This paper proposes an integral sliding mode control that integrates a high-gain observer (HGO) and a radial basis function neural network (RBFNN) for a permanent magnet synchronous motor (PMSM) with uncertainty. Since the second-order motion equation of the PMSM is used to improve the control performance, the speed derivative, which cannot be measured directly, is required. Thus, the HGO is designed to estimate the unknown state (speed derivative). In addition, the RBFNN is designed to approximate the compounded disturbance including the lumped disturbance of system and the HGO error effect. Unlike previous studies, the output of the RBFNN is compensated by both the controller and the HGO to improve the system robustness and observer accuracy. The sliding function and the HGO error are both taken into account in the RBFNN to explicitly guarantee the stability of the whole system. To demonstrate the superiority of the proposed method, comparative simulations and experiments were carried out in different cases.

中文翻译：

---

基于 HGO 和神经网络的具有不确定性 PMSM 的积分滑模控制

本文提出了一种积分滑模控制，它集成了高增益观测器 (HGO) 和径向基函数神经网络 (RBFNN)，用于具有不确定性的永磁同步电机 (PMSM)。由于 PMSM 的二阶运动方程用于提高控制性能，因此需要无法直接测量的速度导数。因此，HGO 旨在估计未知状态（速度导数）。此外，RBFNN 旨在逼近复合扰动，包括系统的集中扰动和 HGO 误差效应。与之前的研究不同，RBFNN 的输出由控制器和 HGO 补偿，以提高系统鲁棒性和观测器精度。RBFNN 中同时考虑了滑动函数和 HGO 误差，以明确保证整个系统的稳定性。为了证明所提出方法的优越性，在不同情况下进行了比较模拟和实验。