SU1686698A1 - Method of displacement-to-digital conversion - Google Patents

Abstract

The invention relates to automation and computing and can be used to connect analog information sources with a digital computing device. In order to improve accuracy by compensating for higher harmonic components errors and simplifying by decreasing. computational operations, in a method of converting movement into a code, based on converting movement into sine-cosine electric signals, measuring the amplitude and phase of these signals, determining the coefficients of the discrete Fourier transform of the correction signal as a function of phase values at each period of the sine-cosine signals, generating correction codes in the form of a trigonometric series and their summation with the corresponding phase values, choose normalized as a corrective the sine signal, and the coefficients of the trigonometric series of correction codes are determined by the corresponding formulas. 1 il. SL

Description

The invention relates to automation and computing and can be used to connect analog information sources with a digital computing device.

The aim of the invention is to improve the accuracy by compensating for the errors of higher harmonic components and simplifying the method by reducing computational operations.

The drawing shows a block diagram of a device for implementing the method.

The device contains a sine-cosine sensor (ACS) 1, a block 2 that converts sine-cosine signals into a phase code,

computing unit 3 and analog-to-digital converter (ADC) 4.

The method for converting movement to code is as follows.

ACS 1 converts the displacement into sine-cosine signals Kc, the normalized values of which Us and Uc can be represented as follows:

Us t sin D8; (1)

Jo

Uc jp Ac, (2)

Uo

Och

oo

about

O

about

00

Where

As bso + asi sin p + bsi costp + + 32 + 02 cos + az sin +

+ Exodus 3 + a4 sin Aip + b4 cos (3) Ac bco + aci sin p + bci cozy +

+32 sin 2 (p + t) + b2COS 2fy + 77) +

+ az sin 3 (# + TJ) + bscos3fy + TJ) +

+ a4sln4 (y + 2) + b4COs4 (p + TJ): (4)

p is the real value of the spatial phase of the ACS signals proportional to the displacement;

Uo is the nominal value of the amplitude of the first harmonic of the ACS signals;

As, Ac is the relative magnitude of the signal distortion Us, Uc, respectively;

bso, asi, bsi, aci, bci, a2, ... a4, b2 .... b4 are the amplitudes of the harmonic components of the distortion.

Here the most significant higher spatial harmonics (up to the fourth inclusive) of the ACS signals are taken into account. In addition, it was assumed that the distortion of the waveform of the ACS by these harmonics is the same.

Then, the measured value V of the spatial phase p is determined from the measured amplitude values of the ACS signals.

V p + Ay arctg -, (5)

where A p is the conversion error due to the presence of distortions of the ACS signals.

In this case, the magnitude of the error, taking into account expressions (1) - (5) after the appropriate transformations, can be in the first approximation as follows;

 2 bs1 - Эс1 + (32 - D2 - 2ЬСО) X

x sin p + (LP + 82 + 2bso) cos p + + (asi-bci) sin + (bsl + aci) xx cos + (32 + 34 + 02 f) sin + + (b2 + b4 - E2 - 34) cos 3ip + 2az sin 4un- + 2Bh cos 4 p (a4 - b4) sin 5y + (a4 + + b4) cos. (6)

Then, in the function V, the Fourier analysis is performed on the correction signal Us ($ from the output of the A / D converter 4, which in the function according to expressions (1), (3), (5), and (6)) can be represented as follows:

Os (t / fl {2bso - b2 - 32 + (4 + 3asi +

+ bci) (bsi + ari) cosi / J + 4 (2bco + 2a2 - a / j - b4) sin 2 + + (2ba - 2bso + 34 - S) cos) + + (bd + 2a3-asi) sin3i / + (2b3-bsi - aci) cos 3l / J f (2a4 - 32 -b2) sin + (2b4 - 32 b2) cos 4 -2az sin 5 -2Bzzo8 5ty + (b4-34) Sin Sch - (34 + b4 ). (7)

As a result of performing a discrete Fourier transform (DFT) of a sequence of functions n. Us ($, the coefficients of the DFT are calculated from the evenly distributed over the period of samples)

A D US (V to) sin I r / v;

n, 0 „n-1

B | rT 2n 0 (V 0 cos I Vk, where V

.0

2YAK

n

(eight)

(9)

(YU)

I-26; n 12.

Then a correction code is formed in the form of a trigonometric series and summed with the corresponding phase values if ()

p V + 2 (A2 + A4 - 2B4 + ZAB -2Be) sln V + (B2 + 2A4 + 84 + + 2Ae + ZVe) cos V + (Az + As) sin 2ty + + (Su + Bs) cos 2 + (A4 + Ae + 2Be) xx sin 3V + (B4 - 2Ae + Be) cos 3V4 + As sin 4V + 85 cos 4V + Ae sin 5V + + Be cos 5V. (11)

The validity of the expression obtained can be justified as follows. The found DFT coefficients are expressed according to the expression (7)

A2 (2HCO + 232 - 34 - b4); Az (bc1 + 2az-a51);

A4 - (2z4 - 32 - b): az.

A5 - 1

2

Ab (b4-34);

B2 {2b2 - 2bso + 34 - b4);

B3 (2b3-bsl-aci);

B4 (2b4 + 32-b2);

50

B5

Be - (a4 + b4).

As a result of solving this system of linear equations, the expressions of the unknowns bso.bco.bsi + 3d, bci - asi, a2, ... 34, b2 .... b4 are determined through the known values of the DFT coefficients. The obtained expressions are substituted into the formula for intra-step error A pb, taking into account the expression (6)

Duev A Jbs1 -Es1

(12)

Transition from full error; internal step is necessary to exclude from consideration the large-period error that cannot be eliminated by this method.

Substituting expression (12) in the formula for calculating the value of the phase with compensated intra-step error, having the form

R". Y -, allows to get the expression you are looking for.

(eleven).

The calculation of the DFT coefficients is repeated for each period of the ACS signals, thereby performing the process of adaptive error correction as the component components of the ACS signal distortion vary from period to period.

Presented in the drawing, the device for implementing the method works as follows.

The ACS generates at its outputs signals of the form (1). (2), which with the help of block 2 (made, for example, in the form of successively connected phase splitters, gated comparators and decoder) are converted into the ip code according to (5), which arrives to computing unit 3 according to a polling signal generated cyclically at the first control output. When the output code of the block reaches 2 values determined according to (10), the computing unit 3 with a signal at its second control output triggers an ADC 4 (built, for example, on a K572PV1 chip), which forms the next readout of the signal Us ($. Transferred to the computational block 3. At the end of the passage of the next full period (when moving forward or backward) computing unit 3 calculates the new values of the DFT coefficients according to expressions (8) and (9). These new values are used when passing the next period for calculating techniques, are corrected desired value r according to expression (11) is performed by the on-demand or cyclically.

The end of the passage of the next full period of the ACS signals is determined by the step change in code 1 / from its maximum value to the minimum (or vice versa).

A single-chip microcomputer of the type PKM1816BE48 is used as the computing unit 3.

The proposed solution is effective when using in the accurate reading channel a multi-dimensional displacement transducer into a code with a multiperiod ACS (for example, a raster photoelectric type), since in it the signal distortions change little from period to period, therefore, the values of the DFT coefficients obtained in the previous the period is also valid for the subsequent period where they are used for correction.

Claims (1)

Invention Formula A method of converting movement into a code, based on converting an object's movement into sine-cosine electrical signals, measuring the amplitude of sine-cosine signals at discrete spatial positions of the object, determining the phase values of sine-cosine signals at the same discrete spatial positions, determining sine AI and cosine Bt coefficients of the discrete Fourier transform of the correcting normalized signal as a function of phase values for each period of sine cosine sig the formation of correction codes in the form of a trigonometric series and their summation with the corresponding phase values of sine-cosine signals, characterized in that, in order to improve the accuracy and simplification of the method, the sinus AJ and cosine B are chosen as the correcting ) The coefficients of a trigonometric series of correction codes are determined by the formulas A I 2 (A2 + A4 - 2B4 + ZAE - 2 Be), 2 (Az + A B); AZ 2 (A4 + A6 + 2B6); A 2As; As 2A6; Bi 2 (82 + 2 А4-В4 + 2А6 + ЗВе); 82 2 (Thu + Be); Burr 2 (B4 - 2Ab - Be): B4 2B5, Bs 2Be, where i 26 are the harmonic numbers of the correction signal; j 1, ..., 5 - harmonic numbers of a trigonometric number and correction codes