A Discrete-Time Filter for the Generation of Signals With Asymmetric and Variable Bounds on Velocity, Acceleration, and Jerk

Reference signals, which are used to drive feedback control loops, are often evaluated on the fly on the basis of the operating conditions. As a consequence, they can be too demanding for the actuation system whose outputs could saturate, thus worsening the tracking performances of the feedback loop. Improved answers can be obtained by smoothing rough references by means of proper filters that are also able to impose bounds on the signal dynamics. This paper proposes a filtering system whose output mimics at best any given input signal compatibly with some smoothness requirements. In particular, generated signals are continuous up to the second time derivative, and their first three time derivatives are constrained between assigned bounds that can be asymmetric and that can also be changed on the fly. The filter, which is internally characterized by minimum time transients, is able to follow, with zero tracking error, piecewise-continuous signals given by combinations of steps, ramps, and parabolas.