Design of Nonlinear Observer for State Estimation of a Bioreactor

Measurement or estimation of process states is critical for process monitoring, advanced process control, and process optimization^1,2. For chemical process whose state information cannot be measured directly, techniques such as state estimation need to be developed. Model-based state estimation is one of the most widely applied methods for estimation of unmeasured states basing on a high-fidelity process model. However, for some complex process, it requires extensive knowledge and effort to build a high-fidelity model to describe the whole system. Certain unmodeled disturbance or unknown inputs will generate model-plant mismatch, and in some case the mismatch is significant. For a case of bioreactor, there are several situations that can generate model-plant mismatch which can be treated as unknown input or disturbance, such as the effect of nutrient limitation, death of cells due to bust of air bubbles, oxygen delivery at high cell density, carbon dioxide stripping, and accumulation of inhibitive compound³. There are several different attempts to address the model-plant mismatch. One of the solutions is to apply parameter estimation for each run of the experiments. However, the adaptive parameter estimation requires extensive measurements of states and cannot be used for state estimation for a new experiment until a new set of parameters is updated. Filter and observer are mathematical methods to extract state information from corrupted measurements, which offer an alternative method for state estimation in the presence of model-plant mismatch.

Unknown input observer was developed to estimate the state in presence of certain types of faults and disturbance³. Comparing to other observers, unknown input observer can eliminate the effect of certain disturbance or fault despite of their size when their possible influences are estimated in the process model. To estimate the process state in presence of process disturbance or unknown inputs, a new design of nonlinear unknown input observer is proposed and it is applied for state estimation of a bioreactor. Design of such observer is provided and sufficient and necessary conditions of the observer are discussed.

Experimental study of batch and fed-batch operation of a bioreactor was performed, which used Saccharomyces cerevisiae strain mutant SM14 to produce β-carotene. Fed-batch experiment was based on the feeding of glucose and ethanol. Based on the mathematical modeling of the process which is demonstrated in our previous study⁵, unknown input observer for the bioreactor was developed. Model-plant mismatch was observed between the original process model and measurements when changing the initial conditions or operating mode of the experiments. State estimation of the process from the designed observer was demonstrated and compared to the experiment measurements. Results indicated that the state estimation from unknown input observer has smaller estimation error compared to the original process model, especially for the fed-batch experiment.

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2. Ricker NL. Model predictive control with state estimation. Industrial & engineering chemistry research. 1990;29(3):374-382.

3. Ozturk S, Hu W-S. Cell culture technology for pharmaceutical and cell-based therapies: CRC Press; 2005.

4.Chen W, Saif M. Unknown input observer design for a class of nonlinear systems: an LMI approach. Paper presented at: American Control Conference, 20062006.

5. M. Carolina Ordoñez, Jonathan P.Raftery, Tejasvi Jaladi , M. Nazmul Karim. Modelling of batch kinetics of aerobic carotenoid production using Saccharomyces cerevisiae. submitted.