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# Proportional-Derivative-Integral (PID) Control

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A simple, widely used control method. This presentation will provide an introduction to PID controllers, including demonstrations, and practise tuning a controller for a simple system.

From the Un-Distinguished Lecture Series (http://ws.cs.ubc.ca/~udls/). The talk was given Mar. 30, 2007.

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### Proportional-Derivative-Integral (PID) Control

1. 1. Proportional-Integral-Derivative Controller Presented by: Sancho McCann
2. 2. Simple Control Loop Control Plant Feedback
3. 3. Examples Control Plant Feedback Throttle Auto-engine Wheel speed Air temp Room temp Thermostat temp Steering direction Car Distance from path Voltage Electric motor Fan speed Fan speed CPU temp CPU temp sensor
4. 4. Speed control: lookup table 10 kph 3% Throttle 20 kph 6% Throttle 40 kph 20% Throttle 80 kph 50% Throttle 140 kph 100% Throttle
5. 5. What to do? Goal (set-point): 21 kph How much should you change your throttle?
6. 6. What to do? Set-point: 80 kph How much should you change your throttle?
7. 7. Proportional Controller • Far from set point? Change throttle more • Close to set point? Change throttle less quot;control = (setpoint # currentState) • pGain
8. 8. Example
9. 9. Proportional-Derivative Control • Approaching set point quickly? Ease off throttle. pTerm = (setPoint quot; currState) • pGain dTerm = (prevState quot; currState) • dGain #control = pTerm + dTerm !
10. 10. Example
11. 11. Problem with Derivative Term Enhances noise
12. 12. Integral Term • Helps state average around the set point • Accumulate historic error • Allow this integral to inform the control decision
13. 13. Examples
14. 14. 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?
15. 15. 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 a small overshoot is noticeable
16. 16. Can be complex: Autopilot Heading Roll Aileron
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