Fractional-Order Sliding Mode Contouring Error Control

This chapter presents a simplified Newton-based contouring error estimation (CEE) and a discrete-time FO 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 Newton extremum seeking algorithm. Compared with existing CEE, SNE method keeps the high precision meanwhile 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 multidimensional system as the designed cost function in SNE takes the vectors into consideration innovatively. To improve the performance further, a discrete-time FO sliding mode CEC (DFSMC) is proposed when the CEC strategy is designed. A novel FO sliding surface is addressed and the conclusion on its stability in LMI form is given out. Furthermore, the dynamics of the entire system are also analyzed in the paper. At last, to validate the effective of the proposed SNE-DFSMC strategy, groups of comparative experiments are implemented on a 2-DOF linear motor table, whose results validate the efficiency of the SNE-DFSMC strategy.