Contouring Control of CNC Machine Tools Based on Linear Parameter-Varying Controllers

This paper proposes a method to design a multi-input multi-output (MIMO) linear parameter-varying (LPV) feedback controller for contour error minimization in two- and three-axis computer-numerical-control (CNC) machines. The design method generates a controller of a special and novel structure, that is, a series connection of a coordinate transformation matrix that varies with the machine tool trajectory angles, and an LPV controller that depends on the trajectory angles and angular velocities. To design the LPV controller part, a well-established gain-scheduled LPV controller design technique based on linear matrix inequalities is applied to the linear time-invariant CNC machine model combined with the parameter-varying coordinated transformation matrix. Simulations in both frequency domain and time domain, as well as experimental results for a two-axis machine, demonstrate a potential of the proposed MIMO LPV control approach for reducing the contouring error further than conventional contouring control methods.