Stability of the reactor which has the external control system

When the reactor is externally controlled, the parameters governing the control must be chosen in close connection with the nuclear and thermal properties and out-put of the reactor, in order to attain stability in the vicinity of operating power. To get this relation, non-linear integral equations containing the effects of fast and slow responding internal feedbacks and delayed neutrons are adopted and connected with the external control system. The method of introducing the special Liapunov function which has been developed by Lur'ye, et al. is applied to the whole system and the required relation is obtained. The results of numerical calculation are presented in the form of diagrams. These relations and diagrams will be useful for the design and operation of external control systems for reactors. This paper also deals briefly with some modifications to the reactor dynamic equations to obtain a more concrete representation of the dynamical behavior of heterogeneous reactors. It is desirable that the equations directly contain the effect of the moderator temperature, which consists of three thermal time constants and is the solution of heat equations between the heterogeneous elements of the reactor. The new equations are solved by expansion, and the region of stability is determined. (author)