級(jí)聯(lián)自適應(yīng)陷波器設(shè)計(jì)及不同步脈沖計(jì)數(shù)補(bǔ)償*

劉桂雄　萬(wàn)勇　黃堅(jiān)　潘云飛

(1.華南理工大學(xué) 機(jī)械與汽車工程學(xué)院, 廣東 廣州 510640; 2.廣州能源檢測(cè)研究院, 廣東 廣州 510170)

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級(jí)聯(lián)自適應(yīng)陷波器設(shè)計(jì)及不同步脈沖計(jì)數(shù)補(bǔ)償*

劉桂雄1萬(wàn)勇2黃堅(jiān)1潘云飛2

(1.華南理工大學(xué) 機(jī)械與汽車工程學(xué)院, 廣東 廣州 510640; 2.廣州能源檢測(cè)研究院, 廣東 廣州 510170)

摘要:為減小計(jì)數(shù)誤差及實(shí)現(xiàn)多路不同步異頻脈沖信號(hào)的高精度測(cè)量,設(shè)計(jì)了一款可實(shí)時(shí)估計(jì)周期脈沖信號(hào)相位的級(jí)聯(lián)自適應(yīng)陷波器(CANF).首先在前端固定一自適應(yīng)因子為0的Liu型自適應(yīng)陷波器(LANF),然后將LANF的輸出作為Mojiri型自適應(yīng)陷波器(MANF)的輸入,再利用MANF的估計(jì)頻率實(shí)時(shí)調(diào)整LANF,最后在流量計(jì)標(biāo)準(zhǔn)裝置中實(shí)現(xiàn)CANF的相位實(shí)時(shí)估計(jì),并對(duì)兩路不同步脈沖信號(hào)進(jìn)行精度補(bǔ)償.仿真實(shí)驗(yàn)結(jié)果表明CANF的計(jì)數(shù)誤差小于±0.047個(gè)脈沖,工程應(yīng)用實(shí)驗(yàn)結(jié)果表明CANF的計(jì)數(shù)誤差小于±0.045個(gè)脈沖,說(shuō)明了文中通過(guò)實(shí)時(shí)計(jì)算信號(hào)相位進(jìn)行計(jì)數(shù)補(bǔ)償?shù)姆椒苡行岣呙}沖計(jì)數(shù)檢定精度和多路并行檢定的實(shí)用性.

關(guān)鍵詞：陷波器;級(jí)聯(lián);自適應(yīng)算法;不同步脈沖;誤差補(bǔ)償

將測(cè)量量轉(zhuǎn)化為計(jì)數(shù)脈沖是工業(yè)生產(chǎn)、實(shí)時(shí)監(jiān)測(cè)、自動(dòng)化控制等領(lǐng)域廣泛使用的技術(shù)手段,但一次檢定多個(gè)頻率、相位不一致的脈沖信號(hào)時(shí),難以應(yīng)用同步計(jì)數(shù)法來(lái)消除計(jì)數(shù)誤差.文獻(xiàn)[1- 2]針對(duì)異頻不同步信號(hào)提出了一種相位補(bǔ)償方法,但只適合測(cè)量?jī)陕凡煌叫盘?hào)的計(jì)數(shù)值,并且需要使用高頻信號(hào)發(fā)生器HP8664A產(chǎn)生輔助測(cè)量信號(hào).使用時(shí)間數(shù)字轉(zhuǎn)換器(TDC)也是提高脈沖計(jì)數(shù)精度的有效方法,但脈沖計(jì)數(shù)測(cè)量對(duì)象通常是低頻脈沖信號(hào),對(duì)時(shí)間精度要求不高(微秒級(jí))[3- 6];TDC應(yīng)用于微秒級(jí)時(shí)間間隔測(cè)量時(shí)存在電路規(guī)模大、動(dòng)態(tài)范圍有限及易受干擾脈沖影響等問(wèn)題.由于周期脈沖信號(hào)可通過(guò)傅里葉級(jí)數(shù)分解為不同頻率正弦信號(hào)的線性疊加,濾除周期信號(hào)3次諧波及以上分量,就可以在獲取同頻基波信號(hào)的同時(shí)濾除隨機(jī)干擾.筆者在前期研究的流量標(biāo)準(zhǔn)裝置中嵌入基于陷波濾波器的脈沖補(bǔ)償算法,計(jì)數(shù)精度提高了0.06個(gè)[7],而自適應(yīng)陷波濾波器(ANF)[8]可自動(dòng)使其陷波頻率跟隨輸入信號(hào)頻率變化、抑制噪聲,并提取信號(hào)幅值、頻率、相位.

為減小計(jì)數(shù)誤差,有效提高計(jì)數(shù)精度,文中在通用數(shù)據(jù)采集卡基礎(chǔ)上,應(yīng)用ANF技術(shù),設(shè)計(jì)了一款可實(shí)時(shí)估計(jì)周期脈沖信號(hào)相位的級(jí)聯(lián)自適應(yīng)陷波器(CANF),并提出了一種多路不同步脈沖計(jì)數(shù)補(bǔ)償方法.

1CANF設(shè)計(jì)

Regalia[9]在局部平均方法、自適應(yīng)律基礎(chǔ)上設(shè)計(jì)了第一類型ANF,但其受正弦信號(hào)幅值、頻率耦合的影響,頻率估計(jì)暫態(tài)響應(yīng)速度受幅值大小的影響明顯.Liu等[10]根據(jù)緩慢積分流形原理設(shè)計(jì)了一種收斂速度幾乎不受幅值影響的全局收斂歸一化ANF(LANF),但LANF僅能處理單正弦輸入信號(hào),不適合測(cè)試計(jì)量領(lǐng)域的周期脈沖信號(hào).Mojiri等[11- 12]采用局部平均方法、Lasalle不變集理論設(shè)計(jì)了一種固定自適應(yīng)增益為γ的ANF(MANF);MANF能很好地處理受諧波干擾的正弦輸入信號(hào),近年來(lái)獲得了廣泛的工程應(yīng)用[13- 16],但均未討論輸入為周期方波的情況.為探討MANF處理周期脈沖信號(hào)的性能,設(shè)周期脈沖幅值為A、初相位為φ、角頻率為ω,則根據(jù)傅里葉級(jí)數(shù)展開(kāi)式可得到信號(hào)在任意t時(shí)刻的測(cè)量值f:

(1)

(2)

(3)

對(duì)于周期輸入信號(hào),動(dòng)態(tài)系統(tǒng)(2)、(3)具有唯一的周期軌道Γ1:

Γ1=(x1,x2,θ)=

若不考慮式(3)的自適應(yīng)率,則式(2)對(duì)應(yīng)的傳遞函數(shù)為

(4)

(5)

由Γ2可以看出,x4與輸入基波信號(hào)同頻、同相.按緩慢積分流形原理設(shè)置γ=0,則LANF為

(6)

式(6)實(shí)際上為一共振器,如果采用級(jí)聯(lián)形式固定θ于MANF頻率估計(jì)值,則對(duì)于頻率為θ的周期脈沖信號(hào),動(dòng)態(tài)系統(tǒng)(4)、(5)可濾除該信號(hào)的3次諧波及以上分量.將x3作為MANF的輸入,可以解決在奇次諧波疊加干擾下MANF狀態(tài)變量x1、x2偏離周期軌道Γ1及收斂速度慢等問(wèn)題,圖1為級(jí)聯(lián)自適應(yīng)陷波器CANF的原理框圖.

圖1　CANF的原理框圖

(7)

圖2　脈沖計(jì)數(shù)補(bǔ)償原理圖

2仿真實(shí)驗(yàn)及工程應(yīng)用實(shí)驗(yàn)

2.1仿真實(shí)驗(yàn)

對(duì)MANF和CANF分別輸入相同的脈沖信號(hào):幅值A(chǔ)=10 V、頻率f=10 Hz、初相φ0=0 rad,設(shè)置ξ=0.7,γ=1,角頻率預(yù)估初值θ0=100 rad/s,則MANF和CANF狀態(tài)變量x1、x2的穩(wěn)態(tài)響應(yīng)曲線、角頻率估計(jì)曲線分別如圖3、4所示.

從圖3(a)可以看出,在奇次諧波疊加干擾下,x1和x2偏離軌道Γ1,算法很難根據(jù)x1和x2估計(jì)相位.從圖3(b)可知,在第25秒處，角頻率估計(jì)值仍在偏離真實(shí)值4.5 rad/s處震蕩,收斂時(shí)間較長(zhǎng),說(shuō)明MANF不能很好地處理周期脈沖輸入信號(hào).從圖4(a)可知,對(duì)于周期脈沖信號(hào)輸入,x1和x2的正弦度好,與預(yù)定周期軌道Γ1相符.從圖4(b)可以看出,角頻率估計(jì)值θ在第3秒處進(jìn)入真實(shí)值附近小幅震蕩.圖3、4說(shuō)明,對(duì)于同頻周期脈沖輸入信號(hào),相同參數(shù)的CANF較MANF大大縮短了收斂時(shí)間,狀態(tài)變量x1和x2更加接近其預(yù)定周期軌道,并在很大程度上提高了頻率估計(jì)的準(zhǔn)確度,其根本原因在于CANF前置的H2(s)濾除了大部分諧波信號(hào).

圖3　MANF的狀態(tài)變量穩(wěn)態(tài)曲線和角頻率估計(jì)曲線

Fig.3Stability curves of status variables and estimated angular frequency curve of MANF

2.2計(jì)數(shù)補(bǔ)償效果實(shí)驗(yàn)

圖4　CANF的狀態(tài)變量穩(wěn)態(tài)曲線和角頻率估計(jì)曲線

Fig.4Stability curves of status variables and estimated angular frequency curve of CANF

表1為對(duì)3路輸入脈沖信號(hào)進(jìn)行計(jì)數(shù)補(bǔ)償?shù)膶?shí)驗(yàn)數(shù)據(jù),測(cè)量時(shí)長(zhǎng)分別為1.0、2.5、5.0 s.可以看出,上升沿檢測(cè)法計(jì)算所得脈沖個(gè)數(shù)在很多情況下均存在±1的計(jì)數(shù)誤差,但經(jīng)過(guò)CANF實(shí)時(shí)估計(jì)相位進(jìn)行計(jì)數(shù)補(bǔ)償后,計(jì)數(shù)誤差小于±0.047個(gè)脈沖.

圖5為CANF狀態(tài)變量x3、x4的80 Hz脈沖響應(yīng)曲線,由于單通道實(shí)際采樣頻率僅為2.5 kHz,80 Hz輸入信號(hào)造成了狀態(tài)變量的正弦度較差,但實(shí)驗(yàn)曲線的幅值、頻率及相位均符合其穩(wěn)態(tài)周期軌道Γ2,故根據(jù)x3、x4計(jì)算的補(bǔ)償脈沖計(jì)數(shù)值具有較高的精度.

2.3工程應(yīng)用實(shí)驗(yàn)

在廣州能源檢測(cè)研究院DN20雙臺(tái)位流量計(jì)標(biāo)準(zhǔn)裝置上進(jìn)行工程應(yīng)用實(shí)驗(yàn).圖6為雙臺(tái)位流量計(jì)標(biāo)準(zhǔn)裝置機(jī)理圖、實(shí)物圖.在流量計(jì)校準(zhǔn)過(guò)程中,流量波動(dòng)導(dǎo)致脈沖信號(hào)頻率在某一范圍內(nèi)波動(dòng),不能以“頻率×?xí)r間”方式獲得脈沖計(jì)數(shù)值.圖7為補(bǔ)償算法效果驗(yàn)證示意圖,實(shí)驗(yàn)中標(biāo)準(zhǔn)流量計(jì)獲得原始脈沖信號(hào),輸出至偶數(shù)分頻器(分頻比為100),并通過(guò)研華工控機(jī)610L上計(jì)數(shù)裝置對(duì)分頻前、后信號(hào)與換向信號(hào)進(jìn)行上升沿計(jì)數(shù)(換向信號(hào)整周期截取),采用阿爾泰PCI8602型數(shù)據(jù)采集卡采集分頻后信號(hào)進(jìn)行脈沖計(jì)數(shù)補(bǔ)償.在2.5、5.0、10.0 m3/h流量下計(jì)數(shù)精度補(bǔ)償算法效果驗(yàn)證實(shí)驗(yàn)結(jié)果見(jiàn)表2.從表中可以看出,在不同流量下,上升沿檢測(cè)法計(jì)算所得脈沖個(gè)數(shù)存在±1的計(jì)數(shù)誤差,經(jīng)補(bǔ)償后計(jì)數(shù)誤差小于±0.045個(gè)脈沖,極大地提升了計(jì)數(shù)精度.

表1　在采樣頻率10 kHz下的計(jì)數(shù)精度補(bǔ)償實(shí)驗(yàn)結(jié)果

圖5　CANF狀態(tài)變量的80 Hz脈沖響應(yīng)曲線

圖6　雙臺(tái)位流量計(jì)標(biāo)準(zhǔn)裝置的機(jī)理圖和實(shí)物圖

Fig.6Mechanism and photo of two-station flowmeter calibration equipment

圖7　計(jì)數(shù)精度補(bǔ)償算法效果驗(yàn)證示意圖

Fig.7Schematic diagram of effect validation for counting precision compensation algorithm

表2計(jì)數(shù)精度補(bǔ)償算法效果驗(yàn)證實(shí)驗(yàn)結(jié)果

Table 2Experimental results of effect validation for counting precision compensation algorithm

流速/(m3·h)分頻前脈沖計(jì)數(shù)分頻后脈沖計(jì)數(shù)計(jì)數(shù)誤差真值不補(bǔ)償補(bǔ)償后不補(bǔ)償補(bǔ)償后2.55.010.020052200.52200200.516-0.52-0.00420152201.52202201.4880.48-0.03220169201.69201201.670-0.69-0.02020149201.49202201.5010.510.01120164201.64202202.6850.360.04520345203.45204203.4660.550.01620252202.52203202.5540.480.03420456204.56204204.572-0.560.01220460204.60205204.5870.40-0.013

3結(jié)論

文中根據(jù)緩慢積分流形原理設(shè)計(jì)了一款級(jí)聯(lián)自適應(yīng)陷波器,并將其應(yīng)用于多路不同步脈沖計(jì)數(shù)補(bǔ)償.仿真與實(shí)驗(yàn)結(jié)果表明:①該級(jí)聯(lián)自適應(yīng)陷波器的諧波干擾抑制能力好,可限制無(wú)限次奇次諧波疊加引起的干擾,很好地解決了LANF僅能處理單正弦輸入信號(hào)、MANF不能處理周期脈沖信號(hào)的問(wèn)題;②該級(jí)聯(lián)陷波器的頻率、相位估計(jì)準(zhǔn)確性在3組不同步計(jì)數(shù)補(bǔ)償實(shí)驗(yàn)中的計(jì)數(shù)誤差小于±0.047個(gè)脈沖;③在雙臺(tái)位流量計(jì)標(biāo)準(zhǔn)裝置上實(shí)現(xiàn)的工程應(yīng)用實(shí)驗(yàn)中的計(jì)數(shù)誤差小于±0.045個(gè)脈沖.這種通過(guò)實(shí)時(shí)計(jì)算信號(hào)相位進(jìn)行計(jì)數(shù)補(bǔ)償?shù)姆椒苡行У靥岣呙}沖計(jì)數(shù)檢定精度和多路并行檢定的實(shí)用性.

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收稿日期:2015- 10- 08

*基金項(xiàng)目:國(guó)家重大科學(xué)儀器設(shè)備開(kāi)發(fā)專項(xiàng)(2013YQ230575);廣州市技監(jiān)局科技計(jì)劃項(xiàng)目(2015KJ35)

Foundation item:Supported by the National Important Scientific Instrument Exploring Foundation of China(2013YQ230575)

作者簡(jiǎn)介:劉桂雄(1968-),男,教授,博士生導(dǎo)師,主要從事先進(jìn)傳感與儀器研究.E-mail:megxliu@scut.edu.cn

文章編號(hào):1000- 565X(2016)05- 0084- 06

中圖分類號(hào)：TH- 3

doi：10.3969/j.issn.1000-565X.2016.05.013

Design of Cascade-Connection Adaptive Notch Filter and Counting Compensation of Asynchronous Pulses

LIUGui-xiong1WANYong2HUANGJian1PANYun-fei2

(1.School of Mechanical and Automotive Engineering,South China University of Technology,Guangzhou 510640,Guangdong,China;2.Guangzhou Institute of Energy Detection,Guangzhou 510170,Guangdong,China)

Abstract:In order to reduce counting error and implement high-accuracy measurement of multi-channel asynchronous impulse signals with different frequencies,a cascade-connection adaptive notch filter(CANF) for real-time phase estimation is proposed.In CANF,firstly,an ANF designed by Liu(LANF) with an adaptive factor of 0 is set in the front of ANF,and the output of LANF is used as the input of an ANF designed by Mojiri(MANF).Secondly, the estimated frequency of MANF is used to adjust the frequency of LANF in real time.Then,CANF is applied to a multi-station flowmeter calibration equipment and is used to calculate the real-time phase of two channels of asynchronous impulse signal.Finally,simulation and practical application of CANF are carried out,with the corresponding counting errors being less than ±0.047 and ±0.045,respectively,which means that the counting error compensation via real-time phase calculation effectively improves the counting accuracy of asynchronous pulses and the practicability of multi-channel parallel calibration.

Key words:notch filters;cascade connections;adaptive algorithms;asynchronous pulse;error compensation