The use of compound actuators in both magnetic and optical disk files has become a means of achieving increased servo actuator bandwidths. A compound actuator, comprised of a fine actuator mounted “piggyback” on a coarse actuator, positions the read/write transducers above a radial track. This paper describes a design methodology for a discrete-time feedback control system for a compound actuator in which the dynamic interaction between the actuator stages is directly considered. The performance of the servosystem, including the range and bandwith limitations of each actuator, is specified in terms of the desired frequency response of the closed-loop transfer functions from the reference track position to the tracking error and to the relative position between the coarse and the fine actuator. Parameter uncertainties and structural resonances are quantified using singular value techniques to form a robustness criterion which sets limits on the attainable tracking performance. Compensator design techniques using linear-quadratic Gaussian optimal control combined with loop transfer recovery are described. The state feedback portion of the compensator is calculated using an automatic procedure, while the state estimator is calculated by solving an associated Kalman filtering problem with colored fictitious noise. The noise is colored to shape the frequency spectrum of the input energy to each actuator, the relative motion between the stages, and the position of the transducer.