Smooth control over jerk with displacement constraint

Abstract

This article investigates the problem of using jerk (the rate-of-change of acceleration) motion control to move a given distance without overshoot. Distance, velocity, and acceleration are all brought to zero simultaneously. Although this problem has been identified in suspension control, it may also be of interest in mechatronics. In this research, particular controls were found that solved this problem. An algorithm was developed which is stable when used in a discretized form, as in a microprocessor continually updated with current state estimations. The control was found serendipitously. A wider range of controls is conjectured to provide the solution to the general minimum-time control problem under distance and jerk constraints. To describe these controls, they are here referred to as ‘skim’ controls. Also, a ‘bang-off-bang’ variant was developed and this was used in a simple test rig. The test developed in this research supports the utility and robustness of the control method.