﻿ Smith预估模糊PID控制算法及其在粉末定量称重中的应用
 光学仪器  2024, Vol. 46 Issue (2): 28-35 PDF
Smith预估模糊PID控制算法及其在粉末定量称重中的应用

1. 上海理工大学 光电信息与计算机工程学院，上海 200093;
2. 上海科源电子科技有限公司，上海 200612

Smith predictive fuzzy PID control algorithm and its application in powder quantitative weighing
CHEN Qi1, YUAN Xujun2, ZHANG Rongfu1, ZHENG Yang1
1. School of Optical-Electrical and Computer Engineering , University of Shanghai for Science and Technology, Shanghai 200093, China;
2. Shanghai Cohere Electronic Technology Co., Ltd., Shanghai 200612, China
Abstract: Aiming at the quantitative weighing system developed by Shanghai Cohere Electronic Technology Co., Ltd. (consisting of a high-precision powder shaking device and a 1/10000 balance), which has nonlinearity and time delay problems due to factors such as powder density, powder fluidity, particle size, humidity, and balance delay during operation, the Smith predictive fuzzy PID controller is used to optimize the control method. Firstly, based on theoretical analysis, the transfer function of the system is obtained, and then a Smith predictive fuzzy PID controller is constructed to adapt to the nonlinearity, time delay, and other characteristics of the system. Finally, this algorithm is substituted into MATLAB to perform simulation, and a 1 g quantitative shaking experiment is carried out in the system. The standard deviation of the Smith predictive fuzzy PID control algorithm and the traditional PID algorithm is 0.0020 and 0.0042, respectively. In conclusion, the Smith predictive fuzzy PID control algorithm has better stability in practical environments and can effectively reduce the weighing error of the system.
Key words: quantitative weighing of powder    Smith predictor    fuzzy PID controller    automation

1 被控对象系统模型建立

 图 1 高精度抖粉装置 Figure 1 High-precision powder shaking device

1.1 抖粉装置运动数学模型

$0 \sim t$时间间隔内粉末下落总质量$W(t)$ 与运动时粉末下落流量率$Q(t)$ 的数学模型为

 $W(t) = \int_0^t {Q(t){\rm{d}}t}$ (1)

 $sW(s) = \rho Q(s)$ (2)

 $a\frac{{\rm{d}}}{{{\rm{d}}t}}Q(t) + bQ(t) = ku(t)$ (3)

 $G(s) = Q(t)/U(s) = k/(as + b)$ (4)

 $Q(s) = (k/as + b)u(s) + \varphi (s)$ (5)
1.2 称重系统模型

 ${Q'}(s) = (k{{\rm{e}}^{ - \tau {s}}}/as + b)u(s) + \varphi (s)$ (6)

1.3 影响因素分析与系统辨识

 ${{\boldsymbol{X}}_m} = {{\boldsymbol{X}}_{m - 1}} + {{\boldsymbol{H}}_m}({{\boldsymbol{Y}}_m} - {\boldsymbol{\alpha}}_m {{\boldsymbol{X}}_{m - 1}})$ (7)
 ${{\boldsymbol{H}}_m} = \frac{{{{\boldsymbol{P}}_m}{\alpha _m}}}{{1 + \alpha _m^{\rm{T}}{{\boldsymbol{P}}_m}{{\boldsymbol{\alpha}} _m}}}$ (8)
 ${{\boldsymbol{P}}_m} = {{\boldsymbol{P}}_{m - 1}} - {{\boldsymbol{H}}_m}{{\boldsymbol{P}}_{m - 1}}{{\boldsymbol{\alpha}} _m}$ (9)

 $\phi (s) = \frac{{Y(s)}}{{R(s)}} = \frac{{{G_{\rm{c}}}(s){G_0}(s)}}{{1 + {G_{\rm{c}}}(s){G_0}(s)}}{{\rm{e}}^{ - {\tau } {\rm{s}}}}$ (13)

2.2 模糊PID控制系统

 图 3 Smith预估模糊PID控制器 Figure 3 Smith predictive fuzzy PID controller

 $\begin{split} & \;\\[-8pt] &\left\{ \begin{gathered} {K_{\rm{P}}} = {K'}_{\rm{P}} + \Delta {k_{\rm{p}}} \\ {K_{\rm{I}}} = {K'}_{\rm{I}} + \Delta {k_{\rm{i}}} \\ {K_{\rm{D}}} = {K'}_{\rm{D}} + \Delta {k_{\rm{d}}} \\ \end{gathered} \right. \end{split}$ (14)
3 系统仿真 3.1 仿真模型构建

 图 4 MATLAB仿真模型 Figure 4 MATLAB simulation model
3.2 给定输入下仿真结果对比

 图 5 给定输入下仿真结果 Figure 5 Simulation results for given input

3.3 添加扰动后仿真结果对比

 图 6 添加扰动后仿真结果 Figure 6 Simulation results with added disturbance

4 实　验

 图 7 模糊PID参数设置程序框图 Figure 7 Block diagram of the fuzzy PID parameter setting program

 图 8 传统PID定量称重数据 Figure 8 Data with conventional PID quantitative weighing

Smith预估模糊PID定量称重数据如图9所示。数据统计如表5所示。

 图 9 Smith预估模糊PID定量称重数据 Figure 9 Data using Smith fuzzy PID quantitative weighing

5 结 论

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