Design of a real-time three-axis controller for contour error reduction based on model predictive control

Abstract

The machining accuracy is mainly indicated by the contour error especially in high-precision processing. Previously, scholars have proposed many controllers to reduce contour errors in real-time machining, such as the cross coupling controller and sliding mode controller. In this paper, we propose a controller based on model predictive control (MPC), and the contour error caused during path tracking can be effectively reduced by this controller. First of all, for two-dimensional (2D) and three-dimensional (3D) tool paths, their contour errors are deduced based on coordinate system transform. Second, the MPC-based controller is designed with the state-space discrete model of a machine tool. The contour error is regarded as a constraint during receding optimization. These are reasons why the presented control scheme is adapted with both bi-axis and three-axis machine tools. Furthermore, in order to improve the efficiency of receding optimization, the contour error of a 3D curve is simplified. Subsequently, the optimization problem is transformed into the standard form of quadratic programming. Finally, a 2D tool path and a 3D tool path are machined to test the proposed controller. Simulations and experiments show satisfactory results which indicate effectiveness of the proposed method.

MPPT Control Algorithm Based on Particle Swarm Optimization and Adaptive Linear Active Disturbance Rejection Control

“…It shows that the output speed curve of the motor under the control of LADRC can rapidly track the reference curve. In addition, LADRC is also used in various other engineering areas due to its wide adaptability [27][28][29].…”