论文标题
连续制药制造中灰色盒模型的减少和观察者设计
Reduction and Observer Design for a Grey-Box Model in Continuous Pharmaceutical Manufacturing
论文作者
论文摘要
在这一贡献中，新型的降低订单模型（ROM）公式对Elkhashap等人提出的灰色框模型。 （2020a）提出了药物连续振动的流体床干燥机（VFBD）。 ROM利用$ \ MATHCAL {H} _2 $ - 基于基于投影的模型订单减少方法，在模型的无限二维部分的特殊解决方案公式之后。这主要是通过在模型部件之间引入矢量场映射，将半分化的PDE铸成双线性形式。然后将产生的ROM集成到基于非线性Kalman滤波的观察者设计中，还可以处理模型代数变量的估计。对FOM，基于ROM，基于ROM的观察者变体和基于FOM的观察者的评估是使用Monte-Carlo模拟以及基于实际系统实验数据的仿真进行的。结果表明，对于实验数据仿真，ROM可以准确地重现FOM状态，相对平方误差低于$ 0.3 \，\％$。这是在达到计算时间缩短到40美元的一倍的同时。显示了具有代数状态校正的基于ROM的观察者（使用Monte-Carlo模拟），无论初始化如何，都可以收敛到所有情况下的真实值。此外，还表明，由于减少而导致的观察者的性能降解实际上微不足道。这是在观察者的计算速度由于降低而达到三阶以上的倍数时。
In this contribution, a novel Reduced Order Model (ROM) formulation of the grey-box model proposed in Elkhashap et al. (2020a) for the pharmaceutical continuous vibrated fluid bed dryer (VFBD) is presented. The ROM exploits the $\mathcal{H}_2$-norm projection-based model order reduction method after a special solution formulation of the model's infinite-dimensional part. This is mainly by introducing a vector field mapping between the model parts casting the semi-discretized PDE into a bilinear form. The ROM produced is then integrated into an nonlinear Kalman Filtering-based observer design also handling the estimation of the model's algebraic variables. Evaluations of the FOM, ROM, ROM-based observer variants, and the FOM-based observer are performed using Monte-Carlo simulations as well as simulations based on experimental data of the real system. It is shown that the ROM could reproduce the FOM states accurately with a relative mean square error below $0.3\,\%$ for the experimental data simulation. This is while reaching a computational-time reduction up to a factor of $40$. The ROM-based observer with algebraic states correction is shown (using Monte-Carlo simulations) to be able to converge to the true values for all cases regardless of initialization. Moreover, it is also shown that the performance degradation of the observer due to reduction is practically insignificant. This is while the computational speedup of the observer due to reduction reached a factor of more than third order of magnitude.
