﻿ 水下航行器低速无刷直流电机调速控制
 舰船科学技术  2023, Vol. 45 Issue (12): 69-72    DOI: 10.3404/j.issn.1672-7619.2023.12.013 PDF

Speed control of low speed brushless dc motor for underwater vehicles
ZHA Jing-zhou, ZHANG Hua
Department of Information and Electronics, Science and Technology College of NCHU, Gongqingcheng 332020, China
Abstract: In order to improve the speed control technology level of low-speed brushless DC motor for underwater vehicle, a speed control method of low-speed brushless DC motor for underwater vehicle is proposed. Through the mathematical model of low-speed brushless DC motor of underwater vehicle, the speed control parameters of the mathematical model of low-speed brushless DC motor are output by this mathematical model, and then the fuzzy PID control parameters are designed, and the fuzzy PID control parameters are adjusted by sparrow search algorithm. By adjusting the deviation between the input value and the actual feedback value, the speed control of low-speed brushless DC motor of underwater vehicle is realized. The experimental results show that the difference between the numerical value and the actual value of the electromagnetic power of the low-speed brushless DC motor of underwater vehicle calculated by this method is small, and the fuzzy PID control parameter setting ability is strong, and the speed of the low-speed brushless DC motor of underwater vehicle can be effectively controlled, with rapid response and small overshoot, and the application effect is good.
Key words: underwater vehicle     speed control     mathematical model     PID controller     sparrow search algorithm
0 引　言

1 低速无刷直流电机调速控制方法 1.1 水下航行器低速无刷直流电机数学模型构建

 $\begin{split} \left[ \begin{gathered} {u_A} \\ {u_B} \\ {u_C} \\ \end{gathered} \right] = &\left[ \begin{array}{*{20}{l}} {R_A}& 0& 0 \\ 0&{R_B}& 0 \\ 0& 0& {R_C} \end{array} \right]\left[ \begin{gathered} {i_A} \\ {i_B} \\ {i_C} \\ \end{gathered} \right] + \frac{\rm d}{{{\rm d}t}}\left[ \begin{array}{*{20}{l}} {Q_A}& {Q_{AB}}& {Q_{AC}} \\ {Q_{BA}}& {Q_B}& {Q_{BC}} \\ {Q_{CA}}& {Q_{CB}}& {Q_C} \end{array} \right] \times \\ & \left[ \begin{gathered} {i_A} \\ {i_B} \\ {i_C} \\ \end{gathered} \right] + \left[ \begin{gathered} {g_A} \\ {g_B} \\ {g_C} \\ \end{gathered} \right] + \left[ \begin{gathered} {u_n} \\ {u_n} \\ {u_n} \\ \end{gathered} \right]。\\[-30pt] \end{split}$ (1)

 $\begin{split} {\left[ \begin{gathered} {u_A} \\ {u_B} \\ {u_C} \\ \end{gathered} \right]^\prime } = &\left[ \begin{array}{*{20}{l}} R & 0 & 0 \\ 0 & R & 0 \\ 0 & 0 & R \end{array} \right]\left[ \begin{gathered} {i_A} \\ {i_B} \\ {i_C} \\ \end{gathered} \right] + \frac{{\rm{d}}}{{{\rm{d}}t}}\left[ \begin{array}{*{20}{c}} Q - M & 0 & 0 \\ 0 & Q - M & 0 \\ 0 & 0 & Q - M \end{array} \right] \times \\ & \left[ \begin{gathered} {i_A} \\ {i_B} \\ {i_C} \\ \end{gathered} \right] + \left[ \begin{gathered} {g_A} \\ {g_B} \\ {g_C} \\ \end{gathered} \right] + \left[ \begin{gathered} {u_n} \\ {u_n} \\ {u_n} \\ \end{gathered} \right]。\\[-30pt] \end{split}$ (2)

${g_a}$ ${g_b}$ ${g_c}$ 分别表示反电动势，当水下航行器低速无刷直流电机在运转时，其电源主要吸收电磁功率、铜和铁的消耗，但其中铜和铁的消耗占比极少，在忽略铜和铁的消耗的情况下，水下航行器低速无刷直流电机电磁功率计算公式如下：

 ${P_e} = \left( {{g_a} \times {i_a} + {g_b} \times {i_b} + {g_c} \times {i_c}} \right) \times {\left[ \begin{gathered} {u_A} \\ {u_B} \\ {u_C} \\ \end{gathered} \right]^\prime }。$ (3)

 ${M_X} = {h_e} + {h_L} + \frac{{{\rm{d}}\omega }}{{{\rm{d}}t}} \times J + {B_v} \times {P_e}。$ (4)

1.2 模糊PID控制参数设计

 ${E_R} = {M_X} \times \left( {{W_1} + {W_2}} \right) \times W'。$ (5)

 $\Delta {K_p} = {E_R} \times {\left[ \begin{gathered} {u_A} \\ {u_B} \\ {u_C} \\ \end{gathered} \right]^\prime } 。$ (6)

PID控制参数运算过程简单，具备较好的适应性和可靠性。PID控制参数通过调节输入值和实际反馈值的偏差，实现目标的控制。使用PID控制参数实现水下航行器低速无刷直流电机的调速控制，PID控制参数数学表达式如下：

 $e(t) = \Delta {K_p} \times \left[ {y^*(t) - y(t)} \right] \times \kappa 。$ (7)

1.3 基于麻雀搜索算法的模糊PID控制参数整定

 $X = e(t) \times {\left[ {{x_1},{x_2}, \cdots ,{x_n}} \right]^{\rm{T}}} 。$ (8)

 ${{F}_x} = X + {\left[ {f({x_1}),f({x_2}), \cdots ,f({x_n})} \right]^{\rm{T}}}。$ (9)

 ${x_{n + 1}} = \cos (k \times \arccos {x_n} \times {{\boldsymbol{F}}_x})。$ (10)

 ${x_{id}} = {l_d} + (1 + {y_{id}}) \times ({u_d} - {l_d})/{x_{n + 1}}。$ (11)

 $x_i^t = \left\{ \begin{array}{ll} {x_i} + {x_{id}} \times t(\lambda ),&{\rm{rand}} < p，\\ {x_i},& {\rm{otherwise}}。\\ \end{array} \right.$ (12)

2 实验分析

 图 1 收敛测试结果 Fig. 1 Convergence test results

 图 2 水下航行器低速无刷直流电机调速控制结果 Fig. 2 Speed control results of low speed brushless dc motor for underwater vehicles

 图 3 控制水下航行器低速无刷直流电机调速响应 Fig. 3 Control the speed control response of low speed brushless DC motor for underwater vehicles

3 结　语

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