There are several controlling factors in nuclear reactors such as:

1. Coolant flow rate.

2. Movement of control rods.

3. Concentration of boric acid.

4. Reaction rate.

5. Error function.

6. Temperature of core.

7. Power of reactor.

8. Core expansion.

9. Fission poisons like Xe and Sm.

10. Fission fragments and fission products.

11. Burn up.

12. Power demand.

13. The kind of fuel.

14. Energy of neutrons.

15. Doppler’s effect.

16. Value of p.

If each system variable as a mathematics variable is considered then can write:

X(t) = Ax(t) + Bu(t) (5)

and:

y(f) = Cx(t)

Where:

x(t) is: variable of system, X(t) is: derivative of system’s variable, y(t) is: output, A is: system’s matrix, B is: control’s matrix, C is: matrix of output and u(t) is: control’s variable.

By taking the laplace conversions from two sides of above equations can write:

sX(s) = AX(s) + Bu(s) (7)

and:

Y(s) = CX(s) (8)

So two last equations that are based on Laplace conversions can be converted to following form:

(sI — A)X(s) = Bu(s)

and:

Y (s) = CX(s) (10)

Therefore:

X(s) = (sI — A)-1 Bu(s) (11)

and:

Y(s) = C(sI — A)-1 Bu(s) (12)

In order to define the transfer function, it will be deduced as shown below:

G(s) = Щ = C(sI — A)-1 B u(s)

Where:
	(sI — A) 1 =p(s)	(14)
and:
	G(s) = Cf(s)B	(15)