Optimal design of Udwadia-Kalaba theory-based adaptive robust control for permanent magnet linear synchronous motor

The control performance of permanent magnet linear synchronous motor (PMLSM) is limited by uncertainty. The uncertainty is bounded by an unknown bound and may be time-varying. The boundary information of uncertainty is unknown but can be described by fuzzy set theory. To mitigate the impact of uncertainty on control performance, this paper proposes a Udwadia-Kalaba theory-based adaptive robust control (UKBARC). The proposed controller contains a Udwadia-Kalaba theory-based controller and an adaptive robust controller. In the Udwadia-Kalaba theory-based controller, the expected trajectory is taken as the expected constraint, and then the control task is converted to make the expected constraint be followed. Additionally, the adaptive robust controller is introduced to handle the system uncertainty without requiring the boundary information of uncertainty. The Lyapunov method is used to show that the performance of uniform boundedness (UB) and uniform ultimate boundedness (UUB) for the PMLSM system is guaranteed. The objective function used to characterize the trade-off between performance and control cost can be derived based on the fuzzy description of uncertainty. Thus, the optimal design of UKBARC (OUKBARC) can be achieved by minimizing the objective function. Simulation and experiment results together verify that high precision motion control can be ensured by using the proposed approach.