Robust control of the A-axis with friction variation and parameters uncertainty in five-axis CNC machine tools

Abstract

A-axis is an essential assembly in the five-axis CNC machine tools, and its positioning precision directly affects the machining accuracy and surface quality of the parts. Considering the influence of parameters perturbation and uncertain cutting force on the control precision of the A-axis, a nonlinear dynamics model of the A-axis system is established, which reveals the relationships among the drive torque, the load torque, the motion direction and the system parameters. Then, two adaptive sliding mode controllers (ASMC) are designed. The first one is based on the bipolar sigmoid function, which can adjust the switching gain and the boundary layer thickness adaptively, then, equilibrium between the tracking error and the chattering can be achieved. The second one is a compound adaptive controller constituted by the traditional sliding mode controller (TSMC) and an internal controller that is based on the hyperbolic tangent function. When the state trajectory comes into the boundary layer, the TSMC will be replaced by the internal controller, thus, the adaptive controller can continuously switch between these two controllers, which can effectively eliminate the high-frequency chattering in the TSMC. Stability of these two controllers is guaranteed by the Lyapunov theory. Experimental results demonstrate the effectiveness and feasibility of the proposed ASMC, which can smooth the input chattering and reduce the tracking error by 16.62% and 21.44%, respectively.