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This paper derives shaped time-optimal servomechanism (STOS) controllers for flexible disk drive systems considering the effect of back electromotive force (back EMF) and coil inductance. To eliminate the vibration due to an unwanted flexible mode, input shaping is used to alter the time-optimal velocity phase-plane profile that moves the third-order nonflexible dynamics from rest to rest. Because the closed-form solution for the time-optimal control of the third-order nonflexible dynamics is not known, the shaped time-optimal velocity phase-plane profiles are derived numerically. By using a curve-fit polynomial to approximate these shaped timeoptimal velocity phase-plane profiles, we obtain an analytical expression for the STOS control. Simulations show that the curve-fit polynomials give high accuracy and the STOS control yields near time-optimal performance without unwanted residual vibration.

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This paper describes the design of closed-loop control laws for undamped flexible structures with friction using a phase-plane approach. The time-optimal control law for a rigid body with friction is shaped using input shaping ideas to address the flexible mode, and then the altered rigid body phase-plane trajectories resulting from this shaping are solved for and used to determine a closed-loop controller. Simulation results show that the resulting controller leads to near time-optimal performance without unwanted residual vibrations.

This paper describes the design of closed-loop control laws for servomechanisms with one dominant flexible mode. An input shaping technique is employed to alter the rigid body phase-plane trajectory that is used in time-optimal servomechanisms. The resulting controllers lead to near time-optimal performance without unwanted residual vibrations. After the basic technique is outlined for a system with one undamped flexible mode, extensions are given considering different acceleration and deceleration capabilities, damping, and slew rate limits.