基于永磁同步电动机(PMSM)的数学模型和状态方程, 为提高其位置控制的动态响应性能和鲁棒性, 提出一种含有整数阶积分以及分数阶积分的复合型非线性滑模面, 并设计了相应的位置滑模控制算法, 其中分数阶积分项的阶次采用模糊推理原则获得. 在控制律输出中加入滑模面的分数阶积分项作为前馈补偿, 进一步增强了抑制负载扰动及削弱系统抖振的能力. 通过Lyapunov定理证明了所设计的复合积分滑模控制方法的稳定性. 对所提控制方法进行模型搭建和数值仿真, 仿真结果证明了所提方法的鲁棒性和有效性.

Based on the mathematical model and state equation of the permanent magnet synchronous motor (PMSM), a composite nonlinear integral sliding surface which contains integer order and fractional order integral was proposed, and the corresponding sliding mode controller was designed in order to improve the dynamic performance and robustness of the PMSM position control system. The order of the fractional integral term is obtained by fuzzy inference. In order to improve the robustness to load disturbance and eliminate the system chattering, the fractional order integral to the sliding surface was considered as a feed forward compensation in the control output. The stability of the proposed method was proved by using the Lyapunov stability theory. The control model was established and the numerical simulation was done. Simulation results show the performance and robustness of the proposed method.