基于经济模型预测控制的金氰化浸出过程动态实时优化

doi:10.11949/0438-1157.20191467

化工学报 ›› 2020, Vol. 71 ›› Issue (3): 1122-1130.DOI: 10.11949/0438-1157.20191467

基于经济模型预测控制的金氰化浸出过程动态实时优化

关宏伟¹(),叶凌箭²(),沈非凡²,顾德³,宋执环⁴

^1. 宁波财经学院机械与电气工程学院, 浙江宁波 315175
^2. 浙江大学宁波理工学院, 浙江宁波 315100
^3. 江南大学轻工过程先进控制教育部重点实验室，江苏无锡 214122
^4. 浙江大学控制科学与工程学院, 浙江杭州 310027

收稿日期:2019-12-03 修回日期:2019-12-10 出版日期:2020-03-05 发布日期:2020-03-05
通讯作者: 叶凌箭
作者简介:关宏伟（1977—），男，博士，讲师，ghw_nit@126.com
基金资助:
国家自然科学基金项目(61673349);浙江省科协育才工程(2017YCGC014);浙江省自然科学基金项目(LQ19F030004);宁波市自然科学基金项目(2018A610188);轻工过程先进控制教育部重点实验室开放课题资助（江南大学）项目(APCLI1802)

Dynamic real-time optimization for gold cyanidation leaching process using economic model predictive control

Hongwei GUAN¹(),Lingjian YE²(),Feifan SHEN²,De GU³,Zhihuan SONG⁴

^1. School of Mechanical and Electrical Engineering, Ningbo University of Finance and Economics, Ningbo 315175, Zhejiang, China
^2. Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, Zhejiang, China
^3. Key Laboratory of Advanced Control for Light Industry Processes of Ministry of Education, Jiangnan University, Wuxi 214122, Jiangsu, China
^4. School of Control Science and Engineering, Zhejiang University, Hangzhou 310027, Zhejiang, China

Received:2019-12-03 Revised:2019-12-10 Online:2020-03-05 Published:2020-03-05
Contact: Lingjian YE

摘要/Abstract

摘要：

针对金氰化浸出过程时间常数大、不确定性强等问题，提出了一种基于经济模型预测控制（EMPC）的动态实时优化方法。不同于传统的模型预测控制，EMPC将经济指标直接作为滚动优化的目标函数，在每个采样时刻求解滚动窗口内的最优操作序列。和稳态优化方法相比，基于EMPC的方法能保证动态最优性，提高经济收益。此外，金氰化浸出过程受随机噪声、未知参数可变等不确定性影响，提出使用扩展卡尔曼滤波（EKF），通过构造增广系统对状态变量及不确定参数进行在线同步估计，加强EMPC的准确性和可靠性。仿真结果表明，提出的EMPC+EKF策略能有效提高金氰化浸出过程的经济性能。

关键词: 金氰化浸出过程, 动态优化, 经济模型预测控制, 不确定性, 卡尔曼滤波

Abstract:

Gold cyanidation leaching processes suffer from slow-dynamics and strong uncertainties. To this end, an economic model predictive control (EMPC) based dynamic real-time optimization scheme is proposed for the gold cyanidation leaching process. Unlike traditional model predictive control, EMCC takes economic indicators directly as the objective function of rolling optimization, and solves the optimal operation sequence within the rolling window at each sampling time. Compared to the static optimization, the EMPC-based scheme ensures dynamic optimality, which enables to obtain a better economic performance. To deal with measurement noise and unknown parameters, the extended Kalman filter (EKF) is employed to identify the states and parameters simultaneously by constructing an extended system, such that the precision and reliability of EMPC are enhanced. Simulation results show that the proposed EMPC+EKF strategy can effectively improve the economic performance of gold cyanidation leaching process.

Key words: gold cyanidation leaching process, dynamic optimization, economic model predictive control, uncertainty, Kalman filter

中图分类号:

TP 273

关宏伟, 叶凌箭, 沈非凡, 顾德, 宋执环. 基于经济模型预测控制的金氰化浸出过程动态实时优化[J]. 化工学报, 2020, 71(3): 1122-1130.

Hongwei GUAN, Lingjian YE, Feifan SHEN, De GU, Zhihuan SONG. Dynamic real-time optimization for gold cyanidation leaching process using economic model predictive control[J]. CIESC Journal, 2020, 71(3): 1122-1130.

图/表 9

图1 金氰化浸出过程

Fig.1 Gold cyanidation leaching process

表1 金氰化浸出过程模型参数

Table 1 Model parameters for gold cyanidation leaching process

参数	标称值	参数	标称值
C _CN _, ₀ ^①/(mg/kg)	200	$d ˉ$ /μm	139
C_l, ₀ ^①/(mg/kg)	0	k ₁	0.0011
C _s _, ₀ ^①/(mg/kg)	100	k ₂	2.13
C _o/(mg/kg)	7	k ₃	0.961
C _w/(kg/kg)	0.39	k ₄	0.228
P _Au/(CNY/mg)	0.226	k ₅	3.6821×10^-9
P _CN/(CNY/mg)	0.000015	k ₆	3.71
P _CNd/(CNY/mg)	0.0000025	ρ _s/(g/cm³)	2.8
Q _s/(kg/h)	2500	ρ_l /(g/cm³)	1
V/m³	68

表1 金氰化浸出过程模型参数

Table 1 Model parameters for gold cyanidation leaching process

参数	标称值	参数	标称值
C _CN _, ₀ ^①/(mg/kg)	200	$d ˉ$ /μm	139
C_l, ₀ ^①/(mg/kg)	0	k ₁	0.0011
C _s _, ₀ ^①/(mg/kg)	100	k ₂	2.13
C _o/(mg/kg)	7	k ₃	0.961
C _w/(kg/kg)	0.39	k ₄	0.228
P _Au/(CNY/mg)	0.226	k ₅	3.6821×10^-9
P _CN/(CNY/mg)	0.000015	k ₆	3.71
P _CNd/(CNY/mg)	0.0000025	ρ _s/(g/cm³)	2.8
Q _s/(kg/h)	2500	ρ_l /(g/cm³)	1
V/m³	68

图2 直接配置法（n=3）

Fig.2 Direct collocation method (n=3)

图3 EKF状态变量估计效果（标称工况）

Fig.5 Estimation performances for state variables and parameters using EKF ( θ =[0.0012 1.917 3.866×10-9]T)

图4 EKF状态及参数估计效果（ θ =[0.0012 1.917 3.866×10-9]T）

Fig.4 Estimation performances for state variables and parameters using EKF ( θ =[0.0012 1.917 3.866×10-9]T)

图5 操作输入Q CN的运行轨迹（标称工况）

Fig.5 Trajectories of control inputs Q CN (nominal condition)

图6 成本函数J的轨迹（标称工况）

Fig.6 Trajectories of cost function J (nominal condition)

图7 操作输入Q CN的运行轨迹（参数θ未知）

Fig.7 Trajectories of control inputs Q CN (unknown parameters θ)

图8 成本函数J的轨迹（参数θ未知）

Fig.8 Trajectories of cost function J (unknown parameters θ)

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基于经济模型预测控制的金氰化浸出过程动态实时优化

Dynamic real-time optimization for gold cyanidation leaching process using economic model predictive control

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