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Control of crystal size distribution in batch crystallization processes governed by partial differential equations

机译：控制批次结晶过程中晶体尺寸分布的控制，由部分微分方程控制

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The paper deals with the simulation of batch crystallization processes and their crystal size distribution controllability by temperature control. The dynamic of crystallization processes under consideration is governed by hyperbolic partial differential equations. We propose simulating the processes of one size variable using the method of characteristics. It turns out that the method of characteristics has no numerical diffusion as compared to the finite difference method. Given a desired crystal size distribution, we investigate its reachability from the null initial condition (i.e. without seeding) by controlling the temperature. Some checkable criterion is established to determine if a desired crystal size distribution is reachable. When it is reachable, an admissible temperature control is constructed to steer the states to the desired distribution in finite time. Our construction is developed based on the discretized model and applied for the original model described by partial differential equations. To ensure a desirable distribution to be reached, we add an output feedback control law to correct possible errors given rise to by uncertainty of parameters.
机译：本文通过温度控制涉及批量结晶方法的模拟及其晶体尺寸分布可控性。所考虑的结晶过程的动态由双曲线偏微分方程控制。我们建议使用特性方法模拟一个尺寸变量的过程。事实证明，与有限差分法相比，特性方法没有数值扩散。考虑到所需的晶体尺寸分布，我们通过控制温度来研究其从零初始条件（不播种）的可达性。建立一些可检测的标准以确定是否可以到达所需的晶体尺寸分布。当它到达时，构造可允许的温度控制以将州转向有限时间的所需分布。我们的施工是基于离散模型开发的，并应用于部分微分方程描述的原始模型。为了确保达到理想的分布，我们添加了输出反馈控制法，以纠正通过参数不确定性升高的可能误差。

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