Download Proportional Control

Systems Control
The function of a heating or air conditioning system is to maintain comfortable conditions within
a space for a specified period of time. This is achieved through the use of a well designed control
system.
A basic control system is shown in figure 1.
heating
coil
Qo
room
flow control
valve
T
s
valve
position
controller
+/error (e)
sp
set
point
Figure 1: a basic room temperature control system.
A sensor (thermostat) feeds a temperature (usually a mix of air and radiant temperature) back to a
controller; this is usually passed in the form of an electrical voltage, where the voltage magnitude
is proportional to the temperature. The controller compares this temperature to a set-point
(desired) temperature and generates an error value:
e   sp   s
The error is the difference between the set-point temperature and the sensed temperature.
Depending on the magnitude of the error, the controller will adjust the output of the heating
system up or down. In practice, this will involve operating a mechanical component such as a
valve to increase or decrease the flow of hot water through a heating coil or radiator. Controllable
components such as valves, pumps, fans and dampers are collectively known as actuators The
controller employs an algorithm to determine the heat output as a function of the error:
Q o (t )  f (e(t ))
This type of control mechanism is commonly termed feedback control, where the controlled
variable (temperature) is fed back to the control system.
ON/OFF Control
This is the simplest type of control used in buildings:
 If the sensed temperature is below the set-point then the heating system is fully ON.
 If the sensed temperature rises above the set-point then the heating system is OFF.
Figure 2 shows the temperature and heat output in a room controlled by an ON/OFF controller. In
practice the use of ON/OFF control can cause problems. As can be seen in Figure 2, the heating
system rapidly switches ON an OFF leading to inefficient system operation and increased
mechanical wear.
oC
OFF
OFF
ON
OFF
ON
ON
upper set point OFF
oC
o
C
heat output
lower set point ON
room air temperature
set point temp.
Qmax
Figure 2: ON/OFF control of air temperature.
To address this deficiency a 'dead band' may be introduced. Effectively this defines an upper and
lower set-point. The control mechanism is now as summarised in Figure 3:
 if the sensed temperature is below the lower set-point then the heating system is ON;
 if the sensed temperature rises above the lower set-point but is still below the upper set-point
then the heating system is ON;
 if the sensed temperature is above the upper set-point then the heating system is OFF; and

if the sensed temperature falls below the upper set-point but is still above the lower set-point
then the heating system is ON.
o
C
heat output
room air temperature
upper temp.
Qmax
lower temp.
Figure 3: ON/OFF control with a dead band.
The addition of the upper and lower set-points acts to reduce the frequency of the plant switching
at the expense of poorer control of the controlled variable (here temperature).
ON/OFF control offers a crude means of controlling conditions in a building and is typically
employed where close control is not required, e.g. temperature control of domestic boilers.
Proportional Control
This is a more advanced control algorithm, where the control action is proportional to the size of
the error:
Q o (t )  Ke(t )
where K is known as the gain of the controller.
Again, taking the example of room temperature control:
 if the temperature is below the set-point then the heating is ON and the output is
proportional to the difference between the sensed temperature and the desired
temperature; and
 if the temperature is above the set-point then the heating is OFF.
Figure 4 shows the operation of a proportional controller. Notice that as the sensed temperature
gets closer to the set-point temperature, so the output of the heating system is reduced
o
C
heat output
room air temperature
upper temp.
Qmax
lower temp.
offset error
Figure 4: Proportional control of room temperature.
In practice the operation of a proportional controller is often limited as the output of the heating
system is limited (i.e. it has a maximum capacity). This is achieved by introducing a 'proportional
band' or 'throttling range'—this is similar to a dead band in that a single set-point is replaced by
an upper and lower limit. With reference to Figure 4, the control action now follows the following
rules:
 if the temperature lies above the throttling range then the heating system is OFF;
 if the temperature lies below the throttling range then the heating system is ON at full
power; and
 if the sensed temperature is within the throttling range then the output is a function of the
error.
Within the throttling range, the output of the heating system is
   s  
Q o   u
Qmax
 u   l 
where, in this case, u = sp and so u - s = e, so.
 Q

Q o   max  e
 u   l 
where K 
Qmax
.
u  l
u & set point
oC
heat output
throttling range
l
0
0
Qmax
Figure 5: Proportional control action.
As with ON/OFF control, proportional control is not a perfect mechanism because the throttling
range affects the operation of the system:

a narrow throttling range gives close control (a small error) at the expense of the system
switching ON/OFF frequently; and

a wide throttling range reduces the ON/OFF switching off the system (cycling) at the
expense of poorer control.
It is impossible to completely eliminate the error between the desired temperature and the sensed
temperature using only proportional control. There is always an offset error, where the controlled
temperature never quite reaches the desired temperature.
PID Control
A PID controller incorporates a mix of proportional, integral and derivative control action. In this
case the control output is a function of the size of the error (e(t)), the rate of change of the error
t
de (t )
1
with time Td
and the integral of the error over time
e(t )dt :
dt
Ti 0
t


de(t ) 1
Q o  K e(t )  Td
  e(t )dt 
dt
Ti o


where Td is the derivative action time (s), Ti the integral action time (s) and K the gain.
As shown in Figure 6, PID control offers close control in that the control action now responds to
the rate of change of the error, while the integral control acts to eliminate the set-point error
experienced with proportional control.
o
C
heat output
room air
temperature
set point
temp.
Qmax
Figure 6: PID control of room air temperature.
Control Location
In the cases considered above control is applied to room temperatures. Many other control targets
may be considered within a building design context. For example:

control of blinds located on the façade;

control of fan speed;

control of damper/valve positions;

control of hot water temperature; and

control of recirculated air .
In conclusion, good control is vital to acceptable performance in terms of comfort and energy
efficiency. The control algorithms considered here—ON/OFF, proportional and PID—must be
configured for optimum performance:

selection of set-points;

selection of proportional/dead band values; and

selection of integral/derivative action times.
Inappropriate control parameters leads to a poorly configured control system, which in turn may
give rise to uncomfortable conditions, energy waste and a reduction in the lifetime of system
components. It is important that a building's control system is well designed, commissioned and
maintained.