Block-oriented non-linear identification of a dynamical equilibrium: Application to a supercritical Hopf bifurcation model

The article deals with the non-linear identification using a block structure to reproduce the behavior of a unknown non-linear system which presents two equilibria: a static equilibrium point, which is in our case unstable, and a dynamic equilibrium, which can correspond, for example, to a Limit Cycle Oscillation (LCO). This non-linear system is representative of a supercritical model which appears in the Hopf bifurcation. The generic proposed methodology is based on three identification steps: firstly the linear identification of the static equilibrium, called the fixed point, secondly, the identification of a Wiener feedback structure to reproduce the LCO, and lastly the tuning of a Wiener-Hammerstein feedback structure to improve the accuracy level of the identified nonlinear model. Finally, time-domain simulations are performed to evaluate and compare results with the original non-linear system.