基于Laguerre的多组分稀土萃取分布式模型预测控制  

Distributed model predictive control for multi-component rare earth extraction based on Laguerre

作　　者：朱建勇 张琳 陆荣秀 杨辉 ZHU Jian-yong;ZHANG Lin;LU Rong-xiu;YANG Hui(School of Electrical and Automation Engineering,East China Jiaotong University,Nanchang 330013,China;Key Laboratory of Advanced Control and Optimization of Jiangxi Province,Nanchang 330013,China)

机构地区：[1]华东交通大学电气与自动化工程学院,南昌330013 [2]江西省先进控制与优化重点实验室,南昌330013

出　　处：《控制与决策》2025年第3期1005-1014,共10页Control and Decision

基　　金：国家自然科学基金项目(62363010);国家自然科学基金重大项目(61991404).

摘　　要：针对多级子工艺稀土萃取生产采用人工根据经验逐级调药的方式,容易导致人工循环调药、生产指标波动大的问题,提出一种基于Laguerre函数的分布式模型预测控制方法调节药剂量.首先,基于多稀土组分萃取机理建立具有串联结构的分布式状态空间方程,拓展成嵌有积分器的增广状态空间模型;其次,利用多组分稀土萃取中各级子工艺仅与其上游子工艺存在耦合的特点,构造一种具有输入约束的非迭代递阶求解分布式药剂量目标优化函数;由于采用较大的预测时域能够实现更高的控制精度,但会急剧增大其计算量,为此,利用Laguerre函数表示控制增量,将原目标函数转化为含有Laguerre系数的目标函数,并利用二次规划进行求解.这种方法使得计算量与预测时域无关,而仅与Laguerre函数的系数数量有关,不会随着预测时域的范围改变.仿真实验表明了所提出方法的有效性.Aiming at addressing the challenges of manual adjustment in drug dosage during multistage sub-process rare earth extraction production,as well as the significant fluctuations in production index caused by such manual adjustments,a distributed model predictive control method based on the Laguerre function is proposed.Firstly,a distributed state-space equation with series structure is established based on the extraction mechanism of multi-rare earth components,followed by the development of an augmented state-space model with embedded integrators.Secondly,a non-iterative hierarchical optimization function with input constraints is constructed to solve the distributed drug dose objective optimization function,taking advantage of the fact that the sub-process of multi-component rare earth extraction is only coupled with its upstream sub-process.Thirdly,while higher control accuracy can be achieved by using a larger prediction time domain,it also leads to significantly increased computational workload.To address this issue,the Laguerre function is utilized to represent control increment and transform the original objective function into one containing Laguerre coefficients for solution through quadratic programming.This approach ensures that computational workload remains independent of prediction time domain scope but is solely related to the number of coefficients in Laguerre function and does not change accordingly.Simulation results demonstrate the effectiveness of the proposed method.

关 键 词：溶剂萃取 预测函数 串联过程 状态空间 约束处理 分布式预测控制 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]