Timing-based servo for determining lateral head velocity

In a servo system for positioning a tape head laterally to follow lateral motion of a longitudinal tape moving in a substantially longitudinal direction with respect to the tape head, the tape having at least one longitudinal defined servo track, the servo track including a longitudinal series of identical servo pattern frames, each servo pattern frame including two pairs of non-overlapping parallel magnetic transitions, the transitions of each pair being spaced apart an equal distance d, the transitions of the first pair forming an azimuth angle to the longitudinal axis of the tape, the transitions of the second pair forming the azimuth angle to the longitudinal axis of the tape but at an opposite slope about the lateral axis of the tape, said servo system including an actuator configured to move the tape head laterally with respect to the longitudinal tape, the tape head including a servo read head configured to read the servo pattern frames in the servo track and produce servo signals, a servo channel configured to receive and process the servo signals, a position error signal loop configured to sense the servo signals, to determine position error between the servo read head and a desired center-line position of the at least one defined servo track based on the servo signals, and to operate the actuator to move the tape head laterally to reduce the determined position error,

• a method to determine a relative lateral movement and velocity between the tape and the tape head, comprising:
• the servo read head reading a servo pattern frame in the servo track, the relative movement of the servo head with respect to the tape forming a trajectory angle with respect to the center-line of the at least one defined servo track, the trajectory of the servo read head intersecting the first and second transitions of the first pair of parallel transitions of the servo pattern frame at times TA and TB, respectively, and intersecting the first and second transitions of the second pair of parallel transitions of the servo pattern frame at times TC and TD, respectively, whereby the servo read head produces servo signals at times TA, TB, TC, and TD;
• and
• the servo channel determining a relative lateral movement LMAB or LMCD between the tape and the actuator between times TA and TB, or times TC and TD, respectively, at least as respective functions of the ratio (TD−TC)/(TB−TA), distance d, and constants proportional to the azimuth angle and the trajectory angle.