Hardware Reference

In-Depth Information

1.5

1

+10% of Track

0.5

0

−10% of track

−0.5

Position Error

−1

−1.5

1

1.5

2

2.5

3

Time (ms)

Figure 2.31: Position error for 100-track seek: Simulation result.

that includes integral control. These two methods are explained later in this

section.

The State Estimator

Considering the rigid body model (
s
2
) of the VCM actuator, corresponding

continuous-time state space model is

∙

¸

∙

¸

dp

dt
=

01

00

0

a

p +

u,

y =[1 0]p,

(2.45)

where u(t)andy(t) are the input and output of the VCM, respectively. The

state vector p =[p
1
p
2
]
T
includes the position (p
1
)andvelocity(p
2
)ofthe

head-slider effectuated by VCM's motion. In this state-space model, the unit

of velocity is tracks per second. Considering the speed of motion in HDD

servomechanism and the magnitude of displacement (maximum velocity can

be hundreds of thousand tracks per second for corresponding displacement of

few tens of tracks), this representation results in large magnitude disparity

between the two states. As a result, one of the feedback gains becomes very

large compared to the other. Such case requires extra care while implementing

the controller using fixed point processor. The issue can be resolved by suitable

transformation of variables. If we redefine the velocity in units of tracks per

sector (time between consecutive sectors is few µs only), its magnitude is scaled

down by a factor of

1

T
S
,whereT
S
is sampling interval. This is equivalent to