Capacitance - Honeywell AUTOMATIC CONTROL SI Edition Engineering Manual

CONTROL FUNDAMENTALS
The difference between repeatability and static error is that
repeatability is the ability to return to a specific condition,
whereas static error is a constant deviation from that condition.
Static error (e.g., sensor error) does not interfere with the ability
to control, but requires that the control point be shifted to
compensate and maintain a desired value.
The dead zone is a range through which the controlled
variable changes without the controller initiating a correction.
The dead zone effect creates an offset or a delay in providing
the initial signal to the controller. The more slowly the variable
changes, the more critical the dead zone becomes.

Capacitance

Capacitance differs from capacity. Capacity is determined
by the energy output the system is capable of producing;
capacitance relates to the mass of the system. For example, for
a given heat input, it takes longer to raise the temperature of a
liter of water one degree than a liter of air. When the heat
source is removed, the air cools off more quickly than the
water. Thus the capacitance of the water is much greater
than the capacitance of air.
A capacitance that is large relative to the control agent tends
to keep the controlled variable constant despite load changes.
However, the large capacitance makes changing the variable to
a new value more difficult. Although a large capacitance
generally improves control, it introduces lag between the time
a change is made in the control agent and the time the controlled
variable reflects the change.
Figure 44 shows heat applied to a storage tank containing a
large volume of liquid. The process in Figure 44 has a large
thermal capacitance. The mass of the liquid in the tank exerts a
stabilizing effect and does not immediately react to changes
such as variations in the rate of the flow of steam or liquid,
minor variations in the heat input, and sudden changes in the
ambient temperature.
LIQUID
IN
STEAM
IN
TANK
Fig. 44. Typical Process with Large Thermal Capacitance.
Figure 45 shows a high-velocity heat exchanger, which
represents a process with a small thermal capacitance. The rate of
flow for the liquid in Figure 45 is the same as for the liquid in
Figure 44. However, in Figure 45 the volume and mass of the
liquid in the tube at any one time is small compared to the tank
shown in Figure 44. In addition, the total volume of liquid in the
exchanger at any time is small compared to the rate of flow, the
heat transfer area, and the heat supply. Slight variations in the
rate of feed or rate of heat supply show up immediately as
fluctuations in the temperature of the liquid leaving the exchanger.
Consequently, the process in Figure 45 does not have a stabilizing
influence but can respond quickly to load changes.
Fig. 45. Typical Process with Small Thermal Capacitance.
Figure 46 shows supply capacitance in a steam-to-water
converter. When the load on the system (in Figure 44, cold air)
increases, air leaving the heating coil is cooler. The controller
senses the drop in temperature and calls for more steam to the
converter. If the water side of the converter is large, it takes
longer for the temperature of the supply water to rise than if
the converter is small because a load change in a process with
a large supply capacitance requires more time to change the
variable to a new value.
CONVERTER
LIQUID
OUT
CONDENSATE
RETURN
CONDENSATE
C2075
RETURN
Fig. 46. Supply Capacitance (Heating Application).
28
LIQUID IN
HEATING
LIQUID OUT
MEDIUM OUT
CONTROLLER
VALVE
HOT WATER SUPPLY
(CONSTANT FLOW,
STEAM
VARYING
TEMPERATURE)
PUMP
HOT WATER
RETURN
COLD AIR
(LOAD)
STEAM
TRAP
ENGINEERING MANUAL OF AUTOMATIC CONTROL
HEATING
MEDIUM IN
C2076
HOT AIR
(CONTROLLED
VARIABLE)
HEATING
COIL
C2077