﻿ 基于滑膜控制的船舶永磁同步推进电机直接转矩控制研究
 舰船科学技术  2022, Vol. 44 Issue (10): 84-88    DOI: 10.3404/j.issn.1672-7649.2022.10.016 PDF

Research on direct torque control of ship permanent magnet synchronous propulsion motor based on sliding mode control
BAI Yan-xiang, ZHANG Yuan-wei, YU Zheng-dong
The 704 Research Institute of CSSC, Shanghai 200031, China
Abstract: With the development of pod propeller, the permanent magnet synchronous motor is widely used as marine propulsion motor. However, due to the complexity of propeller load, in order to improve the control performance of propulsion motor, this paper fully analyzes the basis of direct torque control (DTC). In this paper, a direct torque control based on sliding mode control is proposed. The control rate uses the Super-Twisting algorithm based on second-order sliding mode, and its convergence in torque and flux control is proved. Mathematical models based on traditional DTC and DTC based on sliding mode control are established, and simulation comparison studies are carried out based on Matlab/Simulink. The results show that DTC based on sliding mode control has the characteristics of small torque pulsation, fast response, strong robustness and strong anti-interference ability compared with traditional DTC.
Key words: electric propulsion     permanent magnet synchronous motor     direct torque control     sliding mode control
0 引　言

1 直接转矩控制分析

 图 1 PMSM矢量关系图 Fig. 1 PMSM vector diagram

 $\left\{ \begin{gathered} {\psi _d} = \left| {{\psi _s}} \right|\cos {\delta _{sf}}，\hfill \\ {\psi _q} = \left| {{\psi _s}} \right|\sin {\delta _{sf}}，\hfill \\ \end{gathered} \right.$ (1)

 $\left\{ \begin{gathered} {\psi _d} = {\psi _f} + {L_d}{i_d}，\hfill \\ {\psi _q} = {L_q}{i_q}。\hfill \\ \end{gathered} \right.$ (2)

 ${T_e} = 1.5{p_n}[{\psi _f}{i_q} + ({L_d} - {L_q})]{i_d}{i_q}，$ (3)

 ${T_e} = \frac{3}{2}\frac{{{p_n}}}{{{L_d}}}\left| {{\psi _s}} \right|{\psi _f}\sin {\delta _{sf}} + \frac{3}{4}\frac{{{p_n}({L_d} - {L_q})}}{{{L_d}{L_q}}}{\left| {{\psi _s}} \right|^2}\sin 2{\delta _{sf}}，$ (4)

 ${T_e} = \frac{3}{2}\frac{{{p_n}}}{{{L_s}}}\left| {{\psi _s}} \right|{\psi _f}\sin {\delta _{sf}}。$ (5)

 图 2 传统直接转矩控制系统框图 Fig. 2 The system block diagram of traditional PMSM-DTC
2 基于滑模控制的DTC控制研究

 $\left\{ \begin{gathered} \frac{{{\rm{d}}x}}{{{\rm{d}}t}} = a(x,t) + b(x,t)u ，\hfill \\ y = c(x,t) 。\hfill \\ \end{gathered} \right.$ (6)

 $\left\{ \begin{gathered} u = - {K_p}{\left| y \right|^r}{\rm{sgn}} (y) + {u_1}，\hfill \\ \frac{{{\rm{d}}{u_1}}}{{{\rm{d}}t}} = - {K_i}{\rm{sgn}} (y)。\hfill \\ \end{gathered} \right.$ (7)

 $\left\{ \begin{gathered} {K_p} > \frac{{{A_M}}}{{{B_m}}}，\hfill \\ {K_i} \geqslant \frac{{4{A_M}}}{{B_m^2}} \cdot \frac{{{B_M}({K_p} + {A_M})}}{{{B_m}({K_p} - {A_M})}}。\hfill \\ \end{gathered} \right.$ (8)

 $\frac{{{{\rm{d}}^2}y}}{{{\rm{d}}{t^2}}} = A(x,t) + B(x,t)\frac{{{\rm{d}}u}}{{{\rm{d}}t}}。$ (9)

 $\frac{{{\rm{d}}{T_e}}}{{{\rm{d}}t}} = \frac{3}{2}\frac{{{p_n}}}{{{L_s}}}\left| {{\psi _s}} \right|{\psi _f}\cos {\delta _{sf}}\frac{{{\rm{d}}{\delta _{sf}}}}{{{\rm{d}}t}}，$ (10)
 $\frac{{{{\rm{d}}^2}{T_e}}}{{{\rm{d}}{t^2}}} =\frac{{ - 3p\left| {{\psi _s}} \right|{\psi _f}\sin {\delta _{sf}}}}{{2{L_s}\Delta {T^2}}} + \frac{{3p\left| {{\psi _s}} \right|{\psi _f}\cos {\delta _{sf}}}}{{2{L_s}\Delta T}} \cdot \frac{{{\rm{d}}\Delta {\delta _{sf}}}}{{{\rm{d}}t}}。$ (11)

 $A = \frac{{ - 3p\left| {{\psi _s}} \right|{\psi _f}\sin {\delta _{sf}}}}{{2{L_s}\Delta {T^2}}}，$ (12)
 $B = \frac{{3p\left| {{\psi _s}} \right|{\psi _f}\cos {\delta _{sf}}}}{{2{L_s}\Delta T}}。$ (13)

 ${s_T} = T_e^* - {T_e}，$ (14)

 $\left\{ \begin{gathered} u_d^* = {K_p}{\left| {{s_T}} \right|^r}{\rm{sgn}} ({s_T}) + {u_{sq}}，\hfill \\ \frac{{\rm{d}}}{{{\rm{d}}t}}{u_{sq}} = {K_i}{\rm{sgn}} ({s_T})。\hfill \\ \end{gathered} \right.$ (15)

 $\frac{{{\rm{d}}{\psi _s}}}{{{\rm{d}}t}} = {u_d} - {R_s}{i_d}，$ (16)
 $\frac{{{{\rm{d}}^2}{\psi _s}}}{{{\rm{d}}{t^2}}} = \frac{{R_s^2}}{{{L_s}}}{i_d} - {\omega _r}{R_s}{i_q} - \frac{{{R_s}}}{{{L_s}}}{u_d} + {\dot u_d}。$ (17)

 ${s_\psi } = \psi _s^* - {\psi _s}，$ (18)

 $\left\{ \begin{gathered} u_d^* = {K_p}{\left| {{s_\psi }} \right|^r}{\rm{sgn}} ({s_\psi }) + {u_{sd}}，\hfill \\ \frac{{\rm{d}}}{{{\rm{d}}t}}{u_{sd}} = {K_i}{\rm{sgn}} ({s_\psi })。\hfill \\ \end{gathered} \right.$ (19)

 图 3 基于滑模控制的直接转矩控制系统图 Fig. 3 The system block diagram of PMSM-DTC based on sliding mode control
3 仿真分析 3.1 仿真模型的建立

 图 4 基于滑模控制的DTC仿真程序 Fig. 4 DTC simulation program based on sliding mode control

 图 7 实际转矩变化曲线 Fig. 7 Actual torque curve
3.2 仿真结果分析

 图 5 实际定子磁链变化曲线 Fig. 5 Actual stator flux curve

 图 6 实际转速变化曲线 Fig. 6 Actual speed curve

1）从图5可以看出，在整个仿真过程中，2种控制方式的定子磁链相轨迹都为符合理论的圆形，都可以稳定在参考值上，但基于滑模控制的DTC相对于传统DTC，具有更小的磁链脉动，而且，波动频率相对小，这对降低电磁转矩脉动必然产生有利的作用。

2）从图6可以看出，当电机由零速上升到600 r/min参考转速时，以及在带载时，转速由600 r/min增加到800 r/min时，在2种控制方式下，电机都有一定的转速超调量，但基于滑模控制的DTC与传统DTC相比具有更快的动态响应，而且转速稳定后非常稳定平滑，几乎无波动。

3）从图7可以看出，在加速及突加负载等整个仿真过程中，基于滑模控制的DTC与传统DTC相比，动态响应时间更快，而且当状态稳定后，传统DTC控制较基于滑模的DTC控制的电机电磁转矩波动幅值大而且频率较快，从而说明基于滑模控制的DTC控制相对于传统DTC具有更好的动态性能和抗扰动能力，具有良好的船舶推进电机的控制性能。

4 结　语

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