Optimal force control of a vibro-impact system for autonomous drilling applications

The optimal force control solution for second-order vibro-impact systems with and without friction nonlinearity is introduced and explicitly solved herein. In particular, a finite-step algorithm is developed which generates open-loop force control laws which are designed to minimize the expended control energy per impact cycle, while ensuring that each impact occurs with sufficient impact velocity. When electromagnetic motors are employed to realize the control forces, the performance of the percussive unit becomes heat-limited. The article demonstrates that the controls needed to drive the hammering mechanism with a minimal amount of dissipated energy is a solution that can be derived in closed form. A closed-loop control architecture based on this result is introduced.