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# Integrator for Less Overshoot

IP.com Disclosure Number: IPCOM000115525D
Original Publication Date: 1995-May-01
Included in the Prior Art Database: 2005-Mar-30
Document File: 2 page(s) / 39K

IBM

## Related People

Kimura, J: AUTHOR [+2]

## Abstract

Disclosed is an algorithm to reduce overshoot caused by an integrator for position or velocity control used for a hard disk drive.

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Integrator for Less Overshoot

Disclosed is an algorithm to reduce overshoot caused by an
integrator for position or velocity control used for a hard disk
drive.

A typical integrator algorithm is:
I(n+1) = I(n) + ( y(n) - target ) ........(1)
I(n)  :  an integrator value at time n
y(n)  :  position or velocity at time n
target:  target position or velocity

The equation (1) can be expressed as
I(n) = I(0) + ( y(n-1) - target ) + ( y(n-2) - target ) +...  +
( y(0) - target ) ..........(2)

If there is no external force like friction in a closed loop,
I(n) converges to zero.  If there is external force, I(n) converges
to a value that compensates the force.  This type of an integrator
causes overshoot as described bellow.  In the explanation friction is
assumed to be small enough.

Assuming that y(0)-target is minus and I(0) is zero, there is
y(m) that makes y(m)-target plus.  Otherwise I(n) does not converge
to zero adding only minus value results in minus.  That means
overshoot at y(m).

This new algorithm updates an integrator value as shown below:
I(n+1) = I(n) + ( y(n) - target ) + L ( ( y(n) - tagged ) -
( y(n-1) - target ) ) ............(3)
I(n)  :  an integrator value at time n
y(n)  :  position or velocity at time n
target:  target position or velocity
L :  constant value

The equation (3) can be expressed as:
I  (n) = I(0) + ( y(n-1) - target ) + (...