Cross-coupled control for contour tracking error of free-form curve based on fuzzy PID optimized by improved PSO algorithm

Aiming at the free-form curve contour tracking error problem of CNC machining, a cross-coupled controller based on Fuzzy PID using an improved PSO algorithm is proposed. First, the exact formulas of the linear and circular arc contour errors under a plane trajectory are derived, and an estimation method for the free curve profile error under a plane trajectory based on the principle of approximate approximation of preferred points is designed. Second, a cross-coupled controller based on Fuzzy PID using an improved PSO algorithm is achieved. An improved PSO algorithm, whose learning factor is adjusted with the inertia weight, is used to optimize the controller parameters and achieve contour tracking of the free curve. Finally, a two-dimensional biaxial experimental platform is used to test the proposed method. The results demonstrate that the optimal gain parameters obtained by the proposed strategy can significantly improve contour control accuracy in biaxial contour tracking tasks. The proposed contour error control scheme can achieve not only a nearly perfect contouring error estimation, but also an obvious promotion of contouring accuracy.