Seek time and trajectories of time optimal control for a dual stage optical disk drive actuator

A piecewise expression of the seek time and three kinds of trajectories with their seek distance conditions of the time optimal control of a dual stage disk drive actuator are presented. Necessary conditions for finding the optimal control for the problem with state-variable constraints are applied to derive the solution. The seek time can decrease when the two stages of the actuator are cooperatively controlled as compared with that when the fine actuator locked onto the coarse actuator.