| This paper proposes a robust proximate-time-optimal command shaping technique in the context of scanning probe microscope (SPM) application. It is based on an optimization scheme with least-square method that can easily incorporate various constraints. By including time-unbounded inputs in the derivation of the sufficient condition for zero-residual-vibration input design, the proposed robust command shaping works for both systems with rigid-body mode (as a special case) and systems without rigid-body mode (as a general ease).; After hysteresis nonlinearity inherent to piezoelectric actuators is compensated with the proposed continuous numerical inversion algorithm, the robust command shaping is performed on the linear dynamics. A time-energy optimization is formulated to reduce in maneuver oscillations by making a trade-off between time optimality and energy minimization. Also, the incorporation of EI (extended insensitivity) technique is explored to further reduce maneuver time. Experiments on a floating gantry system have proved the validity of the proposed algorithm.; Application to coordinated contour control is investigated as a preliminary study for possible future work. Both linear and nonlinear contour control are discussed, and a solution for the trajectory reversal problem is proposed by introducing a reversal constraint into the optimization scheme. |
