Page 100 - Dynamics and Control of Nuclear Reactors

94 CHAPTER 8 Reactor control

In this case, the control action is turned off when the error falls in the dead-band
region. Note that, in general, the constant (or gain) K p can be made to change in some
controllers, being large for large errors and small for small errors (often referred to as
a nonlinear gain).
A feature of proportional control is that an error signal must be non-zero for con-
trol action to occur. Therefore, proportional control cannot drive a variable to its set
point following an external disturbance. For example, consider what would happen if
a home thermostat used proportional control rather than on-off control. If the house
cooled to T m because of a drop in outside temperature, the control action would be
K p (T s -T m ). For successful return to the set point, (T s -T m )¼0, the control action
would have to be zero rather than a necessary change in heating or cooling input.

8.3.4 Integral controller
An integral controller (also called reset controller) can eliminate the steady-state
error that occurs with a proportional controller. Integral control action is expressed
as follows:
Z t
f I tðÞ ¼ K i evðÞdv (8.3)
o
f I (t) is the integral control action and K i is the integral constant.
Because of the continuous change in the control action (caused by integration) the
constant K i is often referred to as the reset constant. Integral controllers can reduce
the error to zero, thereby eliminating the problem with proportional controllers. Cau-
tion must be taken in implementing an integral controller to avoid continuous
increase in the control action, caused by the integration of the error. This can be
achieved by limiting the actuator action beyond a certain level. As the error
approaches zero, the magnitude of the integral constant may be reduced, thus ensur-
ing smaller fluctuations in the system output.

8.3.5 Differential controller
As the name suggests, differential control action is proportional to the time rate of
change of the error signal. Because of its sensitivity to fluctuations in the measured
process variable, derivative control is seldom used, but is sometimes applied success-
fully by using a low-pass filter to reduce high-frequency noise in the error signal.
Differential controllers are useful in systems where there is a considerable lag
time between the control action and its effect on the system output. This time lag
can result in an incorrect error term being supplied to the controller, and the system
may go into instability. By combining the proportional and differential components
of the error term, the controller can anticipate the future changes taking place in the
output, in addition to the error itself. Thus, a differential controller could help sta-
bilize a closed-loop system. This controller is expressed as.