磨矿粒度分布的概率密度函数跟踪控制研究

Probability Density Function Tracking Control for Particle Size Distribution of Grinding Circuits

传统的磨矿粒度控制局限于百分比含量这一指标,未考虑粒度具体分布信息,而磨矿产品的粒度分布(PSD)对整个选矿系统能耗和精度的影响不容小视。为解决上述问题,用概率密度函数(PDF)表征PSD信息,对磨矿粒度的PDF进行跟踪控制,使其跟踪给定的最利于选别的粒度PDF。在每个采样时刻,首先测取磨矿产品的多个粒度样本,用核密度方法估算PDF;然后利用跟踪误差建立性能指标函数;最后,用粒子群算法优化性能指标函数,设计最优控制输入。仿真结果验证了所提方法的有效性,可为选矿系统的后续研究和实际应用提供参考。

The traditional index of the particle size control in grinding circuits is limited to the percentage, and does not consider any information about the particle size distribution （ PSD ） in detail. However, the PSD of the grinding circuit output plays a role when it comes to the energy consumption and accuracy of the whole ore dressing system. In this connection, a new control strategy, where the concept of probability density function （PDF） is used to characterize the PSD, was provided here. The new control objective is to make the PDF of the output particle sizes track the optimum PDF, which is determined by the nature of the ores and the techniques of ore dressing. At every sample time, the output PDF was obtained from the particle size samples according to kernel density estimation （KDE）. In order to make the track, the performance function was constructed based on the squared PDF tracking er- rors. With this performance function minimized by particle swarm optimization （PSO） , a PDF tracking control strate- gy was designed. A simulation was finally given to demonstrate the effectiveness of the proposed approach and encour- aging results have been obtained.