永磁同步电动机的有限时间自适应混沌控制

Finite-time adaptive chaos control for permanent magnet synchronous motor

针对永磁同步电动机(PMSM)的混沌吸引子现象以及研究中只能实现平衡状态的周期点的混沌同步控制问题,提出了一种基于自动控制理论与有限时间控制原理的零误差系统算法。首先,通过已建立的PMSM的数学模型,经过数学公式转化得到PMSM各状态变量与其预期设定值之间形成的误差系统模型;然后,利用李雅谱诺夫稳定性理论,对所形成的误差系统模型进行同步控制器与校正率的设计,并证明误差系统在有限时间内快速地收敛至零点;最后,对误差系统施加干扰量,对算法进行鲁棒性分析。理论与仿真结果表明,所提出的算法能实现误差系统到达零点后仍一直维持在零点的平衡状态,有效地抑制PMSM系统中混沌吸引子现象的产生,灵活地调整PMSM的输入输出,在确保PMSM正常运转的基础上,PMSM系统对不定性参量与外部扰动量具有良好的鲁棒特性。

Aiming at the issue that chaotic attractor exists in Permanent Magnet Synchronous Motor （PMSM） and chaotic synchronous control of PMSM cannot be realized except on the cycle of the equilibrium point, a kind of zero error system algorithm based on automatic control theory and finite time control principle was proposed. Firstly, the error system was established by mathematical model of PMSM and a mathematical formula between each state variable and its expected value in PMSM. Secondly, synchronous controller and correction rate were designed for the error system model and the conclusion that the error system could quickly converge to zero in finite time was proved by using Lyapunov＇s stability criterion. Finally, interference was imposed on the error system and the robustness of the algorithm was analyzed. The theoretical analysis and simulation results show that the proposed algorithm can maitain in zero balance after reaching the zero point of the system, which can effectively restrain the chaotic attractor and adjust the input and output of PMSM flexibly; and the PMSM system has good robustness to the uncertainty parameter and external disturbance while ensuring the normal operation of PMSM.