On the feedback stability of linear FNPK equations

The aim of this work is to investigate the stability of linear fractional neutron point kinetics (FNPK) equations with closed-loop feedback. The FNPK model retains the main dynamic characteristics of the neutron movement in which the relaxation time is associated with a variation in the neutron density. The order of FNPK model is fractional (anomalous diffusion coefficient) which can be used to obtain the best representation of the reactor dynamics compared to the classical neutron point kinetics (CNPK), as demonstrated in this work with plant data. The stability of linear FNPK is investigated using three classical techniques: root locus, location of closed-loop poles in the Riemann sheet and evaluation of step response. The analysis is carried out for three values of anomalous diffusion coefficient representing three levels of subdiffusion in reactor core. It has been shown through extensive simulations that all the FNPK models are closed-loop stable.