  In many mechatronic applications, controller input costs are negligible and
time optimality is of great importance to maximize the productivity by
executing fast positioning maneuvers. As a result, the obtained control input
has mostly a bang-bang nature, which excite undesired mechanical vibrations,
especially in systems with flexible structures. This paper tackles the
time-optimal control problem and proposes a novel approach, which explicitly
addresses the vibrational behavior in the context of the receding horizon
technique. Such technique is a key feature, especially for systems with a
time-varying vibrational behavior. In the context of model predictive control
(MPC), vibrational behavior is predicted and coped in a soft-constrained
formulation, which penalize any violation of undesired vibrations. This
formulation enlarges the feasibility on a wide operating range in comparison
with a hard-constrained formulation. The closed-loop performance of this
approach is demonstrated on a numerical example of stacker crane with high
degree of flexibility.
