Everyday closed loop example and importance of feedback

A closed-loop system is one in which the output is measured and fed back to be compared with the desired value; the difference (error) drives the system until the output equals the desired value.

Everyday example: automatic electric iron / water heater with thermostat

Take an electric water heater (geyser):

• Reference: temperature set on the thermostat knob, say 60 °C.
• Sensor (feedback): bimetal strip or thermostat bulb in the water.
• Comparator and controller: thermostat contacts compare actual and set temperature.
• Actuator: heating element switched ON/OFF.
• Plant: water in the tank; output: water temperature.
• Disturbance: cold water entering when hot water is used.

 set temp +   error  +-----------+   +-------+  water temp
 -------->(Σ)------->|Thermostat |-->|Heater |---+------>
           ^ -       |  contacts |   | +tank |   |
           |         +-----------+   +-------+   |
           +-------------[Bimetal sensor]<-------+

When water cools below 60 °C, the error makes the contacts close and heating starts; when 60 °C is reached the heater switches off. The temperature is held near the set point whatever the usage.

Importance of feedback

1. Accuracy: output follows the set point even if the heater ages or supply voltage changes (sensitivity reduced to $1/(1+GH)$).
2. Disturbance rejection: cold-water inflow is automatically corrected.
3. Faster response: time constant reduced from $\tau$ to $\tau/(1+K)$.
4. Safety and automation: no person has to watch the system; overheating is prevented.
5. Smaller steady-state error and ability to stabilize systems that would otherwise run away.