基于GWO的永磁同步电动机Hamilton模型的混沌控制

针对永磁同步电动机中存在的不利于系统运行的混沌现象，利用Hamilton理论首先把永磁同步电动机模型转化为带扰动非线性项的严格耗散广义Hamilton系统模型，依据其模型特点进行了扰动补偿器及跟踪控制器的设计。针对广义Hamilton系统模型中非线性扰动项，设计了带有可调增益矩阵的扰动补偿器，并利用Lyapunov稳定定理证明了加入扰动补偿器后的系统是渐近稳定的。通过任意选取期望平衡点来修正Hamilton能量函数，并结合修正互联和阻尼控制的设计方法，设计了含待定系数矩阵的跟踪控制器，其中的待定系数矩阵为期望结构的修正矩阵。为了更好地增强系统的自适应能力，采用苍狼优化算法（GWO）寻求扰动补偿器中的最佳可调增益及跟踪控制器中的期望结构的修正矩阵的最佳系数，苍狼位置矢量由可调增益参数及修正矩阵的待定系数组成，苍狼捕猎的迭代过程实为有目的的待定参数寻优过程。为了验证以上控制方法的有效性，从系统期望输出、负载扰动输入及交直轴电压输入等3个方面出发，合理设计了相应的仿真比较实验。实验结果表明，被控后的系统混沌现象得到了抑制，系统能较好跟随期望输出，且具有一定的抗负载扰动及电压扰动的能力。同时也验证了苍狼优化算法协助设计控制器参数的有效性，克服了传统的依据经验设定参数的缺点，使参数依目标得到了较优的选择，一定程度上提高了系统自适应能力。

Chaos Control on the Hamilton Model of Permanent Magnet Synchronous Motor Based on GWO

In order to inhibit the harmful chaos of permanent magnet synchronous motor (PMSM),the model of PMSM was transformed to a generalized Hamilton model with some nonlinear disturbance.Then a disturbance compensator and a tracking controller were designed from its Hamilton model.Next a disturbance compensator with adjustable gain matrix was designed for the nonlinear disturbance in the generalized Hamilton model,and the system with the disturbance compensator was proved to have the asymptotic stability by Lyapunov stability theorem.After fixing the Hamilton energy function with freely choosing the desired equilibrium,the tracking controller with undetermined coefficient matrix was designed with the method of modified interconnect and damping control,and the undetermined coefficient matrix was a modified matrix with an expected structure.To improve the adaptive ability of the system,grey wolf optimizer (GWO) was applied to find the best adjustable gains of the disturbance compensator and the optimal coefficients of expecting correction matrix for the tracking controller.The wolf position vector was composed of adjustable gain parameters and the undetermined coefficients of the correction matrix,and the iterative process of GWO was a purposeful optimization one.To verify the validity of the above-controlled method,several contrast experiments were designed from the change of desired output,the load disturbance,as well as the a-axis and d-axis voltage disturbance.The experimental results showed that the chaotic phenomena of the system are suppressed,the system could follow the expected output well and have better capacity in resisting load disturbances and voltage disturbances.The validity of grey wolf optimizer algorithm in assisting the controllers'' parameters on the basis of the optimized objective function,which improves the adaptive ability of the system,was also proved by the experimental results.