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# Connecting Method Between Different Sampling Systems

IP.com Disclosure Number: IPCOM000100096D
Original Publication Date: 1990-Mar-01
Included in the Prior Art Database: 2005-Mar-15
Document File: 3 page(s) / 79K

IBM

## Related People

Kisaka, M: AUTHOR

## Abstract

Disclosed is an algorithm to connect servo systems with different sampling rates. To get a faster access in a digital servo system, there is a method in which the sampling rate of the system is twice as fast in a velocity-control phase than in a track-following phase. To obtain a smooth transition from the velocity-control phase to the track-following phase, a new control algorithm is described.

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Connecting Method Between Different Sampling Systems

Disclosed is an algorithm to connect servo systems with
different sampling rates.  To get a faster access in a digital servo
system, there is a method in which the sampling rate of the system is
twice as fast in a velocity-control phase than in a track-following
phase.  To obtain a smooth transition from the velocity-control phase
to the track-following phase, a new control algorithm is described.

In the figure, a sampling time changes at t=n.  The sampling
rate before t=n is twice as fast and the sampled time is represented
by k.

An equation of motion of a voice coil motor (VCM) at time (n)
with a sampling time Ts and a delay time (d) is
Y(n+1) = 2*Y(n) - Y(n-1) + A1*U(n-1) + A2*U(n-2)
+ B1*U(n)
(1)
where
Y(n)   :  position at time n
A1     :  A*(1+2*Q-2*Q2)
A2     :  A*Q2
B1     :  A*(1-Q)2
Q      :  d/Ts
A      :  Ts2*c
c      :  constant (determined by hardware)
An equation for the controller of the above system at
t=n is
U(n) = K1*Y(n) + K2*Y(n-1) + K3*U(n-1) + K4*U(n-2)
+ K5*I(n)
I(n+1) = I(n) + Y(n)
(2)
where
K1 .. K5 :  constant
I(n)     :  digital integrator

As U(n-1), U(n-2) do not exist, U(n) and also U(n+1) cannot be
obtained from Eq. (2).  That caused improper transition and longer
settling time.  To get a smooth transition, the proper substitutes of
U(n-1) and U(n-2) are chosen as follows:

An equation of motion of a voice coil motor (VCM) at time (k)
with sampling time (Ts/2) and delay time (d) is
Y(k) = 2*Y(k-1) - Y(k-2) + a1*U(k-2) + a2*U(k-3)
+ b1*U(k-1)
(3)
where
Y(k)   :  position at time k
a1     :  a*(1+2*q-2*q2)
a2     :  a*q2
b1     :  a*(1-q)2
q      :  d/(Ts/2)
a      :  (Ts/2)2*c
c      :  consta...