Optimal control of renewable biohydrogen production: A switched system approach*

Abstract

Biohydrogen produced from microorganisms such as cyanobacteria is a promising low cost, sustainable and environmentally friendly energy source. Recent studies have shown that high biohydrogen yield can be obtained from Cyanothece sp. ATCC 51142 in a fed-batch reactor. This system has been accurately described with a modified Droop model that can be used for optimization studies. Searching for the optimal operating conditions and the switching time from batch to fed-batch operation, such that the biohydrogen production is maximized, leads to a challenging singular optimal control problem. In this study, a novel reformulation based on the theory of switched systems and time-scaling transformation is proposed to address the switching of the operating modes and the optimal control structure. Solutions are found by solving an embedded optimal control problem that can be solved efficiently as a nonlinear programming problem. No mesh refinement is required to capture the switching times. Smooth optimal control profiles and clear switching structures that maximize the biohydrogen yield were found for two types of control parametrization.