TW202232057A - Method for calibrating magnetic linear position sensor including moving a magnet along a straight line, and capable of increasing the sensing distance of a magnetic angle-type sensing element - Google Patents
Method for calibrating magnetic linear position sensor including moving a magnet along a straight line, and capable of increasing the sensing distance of a magnetic angle-type sensing element Download PDFInfo
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本發明是有關於一種位置感應器的校正方法,特別是指一種磁性線性位置感應器的校正方法。The present invention relates to a calibration method of a position sensor, in particular to a calibration method of a magnetic linear position sensor.
參見圖1所示,現有獲得一磁性角度型感應元件S(例如AMR、Hall、TMR….)的偵測距離的一種方式是令磁性角度型感應元件S感應沿一直線行程P1運動之磁鐵M的磁場,使產生與磁鐵M之一移動距離相關的一正弦波訊號和一餘弦波訊號並輸出至一訊號處理器10,該訊號處理器10將該正弦波訊號和餘弦波訊號數位化為如圖1所示之由複數正弦訊號值Usin形成的數位化正弦波訊號sin以及如圖1示之由複數餘弦訊號值Ucos形成的數位化餘弦波訊號cos,並對該等正弦訊號值Usin和該等餘弦訊號值Ucos進行反正切函數(ARCTAN)的二階導數(atan2)運算,即atan2(Usin/Ucos),可求得複數曲率值,且該等曲率值形成如圖1所示之一曲率曲線C1,該曲率曲線C1中的一有效線段L1上的每一點的曲率值對應一偵測距離,且因為該有效線段L1的曲率值範圍只有從0.2~1.2,代表磁性角度型感應元件S的一有效偵測距離並不長,例如圖1所示只有6mm,因此,假設需要偵測的長度是6mm的6倍,則至少需要並列6顆磁性角度型感應元件S同時進行偵測。Referring to FIG. 1 , one way to obtain the detection distance of a magnetic angle sensing element S (such as AMR, Hall, TMR....) is to make the magnetic angle sensing element S sense the magnet M moving along a linear stroke P1. The magnetic field generates a sine wave signal and a cosine wave signal related to a moving distance of the magnet M and outputs it to a
因此,本發明之目的,即在提供一種磁性線性位置感應器的校正方法,其能增長該磁性線性位置感應器中之磁性角度型感應元件的偵測距離,進而減少磁性角度型感應元件的使用數量。Therefore, the purpose of the present invention is to provide a calibration method for a magnetic linear position sensor, which can increase the detection distance of the magnetic angle sensing element in the magnetic linear position sensor, thereby reducing the use of the magnetic angle sensing element quantity.
於是,本發明一種磁性線性位置感應器的校正方法,該磁性線性位置感應器設於一直線行程的一側以偵測沿該直線行程往復移動的一磁鐵的位置,該磁性線性位置感應器包含一磁性角度型感應元件及一處理單元;該校正方法包括:(A)令該磁鐵沿該直線行程移動,同時,一訊號處理裝置令該處理單元以一取樣頻率要求該磁性角度型感應元件回傳當下產生的一正弦訊號和一餘弦訊號直到該磁鐵走完該直線行程;(B)該處理單元將該磁性角度型感應元件持續傳來的該等正弦訊號和該等餘弦訊號數位化並輸出至該訊號處理裝置;(C)該訊號處理裝置根據該直線行程的長度和該取樣頻率,獲得該磁鐵在該直線行程中每一個取樣點的位置與數位化的該等正弦訊號值和該等餘弦訊號值的對應關係,且該訊號處理裝置將該等正弦訊號值減去一第一預設值,並將該等餘弦訊號值減去一第二預設值;(D)該訊號處理裝置對減去該第一預設值的該等正弦訊號值和減去該第二預設值的該等餘弦訊號值進行反正切函數的二階導數(atan2)運算,即atan2(減去該第一預設值的該正弦訊號值/減去該第二預設值的該餘弦訊號值),而獲得相對應的複數曲率值,且該等曲率值構成一曲率曲線;(E)該訊號處理裝置以該曲率曲線中的一有效線段做為該磁性角度型感應元件的一特性曲線,並根據該特性曲線決定該磁性角度型感應元件的一有效偵測距離以及相對應的一曲率值範圍;(F)該訊號處理裝置根據該有效偵測距離和該曲率值範圍,藉由曲線擬合和線性迴歸分析決定一擬合該特性曲線的多項式方程式 的m值以及β 0~β m的值,其中i=1,2,3…n,y i代表該磁性角度型感應元件與該磁鐵的一相對距離,xi代表該曲率值,β 0~β m是該磁性角度型感應元件的係數;及(G)該訊號處理裝置將該多項式方程式寫入該處理單元中做為該磁性角度型感應元件的一數學模型。 Therefore, the present invention provides a method for calibrating a magnetic linear position sensor. The magnetic linear position sensor is arranged on one side of a linear travel to detect the position of a magnet that reciprocates along the linear travel. The magnetic linear position sensor includes a Magnetic angle type induction element and a processing unit; the calibration method includes: (A) making the magnet move along the linear stroke, and at the same time, a signal processing device makes the processing unit request the magnetic angle type induction element to return with a sampling frequency A sine signal and a cosine signal are generated at the moment until the magnet completes the linear travel; (B) the processing unit digitizes the sine signals and the cosine signals continuously transmitted from the magnetic angle sensing element and outputs them to the signal processing device; (C) the signal processing device obtains the digitized sine signal values and the cosines of the position of each sampling point of the magnet in the linear stroke according to the length of the linear stroke and the sampling frequency The corresponding relationship between the signal values, and the signal processing device subtracts a first preset value from the sine signal values, and subtracts a second preset value from the cosine signal values; (D) the signal processing device pairs The sine signal values minus the first preset value and the cosine signal values minus the second preset value are subjected to the second derivative (atan2) operation of the arctangent function, namely atan2 (minus the first preset value) setting the sine signal value of the value/subtracting the cosine signal value of the second preset value) to obtain a corresponding complex curvature value, and the curvature values form a curvature curve; (E) the signal processing device uses An effective line segment in the curvature curve is used as a characteristic curve of the magnetic angle sensing element, and an effective detection distance and a corresponding curvature value range of the magnetic angle sensing element are determined according to the characteristic curve; (F ) The signal processing device determines a polynomial equation for fitting the characteristic curve by curve fitting and linear regression analysis according to the effective detection distance and the curvature value range The m value and the value of β 0 ~β m , where i=1,2,3...n, y i represents a relative distance between the magnetic angle induction element and the magnet, xi represents the curvature value, β 0 ~β m is the coefficient of the magnetic angle type sensing element; and (G) the signal processing device writes the polynomial equation into the processing unit as a mathematical model of the magnetic angle type sensing element.
在本發明的一些實施態樣中,該第一預設值是該等正弦訊號值中的最大值與最小值之合的二之一;該第二預設值是該等餘弦訊號值中的最大值與最小值之合的二之一。In some implementation aspects of the present invention, the first preset value is one of the sum of the maximum value and the minimum value among the sine signal values; the second preset value is one of the cosine signal values Either the maximum value or the minimum value.
在本發明的一些實施態樣中,m為6。In some embodiments of the present invention, m is 6.
在本發明的一些實施態樣中,該磁性角度型感應元件具有兩個相差45°的磁阻電橋,其中一磁阻電橋感應該磁鐵的磁場並產生一正弦波訊號,其中另一磁阻電橋感應該磁鐵的磁場並產生一與該正弦波訊號相位差45°的餘弦波訊號。In some embodiments of the present invention, the magnetic angle sensing element has two magnetoresistive bridges with a difference of 45°, wherein one magnetoresistive bridge induces the magnetic field of the magnet and generates a sine wave signal, and the other magnetoresistive bridge induces a sine wave signal. The resistive bridge senses the magnetic field of the magnet and generates a cosine wave signal with a phase difference of 45° from the sine wave signal.
本發明之功效在於:在校正程序中,藉由將該磁性角度型感應元件感應獲得的該等正弦訊號值和該等餘弦訊號適當平移後再對其進行反正切函數(ARCTAN)的二階導數(atan2)運算,能使該磁性角度型感應元件的有效偵測距離增長,而達到減少磁性角度型感應元件的使用數量,並使該磁性線性位置感應器2的偵測距離變長的功效與目的。The effect of the present invention is: in the calibration procedure, the sine signal values and the cosine signals obtained by the induction of the magnetic angle-type sensing element are appropriately shifted and then the second derivative of the arc tangent function (ARCTAN) is performed on them ( atan2) operation can increase the effective detection distance of the magnetic angle sensing element, thereby reducing the number of magnetic angle sensing elements used and making the detection distance of the magnetic
在本發明被詳細描述之前,應當注意在以下的說明內容中,類似的元件是以相同的編號來表示。Before the present invention is described in detail, it should be noted that in the following description, similar elements are designated by the same reference numerals.
參閱圖2所示,是本發明磁性線性位置感應器的校正方法的一實施例的主要流程,且如圖3所示,要被校正的該磁性線性位置感應器2設於一直線行程P2的一側,以偵測沿該直線行程P2往復移動的一磁鐵M的位置,例如該磁鐵M是設於一氣缸1內的一活塞,且該直線行程P2是該活塞在該氣缸1內往復運動的活塞行程。該磁性線性位置感應器2主要包括一磁性角度型感應元件21及一處理單元22,例如一微處理器或一微控制器(MCU)。該磁性角度型感應元件21設於該直線行程P2的一側,例如該氣缸1的外壁面,以感應該磁鐵M的磁場並輸出類比的一正弦訊號和一餘弦訊號;該處理單元22與該磁性角度型感應元件21電連接,以接收該正弦訊號和該餘弦訊號。Referring to FIG. 2, it is the main flow of an embodiment of the calibration method of the magnetic linear position sensor of the present invention, and as shown in FIG. side, to detect the position of a magnet M reciprocating along the linear stroke P2, for example, the magnet M is a piston set in a
而由於每一磁性線性位置感應器2中的該磁性角度型感應元件21的特性都不相同,因此在該磁性線性位置感應器2出廠之前,該磁性線性位置感應器2需先經過一校正程序以找到符合該磁性角度型感應元件21特性的該數學模型;且如圖4所示,該磁性角度型感應元件21(例如AMR、Hall、TMR….)內具有兩個相差45°(即夾45°角)的磁阻電橋(Bridge)211、212;因此,在本實施例的校正方法中,如圖2的步驟S1所示,首先,使磁鐵M從該直線行程P2之遠離該磁性角度型感應元件21的一端朝該磁性角度型感應元件21移動,並通過該磁性角度型感應元件21後朝遠離該磁性角度型感應元件21方向移動至該直線行程P2的另一端,在此過程中,這兩個磁阻電橋211、212會持續感應磁鐵M的磁場而產生相位差45°的一正弦波訊號SIN和一餘弦波訊號COS。Since the characteristics of the magnetic angle-
同時,一訊號處理裝置3,例如但不限於一個人電腦,令該處理單元22以一取樣頻率(例如10次/秒)要求該磁性角度型感應元件21回傳當下產生的該正弦訊號(即該正弦波訊號SIN的某一點的值,類比電壓值)和該餘弦訊號(即該餘弦波訊號COS的某一點的值,類比電壓值),直到該磁鐵M走完該直線行程P2,藉此,該磁性角度型感應元件21每秒將回傳10筆正弦訊號和10筆餘弦訊號給該處理單元22,然後,如圖2的步驟S2,該處理單元22將收到的該等正弦訊號和該等餘弦訊號數位化後輸出至該訊號處理裝置3。該等正弦訊號值Usin和該等餘弦訊號值Ucos的數位化數值可對照圖5左邊縱軸所標示的數值。At the same time, a
因此,該訊號處理裝置3可根據該磁鐵M的一移動距離(即該直線行程P2的長度)以及該取樣頻率,得知該磁鐵M在該直線行程P2中每一個取樣點的位置與數位化的該等正弦訊號值Usin和該等餘弦訊號值Ucos的對應關係,例如圖5所示之由數位化的該等正弦訊號值Usin構成的數位化正弦波訊號sin,以及如圖5所示之由數位化之該等餘弦訊號值Ucos構成的數位化餘弦波訊號cos。Therefore, the
然後,如圖2的步驟S3,該訊號處理裝置3將該等正弦訊號值Usin減去一第一預設值成為Usin’,如圖6所示,相當於將該數位化正弦波訊號sin向下平移(offset)該第一預設值而成為一平移後數位化正弦波訊號sin’,並且該訊號處理裝置3將該等餘弦訊號值Ucos減去一第二預設值成為Ucos’,如圖6所示,相當於將該數位化餘弦波訊號cos向下平移(offset)該第二預設值而成為一平移後數位化餘弦波訊號cos’;且在本實施例中,該第一預設值是該等正弦訊號值Usin中的最大值與最小值之合的二之一,但不以此為限;該第二預設值是該等餘弦訊號值Ucos中的最大值與最小值之合的二之一,但不以此為限。Then, in step S3 of FIG. 2 , the
接著,如圖2的步驟S4,該訊號處理裝置3對減去該第一預設值的該等正弦訊號值Usin’(即平移後數位化正弦波訊號sin’)和減去該第二預設值的該等餘弦訊號值Ucos’(即平移後數位化餘弦波訊號cos’)進行反正切函數(ARCTAN)的二階導數(atan2)運算,即atan2(Usin’/Ucos’),而獲得相對應的複數曲率值,該等曲率值可對照圖7右邊縱軸所標示的數值,而該等曲率值構成如圖7所示的一曲率曲線C2,且該曲率曲線C2的一有效線段L2代表該磁性角度型感應元件21的一特性曲線,並決定該磁性角度型感應元件21的一有效偵測距離以及相對應的一曲率值範圍,例如當曲率值為-1時,可以從該有效線段L2(該特性曲線)得知距離值為-2mm,對照圖3來看,其可以代表磁鐵M是位在該磁性角度型感應元件21的左側且與該磁性角度型感應元件21相距2mm的位置;同理,當曲率值為2時,可以得知距離值為2.6mm,這代表磁鐵M位是在該磁性角度型感應元件21的右側且與該磁性角度型感應元件21相距約2.6mm的位置;且如圖7所示,在本實施例中,由於該曲率值範圍可達到-π~π,因此其相對應的該有效偵測距離可以增長至14mm,由此可知,本實施例透過上述將該磁性角度型感應元件21感應獲得的訊號值平移後,再進行反正切函數(ARCTAN)的二階導數(atan2)運算,能將該磁性角度型感應元件21的偵測距離(14mm)增長至習知技術(6mm)的兩倍以上,因此,假設需要偵測的長度是6mm的6倍,則只需要並列3顆磁性角度型感應元件21同時進行偵測,而能減少磁性角度型感應元件21的使用數量。Next, as shown in step S4 in FIG. 2 , the
然後,如圖2的步驟S6,該訊號處理裝置3以該有效線段L2(即該有效偵測距離與相對應的該曲率值範圍)做為該磁性角度型感應元件21的該特性曲線,而決定該磁性角度型感應元件21的該有效偵測距離以及相對應的該曲率值範圍,且該訊號處理裝置3根據該有效偵測距離和該曲率值範圍,藉由曲線擬合和線性迴歸分析決定一擬合該特性曲線的多項式方程式
的m值以及β
0~β
m的值,其中i=1,2,3…n,y
i代表該磁性角度型感應元件21與該磁鐵M的一相對距離,xi代表該曲率值,β
0~β
m是該磁性角度型感應元件21的係數。
Then, as shown in step S6 of FIG. 2 , the
具體而言,如圖8(A)所示,假設該有效線段L2(該特性曲線)是由對應100個位置(即100個磁鐵M與該磁性角度型感應元件21的距離值,亦即該有效偵測距離) 的100筆曲率值(該曲率值範圍)構成,則在本實施例中,該訊號處理裝置3會先將該有效線段L2的X軸與Y軸的數據置換,使X軸改為呈現該等曲率值而Y軸改為呈現相對應的該等距離值,而使該有效線段L2變成置換後有效線段L2’,如圖8(B)所示。然後,該訊號處理裝置3決定最適合該置換後有效線段L2’的多項式方程式
,例如採用多項式擬合(Polynomial Fitting),以一元m次多項式回歸方程式
來擬合該置換後有效線段L2’,並以如下所示的矩陣解多項式回歸方程式:
Specifically, as shown in FIG. 8(A) , it is assumed that the effective line segment L2 (the characteristic curve) is defined by the distance values corresponding to 100 positions (that is, the distances between 100 magnets M and the magnetic angle
其中y
1~y
n代表該100個距離值,x
1~x
n代表該100個曲率值,β
0~β
m是係數,且由於每個該磁性角度型感應元件21的特性不同,因此其係數β
0~β
m亦不相同,所以藉由上述矩陣運算,可以找出該磁性角度型感應元件21的該等係數β
0~β
m的值,以及決定要採用之擬合該置換後有效線段L2’的多項式方程式。例如,本實施例可以應用METLAB提供的polyfit指令找出上述一元m次多項式方程式的最佳係數(參數)以及最符合該置換後有效線段L2’的多項式方程式。
Wherein y 1 ~y n represent the 100 distance values, x 1 ~x n represent the 100 curvature values, β 0 ~β m are coefficients, and since the characteristics of each of the magnetic
舉例來說,藉由polyfit指令將上述已知的該100筆曲率值(x
1~x
n)與相對應的該100筆距離值(y
1~y
n)分別代入1元1次~1元8次共8個多項式方程式中,將求得這8個多項式方程式各自的最佳係數及其與該置換後有效線段L2’的擬合結果,且從這8個多項式方程式中發現一元6次多項式方程式擬合該置換後有效線段L2’的結果最佳(即一元6次多項式方程式最貼近而最能代表該置換後有效線段L2’)時,該訊號處理裝置3則採用具有最佳擬合結果的一元6次多項式方程式,該方程式例如為y = 2.4431x
6- 8.2418x
5+ 15.967x
4- 10.349x
3+ 7.6091x
2+ 1.567x + 1.0009,其中y代表磁鐵M與該磁性角度型感應元件21的一相對距離(即上述的距離值),x代表曲率值。然後,如圖1的步驟S7,該訊號處理裝置3將該一元6次多項式方程式及該曲率值範圍寫入該處理單元22中做為該磁性角度型感應元件21的該特性曲線的一數學模型,即完成校正程序。
For example, use the polyfit command to substitute the 100 known curvature values (x 1 ~x n ) and the corresponding 100 distance values (y 1 ~y n ) into 1
藉此,當該磁性線性位置感應器2實際應用於例如圖3所示的氣缸1以偵測氣缸1內的活塞(即磁鐵M)位置時,該處理單元22接收到該磁性角度型感應元件21傳來之類比的該正弦訊號和該餘弦訊號時,該處理單元22將該正弦訊號和該餘弦訊號數位化為一正弦訊號值和一餘弦訊號值,且將該正弦訊號值減去該第一預設值以及將該餘弦訊號值減去該第二預設值後,對減去該第一預設值的該正弦訊訊號值和減去該第二預設值的該餘弦訊號值進行反正切函數(ARCTAN)的二階導數(atan2)運算,即atan2(減去該第一預設值的該正弦訊號值/減去該第二預設值的該餘弦訊號值),以獲得一曲率值;然後,該處理單元22判斷該曲率值是在該曲率值範圍內時,將該曲率值代入該數學模型中,即可藉由該一元6次多項式方程式求得一距離值,該距離值即代表該磁性角度型感應元件21與該磁鐵M的該相對距離;然後,該處理單元22可以直接輸出該距離值供後端應用,或者將該距離值轉成相對應的一類比訊號,例如類比電壓(比如1~5V其中的一電壓值)或類比電流(比如4~20mA其中的一電流值)再輸出給後端應用。Therefore, when the magnetic
綜上所述,上述實施例在校正程序中,藉由將該磁性角度型感應元件21感應獲得的該等正弦訊號值和該等餘弦訊號適當平移後再對其進行反正切函數(ARCTAN)的二階導數(atan2)運算,能使該磁性角度型感應元件21的有效偵測距離增長,而達到減少磁性角度型感應元件21的使用數量,並使該磁性線性位置感應器2的偵測距離變長的功效與目的;並且,藉由校正程序,使該磁性線性位置感應器2的該處理單元22中的該數學模型擬合該磁性角度型感應元件21的特性曲線,並決定該磁性角度型感應元件21的一有效偵測距離及相對應的一曲率值範圍;藉此,該處理單元22只需將該磁性角度型感應元件21傳來的該正弦訊號和該餘弦訊號數位化後,對減去第一預設值的該正弦訊號值和減去第二預設值的該餘弦訊號值進行atan2(減去該第一預設值的該正弦訊號值/減去該第二預設值的該餘弦訊號值)運算,獲得對應的一曲率值後,將該曲率值輸入計算距離的該數學模型,即可透過容易計算的一元m次多項式方程式快速地求得該磁性角度型感應元件21與該磁鐵M的一相對距離。To sum up, in the calibration procedure of the above embodiment, the sine signal values and the cosine signals obtained by the induction of the magnetic
惟以上所述者,僅為本發明之實施例而已,當不能以此限定本發明實施之範圍,凡是依本發明申請專利範圍及專利說明書內容所作之簡單的等效變化與修飾,皆仍屬本發明專利涵蓋之範圍內。However, the above are only examples of the present invention, and should not limit the scope of the present invention. Any simple equivalent changes and modifications made according to the scope of the application for patent of the present invention and the content of the patent specification are still within the scope of the present invention. within the scope of the invention patent.
1:氣缸
2:磁性線性位置感應器
21:磁性角度型感應元件
211、212:磁阻電橋
22:處理單元
3:訊號處理裝置
M:磁鐵(活塞)
P2:直線行程
SIN:正弦波訊號
COS:餘弦波訊號
sin:數位化正弦波訊號
cos:數位化餘弦波訊號
sin’:平移後數位化正弦波訊號
cos’:平移後數位化餘弦波訊號
C2:曲率曲線
L2:有效線段
L2’:置換後有效線段
S1~S7:步驟
1: Cylinder
2: Magnetic Linear Position Sensor
21: Magnetic
本發明之其他的特徵及功效,將於參照圖式的實施方式中清楚地顯示,其中: 圖1說明現有獲得磁性角度型感應元件的偵測距離的一種方法; 圖2是本發明磁性線性位置感應器的校正方法的一實施例的流程圖; 圖3說明本實施例所要校正的磁性線性位置感應器包含的元件及其設置方式; 圖4是本實施例的磁性線性位置感應器包含的磁性角度型感應元件的細部電路示意圖; 圖5是經由本實施例的處理單元數位化後的數位化正弦波訊號sin和數位化餘弦波訊號cos的波形示意圖; 圖6說明將圖5的數位化正弦波訊號sin和數位化餘弦波訊號cos分別向下平移一第一預設值和一第二預設值; 圖7說明對圖6所示的正弦波訊號sin’和餘弦波訊號cos’進行反正切函數(ARCTAN)的二階導數(atan2)運算以獲得相對應的複數曲率值,該等曲率值構成一曲率曲線C2;及 圖8說明將圖7所示的曲率曲線C2之有效線段L2的X軸數據與Y軸數據置換,而變成置換後有效線段L2’。 Other features and effects of the present invention will be clearly shown in the embodiments with reference to the drawings, wherein: FIG. 1 illustrates a method for obtaining the detection distance of the magnetic angle sensing element in the prior art; 2 is a flowchart of an embodiment of a calibration method for a magnetic linear position sensor of the present invention; FIG. 3 illustrates the components included in the magnetic linear position sensor to be calibrated in this embodiment and its arrangement; FIG. 4 is a detailed circuit schematic diagram of the magnetic angle-type sensing element included in the magnetic linear position sensor of the present embodiment; 5 is a schematic diagram of waveforms of the digitized sine wave signal sin and the digitized cosine wave signal cos after being digitized by the processing unit of the present embodiment; 6 illustrates that the digitized sine wave signal sin and the digitized cosine wave signal cos of FIG. 5 are shifted downward by a first predetermined value and a second predetermined value, respectively; 7 illustrates the operation of the second derivative (atan2) of the arc tangent function (ARCTAN) on the sine wave signal sin' and the cosine wave signal cos' shown in FIG. 6 to obtain corresponding complex curvature values, which constitute a curvature curve C2; and Fig. 8 illustrates that the X-axis data and the Y-axis data of the effective line segment L2 of the curvature curve C2 shown in Fig. 7 are replaced to become the post-replacement effective line segment L2'.
S1~S7:步驟 S1~S7: Steps
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