Takagi-Sugeno Fuzzy Observer for a Switching Bioprocess: Sector Nonlinearity Approach

In a bioprocess it is desired to produce high amounts of biomass or metabolites such as vitamins, antibiotics, and ethanol, among others. The measurement of biological parameters as the cell, by-product concentrations and the specific growth rate are essential to the successful monitoring and control of bioprocesses (Horiuchi & Kishimoto, 1998). Adequate control of the fermentation process reduces production costs and increases the yield while at the same time achieve the quality of the desired product (Yamuna & Ramachandra, 1999). Nevertheless, the lack of cheap and reliable sensors providing online measurements of the biological state variables has hampered the application of automatic control to bioprocesses (Bastin & Dochain, 1990). This situation encourages the searching of new software sensors in bioprocesses. A state observer is used to reconstruct, at least partially the state variables of the process. Two classes of state observers or software sensors for (bio)chemical processes can be found in the literature (Dochain, 2003). A first class of observers called asymptotic observers, is based on the idea that the uncertainty in bioprocess models is located in the process kinetics models. A second class is based on the perfect knowledge of the model structure (Luenberger, Kalman observers and nonlinear observers). Different applications of state observers in bioprocess are reported in the literature (Cazzador & Lubenova, 1995; Farza et al., 2000; Guay & Zhang, 2002; Lubenova et al., 2003; Oliveira et al., 2002; Soh & Cao, 1999; Veloso et al., 2007). Fuzzy logic has become popular in the recent years, due to the fact that it is possible to add human expertise to the process. Nevertheless, in the case where the nonlinear model and all the parameters of a process are known, a fuzzy system may be used. A first approach can be done using the Takagi-Sugeno fuzzy model (Takagi & Sugeno, 1985), where the consequent part of the fuzzy rule is replaced by linear systems. This can be attained, for example, by linearizing the model around operational points, getting local linear representation of the nonlinear system.