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.

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:

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:

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 OFFleading to inefficient system operation and increased mechanical wear.

Figure 2: ON/OFF control of air temperature.

Toaddress 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.


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:

where K is known as the gain of the controller.

Again, taking the example of room temperaturecontrol:

  • 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


Figure 4: Proportional control of room temperature.

In practice the operation of a proportional controlleris 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 throttlingrange then the heating system is OFF;
  • if the temperature lies below the throttlingrange 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

where, in this case, u = sp and so u - s= e, so.

.

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 ofproportional, 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 with time Td and the integral of the error over time :

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.

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 toacceptableperformance 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.