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Optimizing Control of a Tubular Polymerization Reactor: Comparison of Single Shooting and Full Discretization

机译：管状聚合反应器的优化控制：单射和全离散比较

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The goal of this contribution is to study numeric solution techniques for implementing optimizing control of polymerization processes in tubular reactors with multiple side injections of monomer along the reactor. The configuration of the reactor causes long delays between the inputs and the measurements at the reactor outlet and sharp moving fronts when the inflows are changed. Moreover, the polymerization kinetics are strongly nonlinear. The process is described by 1D partial differential equations along the reactor length. This makes the application of optimizing control based on a rigorous process model challenging. The so called weighted essentially non-oscillatory scheme (WENO) is used to discretize the spatial dimension of the plant model. This method avoids the need for a very large number of discretization points and still the model can be simulated sufficiently accurately. The resulting ode model contains 1600 states and comprises five manipulated variables. We implement the optimizing controller using two different approaches: At first single shooting with control vector parametrization is used which is simple to implement and has fewer decision variables. This is compared to full discretization scheme using orthogonal collocation on finite elements which results in a very large but very sparse and structured nonlinear programing problem. The simulation results show that both approaches have a similar performance and drive the system to a significantly more productive steady state.
机译：该贡献的目的是研究数值解决方案技术，该技术用于在沿着反应器进行单体多次侧注入的管式反应器中实现对聚合过程的优化控制。反应堆的配置会导致输入和反应堆出口处的测量之间的长时间延迟，以及流入量变化时尖锐的移动前沿。而且，聚合动力学是强烈非线性的。该过程由沿反应堆长度的一维偏微分方程描述。这使得基于严格过程模型的优化控制的应用具有挑战性。所谓的加权基本非振荡方案（WENO）用于离散化工厂模型的空间维度。这种方法避免了大量离散点的需要，并且仍然可以足够准确地模拟模型。生成的ode模型包含1600个状态，并包含五个可操作变量。我们使用两种不同的方法来实现优化控制器：首先，使用具有控制矢量参数化功能的单发射击，它易于实现且决策变量更少。这与在有限元上使用正交配置的完全离散化方案相比较，这会导致非常大但非常稀疏和结构化的非线性编程问题。仿真结果表明，这两种方法都具有相似的性能，并将系统驱动到明显更高的稳定状态。

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