Single-use anion-exchange resins can reduce hazardous chromates to safe levels in drinking water. However, since most process control strategies monitor effluent concentrations, detection of any chromate leakage leads to premature resin replacement. Furthermore, variations in the inlet chromate concentration and other process conditions make process control a challenging step. In this work, we capture the uncertainty of the process conditions by applying the Ito process of Brownian motion with drift into a stochastic optimal control strategy. The ion exchange process is modeled using the method of moments which helps capture the process dynamics, later formulated into mathematical objectives representing desired chromate removal. We then solved our developed models as an optimal control problem via Pontryagin's maximum principle. The objectives enabled a successful control via flow rate adjustments leading to higher chromate extraction. Such an approach maximized the capacity of the resin and column efficiency to remove toxic compounds from water while capturing deviations in the process conditions.

翻译：单次使用的阴离子交换树脂可将饮用水中的有害铬酸盐降低至安全水平。然而，由于大多数过程控制策略监测出水浓度，任何铬酸盐泄漏的检测都会导致树脂过早更换。此外，进水铬酸盐浓度及其他工艺条件的变化使过程控制成为一项具有挑战性的步骤。在本工作中，我们通过将带漂移的布朗运动伊藤过程应用于随机最优控制策略，来捕捉工艺条件的不确定性。离子交换过程采用矩量法进行建模，该方法有助于捕捉过程动态特性，随后将其表述为表示期望铬酸盐去除效果的数学目标。然后，我们通过庞特里亚金最大值原理将所开发的模型求解为最优控制问题。这些目标通过流量调节实现了成功的控制，从而提高了铬酸盐的提取效率。该方法在捕捉工艺条件偏差的同时，最大化了树脂容量和柱效率，以去除水中的有毒化合物。