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

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

3. 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 Measurement Comparator 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 Measurement Comparator 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