Optimal control of nonlinear fed-batch process using direct transcription method

Abstract

In this paper, we investigate the direct transcription method for dynamic optimization applied to fed-batch processes. The performance index proposed for optimization has a more general form than the classical ones. As a result, more design characteristics such as the minimum time, maximum production, desired production, and minimum energy are provided. As a matter of fact, abrupt changes in the feed profiles can lead to undesirable behaviors in bioprocesses, such as decreasing the productivity. To handle the mentioned drawback, a novel idea is presented that results in achieving smooth control policies by limiting the higher-order derivatives of the feed rates. Owing to the nonlinear model of the fed-batch processes, the presence of constraints and free final time analysis, the problem is reformulated as a nonlinear programming optimization by the direct trapezoidal method. Finally, the proposed method is applied to the invertase and PHB production processes and the effectiveness of the presented approach is demonstrated by comparing with several works in the literature.