Page 103 - Dynamics and Control of Nuclear Reactors

8.4 Control of a zero-power reactor 97

The closed-loop transfer function of a system with transfer function, 1/(s+a) and
with integral controller is given by

YsðÞ K i
¼ (8.14)
2
Xs ðÞ ð s + as + K i Þ
Note that the closed-loop system becomes a second-order dynamic system, with the
potential for the system response to have an oscillatory characteristic, as K i becomes
large. The system error is given by
ð
ss + aÞXsðÞ
EsðÞ ¼ 2 (8.15)
ð s + as + K i Þ
The steady-state error for a unit step input is
lim
etðÞ ¼ sE sðÞ ¼ 0 (8.16)
s ! 0
The integral control thus results in a zero steady-state error for the above system.
For a¼0.02, the closed-loop transfer function is given by.

Ys ðÞ K i
¼ (8.17)
2
XsðÞ ð s +0:02s + K i Þ
For K i > 0.0001, the roots of the denominator polynomial are complex, resulting in
an oscillatory response of to a step input. Thus, extreme caution must be exercised in
choosing K i for a general system. A large value of K i results in a highly oscillatory
behavior, and quite likely makes the system unstable. Thus, the choice of an appro-
priate value of K i is important, rather than the use of an arbitrary absolute value.

8.3.8 Advanced controllers
Advanced control strategies use computed estimates of future consequences of cur-
rent control actions rather than current consequences as in classical control.
Advanced model-based controllers are necessary in some applications (such as con-
trolling missile trajectories). Sophisticated advanced control software is available,
but is not currently needed for reactor control. The next generation reactors may find
use for advanced control implementation.

8.4 Control of a zero-power reactor

This section illustrates system control by simulation of a zero-power reactor with
proportional control, integral control, and proportional plus integral (PI) control.
Included are responses to a reactivity step input and a power set point change.
The reader should note the effectiveness of the controller in driving the response
to the desired final value.