As already mentioned the feedback of the control system on the reactor core acts through two quantities: the control-rod position and the coolant mass flow. For accident analysis (short-time dynamics) it is not usually necessary to introduce a description of the control system in the already complicated system of equations describing the core dynamic behaviour. It is then sufficient to suppose that when a given quantity (e. g. neutron flux, coolant outlet temperature, etc.) exceeds a previously determined threshold value, a scram occurs. This means that a negative Дkc and a reduction of the coolant mass flow are introduced as given functions of time.

In the reactor operation and stability studies (long-time dynamics) the control system has to be simulated in the dynamics equations. It is usually required that the power Qr(t) released by the reactor follows a given power diagram Q(t) while a given gas-outlet temperature Tg must be maintained. Various methods of regulation can be used. A regulation of the thermal power through the coolant mass flow would be in general represented by

(12.22)

where KP, Ki and KD are the coefficients of the proportional, integral and differential member respectively, and

Qr = cPm(T, 2- T,,).

A regulation of the gas outlet temperature through the control rod reactivity Дkc would
be represented by

Дкс = KP(Tg — Tc2) + KiJ (Ts-Tc2)dt+KD-^(Tg-Tc2). (12.23)

See also § 12.14 for details on spatial instability and sector controllers.