Simplified Newton-Based CEE and Discrete-Time Fractional-Order Sliding-Mode CEC

Abstract

This paper presents a simplified Newton-based contouring error estimation (CEE) method and a discrete-time fractional-order sliding-mode contouring error control (CEC) strategy to obtain an excellent contouring motion performance for multidimensional systems. Specifically, the simplified Newton-based CEE (SNE) is modified from the Newton extremum seeking algorithm. Compared with existing CEE, the SNE method keeps the high precision; meanwhile, it requires less computing resources and avoids the possible singularity as no derivatives are demanded during the calculation. Moreover, the form of SNE is rather simple in a multidimensional system as the designed cost function in the SNE takes the vectors into consideration innovatively. To improve the performance further, a discrete-time fractional-order sliding-mode CEC (DFSMC) is proposed when the CEC strategy is designed. A novel fractional-order sliding surface is addressed, and the conclusion on its stability in a linear matrix inequality form is given out. Furthermore, the dynamics of the entire system are also analyzed in this paper. At last, groups of comparative experiments are implemented on a 2-degree-of-freedom linear-motor table, whose results validate the efficiency of the SNE-DFSMC strategy.