amplifier, actuator, control rod

Reactor transfer function with on

A simplified block diagram is shown below, for a reactor with a single$-$path temperature

feedback loop, together with the amplifier, actuator, control rod mechanism and the neutron

flux measurement device.

In this block diagram, the reactor transfer function with one group of delayed neutrons, and

the transfer function for single$-$path temperature feedback were derived in the class. The

transfer function for the amplifier, actuator, control rod mechanism is used because $1)$ it is an

excellent approximation of some of the practical servo systems now used in reactor control

systems, and $2)$ a quadratic form of this should closely approximate the behavior of almost

any type of physical equipment which might be chosen to drive a control rod.

The meaning of the symbols in the block diagram is as below:

k : gain

w$\_($n$)=2\backslash$pi f$\_($n$)$

f$\_($n$)$ : undamped natural resonant frequency of control rod servo system

$\backslash$zeta : damping ratio of servo system

A : a constant $($depending on power level, moderator and coolant$)$

$\backslash$alpha : lumped temperature coefficient

$\backslash$tau : time constant $($dependent upon mass and specific heat capacity of the moderator$)$

K$\_(0)$ : proportional gain of the neutron flux detector

n$\_(0)$ : original neutron density

$\backslash$lambda : precursor decay constant

$\backslash$Lambda $=($l$)/($k$\_($eff $))$

l : effective time between succeeding generations

k$\_($eff$)=1+(\backslash$Delta n$)/($n$)$

n :neutron density

B : fraction of delayed neutrons

Question: Simplify this block diagram to obtain the transfer function $(($n$($s$))/($n$\_($d$)($s$)))$ of the entire system.