For many dynamic processes, improved time-average performance could be achieved by periodic operations, which introduce periodic variations to the state-variables deliberately. In this paper, a bioreactor is adopted as case-study where periodic operations are realized through both external and internal oscillations. Since the mechanism for generating external and internal oscillations vary significantly, different mathematical tools are discussed. Specifically, to understand the influence of external oscillations, a nonlinear analysis method is proposed which relies on Laplace-Borel transform; then, numerical solution of a self-oscillator using a collocation technique is detailed to study internal oscillations. Next, scenarios that elucidate the integration of internal and external oscillations are offered. Finally, the potential elimination of oscillations through a membrane bioreactor is explored. Through this study, the analysis methods offer an integrated framework which could be used to analyze a number of periodic operation scenarios, facilitating the implementation of novel operational strategies for the process industries.

对于许多动态过程，可以通过周期性的操作来提高时间平均性能，这种操作会故意将状态变量引入状态变量。本文采用生物反应器作为案例研究，通过外部和内部振荡实现周期性操作。由于产生内部和内部振荡的机制差异很大，因此讨论了不同的数学工具。具体而言，为了解外部振荡的影响，提出了一种基于拉普拉斯-伯雷尔变换的非线性分析方法。然后，详细介绍了使用搭配技术的自激振荡器的数值解，以研究内部振荡。接下来，提供了阐明内部和外部振荡的集成的方案。最后，探索了通过膜生物反应器消除振荡的可能性。通过这项研究，分析方法提供了一个可用于分析许多定期操作方案的集成框架，从而为过程工业实施新颖的操作策略提供了便利。