Evolutionary algorithms and orthogonal basis for dynamic optimization in L2 space for batch biodiesel production

Abstract

In this work, a novel methodology for the dynamic optimization of biodiesel batch production is developed. Two problem statements are carried out. In the first approach, only the final concentration of biodiesel is optimized. In the second, the signal energy is also considered, which is measured as the integral of the square reactor temperature over the reaction time and represents an indirect way to contemplate the energy employed. The proposed strategy to solve the optimal control problem is based on the Fourier series for the reactor temperature parameterization. The main advantage of this Fourier-based sequential approach over competing methods is that the obtained profiles are smooth and continuous, which is relevant since smoothing techniques are not required for implementation in real systems. Besides, a minimum number of parameters to optimize is required. The process is modeled and simulated in Matlab and Simulink. The results are compared with data reported in the literature. An improvement of over 5% in biodiesel production is achieved without energy contemplation. In the second case, an increase of 3% in the final biodiesel production is achieved with a 10% lower energy, in both cases employing only three parameters.