﻿ 基于混合粒子群算法的船用离心泵电机优化研究
 舰船科学技术  2022, Vol. 44 Issue (18): 134-138    DOI: 10.3404/j.issn.1672-7649.2022.18.027 PDF

Optimization of marine centrifugal pump motor based on hybrid particle swarm optimization
FU Rong-he, XING Ji-sheng
School of Electrical and Information Engineering, Beihua University, Jilin 132021, China
Abstract: In the marine system, the centrifugal pump plays a key role in operation, and whether the driving motor runs reliably is the premise for the pump to work stably. The traditional PID manual parameter adjustment method has the disadvantages of long setting time and great difficulty, so it is difficult to achieve the ideal control results. To solve the above problems, a method of using hybrid particle swarm optimization (HPSO) to optimize the parameters of PID controller is proposed. The concept of random movement in bat algorithm (BA) is introduced into particle swarm optimization algorithm, which is compared with PSO algorithm and traditional methods, and the PID control model is established by MATLAB software. The simulation results show that the PID controller optimized by HPSO can overcome the disadvantage that the traditional particle swarm optimization (PSO) is easy to fall into local optimization, and can find the best parameters of the PID controller efficiently, accurately and quickly. It shows the advantages of good robustness, less adjustment time and relatively stable operation, and the system can run more stably.
Key words: PID controller     hybrid particle swarm optimization     parameter optimization     centrifugal pump motor
0 引　言

PID控制由于应用广泛，原理易懂，因而得到了普遍运用[3]。PID控制器参数整定优化的结果对于离心泵电机的控制效果起决定作用，然而在传统PID参数整定过程中含有复杂棘手、难度大等缺点[4]，传统方式很难在复杂系统中整定出理想的最优值，致使其控制效果不佳，不能满足系统的控制要求。

1 PID控制

PID控制器由3部分构成，分别为比例、积分和微分等[5]，一般形式下式：

 $u(t) = {K_p}e(t) + {K_i}\int_0^t {e(\tau )} + {K_d}\frac{{{\rm{d}}e(t)}}{{{\rm{d}}t}}。$ (1)

 ${G_{\left( s \right)}} = \frac{{{N_{\left( s \right)}}}}{{{U_{\left( s \right)}}}} = Kp\left( {1 + \frac{1}{{{T_i}s}} + {T_d}s} \right)。$ (2)

 $J = \int_0^\infty {{{t}}\left| {{e_{\left( t \right)}}} \right|} {\rm{d}}t。$ (3)
2 PID控制模型 2.1 船用离心泵电机研究

 图 1 离心泵结构图 Fig. 1 Structure diagram of centrifugal pump

2.2 电机传递函数

 图 2 永磁直流电机等效电路图 Fig. 2 Equivalent circuit diagram of permanent magnet DC motor

 ${T_e} = {T_2} + J\frac{{{{\rm{d}}\omega }}}{{{{\rm{d}}t}}} + {M_L}\omega 。$ (4)

 ${M_l} = {C_m} \times {I_a}。$ (5)

 ${U_a} = {E_a} + {I_d}{R_a} + {L_a}\frac{{{\rm{d}}{l_a}}}{{{{\rm{d}}t}}} + {{\Delta }}{{{U}}_{{b}}} 。$ (6)

${T_b} = \dfrac{{J \times {R_a}}}{{{K_e} \times {C_m}}}$ 为电机电气机械时间常数， ${K_e}$ 为电动势常数； ${T_c} = \dfrac{{{L_a}}}{{{R_a}}}$ 为电机的电气时间常数。不考虑粘性摩擦负载，则ML=0。根据自动控制理论知识能快速得到其传递函数表达式[9]，化简后如下式：

 ${G_{\left( {\text{s}} \right)}} = \frac{{{K_{\text{e}}}}}{{J{L_a}{s^2} + J{R_a}s + {K_{\text{e}}}{C_{\text{m}}}}}。$ (7)
2.3 传递函数的确定

 ${G_{\left( {\text{s}} \right)}} = \frac{{68}}{{{s^2} + 4.5s + 1}}。$ (8)

3 智能算法 3.1 粒子群算法

 ${v_{t + 1}} = \omega {v_t} + {c_1}{r_1}\left( {{P_{prime}} - {x_t}} \right) + {c_2}{r_2}\left( {{G_{prime}} - {x_t}} \right)，$ (9)
 ${x_{t + 1}} = {x_t} + {v_{t + 1}}。$ (10)

 图 4 PSO优化PID过程图 Fig. 4 PSO Optimization PID process diagram
3.2 蝙蝠算法

 ${f_i} = {f_{\min}} + \left( {{f_{\max}} - {f_{\min}}} \right) \xi，$ (11)
 ${\nu _i}^{t + 1} = {\nu _i}^t + \left( {{x_{{\rm{prime}}}} - {x_i}^t} \right){f_i}，$ (12)
 ${x_i}^{t + 1} = {x_i}^t + {\nu _i}^{t + 1}。$ (13)

 ${x_n} = {x_o} + \tau {A^t}。$ (14)

3.3 混合粒子群算法（HPSO）

 $\begin{split} & {\nu _i}^{t + 1} = \omega {v_i}^t + \omega \left( {{P_{prime}} - {x_i}^t} \right){f_i} + {c_1}{r_1}\times \\ & \left( {{P_{prime}} - {x_0}^t} \right) + {c_2}{r_2}\left( {{G_{prime}} - {x_0}^t} \right)，\end{split}$ (15)
 ${y_i}^{_{t + 1}} = {x_i}^{_{t + 1}}{x_0} + \tau {A^t} + {v_i}^{_{t + 1}}。$ (16)

 图 5 HPSO整定PID参数控制图 Fig. 5 HPSO tuning PID parameter control diagram

4 仿真结果与对比分析

 图 6 适应值收敛曲线 Fig. 6 fitness convergence curve

 图 7 系统阶跃响应输出曲线 Fig. 7 System step response output curve

HPSO到达稳定所用的调节时间为1.81 s，优于PSO稳定的调节时间2.09 s和传统方法的3.54 s，因此系统的调节速度更快，能很快达到稳定状态。经过HPSO优化的PID最佳参数，使其选出的3个K值恰当，能够很好将调节时间和超调量等优化到尽可能少，使得系统能得到良好的控制效果，因而证明此方法的可行性。

5 结　语

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