A kind of certain kinds harmonic wave of the present invention repetitive controller; Comprise repetition ride gain module, positive feedback gain module, addition ring, two time delay modules that the subtraction ring is identical with two; Wherein repeat the input end 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 end of very first time Postponement module; The input end of the output termination second time delay module of very first time Postponement module and the input end 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 end of the output termination addition ring of the second subtraction ring.

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

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

A kind of control method of certain kinds harmonic wave repetitive controller is following:

Repeat the ride gain module: the input quantity of repetitive controller is obtained repetition ride gain module output quantity through the repetition ride gain, realize regulating the speed that the certain kinds harmonic wave was followed the tracks of or eliminated to said repetitive controller through regulating the repetition ride gain;

The addition ring: the output quantity addition that will repeat the ride gain module output quantity and the second subtraction ring obtains addition ring output quantity;

Very first time Postponement module: addition ring output quantity is postponed output;

The second time delay module: the addition ring output quantity that very first time Postponement module is postponed output postpones output again;

Positive feedback gain module: very first time Postponement module output quantity is obtained positive feedback gain module output quantity through the positive feedback gain; Parameter in the positive feedback gain module by the harmonic frequency number of times that will follow the tracks of or eliminate confirm, can realize following the tracks of or eliminating the certain kinds harmonic wave;

The first subtraction ring: the addition ring output quantity and the second time delay module output quantity are subtracted each other the output quantity that obtains repetitive controller.

The second subtraction ring: the output quantity of the positive feedback gain module output quantity and the second time delay module is subtracted each other back output;

Preferably, said time delay module is an analog or digital time delay module, and then said repetitive controller transport function is following:

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

Or

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

Wherein c () is the output quantity of repetitive controller, and e () is the input quantity 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, and s is Laplce (Laplace) variable of continuous 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.

Preferably, said time delay module is the simulated time Postponement module, the limit of controller is positioned at ± and (ω of nk ± m) _oThe frequency place is positioned at the midpoint frequency place of two adjacent extreme points zero point, and the repetitive controller transport function of then eliminating nk ± m subharmonic can change into following form:

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

$=k_{\mathrm{rc}}\·\frac{\sinh \left(\frac{s{T}_o}{n}\right)}{\cosh \left(\frac{s{T}_o}{n}\right)-\cos \left(\frac{2\mathrm{\π}}{n}m\right)}=k_{\mathrm{rc}}\·\frac{\frac{\mathrm{s\π}}{n{\mathrm{\ω}}_o}\·\underset{k=1}{\overset{\∞}{\mathrm{\Π}}}[1+\frac{s^2}{{\left(\frac{n}{2}k\right)}^2{\mathrm{\ω}}_0^2}]}{{\sin }^2\left(\frac{\mathrm{\π}}{n}m\right)\·\underset{k=-\∞}{\overset{\∞}{\mathrm{\Π}}}[1+\frac{s^2}{{(\mathrm{nk}+m)}^2{\mathrm{\ω}}_o^2}]}$

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

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

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

$=k_{\mathrm{rc}}\&CenterDot;\frac{\underset{k=0}{\overset{\&infin;}{\mathrm{\&Pi;}}}[1+\frac{s^2}{n^2{\left(\frac{2k+1}{2}\right)}^2{\mathrm{\&omega;}}_o^2}]}{\frac{\mathrm{s\&pi;}}{n{\mathrm{\&omega;}}_o}\&CenterDot;\underset{k=1}{\overset{\&infin;}{\mathrm{\&Pi;}}}[1+\frac{s^2}{n^2{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HSA00000425445800011.png,HSA00000425445800012.png"\; state="\{\{state\}\}">k</figure-callout>}}^2{\mathrm{\&omega;}}_o^2}]}$

Comprehensive above-mentioned two formulas can get certain kinds harmonic wave repetitive controller that the present invention proposes and comprise frequency and be (the ω of nk ± m) _oLimit, therefore also be called nk ± m subharmonic repetitive controller.

Preferably, said two identical time delay modules have damping gain coefficient K respectively, and the output terminal of said two identical time delay modules is connected in series low-pass filter Q () respectively and carries out filtering, and then its repetitive controller transport function is following:

$G_{\mathrm{rc}}\left(s\right)=\frac{c\left(s\right)}{e\left(s\right)}=k_{\mathrm{rc}}\&CenterDot;\frac{1-{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="HSA00000425445800011.png,HSA00000425445800012.png"\; state="\{\{state\}\}">K</figure-callout>}}^2\&CenterDot;e^{-\frac{2s{T}_o}{n}}\&CenterDot;Q^2\left(s\right)}{1-2K\&CenterDot;\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)e^{-\frac{s{T}_o}{n}}\&CenterDot;Q\left(s\right)+{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="HSA00000425445800011.png,HSA00000425445800012.png"\; state="\{\{state\}\}">K</figure-callout>}}^2\&CenterDot;e^{-\frac{2s{T}_o}{n}}\&CenterDot;Q^2\left(s\right)}$

Or

$G_{\mathrm{rc}}\left(z\right)=\frac{c\left(z\right)}{e\left(z\right)}=k_{\mathrm{rc}}\&CenterDot;\frac{1-{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="HSA00000425445800011.png,HSA00000425445800012.png"\; state="\{\{state\}\}">K</figure-callout>}}^2\&CenterDot;z^{-2\frac{N}{n}}\&CenterDot;Q^2\left(z\right)}{1-2K\&CenterDot;\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)z^{-\frac{N}{n}}\&CenterDot;Q\left(z\right)+{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="HSA00000425445800011.png,HSA00000425445800012.png"\; state="\{\{state\}\}">K</figure-callout>}}^2\&CenterDot;z^{-2\frac{N}{n}}\&CenterDot;Q^2\left(z\right)}$

0＜K≤1 wherein.

Beneficial effect:

1, nk ± m subharmonic repetitive controller proposed by the invention carries out error free tracking or disturbance elimination to nk ± m rd harmonic signal specially, 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 to 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 storage unit 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 like 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 nk of the present invention ± special case of m subharmonic repetitive controller when n=6 and m=1; The patent documentation " Repetitive Controller to Compensate for odd Harmonics " that Jesus Leyva Ramos etc. is applied for; US 2007/0067051A1; Mar.22, applied odd harmonic repetitive controller is the nk of the present invention ± 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 2007/0055721A1; Mar.8, applied conventional repetitive controller is the nk of the present invention ± 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 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 present invention 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 invention:

Nk proposed by the invention ± m subharmonic repetitive controller structured flowchart is as shown in Figure 1, and its transport function is:

$G_{\mathrm{rc}}\left(s\right)=\frac{c\left(s\right)}{e\left(s\right)}=k_{\mathrm{rc}}\&CenterDot;\frac{1-e^{-\frac{2s{T}_o}{n}}}{1-2\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)e^{-\frac{s{T}_o}{n}}+e^{-\frac{2s{T}_o}{n}}}$

Wherein c (s) is the output quantity of repetitive controller, and e (s) is the input quantity 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.Through regulating repetition ride gain coefficient k _RcNumerical value, can change the speed of convergence of system, k _RcBig more, system's convergent speed 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 much faster than general repetitive controller, and this is (the big advantage of subharmonic repetitive controller of nk ± m).

The transport function of the repetitive controller that the present invention is shown in Figure 1 can be rewritten as follows:

$G_{\mathrm{rc}}\left(s\right)=\frac{c\left(s\right)}{e\left(s\right)}=k_{\mathrm{rc}}\&CenterDot;\frac{1-e^{-\frac{2s{T}_o}{n}}}{1-2\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)e^{-\frac{s{T}_o}{n}}+e^{-\frac{2s{T}_o}{n}}}=k_{\mathrm{rc}}\&CenterDot;\frac{e^{\frac{s{T}_o}{n}}-e^{-\frac{s{T}_o}{n}}}{e^{\frac{s{T}_o}{n}}+e^{-\frac{s{T}_o}{n}}-2\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)}$

$=k_{\mathrm{rc}}\&CenterDot;\frac{\sinh \left(\frac{s{T}_o}{n}\right)}{\cosh \left(\frac{s{T}_o}{n}\right)-\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)}=k_{\mathrm{rc}}\&CenterDot;\frac{\frac{\mathrm{s\&pi;}}{n{\mathrm{\&omega;}}_o}\&CenterDot;\underset{k=1}{\overset{\&infin;}{\mathrm{\&Pi;}}}[1+\frac{s^2}{{\left(\frac{n}{2}k\right)}^2{\mathrm{\&omega;}}_0^2}]}{{\sin }^2\left(\frac{\mathrm{\&pi;}}{n}m\right)\&CenterDot;\underset{k=-\&infin;}{\overset{\&infin;}{\mathrm{\&Pi;}}}[1+\frac{s^2}{{(\mathrm{nk}+m)}^2{\mathrm{\&omega;}}_o^2}]}$

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

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

$=k_{\mathrm{rc}}\&CenterDot;\frac{(1-e^{-\frac{s{T}_o}{n}})(1+e^{-\frac{s{T}_o}{n}})}{{(1-e^{-\frac{s{T}_o}{n}})}^2}=k_{\mathrm{rc}}\&CenterDot;\frac{1+e^{-\frac{s{T}_o}{n}}}{1-e^{-\frac{s{T}_o}{n}}}=k_{\mathrm{rc}}\&CenterDot;\frac{e^{\frac{s{T}_o}{2n}}+e^{-\frac{s{T}_o}{2n}}}{e^{\frac{s{T}_o}{2n}}-e^{-\frac{s{T}_o}{2n}}}=k_{\mathrm{rc}}\&CenterDot;\frac{\cosh \left(\frac{s{T}_o}{2n}\right)}{\sinh \left(\frac{s{T}_o}{2n}\right)}$

$=k_{\mathrm{rc}}\&CenterDot;\frac{\underset{k=0}{\overset{\&infin;}{\mathrm{\&Pi;}}}[1+\frac{s^2}{n^2{\left(\frac{2k+1}{2}\right)}^2{\mathrm{\&omega;}}_o^2}]}{\frac{\mathrm{s\&pi;}}{n{\mathrm{\&omega;}}_o}\&CenterDot;\underset{k=1}{\overset{\&infin;}{\mathrm{\&Pi;}}}[1+\frac{s^2}{n^2{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HSA00000425445800011.png,HSA00000425445800012.png"\; state="\{\{state\}\}">k</figure-callout>}}^2{\mathrm{\&omega;}}_o^2}]}$

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, i.e. the certain kinds harmonic wave repetitive controller of the present invention proposition is called nk ± m subharmonic repetitive controller.In the middle of the practical application, can give n and m with different numerical, can realize error free tracking or Disturbance Rejection specific nk ± m subharmonic to the demand of different occasions.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. strange inferior); 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 realizes and is able to using with digital form.The pairing Digital Implementation of repetitive controller shown in Figure 1 is as shown in Figure 2, and its transport function is:

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

Wherein c (z) is the output quantity of repetitive controller, and e (z) is the input quantity 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 storage 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 practical application; For improving the stability and the antijamming capability of control system; Usually need improve 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, and like Fig. 3 and shown in Figure 4, wherein Fig. 4 is the Digital Implementation form of Fig. 3.The transport function of improved nk shown in Figure 3 ± m subharmonic repetitive controller can be write as following form:

$G_{\mathrm{rc}}\left(s\right)=\frac{c\left(s\right)}{e\left(s\right)}=k_{\mathrm{rc}}\&CenterDot;\frac{1-{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="HSA00000425445800011.png,HSA00000425445800012.png"\; state="\{\{state\}\}">K</figure-callout>}}^2\&CenterDot;e^{-\frac{2s{T}_o}{n}}\&CenterDot;Q^2\left(s\right)}{1-2K\&CenterDot;\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)e^{-\frac{s{T}_o}{n}}\&CenterDot;Q\left(s\right)+{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="HSA00000425445800011.png,HSA00000425445800012.png"\; state="\{\{state\}\}">K</figure-callout>}}^2\&CenterDot;e^{-\frac{2s{T}_o}{n}}\&CenterDot;Q^2\left(s\right)}$

0＜K≤1 wherein.

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

$G_{\mathrm{rc}}\left(z\right)=\frac{c\left(z\right)}{e\left(z\right)}=k_{\mathrm{rc}}\&CenterDot;\frac{1-{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="HSA00000425445800011.png,HSA00000425445800012.png"\; state="\{\{state\}\}">K</figure-callout>}}^2\&CenterDot;z^{-2\frac{N}{n}}\&CenterDot;Q^2\left(z\right)}{1-2K\&CenterDot;\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)z^{-\frac{N}{n}}\&CenterDot;Q\left(z\right)+{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="HSA00000425445800011.png,HSA00000425445800012.png"\; state="\{\{state\}\}">K</figure-callout>}}^2\&CenterDot;z^{-2\frac{N}{n}}\&CenterDot;Q^2\left(z\right)}$

0＜K≤1 wherein.

Claims (7)

1. certain kinds harmonic wave repetitive controller; It is characterized in that comprising repetition ride gain module, positive feedback gain module, addition ring, two time delay modules that the subtraction ring is identical with two; Wherein repeat the input end of the output termination addition ring of ride gain module; The output terminal of addition ring connects the positive input terminal of the first subtraction ring and the input end of very first time Postponement module respectively; The output terminal of very first time Postponement module connects the input end of the second time delay module and the input end of positive feedback gain module respectively; The output terminal 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 end 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 said two identical time delay modules have the damping gain coefficient, and the output terminal of said 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 said time delay module is an analog or digital time delay module.

4. control method based on the described a kind of certain kinds harmonic wave repetitive controller of claim 1 is characterized in that said method is following:

Repeat the ride gain module: the input quantity of repetitive controller is obtained repetition ride gain module output quantity through the repetition ride gain, realize regulating the speed that the certain kinds harmonic wave was followed the tracks of or eliminated to said repetitive controller through regulating the repetition ride gain;

The addition ring: the output quantity addition that will repeat the ride gain module output quantity and the second subtraction ring obtains addition ring output quantity;

Very first time Postponement module: addition ring output quantity is postponed output;

The second time delay module: the addition ring output quantity that very first time Postponement module is postponed output postpones output again;

Positive feedback gain module: very first time Postponement module output quantity is obtained positive feedback gain module output quantity through the positive feedback gain; Parameter in the positive feedback gain module by the harmonic frequency number of times that will follow the tracks of or eliminate confirm, can realize following the tracks of or eliminating the certain kinds harmonic wave;

The first subtraction ring: the addition ring output quantity and the second time delay module output quantity are subtracted each other the output quantity that obtains repetitive controller;

The second subtraction ring: the output quantity of the positive feedback gain module output quantity and the second time delay module is subtracted each other back output.

5. the control method of a kind of certain kinds harmonic wave repetitive controller according to claim 4 is characterized in that said time delay module is an analog or digital time delay module, and then said repetitive controller transport function is following:

$G_{\mathrm{rc}}\left(s\right)=\frac{c\left(s\right)}{e\left(s\right)}=k_{\mathrm{rc}}\&CenterDot;\frac{1-e^{-\frac{2s{T}_o}{n}}}{1-2\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)e^{-\frac{s{T}_o}{n}}+e^{-\frac{2s{T}_o}{n}}}$

Or

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

Wherein c () is the output quantity of repetitive controller, and e () is the input quantity 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, and s is the Laplce Laplace variable of continuous 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.

6. the control method of a kind of certain kinds harmonic wave repetitive controller according to claim 5 is characterized in that adopting the simulated time Postponement module, and the limit of controller is positioned at ± (the ω of nk ± m) _oThe frequency place is positioned at the midpoint frequency place of two adjacent extreme points zero point, and the repetitive controller transport function of eliminating nk ± m subharmonic can change into following form:

$G_{\mathrm{rc}}\left(s\right)=\frac{c\left(s\right)}{e\left(s\right)}=k_{\mathrm{rc}}\&CenterDot;\frac{1-e^{-\frac{2s{T}_o}{n}}}{1-2\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)e^{-\frac{s{T}_o}{n}}+e^{-\frac{2s{T}_o}{n}}}=k_{\mathrm{rc}}\&CenterDot;\frac{e^{\frac{s{T}_o}{n}}-e^{-\frac{s{T}_o}{n}}}{e^{\frac{s{T}_o}{n}}+e^{-\frac{s{T}_o}{n}}-2\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)}$

$=k_{\mathrm{rc}}\&CenterDot;\frac{\sinh \left(\frac{s{T}_o}{n}\right)}{\cosh \left(\frac{s{T}_o}{n}\right)-\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)}=k_{\mathrm{rc}}\&CenterDot;\frac{\frac{\mathrm{s\&pi;}}{n{\mathrm{\&omega;}}_o}\&CenterDot;\underset{k=1}{\overset{\&infin;}{\mathrm{\&Pi;}}}[1+\frac{s^2}{{\left(\frac{n}{2}k\right)}^2{\mathrm{\&omega;}}_0^2}]}{{\sin }^2\left(\frac{\mathrm{\&pi;}}{n}m\right)\&CenterDot;\underset{k=-\&infin;}{\overset{\&infin;}{\mathrm{\&Pi;}}}[1+\frac{s^2}{{(\mathrm{nk}+m)}^2{\mathrm{\&omega;}}_o^2}]}$

Following formula requires m ≠ 0; When m=0, the repetitive controller transport function of eliminating nk ± m subharmonic can turn to following form:

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

$=k_{\mathrm{rc}}\&CenterDot;\frac{(1-e^{-\frac{s{T}_o}{n}})(1+e^{-\frac{s{T}_o}{n}})}{{(1-e^{-\frac{s{T}_o}{n}})}^2}=k_{\mathrm{rc}}\&CenterDot;\frac{1+e^{-\frac{s{T}_o}{n}}}{1-e^{-\frac{s{T}_o}{n}}}=k_{\mathrm{rc}}\&CenterDot;\frac{e^{\frac{s{T}_o}{2n}}+e^{-\frac{s{T}_o}{2n}}}{e^{\frac{s{T}_o}{2n}}-e^{-\frac{s{T}_o}{2n}}}=k_{\mathrm{rc}}\&CenterDot;\frac{\cosh \left(\frac{s{T}_o}{2n}\right)}{\sinh \left(\frac{s{T}_o}{2n}\right)}$

$=k_{\mathrm{rc}}\&CenterDot;\frac{\underset{k=0}{\overset{\&infin;}{\mathrm{\&Pi;}}}[1+\frac{s^2}{n^2{\left(\frac{2k+1}{2}\right)}^2{\mathrm{\&omega;}}_o^2}]}{\frac{\mathrm{s\&pi;}}{n{\mathrm{\&omega;}}_o}\&CenterDot;\underset{k=1}{\overset{\&infin;}{\mathrm{\&Pi;}}}[1+\frac{s^2}{n^2{k}^2{\mathrm{\&omega;}}_o^2}]}$

7. the control method of a kind of certain kinds harmonic wave repetitive controller according to claim 5; It is characterized in that two identical time delay modules have damping gain coefficient K respectively described in the practical application; The output terminal of said two identical time delay modules is connected in series low-pass filter Q () respectively and carries out filtering, and then its repetitive controller transport function is following:

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

Or

$G_{\mathrm{rc}}\left(z\right)=\frac{c\left(z\right)}{e\left(z\right)}=k_{\mathrm{rc}}\&CenterDot;\frac{1-K^2\&CenterDot;z^{-2\frac{N}{n}}\&CenterDot;Q^2\left(z\right)}{1-2K\&CenterDot;\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)z^{-\frac{N}{n}}\&CenterDot;Q\left(z\right)+K^2\&CenterDot;z^{-2\frac{N}{n}}\&CenterDot;Q^2\left(z\right)},$

0＜K≤1 wherein.

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