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A three-degree-of-freedom (3-DOF) dynamic model-based intelligent nonsingular terminal sliding mode control (INTSMC) system is proposed in this study for the precision contours tracking of a gantry position stage. A Lagrangian equation-based 3-DOF dynamic model for the gantry position stage is derived first. Then, to minimize the synchronous error and tracking error in the precision contours tracking, the 3-DOF dynamic model-based INTSMC system is proposed. In this approach, a nonsingular terminal sliding mode control is designed for the gantry position stage to achieve finite time tracking control. Moreover, to increase the robustness and to improve the control performance, an interval type-2 recurrent fuzzy neural network, and asymmetric membership function, which combines the advantages of interval type-2 fuzzy logic system, recurrent neural network, and asymmetric membership function, is developed as an estimator to approximate a lumped uncertainty. Finally, some experimental results of the gantry position stage for optical inspection application are obtained to show the validity of the proposed control approach.