Friction existing between any two surfaces having relative motion is nonlinear,
multiform, and is difficult to model. Nonlinear friction in the actuator pivot
of a hard disk drive (HDD) limits the low frequency gain, which prevents the system
positioning accuracy from further improvement. This problem is much more pronounced
for the severe nonlinearity at the micrometer level. The conventional two-mode
proximate time optimal servomechanism (PTOS) is inadequate for immediate future
hard disk drives because of the existence of restrictions in the particular design
approach. A triple-mode control scheme, and its variations, as presented herein,
include (a) a proximate time-optimal controller (PTOC) having a relatively large
output is used for track seeking, (b) a robust compensator having a relatively
small output is used for track following to compensate for friction and other nonlinearities,
and (c) a bridging (connection) control to guarantee the continuity of the control
signals. Because of the introduction of an extra mode, additional freedoms for
controler design are made available for improved performance. The robust compensator
is non-model based in the sense that it does not depend on the models of friction
and other nonlinearities. This makes the invention simpler and more practical than
conventional systems.