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We present a data-based approach for modeling and controller design of a dual-stage tape servo actuator. Our method uses step response measurements and a generalized realization algorithm to identify a multivariable discrete-time model of the actuator. The data acquisition and modeling can be implemented in the servo firmware of a tape drive. We have designed a dual-stage controller, based on the model, using loop shaping techniques adopted for multivariable control problems. We applied the procedure to the prototype of a dual-stage actuator tape head to reduce the effect of lateral tape motion. The prototype consists of a conventional voice coil motor for coarse positioning and a micro-actuator for fine positioning. The micro-actuator, which is mounted on the voice coil motor, uses a piezo crystal to follow high-frequency lateral tape motion (up to the kilohertz regime), while the voice coil motor follows only low-frequency lateral tape motion. Compared to a single-stage design, the dual-stage servo design provides a 25% bandwidth improvement and a voice coil motor control signal that is much smaller in magnitude.