Extended Luenberger observer for a biodiesel production process with heterogeneous catalyst

Abstract

The biodiesel production process requires low-cost and real-time monitoring. In this document, an extended Luenberger observer was designed to provide on-line estimation of the concentration of triglycerides, methanol, biodiesel, and glycerol. To this end, a mathematical model based on energy and mass balance equations as well as the global transesterification reaction in a batch reactor was considered. The model consists of two nonlinear differential equations, one output equation, and four complementary equations. The simplification of the model was used through a linearization procedure, considering two state variables (reaction rate and temperature) and one output variable (temperature). This procedure allowed to use estimation strategies typical of linear systems. The LQR method was used to calculate the gain observer. A fast convergence (compared to the total reaction time) of the observer was obtained despite varying the initial conditions up to 30%. Thus, it was concluded that the extended Luenberger observer, using temperature as the only output, allows estimating the conversion of triglycerides to biodiesel.