Advanced contouring error compensation in high performance motion control systems

Because of nonlinearities, uncertainties and inherent performance limitations of the mechatronic system, there is a trade-off between tracking error minimization and robust stabilization. This implies that the tracking error is unavoidable in practice. Fortunately, in the path following motion control system, it is the geometric error that measures the quality of the product. Since the tracking error gives an upper bound on the geometric error, by the principle of uncertainty, more preference can be given to the geometric error dynamics to improve the quality of the product. For generic parametric tool path, although the geometric error is hard to be computed numerically, it can be estimated by a projection operator on the tracking error vector. Then the tasks of contouring error compensation are twofold: to internally stabilize the feedback system, and to minimize the estimated contouring error. A novel multiple-loop structure is proposed in this paper. By using this structure, the internal stability of the feedback system is guaranteed, if the norm of the compensator is less than a function value on the infinity norm of the tracking error dynamics. Experiments were done on milling machines to verify the feasibility of the proposed structure. Low order compensators were designed and compared with each other. In the experiments, the estimated contouring error was reduced by more than 20%, while the tracking error did not change too much.