Iterative learning contouring controller based on trajectory generation with linearly interpolated contour error estimation and Bézier reposition trajectory for computerized numerical control machine tool feed drive systems

Abstract

In industrial applications, highly accurate mechanical components are generally required to produce advanced mechanical and mechatronic systems. In machining mechanical components, contour error represents the product shape quality directly, and therefore it must be considered in controller design. Although most existing contouring controllers are based on feedback control and estimated contour error, it is generally difficult to replace the feedback controller in commercial computerized numerical control machines. This article proposes an embedded iterative learning contouring controller by considering the linearly interpolated contour error compensation and Bézier reposition trajectory, which can be applied in computerized numerical control machines currently in use without any modification of their original feedback controllers. While the linearly interpolated contour error compensation enhances tracking performance by compensating the reference input with an actual value, the Bézier reposition trajectory enables smooth velocity transitions between discrete points in the reference trajectory. For performance analysis, the proposed controller was implemented in a commercial three-axis computerized numerical control machine and several experiments were conducted based on typical three-dimensional sharp-corner and half-circular trajectories. Experimental results showed that the proposed controller could reduce the maximum and mean contour errors by 45.11% and 54.48% on average, compared to embedded iterative learning contouring controller with estimated contour error. By comparing to embedded iterative learning contouring controller with linearly interpolated contour error compensation, the maximum and mean contour errors are reduced to 20.54% and 26.92%, respectively.

Development of Pitch Cycle-Based Iterative Learning Contour Control for Thread Milling Operations in CNC Machine Tools

“…Although many CEV estimation methods have been proposed in recent decades, the accuracy, complexity, and calculation time of the estimated CEV must be carefully considered in the PCB-ILCC design. Therefore, this study used the interpolated positions on a helical path to estimate the CEV [27]. As shown in Figure 4, R denotes the response position on the response path; i H and…”

“…Although many CEV estimation methods have been proposed in recent decades, the accuracy, complexity, and calculation time of the estimated CEV must be carefully considered in the PCB-ILCC design. Therefore, this study used the interpolated positions on a helical path to estimate the CEV [27]. As shown in Figure 4 to the geometric relationship shown in Figure 4, the distance relations can be obtained as Equations ( 1) and ( 2): Let d i−1 and d i , respectively, denote the distance from R to H i−1 and H i , and let D i−1 and D i , respectively, denote the distance from H c to H i−1 and H i .…”

“…Thus, the control parameters K 1 and K 0 were tuned to rapidly attenuate errors without significant oscillations. Referring to Equation (27), because the threshold constant σ affects the chattering phenomenon of the solution trajectory, the threshold constant σ was tuned to suppress chattering. Furthermore, the larger the bounded value ρ, the more stable control is achieved; however, a large bounded value usually increases the response time and steady-state errors of the PMSM driving control.…”

A corner smoothing algorithm using Trajectory Pattern Method (TPM) for high-speed and high-quality machining

“…To this end, several researchers have investigated methods for smooth tool path generation. 1,2 Some researchers have focused on the Local Smooth Method (LSM), in which transition curves are constructed at the junction of small line-segments to improve corner smoothness and velocity since it is simple to implement and is easily controlled. For example, Lv et al 3 used arcs to blend small line-segments.…”