Elliptic Jerk Motion Profile: Nondimensional Frequency-Domain and Time-Domain Analysis of Second-Order Linear Systems

Recently, the elliptic jerk motion profile, developed based on a jerk function with elliptic shape, has been proposed as an alternative to other laws for rest-to-rest motions of inertial loads. In this article, a nondimensional frequency-domain comparison of the proposed profile with other motion laws is presented. Then, a nondimensional approach is employed to compare the performance of different motion profiles when applied to second-order dynamic systems, for example translating or rotating systems connected to a moving base with imposed motion, or mechatronic devices controlled in position with the PD scheme. After an experimental validation through the application to a position-controlled rotor, the nondimensional model has been used to obtain a generalized comparison of the motion profiles in terms of maximum induced displacement, velocity, acceleration, and force/torque, producing 3D maps of these performance indexes as functions of the system damping ratio <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\zeta $</tex-math></inline-formula> and of the ratio <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\bm{\tau }}$</tex-math></inline-formula> between motion duration and system’s natural period. Possible application areas for the proposed elliptic jerk profile and nondimensional approach include industrial automation, robotics, and the control of rotating bodies.