A dynamic flotation model for predictive control incorporating froth physics. Part II: Model calibration and validation
A dynamic flotation model for predictive control incorporating froth physics. Part II: Model calibration and validation
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DOI：
10.1016/j.mineng.2021.107190
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发表时间：
2021-09-21
影响因子：
4.8
通讯作者：
Brito-Parada, Pablo R.
中科院分区：
文献类型：
--
作者：
Quintanilla, Paulina;Neethling, Stephen J.;Brito-Parada, Pablo R.
浮选控制的建模是基于模型的预测控制器实现的关键阶段。在本文的第一部分中，我们介绍了浮选过程的动态模型，适用于控制的目的，沿着的拟合参数的灵敏度分析和模拟的重要控制变量。我们提出的模型是第一个，因为它包括关键的泡沫物理方面。包括泡沫物理学的重要性在于，它改进了对精矿中的材料（贵重物品和夹带的脉石）的量的估计，这可以在控制策略中用作估计品位和回收率的代理。在本系列的第二部分中，使用实验数据来估计拟合参数并验证模型。进行模型校准以估计提供过程行为的良好描述的一组模型参数。通过将模型预测与感兴趣变量的实际测量值进行比较来进行模型校准。然后进行模型验证，以确保校准模型正确评估可能影响模型结果的所有变量和条件。验证还允许进一步评估模型的预测能力。为了模型校准和验证的目的，在87升实验室规模的浮选槽中进行实验。实验设计为随机32全因子设计，操纵表观气体速度和尾矿阀位置。所有实验都在三相系统（固液气）中进行，以确保获得的结果以及浮选操作的行为尽可能与工业浮选槽中发现的结果相似。总共校准了来自模型的六个拟合参数：来自溢流气泡尺寸方程的两个项;来自爆破速率方程的三个参数;以及纸浆气泡尺寸类别的数量。在模型校准之后，进行模拟以针对实验数据验证模型的预测。验证结果表明，实验数据和模型预测的重要浮选变量，如纸浆水平，空气回收率，和溢出泡沫速度之间的良好协议。高精度的预测表明，该模型可以成功地实施预测控制策略。
Modelling for flotation control purposes is the key stage of the implementation of model-based predicted controllers. In Part I of this paper, we introduced a dynamic model of the flotation process, suitable for control purposes, along with sensitivity analysis of the fitting parameters and simulations of important control variables. Our proposed model is the first of its kind as it includes key froth physics aspects. The importance of including froth physics is that it improves the estimation of the amount of material (valuables and entrained gangue) in the concentrate, which can be used in control strategies as a proxy to estimate grade and recovery. In Part II of this series, experimental data were used to estimate the fitting parameters and validate the model. The model calibration was performed to estimate a set of model parameters that provide a good description of the process behaviour. The model calibration was conducted by comparing model predictions with actual measurements of variables of interest. Model validation was then performed to ensure that the calibrated model properly evaluates all the variables and conditions that can affect model results. The validation also allowed further assessing the model's predictive capabilities. For model calibration and validation purposes, experiments were carried out in an 87-litre laboratory scale flotation tank. The experiments were designed as a randomised 32 full factorial design, manipulating the superficial gas velocity and tailings valve position. All experiments were conducted in a 3-phase system (solidliquid-gas) to ensure that the results obtained, as well as the behaviour of the flotation operation, are as similar as possible to those found in industrial flotation cells. In total, six fitting parameters from the model were calibrated: two terms from the equation for overflowing bubble size; three parameters from the bursting rate equation; and the number of pulp bubble size classes. After the model calibration, simulations were performed to validate the predictions of the model against experimental data. The validation results revealed good agreement between experimental data and model predictions of important flotation variables, such as pulp level, air recovery, and overflowing froth velocity. The high accuracy of the predictions suggests that the model can be successfully implemented in predictive control strategies.