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 $3^2$ full factorial design, manipulating the superficial gas velocity and tailings valve position. All experiments were conducted in a 3-phase system (solid-liquid–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.

为浮选控制目的建模是实现基于模型的预测控制器的关键阶段。在本文的第一部分，我们介绍了适合控制目的的浮选过程的动态模型，以及拟合参数的敏感性分析和重要控制变量的模拟。我们提出的模型是同类模型中的第一个，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材料（贵重物和夹带的脉石）数量的估计，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，实验数据用于估计拟合参数并验证模型。执行模型校准以估计一组模型参数，这些参数提供了对过程行为的良好描述。模型校准是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的。然后执行模型验证以确保校准模型正确评估所有可能影响模型结果的变量和条件。验证还允许进一步评估模型的预测能力。

出于模型校准和验证的目的，实验在 87 升实验室规模的浮选罐中进行。实验设计为随机$3^2$全因子设计，操纵表观气体速度和尾矿阀位置。所有实验均在三相系统（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的结果相似。

总共校准了模型中的六个拟合参数：来自溢出气泡大小方程的两项；爆破率方程中的三个参数；和纸浆气泡大小等级的数量。模型校准后，进行模拟以验证模型对实验数据的预测。验证结果表明，实验数据与重要浮选变量（如矿浆液位、空气回收率和溢流泡沫速度）的模型预测之间具有良好的一致性。预测的高精度表明该模型可以在预测控制策略中成功实施。