Error-bounded reference tracking MPC for machines with structural flexibility

For industrial contouring and machining applications such as laser cutting, it is desirable to be able to bound errors without unduly compromising machine throughput. Traditional control architectures in machining are unable to explicitly bound tracking errors, and therefore, conservative operation is required to ensure satisfactory performance of the overall system. This is particularly relevant in contouring applications when the end effector is connected to the drive via a flexible link, and no direct feedback measurement about the end-effector position is available. In this article, a model predictive approach is proposed, which guarantees that a desired level of tracking error is met for the case where the structure is flexible and the end-effector position is estimated. To achieve this, a robust control invariant set is estimated using a computationally tractable algorithm and incorporated into the problem formulation. The applicability of the proposed approach is successfully demonstrated via simulation and experiments conducted on a commercial single axis system.