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

doi:10.11949/0438-1157.20191467

Abstract

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

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

CLC Number:

TP 273

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.

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.

Figures/Tables 9

Fig.1 Gold cyanidation leaching process

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

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

Fig.2 Direct collocation method (n=3)

Fig.5 Estimation performances for state variables and parameters using EKF ( 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)

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

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

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

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

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