Third Order System for the Generation of Minimum-Time Trajectories with Asymmetric Bounds on Velocity, Acceleration, and Jerk

Reference signals used to drive feedback control loops are often evaluated on-the-fly on the basis of the systems operating conditions. As a consequence, it is very difficult to guarantee a priori properties like continuity or the existence of bounds on the signal dynamics and, therefore, control systems performances could deteriorate. Improved answers can be obtained if input signals are properly smoothed. The paper proposes a possible filtering system which 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. Differently from analogous solutions proposed in the past, it also handles asymmetric bounds.