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: 浓密机是矿物加工与湿法冶金工艺中的关键设备,其运行状态直接关系到生产效率和资源回收率. 然而,由于浓密机具有强非线性、高时滞、多变量耦合以及易受外部干扰等复杂特性,传统控制方法往往难以实现对其底流浓度的精准稳定控制. 为此,本文以提高底流浓度控制性能为研究目标,提出一种结合机理建模与智能补偿的复合控制策略. 首先,基于沉降–分离理论,建立浓密机的状态空间模型,并设计一种非线性模型预测控制(NMPC)方法,以实现对设定底流浓度的有效跟踪. 进一步地,考虑到实际过程中存在的未建模动态、参数摄动和外部干扰等不确定因素,引入径向基函数(RBF)神经网络作为在线补偿器,用于实时修正机理模型的预测输出,从而增强系统在复杂工况下的预测精度与控制鲁棒性. 最后,通过浓密机仿真实验将所提NMPC–RBF策略与比例积分微分控制(PID)、模型预测控制(MPC)及NMPC方法进行对比. 结果表明,NMPC–RBF在底流浓度跟踪中表现最优,其引入的RBF补偿机制通过提前修正系统输出,有效克服了模型失配问题,显著提升了跟踪精度与鲁棒性,为复杂工业过程中浓密机的优化控制提供了可行方案.

     

    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 control 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.

     

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