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# Digital Velocity From Two-Phase Optical Encoder

IP.com Disclosure Number: IPCOM000120850D
Original Publication Date: 1991-Jun-01
Included in the Prior Art Database: 2005-Apr-02
Document File: 3 page(s) / 98K

IBM

## Related People

Mery, HE: AUTHOR [+2]

## Abstract

An optical encoder can be used as a digital tachometer in the servo system of a disk or tape drive. This article discloses a new numerical technique which uses both phases of a 2-phase optical encoder to derive an improved digital velocity measurement over the sample period of just one of the phases. The traditional sample period for a single phase of the encoder, h, along with the offset in time between the two phases, h/4, is shown in the figure.

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Digital Velocity From Two-Phase Optical Encoder

An optical encoder can be used as a digital tachometer in
the servo system of a disk or tape drive.  This article discloses a
new numerical technique which uses both phases of a 2-phase optical
encoder to derive an improved digital velocity measurement over the
sample period of just one of the phases.  The traditional sample
period for a single phase of the encoder, h, along with the offset in
time between the two phases, h/4, is shown in the figure.

The new numerical technique is derived by using the
single-variable, second order, Taylor series to extrapolate backward
in time from the latest displacement, d(j), of the encoder.  Equation
1 relates phases A and B.  Equation 2 describes only phase A.
d(j - 1/4) - d(j) - (h/4)d'(j) + (h/42d''(j)/2 - (h/4)3d'''/6   (1)
d(j - 1) = d(j) - hd'(j) + h2d''(j)/2 - h3d'''/6 (2)
where h      = time interval between encoder pulses of the same phase
j      = integer representing discrete increments in time
d(j)   = displacement function at time j
d'(j)  = first derivative of displacement at time j
d''(j) = second derivative of displacement at time j
d'''   = third derivative of displacement

By multiplying Equation 1 by -16 and then adding Equation 2,
Equation 3 is derived.  Note that the second-derivative
(acceleration) terms, d''(j) disappear in Equation (3).
15d(j) - 16d(j - 1/4) + d(j-1) = 3hd'(j) - h3d'''/8 (3)

By dividing Equation 3 by three times the time interval, h, the
initial form of the precision digital velocity formula for the
2-phase encoder is derived; see Equation 4.

(Image Omitted)

The derivative of displacem...