An online generation of time-optimal trajectories via simple feedforward filter and its implementation with two-degree-of-freedom system

Step response is usually 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. In such situations, some limitations on the acceleration and/or velocity of the plant would be necessary. In addition, any actual system has some limitations on their state variables and/or inputs usually caused by input saturation. For these actual systems, step function is not an achievable trajectory and in the worst cases, it makes the system unstable. Therefore, a moderated reference whose velocity and acceleration are constrained in certain values is important. 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 acceleration and velocity guarantee the limitations that are given a priori. Furthermore, a synthesis method of the two-degree-of-freedom system with the proposed filter is discussed and the effectiveness is substantiated with experimental results.