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# Digital Integrator

IP.com Disclosure Number: IPCOM000102312D
Original Publication Date: 1990-Nov-01
Included in the Prior Art Database: 2005-Mar-17
Document File: 5 page(s) / 110K

IBM

## Related People

Kisaka, M: AUTHOR

## Abstract

Disclosed is an algorithm that enables a digital serial integrator in a VCM servo system in a hard disk file where only a position error signal is available. To eliminate error from a target value in the steady state, a digital integrator is used in a digital servo controller. In the past, the integrator used to be placed parallel to other controller terms (Fig. 1). This parallel integrator caused overshoot, so that in some cases, such as a velocity control, employing a parallel integrator is improper. However, a digital serial integrator can reduce overshoot, so it can be used in a velocity control. To enable a digital serial integrator, a new algorithm in velocity control mode is described. An algorithm of a parallel integrator is: I(n+1) = I(n) + error(n) .....

This text was extracted from an ASCII text file.
This is the abbreviated version, containing approximately 45% of the total text.

Digital Integrator

Disclosed is an algorithm that enables a digital serial
integrator in a VCM servo system in a hard disk file where only a
position error signal is available.  To eliminate error from a target
value in the steady state, a digital integrator is used in a digital
servo controller. In the past, the integrator used to be placed
parallel to other controller terms (Fig. 1).  This parallel
integrator caused overshoot, so that in some cases, such as a
velocity control, employing a parallel integrator is improper.
However, a digital serial integrator can reduce overshoot, so it can
be used in a velocity control.  To enable a digital serial
integrator, a new algorithm in velocity control mode is described.
An algorithm of a parallel integrator is:
I(n+1) = I(n) + error(n) ..... (1)
where
I(n) is integrator value at time n
'error' is
current value - target value  ..... (2)
and current value may be position or
velocity.

If I(0) is equal to zero, error(0) is negative, and I(n) is
equal to zero in the steady state, then error must become positive
for a certain period because from eq.(1), I(1) is negative and only
positive value of error(n) can make I(n) equal to zero in steady
state.  This means that overshoot is inevitable in this algorithm
(Fig. 2).  If input for the integrator is not error(n) but system
input U(n), then there is no restriction on error(n).  This means
that a digital serial integrator can reduce overshoot.

A block diagram of the system with a serial integrator is shown
in Fig. 3.  Though a serial integrator is actually in a controller,
it can be considered to be theoretically included in the VCM system
for designing a stable controller.  A stable controller in velocity
control mode can be obtained as follows:

A transfer function H(z) of a voice coil motor (VCM) from U(z)
to Y(z) at time (n) with a sampling time Ts and delay time (d) is:
A1 * (1/z) + A2 * (1/z)2 + B1
H(z) = 1/z * -----------------------------------
( 1 - 1/z )2
..... (3)
where
A1 : A*(1+2*Q-2*Q2)
A2 : A*Q2
A1 : A*(1-Q)2
Q  : d/Ts
A  : Ts2*c
...