N-PID controller with feedforward og generalized maxwell-slip and static friction model for for friction compensation in machine tools - Tsung Heng, Chiew (2014)
Increasing demand for accuracy and precision in machine tools application has placed greater pressure on researchers and machine developers for better products performance. Several factors that have been identified in literature that could affect machine performance are the active presence of disturbance forces such as cutting forces and friction forces. This research focuses only on the effect of friction forces as disturbance in a positioning system. “Spikes” on milled surface are normally observed in computer numerical control machine based on recent research and analysis. These “spikes” are known as quadrant glitches and is mainly due to the friction forces, which is an undesirable and nonlinear phenomenon that cannot be avoided during positioning process. The main objective of this research is the compensation of these friction forces to improve tracking performance of system by utilizing two different approaches, namely; non-model based method and friction model-based feedforward method. Two controllers, namely, proportional-integral-derivative (PID) controller and nonlinear PID (N-PID) controller, were designed, implemented and validated as non-model based technique to compensate friction forces on a XYZ-Stage, which is a fundamental block of a milling machine. In friction model-based method, two friction models, namely; static friction model and Generalized Maxwell-slip (GMS) model, were identified, modeled and applied as friction model-based feedforward. The system frequency response function was identified using a data acquisition unit, dSPACE 1104 with MATLAB software and H1 estimator, a nonlinear least square frequency domain identification method. Parameters for static friction and GMS model were identified using heuristic method and virgin curve respectively. PID and N-PID controllers were designed based on traditional loop shaping frequency domain approach and Popov stability criterion respectively. Numerical simulation and experimental validation for non-model based method showed that N-PID controller provided 25.0% improved performance in terms of quadrant glitches magnitude reduction than the PID controller. This is due to its automatic gain adjustment based on the chosen nonlinear function. For friction model-based feedforward method, the static friction model produced 95.9% reduction in tracking errors using PID controller and 95.8% reduction using the N-PID controller. For GMS friction model feedforward, the quadrant glitches magnitude was reduced by 33.3% using PID controller and 30.0% while using the N-PID controller. Finally, a combined feedforward of static and GMS friction models with the N-PID controller has resulted in the best performance that was a 96.5% reduction in tracking errors, and a 50.0% reduction in quadrant glitches magnitude. It is concluded that this combined approach would benefits to machine tools manufacturers and users as it improves the tracking performance as well as precision especially during circular motion and low tracking velocity.