Hardware Reference

In-Depth Information

be greater than 0, resulting in more attenuation of vibration than amplification

with a continuous time controller. Additionally, we note that Clegg integrator

has 39 degree phase lag instead of the usual 90 degree phase lag. As a result, it

provides the necessary integral action but does not add the amount of phase lag

found in the usual linear controls. Henceitispossibletoavoidthewaterbed

effect. Nevertheless, with limited sampling frequency, a digital servo loop will

have more vibration amplification than a continuous time servo loop of the

same bandwidth.

3.3.3 Bandwidth Limitations

Assumingatypicalservoloopshape(Section 3.2) and stability margin require-

ments, the two major factors thet limit the achievable servo bandwidth are (1)

the uncertainties related to the actuator, and (2) various delays in the control

system.

The phase margin of a control system defines the extent of additional phase

lag that can be tolerated before the stability is lost, and the gain margin defines

the amount of increase in gain that makes the loop unstable. So the servo loop

can be pushed to the point that enough margin is left for the actuator's phase

and gain uncertainty. Since the control systems are typically designed to have

6 dB gain margin, the servo bandwidth attainable is limited to the frequency

where the uncertainty of actuator gain is equal to 6 dB. In general, a rule of

thumb states that a servo bandwidth of 1/4 of the critical resonant frequency

(beyond which, the frequency response will show uncertain behavior at different

excitation level) can be achieved [144].

The PES sampling frequency and the achievable servo bandwidth are in-

terrelated. It is generally preferred to have PES sampling frequency roughly

10 times the open loop servo bandwidth or higher for effective suppression of

vibration. The sampling frequency depends on the number of servo sectors

per revolution which, in turn, is limited by the space on the disk allocated

for servo bursts. Increasing the rotating speed of disk increases the sampling

frequency, but it also increases the level of internal vibrations and therefore

demands for better servo design, which in turn requires a even higher PES

sampling frequency. Similar to the limitations on control performance due to

the sampling frequency, the computation delay and more importantly the de-

lay introduced by the ADC limit the achievable performance by adding extra

phase lag. These delays must be kept less than a fraction of the PES sampling

period.

The success in achieving the objective of the HDD servo control to meet the

requirements on tracking accuracy and response time demanded by the system

depends on many factors including the limitations of actuator's performance

(plant uncertainty), lack of accurate disturbance model, and insuļ¬cient feed-

back information due to limited sampling frequency. It is obvious that no single

solution exists that can tackle all these limitations, and optimization plays an