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Shaped time-optimal control for disk drive systems with back EMF, slew rate limits, and different acceleration and deceleration rates

This paper derives shaped time-optimal servomechanism (STOS) controllers for flexible structures consisting of a second-order rigid body with damping and a damped flexible mode. The approach uses input shaping to account for the damped flexible mode by altering the time-optimal velocity profile that moves the second-order rigid body with damping from rest to rest. Considering the slew rate limit constraints, the maneuver is categorized into three ranges due to their different shaped input profiles. For one of the maneuver ranges, when systems have different acceleration and deceleration capabilities, the time-optimal control for the second-order with damping rigid body portion has to be solved numerically. However, the STOS control for this maneuver range can still be derived analytically by using the curve-fit approximation of the switching time of the time-optimal control. Simulation show that the derived STOS control laws yield near time-optimal performance without unwanted residual vibration at the end of the maneuver.