1. Uncontrolled System
Disturbance or Change in Exogenous
variable
Input
Output
System

2. Examples of “measurements” -air temperature -body temperature
Controlled System
Disturbance
Input
Output
System
Measurement
Examples of “measurements”
-air temperature
-body temperature
-car velocity

3. Comparator is “device” that compares measurement with setpoint
Controlled System
Setpoint
Disturbance
Input
Output
System
Comparator
Measurement
Comparator is “device” that compares measurement with setpoint
-thermostat
-human brain
-cruise control computer

4. Controlled System Setpoint Disturbance Input Output System
Compensator
Comparator
Measurement
Compensator is “device” that computes appropriate action to take
-thermostat – simple on/off switch
-human brain – determine whether to shiver, increase metabolism
-cruise control computer – determines how much gas to give

5. Controlled System Setpoint Disturbance Input Output System
Actuator
Compensator
Comparator
Measurement
Actuator is “device” that translates signal from compensator into action
-house heating system
-piloerectors, muscles shiver, metabolism increases
-gas pedal linkage system

6. House Thermostat/Heating System
Outside Temperature= O
dI/dt = C (I - O)
where C is related to insulation
and thermal inertia of house
Inside
Temperature = I
Uncontrolled
System
Note: daily temperature fluctuation can
be thought of as a disturbance or perturbation

7. Outside Temperature= O
dI/dt = (C (I - O)) + Heat applied
The key question is how much
heat (or cooling) to apply and when
Inside
Temperature = I

8. Walk through first few Excel spreadsheets

9. Proportional Control exerts control related to difference
between target and observed temperature

10. Integral Control exerts control related to ACCUMULATED
difference between target and observed temperature

11. Rate
High
Rate
Lower
Derivative Control exerts control related to RATE OF CHANGE
of difference between target and observed temperature