Due to extremely rapid progress of computer and information technology and related products in recent years, the storage capacity of magnetic Hard Disk Drives(HDDs) continues increasing, and the growth rate of data storage density has been almost 100% a year. At present, the data storage density is increasing toward 40 Gbit/in² which requires the interval between adjacent tracks to be less than 0.5 micro-meters.

The technological advance of magnetic disks makes conventional actuators impossible to achieve desirable head positioning servomechanism of high accuracy and high speed. Recently, the new architecture of the dual-stage actuator made of the pair of a conventional Voice Coil Motor(VCM) and a micro-actuator has been proposed. The micro-actuator which is placed on the tip of the VCM renders the open-loop bandwidth of the overall dual-stage actuator large enough to seek high-speed and high-precision tracking and following of the magnetic head. Thus, the necessary advance of HDDs is up to the development of effective ways of utilizing the dual-stage architecture in the head positioning control.

The topic of this thesis is the design of multirate control which makes the best use of the potential dual-state actuator. To this end, this thesis pays attention to the difference between the bandwidth of two actuators and introduces the idea of frequency separative control to the feedback and forward multirate control design. Much effort is made to redesign direct-feedthrough compensation toward achieving shorter settling time by moving the actuators as early as possible after the target track command. Calculation of parameters of the direct-feedthrough compensation is formulated in the form of linear matrix inequalities which are amenable to a standard software of numerical optimization. This thesis first shows the result of a multirate controller designed by incorporating frequency separation into the multirate sampled-data H_infinity control theory. Then, a redesign of the direct-feedthrough parameters of the controller is performed. The result of the redesign is compared with the controller without the redesign, and the potential of redesigning direct-feedthrough compensation aiming at more accurate and swift head positioning is demonstrated.