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

Abstract

To achieve a maximum production of biodiesel in the batch transesterification, an optimal operating condition and an effective control strategy are needed to improve the quality of product. An off-line optimization is prior determined by maximizing productivity for the batch transesterification to modify optimal temperature set point. Model based control, model predictive control (MPC) with an estimator has been implemented to drive the reactor temperature tracking to the desired profile. An extended Kalman filter (EKF) has been designed to estimate the uncertain parameter and unmeasurable states variable. In this work, improvement of batch transesterification process under uncertain parameters on the overall heat transfer coefficient has been proposed. Simulation results demonstrate that the EKF can still provide good estimates of the overall heat transfer coefficient and heat of reaction. The control performance of MPC is better than that of PID. Moreover, MPC with the EKF estimator can control the transesterification according to the optimal trajectory and then can achieve maximum product as determined. As a result, the MPC with EKF is still robust and applicable in real plants.

Appendix A

The model assumptions to design EKF estimator based on simplified mathematical models of batch reactor [18]. In this work, the heat of reaction and the overall heat transfer coefficient are the state and parameter that have to be study. The design of the state estimation bases on simplified mathematical models are given by

$$ \frac{{dT_{R} }}{dt} = \frac{{M_{R} Q_{R} + UA(T_{j} - T_{R} )}}{{V\rho_{R} c_{m,R} }} $$

(A.1)

$$ \frac{{dT_{j} }}{dt} = \frac{{F_{j} \rho_{j} c_{j} (T_{jsp} - T_{j} ) - UA(T_{j} - T_{R} )}}{{V_{j} \rho_{j} c_{j} }} $$

(A.2)

$$ \frac{dN}{dt} = - bNT_{R} $$

(A.3)

$$ \frac{{dQ_{R} }}{dt} = N\frac{{dT_{R} }}{dt} + T_{R} \frac{dN}{dt} $$

(A.4)

$$ \frac{{dQ_{R} }}{dt} = N\frac{{dT_{R} }}{dt} + T_{R} \frac{dN}{dt} $$

(A.5)

$$ \frac{db}{dt} = 0 $$

(A.6)

$$ \frac{dUA}{dt} = 0 $$

(A.7)

The initial condition and parameters to support in the EKF estimator is presented by Chanpirak, and Weerachaipichasgul [18]. Detailed regarding the EKF algorithm is given in [12,13,14, 18].