Bifurcation Control on the Un-Linearizable Dynamic System via Washout Filters

Abstract

Information fusion integrates aspects of data and knowledge mostly on the basis that system information is accumulative/distributive, but a subtle case emerges for a system with bifurcations, which is always un-linearizable and exacerbates information acquisition and presents a control problem. In this paper, the problem of an un-linearizable system related to system observation and control is addressed, and Andronov–Hopf bifurcation is taken as a typical example of an un-linearizable system and detailed. Firstly, the properties of a linear/linearized system is upon commented. Then, nonlinear degeneracy for the normal form of Andronov–Hopf bifurcation is analyzed, and it is deduced that the cubic terms are an integral part of the system. Afterwards, the theoretical study on feedback stabilization is conducted between the normal-form Andronov–Hopf bifurcation and its linearized counterpart, where stabilization using washout-filter-aided feedback is compared, and it is found that by synergistic controller design, the dual-conjugate-unstable eigenvalues can be stabilized by single stable washout filter. Finally, the high-dimensional ethanol fermentation model is taken as a case study to verify the proposed bifurcation control method.

Global Stabilizing Control of a Continuous Ethanol Fermentation Process Starting from Batch Mode Production

“…But a typical drawback of the continuous fermentation is the presence of multiple outputs (which would easily shift the process to the washout condition), as well as oscillations under certain conditions (the effect being the decrease in ethanol productivity, the loss of a high quantity of substrate). To stabilize the process, the cause of the reactor instability [8][9][10][11][12] is investigated; and, in view of the fact that the osmotic pressure formed at high ethanol concentrations (~50-60 g/L [13,14]) might inhibit or even kill yeast cells, hybrid designs through in situ ethanol removal to alleviate ethanol stress [15] are proposed. However, the accompanied instrumental cost as well as possible membrane fouling and degeneration are unbearable in industry.…”