Bioprocess Modelling and Control by Constraint-based Optimization Methods

A recent trend for bioprocess modelling consist of using more complex models to better capture the metabolic behavior of micro-organisms.
In this work, dynamic enzyme-cost flux balance analysis (deFBA), a resource allocation model, is used as framework to describe biotechnological processes.
In addition to making a distinction for multiple biomass components, this method explicitly accounts for a limited enzyme capacity.
The work consists of two parts: (1) the development of a deFBA solution strategy compatible with Luenberger like observers, and (2) the application of the developed methods on a methane bioconversion process by \textit{Methylotuvimicrobium buryatense}. 
To establish the theoretical foundations of observer design for deFBA models, a new solution approach is developed.
The direct approach (DA) describes the deFBA model as a set of ordinary differential equations (ODEs) with an embedded linear programming  problem in the right-hand side. 
When a basis variable of the optimization problem becomes zero, the dynamics of the system change.
By employing this method, the deFBA problem has been rewritten as a switched system, i.e., a system with changing dynamics, for which mode switches are triggered by the state values. 
The deFBA solution method has provided satisfactory simulation results for a simple substrate-product model for which the product catalyzes substrate uptake. 
The simulation perfectly corresponds to the analytic solution. Furthermore, the metabolism of a carbon core model has been successfully simulated.

The switched system representation of the deFBA problem allows for the design of Luenberger like observers. 
Two approaches have been developed: (1) the ensemble observer and (2) the switch observer. 
For the ensemble observer, a bank of Luenberger observers is designed, one for each mode. 
Simultaneously, for each of the observers a moving average error is tracked. 
The system is estimated to be in the mode with the lowest moving average error. 
In case of a correct mode estimation, it is proven that the error dynamics are asymptotically stable.
The switch observer exploits the switching nature of the model formulation and integrates the observer dynamics until a statistically significant output estimation error with respect to the measurement noise is detected.
After a mode switch has been detected, the mode identification algorithm starts by applying a forward-backward Luenberger observer.
The mode that corresponds best with the measurements in the post-switch interval is chosen as the new optimal mode from which integration resumes.
Extending the concept of observability, the concept of mode distinguishability is introduced. 
When modes are distinguishable from each other, the mode identification algorithm is capable of making a difference between two modes solely based on the the given output measurements.
A mode distinguishability rank criterion is defined.
The ensemble and switch observes have been successfully applied on a small-scale two-species biofilm model.

The purpose of the second part of the thesis is constructing a deFBA model for wild-type \textit{M. buryatense} fermentations and applying the switch observer algorithm to this process.
The constructed deFBA model contains a total of 549 reactions and 564 metabolites, including 6 quota compounds, 147 enzymes and the ribosome.
Starting from an annotated genome, the metabolic network model is extended with the enzyme, quota and ribosome synthesis reactions.
A parameter sensitivity analysis pointed out that only a limited subset of turnover numbers has a significant influence on the predicted biomass amount. 
Using experimental data, a growth curve analysis shows that after a lag phase, the micro-organisms grow exponentially, followed by a linear growth phase. 
The most sensitive turnover numbers are estimated by nonlinear least squares fitting to the total biomass amount and dissolved oxygen concentration measurements.
The model is capable of describing the exponential growth phase.
The linear growth phase is only predicted by the model due to substrate depletion within the time horizon.
Since the size of the \textit{M. buryatense} model is relatively large, a reduced model is constructed for observer design. 
This reduced model contains 31 reactions and 35 metabolites.
The reduced model is capable of predicting the experimental values with reasonable accuracy. 
Both for simulation data with artificial noise and for experimentally determined data during exponential growth, the switch observer is capable of accurately estimating the extracellular metabolite amounts and the biomass component amounts.

For benchmarking reasons, extended and unscented Kalman observers are developed for both a laboratory and industrially relevant combination of sensors starting from an unstructured ODE model for the continuously operated methane bioconversion process.
The extended Kalman filter was shown to have a better performance for the model of interest.
An LQR controller in combination with the extended Kalman filter shows accurate biomass tracking results for simulated data.
An observability analysis with empirical Gramians shows that at least three measurements are required for model observability.
A similar controllability analysis shows that the methane and air flow, and dilution rate are required inputs to track the biomass concentration.