2.1 Analyzing the theory by mathematical model

In this work the value of Keff as a comparable value is supposed and attributed to input parameter block (H) and then this value with the received feedback value is compared.

The unit of the control rod velocity (v) can be mm/ s, the rate is steady, and the control rod movement is only to up and down directions, so: x(0) =0 (Shirazi et al., 2010).

Since the sgn(x) function is nonlinear; so conversion function can not be calculated; thus in this stage arguing the frequency response is not meaningful. Therefore the steady state must be considered for this nonlinear function; though it is rather complicated (Marie and Mokhtari, 2000).

To analyze the controlling system theory these are assumed:

If: Input=H; Output=x(t); in the top of control rod: x=0; in the bottom of the control rod:

x=xmax;

F = kHx(t) + K0

Where:

F : Function, k: constant coefficient, H : input parameter, x(t): the control rod position, K0: initial value of Keff.

Ax = v sgn(F — Ksp ).At

Where Ax is: the amount of control rod movement, At is: time.

Where — is: the velocity of control rod from the movement aspect to up and down, Ksp : the secondary value of Keff in the recent position of control rod.

x(t) = 10 vsgn[kx(t)H(t — tD) + Ko — Ksp ]dt

Supposition: x(0) = 0, So:

x(t) = X0 ± vtsgn(t — tD) (78)

Where x is: absolutely descending, x0 is: the initial value of x and tD is: the innate delay time.

The SIMULINK of MATLAB is an appropriate software to analyze the performance of this simulation (Tewari, 2002).

The simulated model is considered according to Fig.3: