Uncontrolled System Disturbance or Change in Exogenous variable

Uncontrolled System Disturbance or Change in Exogenous variable Input System Output

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

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

Controlled System Setpoint Disturbance Input Comparator Compensator System Output 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

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

House Thermostat/Heating System Outside Temperature= O d. I/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

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

Walk through first few Excel spreadsheets

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

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

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