Proportional-Integral-DerivativeController

Presented by: Sancho McCann

Simple Control Loop

Control Plant Feedback

Examples

CPU temp sensorCPU tempFan speed

Fan speedElectric motorVoltage

Distance from pathCarSteering direction

Thermostat tempRoom tempAir temp

Wheel speedAuto-engineThrottle

FeedbackPlantControl

Speed control: lookup table

100% Throttle140 kph

50% Throttle80 kph

20% Throttle40 kph

6% Throttle20 kph

3% Throttle10 kph

What to do?

Goal (set-point): 21 kph

How much should you change your throttle?

What to do?

Set-point: 80 kph

How much should you change your throttle?

Proportional Controller

• Far from set point? Change throttle more• Close to set point? Change throttle less

!

"control = (setpoint # currentState)•pGain

Example

Proportional-Derivative Control

• Approaching set point quickly? Ease offthrottle.

!

pTerm = (setPoint " currState) •pGain

dTerm = (prevState " currState) •dGain

#control = pTerm + dTerm

Example

Problem with Derivative Term

Enhances noise

Integral Term

• Helps state average around the set point

• Accumulate historic error• Allow this integral to inform the control

decision

Examples

Extremes

• What if– P term is too low?– P term is too high?– D term is too low?– D term is too high?– I term is too low?– I term is too high?

Tuning (one manual method)• Start with low pGain (< 1)• Set dGain ~ 100x pGain• Increase dGain until oscillation

– Halve until no oscillation reduced

• Increase pGain until oscillation– Halve that value

• Set iGain very low and increase until asmall overshoot is noticeable

Can be complex: Autopilot

Heading AileronRoll