An adaptive 2DoF P-PI controller based on an improved just-in-time learning technique for ultra-low-velocity linear stages driven by PMLSMs

In this paper, an adaptive two-degree-of-freedom (2DoF) proportional/proportional-integral (P-PI) controller is presented for ultra-precise linear motion stages driven by permanent magnet linear synchronous motors (PMLSMs) under ultra-low-velocity conditions. The adaptive 2DoF P-PI controller is designed based on reliable position output predictions obtained via just-in-time learning (JITL). To implement the JITL method, the current velocity commands, current position outputs and former position outputs are employed to formulate the JITL model. To guarantee high real-time performance and high prediction accuracy, the JITL method with an improved database (JITLIDB) is presented. Through comparative experiments, JITLIDB is shown to effectively reduce computation time by virtue of its use of a layered database structure to decrease the computational burden and a forgetting factor to prevent the JITL database from infinitely increasing in size. Based on the JITL predictions, a 2DoF P-PI parameter updating algorithm is designed, which is proven to guarantee that the system position errors converge to zero using the Lyapunov method. Through ultra-low-velocity simulations using the proposed adaptive 2DoF P-PI controller based on JITLIDB, it is shown that the proposed controller achieves satisfying performance. These simulations correspond to experiments performed on an ultra-precision air-bearing linear stage driven by a PMLSM. Finally, comparative experiments are presented, in which the proposed adaptive 2DoF P-PI controller based on JITLIDB achieves superior ultra-low-velocity error performance compared with a traditional 2DoF P-PI controller with fixed parameters.