In this simulation the input parameter value (H) is attributed to arbitrary Keff. So if the favorite Kgff is: 1 then the value of H will be defined: 100 and it is also for Set point (reference Keff). So Set Point: 50 means the reference K, ff is: 0.50 and in this situation this K, ff is enumerated as the arbitrary and favorite Keff that stability of reactor in this situation is based on it. This arbitrary Keff with output of Zero-Order Hold block is compared for performance of simulation by SIMULINK software. Also for example velocity: 3 means the velocity of control rod in this simulation is: 3 units per second (for example: 3mm/ s). In this state the velocity of control rod is increased comparing to the last stage which was: 1 unit per second. The velocity of control rod belongs to Speed block which is an input to Tsp Sum block in the block diagram.

By changing the values of the cited parameters (which were: Set Point, the velocity of control rod (v), H and the delay time), the different states of the graphs can be shown according to Figs.4, 5, 6 and 7:

The Figs.4, 5, 6 and 7 show if the velocity of control rod for upward and downward movements is increased then the Keff will be pendulous surrounds of defined Set Point (reference Keff) and also the oscillation amplitude will be more than lower velocity situations. For low velocities the oscillation amplitude is slight and acceptable. Another effective factor is inherent delay (such as derived delay of control rod mechanism) and its inordinate increasing can cause unstable states.

3. Conclusion

By this simulation the best response and operation which a reactor can have from stability aspect, according to its control rod velocity is derived.

According to Figs.4-8 the best status in the Fig.4 is observed in which there is no vibration in response. In this simulation the stability of reactor depends on either velocity or delay time values directly because delay time plays a key role. Therefore in this simulation the admissible ranges of velocity and delay time which can be caused to stable the reactor are respectively: low velocity of control rod around 1-3 units per second and short delay time (10ms). However in this case reach critical state (Keff=1) for nuclear reactor will be taken more than modes Figs.5-8. As in all the figures is observed, so can deduce the velocity of control rod plays the more important role than delay time of mechanism in stability of nuclear reactor. Whereas for minor and major changes of reactivity and shut down of reactor in emergency states, there are some kinds of control rods at nuclear reactors cores such as regulating rods, safety rods and shim rods, therefore this simulation can be applied for each control rod in either LWR nuclear reactor or research reactor cores which have vertical control rods. Also this simulation can be applied for each batch control rods which

act in the same way as the cluster at fuel assembly at core of nuclear power reactors though

the moving speed of regulating rod is much less than the safety rod.

4. Acknowledgment

This book chapter is related to a research project entitled: "The Simulation of a Model by

SIMULINK of MATLAB for Determining the Best Ranges for Velocity and Delay Time of

Control Rod Movement in LWR Reactors" that by financial supporting the Islamic Azad

University-South Tehran Branch has been carried out.