Time-optimal trajectory generator under jerk constraints

Step response is widely used as the performance index of controlled systems. Thus, the ideal system would be one that has an output which approaches to the step signal quickly without error or over-shoot. However, if the output of an actual plant converges to the reference signal in a very short period, it can be dangerous to the surrounding environment as well as the operators. Furthermore, the smooth trajectories are required in some cases like vehicle or elevator systems. It is known that some limitations on the jerk of the plant would be necessary in such situations which require ride quality. In this paper, a non-linear feedforward filter for the step signal is proposed. The proposed filter, which has simple structure and requires less computational burden, produces time-optimal trajectories whose jerk guarantees the limitations that are given a priori. The effectiveness is substantiated with numerical examples.