Control of an anaerobic digester through normal form of fold bifurcation

Nonlinear dynamics is ubiquitous in engineering systems. As some parameters are varied bifurcations arise in the state variables. Generically, when one parameter changes, Hopf and fold bifurcations are found. Other ones can also be present due to special systems characteristics, such as symmetries. Knowing in advance the significant bifurcation scenario, a novel approach to control can be considered. We compute the normal form corresponding to such a bifurcation and we take this model as the nominal model of the plant. Then we design a nonlinear control which takes advantage of the precise bifurcation scenario. This general method is applied, in this paper, to an anaerobic digester. We will control the process with an adaptive controller.Specifically, we want to compare with the case that the nominal plant is considered as a linear model, such as it is typical in adaptive control techniques. Our proposed method has more benefits in signal control effort, faster convergence rate and low error.This paper shows how the combination of appropriated nonlinear dynamic techniques such as bifurcations and normal forms, and nonlinear control, can give rise to an improvement of the traditional methodology.