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This paper proposes an optimization based control scheme for a dual-stage hard disk drive servo system to maximize the tracking accuracy given the actuator bandwidth limitations without knowing the mechanical disturbance model. We proposed to add an outer loop, selected based on optimization of the Youla parameters, to the usual dual-stage controller for tracking accuracy improvement. The Youla parameters are bounded based on specifications of minimum bandwidth, phase margin, and gain margin, and maximum bandwidth limitations. Time domain and frequency domain simulations were performed to show the effectiveness of the design. The tracking accuracy with respect to various noise and disturbance levels was considered. The results suggested that for the noise and disturbance model considered, the mechanical disturbance must be reduced considerably to achieve higher TPI.