﻿ 船舶永磁同步电机在线惯量辨识研究
 舰船科学技术  2024, Vol. 46 Issue (5): 103-108    DOI: 10.3404/j.issn.1672-7649.2024.05.019 PDF

Research on on-line inertia identification of marine permanent magnet synchronous motor
DAI Lei, ZHANG Yong-lin, ZHAO Jin, WU Meng-yu, LIU Ni
College of Automation, Jiangsu University of Science and Technology, Zhenjiang 212100, China
Abstract: The moment of inertia and load torque of Marine permanent magnet synchronous motor propulsion system are disturbed. To solve the above problems, an online inertia identification algorithm based on the combination of gradient correction method and extended Kalman filter is proposed. The gradient correction method is used to identify the moment of inertia, and the extended Kalman filter is used to observe the load torque, and the identified inertia value is used to correct the coefficient matrix of the filter. The observed load torque is used as input parameter of gradient correction method and feedforward compensation of current loop. Simulation and experiments verify the feasibility of the inertia identification algorithm and the anti-disturbance performance of the system for load torque variation.
Key words: rotational inertia     load torque     gradient correction method     extended Kalman filter     anti-disturbance
0 引　言

1 PMSM的数学模型

 $\left\{ \begin{gathered} {u_d} = R{i_d} + {L_d}\frac{{\rm{d}}}{{{\rm{d}}t}}{i_d} - {\omega _e}{L_q}{i_q}，\\ {u_q} = R{i_q} + {L_q}\frac{{\rm{d}}}{{{\rm{d}}t}}{i_q} + {\omega _e}({L_d}{i_d} + {\psi _f}) 。\\ \end{gathered} \right.$ (1)

 图 1 船舶推进系统惯量辨识框图 Fig. 1 Block diagram of inertia identification of ship propulsion system

 $F[x(t)] = {\left. {\dfrac{{\delta f}}{{\delta x}}} \right|_{x = x(t)}} = \left[ {\begin{array}{*{20}{c}} {{{ - }}\dfrac{{{B}}}{{{J}}}}&{{{ - }}\dfrac{{{1}}}{{{J}}}} \\ {{0}}&{{0}} \end{array}} \right]，$ (18)
 $H[x(t)] = {\left. {\frac{{\delta h}}{{\delta x}}} \right|_{x = x(t)}} = \left[ {\begin{array}{*{20}{c}} {{1}}&{{0}} \end{array}} \right]。$ (19)

 $\left\{ \begin{gathered} x(k + 1) = {A_k}x(k) + {B_k}u(k) + w(k)，\\ y(k) = {H_k}x(k) + v(k) 。\\ \end{gathered} \right.$ (20)

 $\left\{ \begin{gathered} \cos (w) = E\left\{ {w{w^{\rm{T}}}} \right\} = Q = \left[ {\begin{array}{*{20}{c}} {{{{q}}_{{w}}}}&{{0}} \\ {{0}}&{{{{q}}_{{{{T}}_{{L}}}}}} \end{array}} \right]，\\ \cos (v) = E\left\{ {v{v^{\rm{T}}}} \right\} = R 。\qquad\qquad\qquad\quad\\ \end{gathered} \right.$ (21)

 $\widetilde x(k + 1) = \widehat x(k) + {T_s}[f(\widehat x(k)) + B(k)u(k)]。$ (22)

 $\widetilde p(k + 1) = F(k)\widehat p(k + 1)F{(k)^{\rm{T}}} + Q。$ (23)

 $K(k + 1) = \widetilde p(k + 1){H^T}{[H\widetilde p(k + 1){H^T} + R]^{ - 1}}。$ (24)

 $\widehat x(k + 1) = \widetilde x(k + 1) + K(k + 1)[y(k + 1) - \widetilde y(k + 1)]。$ (25)

 $\widehat p(k + 1) = \widetilde p(k + 1) - K(k + 1)H\widetilde p(k + 1)。$ (26)
3 仿真分析

3.1 定惯量辨识仿真

 图 2 $\lambda$取不同值的辨识效果 Fig. 2 Identification effect of different values of $\lambda$

3.2 变惯量辨识仿真

${\text{Matlab/Simulink}}$软件中，根据PMSM的数学方程自定义创建电机模型，目的是把转动惯量$J$的端口引出，从而可以接任何信号，达到变惯量仿真的效果。为测试算法在转动惯量发生突变时的性能，开始电机空载运行，设定在$t = 0.5\;{\text{s}}$时，突然加入 $1$ 倍和 $4$ 倍电机转子惯量的负载惯量，则系统总的转动惯量${J'_1} = J + {J_{L1}} = 1.118 \times {10^{ - 4}}\;{\rm{kg \cdot {m^2}}}$${J'_2} = J + {J_{L2}} = 2.795 \times$${10^{ - 4}}\;{\rm{kg \cdot {m^2}}}。$

 图 4 突加1倍惯量的仿真效果 Fig. 4 The simulation effect of adding 1 times of inertia suddenly

 图 5 突加4倍惯量的仿真效果 Fig. 5 The simulation effect of adding 4 times of inertia suddenly
3.3 负载扰动仿真

 图 6 参数突变的辨识结果 Fig. 6 Identification results of parameter mutation

 图 8 空载条件下辨识值 Fig. 8 Identification value under no-load condition

 图 9 带载条件下辨识值 Fig. 9 Identification value under load condition

 图 10 负载转矩观测值 Fig. 10 Observed load torque
5 结　语

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