Optimal Output Feedback Controller Design of Permanent Magnet Synchronous Motor Speed Servo System
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摘要: 针对永磁同步电动机(Permanent magnet synchronous motor, PMSM)模型参数未知以及电枢电流和负载转矩无法直接测量的问题, 设计一种基于自适应动态规划(Adaptive dynamic programming, ADP)的输出反馈控制方案, 实现PMSM最优速度跟踪控制. 首先, 根据PMSM内部特性确定其数学模型的结构, 构建与原始系统相对应的辅助系统, 引入新的线性二次指标来实现速度最优跟踪调节. 其次, 设计一种嵌入式观测器, 该观测器能够在系统模型未知情况下用可测量数据重构系统全部状态. 此外, 提出一种离线策略的ADP方法逼近最优控制增益的解. 最后, 仿真结果验证所提控制方案在模型参数未知以及电枢电流和负载转矩不可测量的情况下, 实现了精确的速度跟踪性能和良好的瞬态响应, 同时降低了电压的冲击.Abstract: In response to the problems of unknown model parameters of permanent magnet synchronous motor (PMSM) and inability to directly measure armature current and load torque, this paper designs an output feedback control scheme based on adaptive dynamic programming (ADP) to achieve optimal speed tracking control for PMSM. Firstly, based on the internal characteristics of the PMSM, the mathematical model＇s structure is determined. An auxiliary system corresponding to the original system is constructed, and a new linear quadratic index is introduced to achieve optimal speed tracking adjustment. Next, an embedded observer is designed that can reconstruct all system states with measurable data in the presence of unknown system models. In addition, this paper proposes an off-policy ADP method to approximate the solution of the optimal control gain. Finally, the simulation results verify that the proposed control scheme achieves precise speed tracking performance and good transient response in the presence of unknown model parameters and unmeasurable armature current and load torque, while reducing voltage shocks.
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图 4 不同控制方法下转子速度的跟踪效果
Fig. 4 Tracking effect of rotor speed under different control methods
图 8 方法2和方法4下的$ q $轴电压响应局部放大
Fig. 8 Partial amplification of q-axis voltage response under method 2 and method 4
图 9 不同权重$ Q $下的转子速度跟踪效果
Fig. 9 Tracking effect of rotor speed under different weights $ Q $
图 10 不同权重$ Q $下的$ q $轴电压响应
Fig. 10 q-axis voltage response under different weights $ Q $
图 11 不同权重$ R $下的转子速度跟踪效果
Fig. 11 Tracking effect of rotor speed under different weights $ R $
图 12 不同权重$ R $下的$ q $轴电压响应
Fig. 12 q-axis voltage response under different weights $ R $
表 1 PMSM系统参数设置
Table 1 PMSM system parameters setting
参数 大小 单位 转动惯量$J$ $2.10\times 10^{-3}$ ${{\rm{kg}}{\cdot}{\rm{m}}}^2$ 粘性摩擦系数$B_s$ $5.71\times 10^{-3}$ ${{\rm{N}}{\cdot}{\rm{s/rad}}}$ 极对数$n_p$ $4$ — 永磁通链$\varphi$ $8.10\times 10^{-2}$ Wb 定子电感$L_s$ $9.80\times 10^{-3}$ H 定子电阻$R_s$ $1.06$ $\Omega$ 
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