In this paper, we describe the design of closed-loop control laws for disk-drive systems that account for back-electromotive force (back-EMF) by using a phase-plane approach. The time-optimal control law for a rigid body is shaped by using input shaping ideas to address the flexible mode, and then the altered rigid body phase-plane trajectories resulting from this shaping are calculated and used to determine a closed-loop controller. Extensions are made to account for damping and slew rate limits. Simulation results show that this control approach leads to near-time-optimal performance without unwanted residual vibrations, good robustness to modeling errors, and faster time response than the previously developed extended proximate time-optimal servomechanism (XPTOS) control, especially when the flexible dynamics are dominant.
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