Model Reduction, Control and State Estimation of Two-Time-Scale Nonlinear Systems with the Application to Bioreactors

A two-time-scale system demonstrates both fast and slow dynamic properties. Modeling this type of system sometimes does not only introduce unnecessary extra orders, but also poses challenges to process simulations due to stiffness and is thereby computationally costly for optimization, controller synthesis and state estimation. To overcome this, one option is to perform model reduction and properly eliminate the fast modes. Bioreactors are widely used in the areas of biochemical engineering, environmental engineering and the pharmaceutical industry. The reliability of bioprocess operations is a key issue to be addressed. This has attracted interests of the biochemical and control communities, with a number of research projects focused on modeling, control and state estimation studies for bioreactors. In fact, many bioreactors are two-time-scale systems that involve both fast and slow dynamics owing to the presence of multiple microbial cultures. In this dissertation, two different bioreactor systems with large spectral gaps are studied. Particularly, one is a continuous two-stage anaerobic digestion process, whose optimal configuration is obtained through global nonlinear optimization. The other aerobic bioprocess is studied under both continuous and fed-batch operations. Slow invariant manifold based model reduction is applied to both systems. With the stabilization study and an observer design example of reduced order systems, it also demonstrates how the model reduction can be used to facilitate the control and state estimation studies of such two-time-scale systems. Inspired by the reduced-order observer example for the reduced model, the dissertation also presents two nonlinear observer design approaches for a general two-time-scale system. Depending on the importance and availability of the fast dynamics, either a reduced-order or full-order nonlinear observer can be designed following the proposed algorithms to reconstruct the unmeasurable state variables