Adaptive Robust Position Control for Permanent Magnet Linear Synchronous Motor Based on Udwadia-Kalaba Theory

To realize the accurate motion control for permanent magnet linear synchronous motor (PMLSM) with uncertainty, this article develops an adaptive robust control based on the Udwadia-Kalaba theory (UKARC). The uncertainty is time-varying but within a bounded region, while the boundary value of the region is not known. In this paper, the control objective of PMLSM is considered as the servo constraint, then a UKARC is designed such that the constraint is satisfied. The dynamic model of PMLSM can be represented by the nominal portion and uncertain portion. For the nominal portion, a nominal control based on Udwadia-Kalaba (U-K) theory is constructed to ensure that obedience to the expected constraint can be achieved. For the uncertain portion, to mitigate the effect of uncertainty, adaptive robust control is constructed. The performance of uniformly bounded (UB) and uniformly ultimately bounded (UUB) for PMLSM is deduced based on the Lyapunov method. Furthermore, the validation of simulation and experiment are conducted to verify the accurate position tracking performance can be realized with the proposed method.