Minimum-time open-loop smooth control for point-to-point motion in vibratory systems

We present an approach for motion planning of servosystems endowed with elastic transmission. The open-loop control strategy proposed is based on noncausal system inversion and guarantees the absence of vibration both during and at the end of the point-to-point motion. The idea is to calculate the command input of the system after having determined a suitable parametrized motion law of the load. It can be demonstrated that, with an opportune choice of the motion law, the input function has a continuous derivative of a predefined order. Moreover, the time of the motion can be optimized with the purpose to minimize it, taking into account constraints on the actuators. The whole technique is explained in the paper and simulation results are given in order to show its feasibility