Integral sliding mode control (ISMC) has been employed and shown to improve contouring accuracy in the presence of external disturbances and model uncertainties. An ISMC controller directly reduces the tracking errors of each individual axis, thereby reducing the overall contour errors indirectly. An ISMC controller drives the system dynamics back onto the sliding surface if there exists a deviation from the predefined surface. In the design of an ISMC controller, it is crucial to choose an appropriate sliding surface as this has a great impact on system performance and on chattering. In current approaches, the sliding surface is chosen largely based on a rule of thumb which is only applicable for systems with open-loop poles having imaginary parts. In this paper, an approach is presented to design the sliding surface using principles of robust digital control so that both the regulation and robustness requirements can be satisfied. The natural frequency of the dominant closed-loop poles is chosen such that the modulus of the output sensitivity function lies within the robustness bounds. Resonant pole-zero filters are then used to reshape the output sensitivity function in specific frequency regions. Experiments showed that when the modulus of the output sensitivity function is kept within the robustness bounds, chattering can be avoided and the contour errors resulting from vibrations can be reduced. The introduction of a resonant pole-zero filter also allowed the attenuation band to be expanded so that the low frequency components of the contour errors are attenuated.
Xi, X. C., Zhao, W. S., & Poo, A. N. (2015). Improving CNC contouring accuracy by robust digital integral sliding mode control. International Journal of Machine Tools and Manufacture, 88, 51–61. https://doi.org/10.1016/j.ijmachtools.2014.08.005