工程科学学报2026，Vol.48Issue(6)：1207-1219,13.DOI:10.13374/j.issn2095-9389.2025.12.12.001
基于径向基函数神经网络在线补偿的浓密机底流浓度鲁棒非线性模型预测控制
Robust nonlinear model predictive control of thickener underflow concentration with online RBF neural network compensation
摘要
Abstract
Thickeners are critical components in mineral processing and hydrometallurgical circuits.Their operational performance directly determines the production efficiency and resource recovery rates.However,maintaining precise control of the underflow concentration presents considerable challenges owing to inherently strong nonlinearities,significant time delays,multivariable coupling,and pronounced sensitivity to external disturbances.Traditional control methods are often inadequate to achieve accurate and stable regulation under complex dynamic conditions.To address these challenges,we developed an advanced composite control strategy that synergistically integrates mechanistic modeling with intelligent compensation.This study aims to enhance the underflow concentration c ontrol performance through a novel framework that combines theoretical foundations with adaptive learning capabilities.The methodological implementation proceeded in two systematically coordinated phases.Initially,based on the sedimentation separation theory,a comprehensive state-space model of the thickener process was established.This model captures the fundamental dynamics of solid-liquid separation,including the particle settling behavior,sediment compression mechanisms,and continuous discharge characteristics.This mechanistic foundation supports the formulation of a nonlinear model predictive control(NMPC)framework.NMPC employs repeated finite-horizon optimization to compute optimal control actions while explicitly handling process constraints.Subsequently,considering the practical challenges posed by unmodeled dynamics,parameter perturbations,and external disturbances,a radial basis function(RBF)neural network was incorporated as an online compensator.This intelligent component continuously identifies discrepancies between mechanistic model predictions and actual process behavior.It generates real-time corrections to enhance prediction accuracy.The RBF architecture leverages Gaussian activation functions.The network parameters are adaptively tuned using online learning algorithms to ensure optimal performance under varying operational conditions.The experimental validation included realistic industrial scenarios.Both feed flow rate and feed concentration from upstream processes were set as continuously fluctuating variables.The disturbance input increments followed a Gaussian distribution.The relationship between disturbance variation and time was mathematically characterized.Model errors were represented by a sinusoidal error signal with Gaussian noise established from the mechanistic model output and actual measured output.The compensation effectiveness of the RBF neural network for unmodeled system dynamics demonstrated excellent tracking characteristics.Although minor time delays were observed,the compensation signal maintained high consistency with the disturbance signal in terms of amplitude variation trend.This indicates the effective learning and approximation capabilities of the RBF neural network in uncertain system dynamics.Comparative case studies were conducted for four control strategies:PID,MPC,standard NMPC,and the proposed NMPC-RBF.The underflow concentration tracking results clearly demonstrated that the NMPC-RBF controller achieves the best performance.The PID controller exhibits significant steady-state errors and lower overall tracking accuracy.Both the MPC and standard NMPC controllers maintain the output near the reference,but undergo apparent oscillatory phenomena.The standard NMPC is particularly prone to large overshoot.In contrast,the NMPC-RBF output curve maintains a high degree of coincidence with the reference throughout the entire time domain.This demonstrates its superior tracking precision.This enhancement is attributed to the introduced RBF compensation mechanism.This mechanism proactively corrects the system output during rolling optimization.It effectively overcomes the performance limitations caused by model mismatch and provides more accurate prediction information for optimal decision making.Notably,within the NMPC-RBF framework,the flocculant dosage input remains stable at relatively low levels.Concentration control is primarily achieved through modulated adjustments to the underflow rate.This operational pattern aligns closely with key industrial objectives.The aim is to maintain a stable discharged solid concentration while simultaneously minimizing flocculant consumption.This contributes to a reduction in operational costs and environmental impact.These comprehensive results confirm that the integrated NMPC-RBF approach substantially enhances control accuracy,adaptive capability,and operational robustness of thickener operations.This presents a viable advanced solution for optimizing thickener performance in complex industrial environments.关键词
模型预测控制/沉降-分离理论/浓密机控制/神经网络/矿物加工Key words
model predictive control/sedimentation theory/thickener control/neural networks/mineral processing分类
信息技术与安全科学引用本文复制引用
吴逸帆,王家胜,孙亮,贺威..基于径向基函数神经网络在线补偿的浓密机底流浓度鲁棒非线性模型预测控制[J].工程科学学报,2026,48(6):1207-1219,13.基金项目
国家自然科学基金资助项目(62373038,52304121) （62373038,52304121）
