Editing Proportional–integral–derivative controller (section)

===Manual tuning===
If the system must remain online, one tuning method is to first set <math>K_i</math> and <math>K_d</math> values to zero. Increase the <math>K_p</math> until the output of the loop oscillates; then set <math>K_p</math> to approximately half that value for a "quarter amplitude decay"-type response. Then increase <math>K_i</math> until any offset is corrected in sufficient time for the process, but not until too great a value causes instability. Finally, increase <math>K_d</math>, if required, until the loop is acceptably quick to reach its reference after a load disturbance. Too much <math>K_p</math> causes excessive response and overshoot. A fast PID loop tuning usually overshoots slightly to reach the setpoint more quickly; however, some systems cannot accept overshoot, in which case an [[overdamped]] closed-loop system is required, which in turn requires a <math>K_p</math> setting significantly less than half that of the <math>K_p</math> setting that was causing oscillation.{{Citation needed|date=June 2012}}
[[File:PID Compensation Animated.gif|right|thumb|400px|Effects of varying PID parameters (K<sub>p</sub>,K<sub>i</sub>,K<sub>d</sub>) on the step response of a system]]
{| class="wikitable"
|+ Effects of ''increasing'' a parameter independently<ref>{{Cite journal |doi = 10.1109/TCST.2005.847331|title = PID control system analysis, design, and technology|journal = IEEE Transactions on Control Systems Technology|volume = 13|issue = 4|pages = 559–576|year = 2005|last1 = Kiam Heong Ang|last2 = Chong|first2 = G.|last3 = Yun Li|s2cid = 921620|url = http://eprints.gla.ac.uk/3817/1/IEEE3.pdf}}</ref><ref>{{cite journal |url=http://saba.kntu.ac.ir/eecd/pcl/download/PIDtutorial.pdf |title=PID Controller Tuning: A Short Tutorial |author=Jinghua Zhong |date=Spring 2006 |access-date=2011-04-04 |archive-url=https://web.archive.org/web/20150421081758/http://saba.kntu.ac.ir/eecd/pcl/download/PIDtutorial.pdf |archive-date=2015-04-21 |url-status=dead }}</ref>
! Parameter
! Rise time
! Overshoot
! Settling time
! Steady-state error
! Stability
|- style="text-align:center;"
! <math>K_p</math>
| Decrease
| Increase
| Small change
| Decrease
| Degrade
|- style="text-align:center;"
! <math>K_i</math>
| Decrease
| Increase
| Increase
| Eliminate
| Degrade
|- style="text-align:center;"
! <math>K_d</math>
| Minor change
| Decrease
| Decrease
| No effect in theory
| Improve if <math>K_d</math> small
|}