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Proportional–integral–derivative controller
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===Tuning software=== Most modern industrial facilities no longer tune loops using the manual calculation methods shown above. Instead, PID tuning and loop optimization software are used to ensure consistent results. These software packages gather data, develop process models, and suggest optimal tuning. Some software packages can even develop tuning by gathering data from reference changes. Mathematical PID loop tuning induces an impulse in the system and then uses the controlled system's frequency response to design the PID loop values. In loops with response times of several minutes, mathematical loop tuning is recommended, because trial and error can take days just to find a stable set of loop values. Optimal values are harder to find. Some digital loop controllers offer a self-tuning feature in which very small setpoint changes are sent to the process, allowing the controller itself to calculate optimal tuning values. Another approach calculates initial values via the Ziegler–Nichols method, and uses a numerical optimization technique to find better PID coefficients.<ref name=Hein>{{cite book |last1=Heinänen |first1=Eero |title=A Method for automatic tuning of PID controller following Luus-Jaakola optimization |date=October 2018 |publisher=Tampere University of Technology |location=Tampere, Finland |edition=Master's Thesis |url=https://ahelp.com/wp-content/uploads/2025/02/Heinanen.pdf |access-date=Feb 1, 2019 |ref=Hein}}</ref> Other formulas are available to tune the loop according to different performance criteria. Many patented formulas are now embedded within PID tuning software and hardware modules.<ref>{{cite journal |first1=Yun |last1=Li |first2=Kiam Heong |last2=Ang |first3=Gregory C.Y. |last3=Chong |title=Patents, software, and hardware for PID control: An overview and analysis of the current art |journal=IEEE Control Systems Magazine |volume=26 |issue=1 |pages=42–54 |date=February 2006 |url=http://eprints.gla.ac.uk/3816/1/IEEE2pdf.pdf |doi=10.1109/MCS.2006.1580153|s2cid=18461921 }}</ref> Advances in automated PID loop tuning software also deliver algorithms for tuning PID Loops in a dynamic or non-steady state (NSS) scenario. The software models the dynamics of a process, through a disturbance, and calculate PID control parameters in response.<ref>{{cite thesis |title=On Automation of the PID Tuning Procedure |first=Kristian |last=Soltesz |publisher=[[Lund university]] |date=January 2012 |type=[[Licentiate (degree)|Licentiate]] theis |url=https://www.researchgate.net/publication/319183200 |id=[http://lup.lub.lu.se/record/2293573 847ca38e-93e8-4188-b3d5-8ec6c23f2132]}}</ref>
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