An online generation of time-optimal trajectories for piecewise step references

In this paper, a feedforward filter is proposed for piecewise step references, which produces time-optimal trajectories under constraints on acceleration. 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 overshoot. 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. For this issue, we have already proposed a feedforward filter for a given single step reference, which produces time-optimal trajectories under constraints on acceleration and velocity. In this paper, a new filter is proposed for piecewise step references.