Contouring error control of the tool center point function for five-axis machine tools based on model predictive control

Abstract

In five-axis machining processes, tool center point (TCP) control is often used to adjust the orientation of the ball end milling while maintaining constant tool center point coordinates in the workpiece frame. Therefore, TCP contouring error decreases the quality of the machined surface, but very few efforts have been made so far to minimize the contouring error of five-axis TCP by feedback control. To this end, a model predictive control (MPC) method is developed here for rolling optimization. More precisely, the contouring error model of five-axis TCP function is developed, where a Jacobian matrix is used to approximate the relationship between the contouring error and five drivers' tracking errors. The MPC algorithm is afterwards derived, where constraints of control signals are considered as well to avoid violation of the power limitation of the drivers. Finally, the proposed MPC method is examined by extensive experiments using testing tool path of ISO 10791-6: 2014 to verify its effectiveness and superiority.

MPC‐based robust contouring control for a robotic machining system

“…The PPI‐FF consists of an inner PI velocity feedback loop and an outer P position feedback loop that are injected by acceleration and velocity feed forwards, respectively, as shown in Figure 7. Tool Center Point Model Predictive Contouring Control (TCP‐MPCC): TCP‐MPCC [29] defines contour error as an error vector between the desired position P d and the actual one P . The contour error is estimated as [27] where J p is a Jacobian function of the forward kinematics of the dual‐arm robot. TCP‐MPCC is designed to minimize the joint tracking error ( q Ld − q L ) and the contour error by optimizing the change of the control action (Δ u ).…”

“…Shi et al [27] proposed a model predictive contouring control (MPCC) based on unified modeling, while Yang et al [28] presented a method that utilize the main function of MPC to predict the contour errors for pre‐compensation. So far, only the MPCC of a tool center point (TCP) function developed by Yang et al [29] was experimentally implemented to a five‐axis CNC machine tools. However, only approximated position contour errors are used, and the orientation contour errors are not taken into account.…”

“…Second, ISMC is incorporated into the MPCC to establish the robustness. Finally, compared with two existing contouring control methods [29, 31], experiments are conducted to evaluate the performance of the proposed control scheme.…”

Data‐Driven Performance Monitoring for Model Predictive Control Using a mahalanobis distance based overall index

“…As the PID range for the flow rate of pump and proportional valve are 1.7~3.7 and 0.65~1 L/min respectively, the constraints of the manipulated variables are (1.7, 3.7) and (0.65, 1) L/min respectively. Since the maximum level of the Tank is 22 cm, the constraints of the controlled variables are (7,22) and (11,22) cm respectively by taking into account the application scope of the model. The control performance of the system is shown in Fig.…”

“…Model Predictive Control (MPC), as one of the advanced control methods [1,2], has made considerable applications in complex industrial processes such as oil refining, chemical, metallurgical, power [3,4], machining processes [5][6][7], and complex systems such as artificial pancreas (AP) systems [8]. It is noted that the MPC algorithms can meet design requirements with good performance during the early operation period.…”