Parameter estimation of models with limit cycle based on the reformulation of the objective function

Many processes show limit cycles, meaning that the system presents oscillatory behavior. The parameter estimation of such kind of systems is not a simple task, due to the non-convexity of the optimization problem. This paper proposes the inclusion of a driving term based on the damping factor in the classical objective function formulation, reducing the non-convexity of the problem. This driving term is reduced after each iteration until its complete elimination, as the system starts to have oscillatory behavior close to the limit cycle. Two case studies illustrate the strengths of the proposed approach: the Jöbses's dynamic model for ethanol fermentation with Zymomonas mobilis and the Di Meglio et al. (2009) model, which represents the slugging flow regime appearing in vertical risers. The results showed that the proposed approach was able to ensure the oscillatory behavior, forcing the dynamical behavior of the system to produce the limit cycle.