Hardware Reference
In-Depth Information
are designed independent of one another, continuity of the control signal is not
guaranteed at the time of switching from one mode to the other.
A controller is usually designed with an assumption that the initial values of
the states are zero. This assumption is not valid for the HDD servomechanism.
When the states of the closed loop system move from one mode to the other,
the initial states are not guaranteed to be zero-valued for the second controller.
It may be pointed out that, in HDD servomechanism, switching always takes
place from track-seek mode to track-following mode and not vice versa.There-
fore, one can design the track-following controller using a technique that takes
the non-zero initial conditions into consideration. The mode switching con-
trol with Initial Value Compensation (IVC) is a method that ensures smooth
hand over between the two controllers [218]. The validity of the MSC-IVC de-
sign depends on two assumptions - (i) the track-following controller is a stable
single-input single-output system, and (ii) the transfer functions of the plant
and the controller are proper. The MSC-IVC design will be elaborated later
in chapter 3.
Let the plant and controller be described by the following discrete-time
state equations.
X
p
(k +1) = A
p
X
p
(k)+B
p
u(k),
y(k)=C
p
X
p
(k),
X
c
(k +1) = A
c
X
c
(k)+B
c
(r(k)−y(k)),
u(k)=C
c
X
c
(k)+D
c
(r(k) −y(k)),
(2.58)
where X
p
and X
c
are the m
th
− order and n
th
− order state vectors of the
plant and controller, respectively. The variables u(k) is the control input to the
plant, y(k) is the output of the plant, and r(k) is the reference. The matrices
and vectors A
p
,B
p
,C
p
,A
c
,B
c
,C
c
and D
c
are of appropriate dimensions. The
instant of mode switching is the sampling instant k = 0. During the track
following mode, r(k) is the reference of the track-center which is not measured
directly. It is the error signal e(k)=r(k) −y(k)thatisavailableintheHDD
servomechanism.
In transform domain, the system of equation 2.58 can be
written as
Y (z)=
N
p
(z)
D(z)
X
p
(0) +
N
c
(z)
D(z)
X
c
(0)
(2.59)
where N
p
,N
c
and D are polynomials in z of appropriate dimensions. The states
of the track-following controller can be initialized to desired initial values using
arealcoefficient matrix (K
ivc
)suchthatX
c
(0) = K
ivc
X
p
(0). Then
Y (z)=
N
p
(z)+K
ivc
N
c
(z)
D(z)
X
p
(0).
(2.60)
An appropriate selection of K
ivc
can improve the transient characteristics fol-
lowed by the mode-switching. The track following controller is designed to
