Time-optimal bang-bang driven rest-to-rest motion through an angular switching point

For economic reasons, machine builders are increasingly challenged to make single-axis driven machines perform rest-to-rest movements as fast as possible over time. In terms of control, a time-optimal motion is performed by injecting a bang-bang torque profile, characterized by a discrete switching point. However, the state-of-the-art to obtain the ideal application-dependent switching point is often computationally demanding and lacks robustness, hampering smooth system implementation. Moreover, machine builders invariably design their machines using CAD software, which automatically provides good knowledge about, e.g., the machine’s load torque profile. Therefore, in this work, based on Newton’s work-energy principle, a framework for variable inertia systems is derived and used as a starting point to estimate the optimal bang-bang switching point efficiently, employing CAD extracted data. In addition, a self-learning control structure is proposed to correct for the initial switching point so that the application continues to move time-optimally, regardless of system influences such as temperature variation. A case study is used to validate the proposed methodology and associated control structure through simulation.