There are several methods for investigation of nuclear reactors dynamics.

One of the most important methods to study reactor dynamics and the stability of nuclear reactor is define of transfer’s functions and application of it to analyze the closed loop function.

According to following figure a closed loop system including transfer function, feedback and related applied reactivity are shown:

Where:

Pi (s) is: input reactivity in frequency field, Pf (s) is: reactivity due to feedback in frequency field, pe (s) is: error reactivity in frequency field that is as input reactivity to transfer function, G(s) is: transfer function, H(s) is: feedback function and n(s)is: output of closed loop conversion function that means the density of neutrons.

There is also:

Pe (s) = Pi (s) -Pf (s) (1)

According to Fig.1 for both transfer function and feedback function existing in closed loop can write:

In order to survey the stability of a closed loop system the term of [1 + G(s).H(s)] must be set zero and by solving this equation, all the roots that are as zero and pole for closes loop system, will be defined. The stability condition of a closed loop system is lack of positive real part of poles. It means all the poles must be the left side of real-imagine graph.

Reactivity feedback causes the steady operation of nuclear reactor and equilibrium of its dynamical system.

A transfer function can be either linear or not. Each system variable can be affected as an input reactivity to transfer function as shown in Fig.2 :