In two-degree-of-freedom (2-DOF) servo positioning control of mechanical structures, the profile of reference trajectories is extremely important. In some cases, taking constraints on control problems into account, these trajectories are designed a priori by off-line calculations. Especially, such trajectories are effective in positioning control of flexible structures. Generally, the number of the profiles is limited such that the profiles comprise only some typical positioning distance cases. Therefore, an adjustment is required for realizing the positioning of an arbitrary distance. For this problem, this study proposes SMART adjustment method based on the idea of "Structural vibration Minimized AcceleRation Trajectory (Mizoshita, et al., 1991)." SMART is an optimal control solution for the motion of the double integrator dynamical model. SMART adjustment maintains the characteristics of off-line designed trajectories. By applying this method to 2-DOF H∞ servo positioning control of a flexible structure, the effectiveness of it is verified by numerical calculations and experiments.
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Susumu Hara (2000) studied this question.