Improvement of Maximum Production in the Batch Transesterification Reactor of Biodiesel by Using Nonlinear Model Based Control

Indirect Measurement of Variables in a Heterogeneous Reaction for Biodiesel Production

“…State observers have already been used as a strategy to estimate variables [5,9,[19][20][21][22], parameters [21], and even the reaction heat [10] in the homogeneous transesterification of oils for biodiesel production. The estimated variables are used as soft sensors in supervision systems or as elements in control strategies [21]; the final objective is to enhance the performance of reactors for biodiesel production.…”

“…The methodology of implementing an extended Luenberger observer to estimate the concentration of TG, M, E, and G throughout the transesterification reaction may be the easiest one and offers a balance between precision and complexity. In comparison with other methods such as the EKF [5,10,38], fuzzy methods [19,20], and multimodel methods [22,23], the computational load of Luenberger observers is lower since no recurrent calculations are required. The reported observers consider six [5,10,20] or four [19,21] differential equations; multiobservers consider two equations or set of models with two equations [9,22], but these are reduced models, and only two variables are estimated.…”

“…In comparison with other methods such as the EKF [5,10,38], fuzzy methods [19,20], and multimodel methods [22,23], the computational load of Luenberger observers is lower since no recurrent calculations are required. The reported observers consider six [5,10,20] or four [19,21] differential equations; multiobservers consider two equations or set of models with two equations [9,22], but these are reduced models, and only two variables are estimated. The Luenberger observer presented in this paper considers only two differential equations instead of six or four as usual; the estimation of the concentrations of products is performed by algebraic equations.…”

“…They also allow for formalizing and incorporating the The goal of the observer is to obtain an accelerated process dynamic, allowing us to predict (estimate) the behavior of variables; then, a mathematical model is required. Usually, the models considered are based on the general equation of the transesterification reaction [7] since it describes the different steps to transform triglycerides in biodiesel and crude glycerol, regardless of the reaction phase (homogeneous or heterogeneous transesterification); kinetics, conversion rate, reaction mechanism, and mass and energy balance are usually included in the models for variables' estimation [5,[8][9][10]. Once the models are formulated, it is necessary to adapt their structure according to the state space theory, since this is the basis for observer development.…”

“…Regarding transesterification for biodiesel production, Table 1 summarizes the research related to the implementation of state observers. The extended Kalman filter is used to obtain fast estimations based on probability theory; however, its implementation online can cause an excessive computational load because the method is complex [5,10]. On the other hand, observers based on artificial intelligence (Fuzzy and Takagi-Sugeno) are suitable for highly nonlinear systems with incomplete or unknown models.…”