Identification of Biochemical Reactors Using Fractional Differential Equations

Identification of Biochemical Reactors Using Fractional Differential Equations

L. A. D. Isfer, M. K. Lenzi, E. K. Lenzi, Latin American Applied Research 40, 193 (2010). PDF | DOI

High production meeting product quality, process safety and environmental regulation provide to control systems a key role in biochemical plants operation. As a suitable mathematical model is essential for process control, this work reports an alternative tool, based on the use of fractional order differential equations, for biochemical reactor identification using previously reported experimental data. Three different approaches were considered: i) solving the nonlinear set of algebraic equations obtained from the derivatives of the objective function with respect to the parameters; ii) solving a multivariable nonlinear deterministic optimization problem; iii) solving a multivariable nonlinear heuristic optimization problem. All identified models were submitted to statistical fitting tests and the second approach (ii) proved to be the most efficient for process identification, satisfying all statistical tests. Common integer order models were identified, leading to poorer data fit when compared to the fractional model, proving the usefulness and success identification tool proposed.