Model-based control of the dynamics during fine grinding in wet-operated stirred media mills

搅拌介质磨用于各种超细粉碎工艺。所选择的运行参数与悬浮液的性质相结合，决定了研磨介质的动能，在连续运行的情况下，还决定了颗粒的输送以及研磨介质在磨机内的不均匀轴向分布。这决定了粉碎行为和功耗。为了将产品颗粒超细粉碎至纳米级，磨机通常使用搅拌容器进行回路操作。因此，搅拌容器和磨机中的粒度分布是动态变化的。由于比表面积随着粒径的减小而不断增大，因此颗粒间的相互作用及其对悬浮稳定性和粘度的影响在超细粉碎过程中起着至关重要的作用。悬浮液粘度的增加对研磨介质的相对速度有直接影响，从而对传递给产品颗粒的能量有直接影响。此外，悬浮液粘度影响磨矿介质的轴向分布，从而影响磨矿介质的运动特性。因此，在过程控制中，除了控制搅拌器尖端速度或流量外，还必须考虑静电或空间稳定添加剂。此外，随着粒度的变化，理想破碎所需的应力能，即磨机的最佳工作点，向较低的应力能偏移。在湿式磨机中控制细磨过程时，必须考虑粘度增加对磨矿介质的阻尼作用、粒度减小对颗粒强度的提高以及应力强度增加对最佳工作点的偏移等因素的相互作用。最后，自发再团聚或再结晶过程对在线测量技术和过程控制提出了很高的要求。虽然存在搅拌介质磨机的捷径模型和建模方法，但目前还没有模型可以动态控制粒度分布、最佳能量利用或最大生产率等变化的细粉碎过程。在这个项目中，另一种可能的控制是通过结合非线性模型预测控制（NMPC）策略的人口平衡模型（PBM）进行描述。因此，PBM将通过机械粉碎模型来描述。

Stirred media mills are used in various ultra-fine comminution processes. The selected operating parameters in combination with the suspension properties determine the kinetic energy of the grinding media and, in the case of continuous operation, also the transport of the particles as well as the non-uniform axial distribution of the grinding media within the mill. This determines comminution behavior and power consumption. For ultra-fine comminution of the product particles down to the nanoscale, mills are often circuit-operated with an agitated vessel. Hereby, the particle size distributions in the agitated vessel and mill change dynamically. Due to a constant in-crease in specific surface area with decreasing particle size, particle interactions and their influence on suspension stability and viscosity play a fundamental role in ultra-fine comminution. The increase in suspension viscosity has a direct influence on the relative grinding media velocity and thus on the energy transferred to the product particles. In addition, the suspension viscosity influences the axial distribution and thus the movement behavior of the grinding media. Hence, electrostatically or sterically stabilizing additives must be considered in the process control in addition to the control of, e.g., stirrer tip speed or flow rate. Moreover, with changing particle size, the stress energy required for ideal particle breakage, i.e. the optimal operating point of the mill, shifts towards lower stress energies. When controlling a fine grinding process in a wet-operated mill, the interplay between damping of the grinding media through the increase in viscosity, in-crease in particle strength with decreasing particle size and shift in the optimum operating point due to the increase in stress intensity must be considered. Finally, spontaneous reagglomeration or recrystallization processes place high demands on online measurement technology and process control. Although short-cut models and modelling approaches for stirred media mills exist, there currently is no model that allows for dynamic control of changing fine comminution processes with regard to particle size distribution, optimum energy utilization, or maximum production rate. One possibility of control also pursued in this project is the description via population balance models (PBM) in combination with a Nonlinear Model Predictive Control (NMPC) strategy. Thereby the PBM will be described via a mechanistic comminution modell.