en>Rjwilmsi: /* The sum and duality conjectures */Journal cites:, added 1 DOI using AWB (10473)

2014-10-03T06:39:18Z

The sum and duality conjectures<ref name="hof"/>: Journal cites:, added 1 DOI using AWB (10473)

en>Pinazza: /* Other results */ added some derivate formulas (ref in note 3)

2013-11-07T23:19:24Z

Other results: added some derivate formulas (ref in note 3)

← Older revision		Revision as of 01:19, 8 November 2013
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	~~La crainte n~~'a ~~pas sa place ici car les erreurs font partie du jeu~~. L'~~agent est mandataire c~~'~~est~~ -~~dire qu~~'~~il agit au nom pour le compte et aux risques de l~~'~~entreprise mandante~~.<br><br>~~Also visit my web page~~: [http://www.~~gagnerdelargent~~.tv/ ~~bourse binaire en ligne~~]		{{main\|PID controller}}
			The '''Ziegler–Nichols tuning method''' is a [[heuristic]] method of tuning a [[PID controller]]. It was developed by [[John G. Ziegler]] and [[Nathaniel B. Nichols]]. It is performed by setting the ''I'' (integral) and ''D'' (derivative) gains to zero. The "P" (proportional) gain, <math>K_p</math> is then increased (from zero) until it reaches the '''ultimate gain''' <math>K_u</math>, at which the output of the control loop oscillates with a constant amplitude. <math>K_u</math> and the oscillation period <math>T_u</math> are used to set the P, I, and D gains depending on the type of controller used:

			{\| class="wikitable"
			\|-----
			\| align="center" colspan="5" border="1" \| Ziegler–Nichols method<ref>{{cite journal\|title=Optimum settings for automatic controllers\|author=Ziegler, J.G and Nichols, N. B.\|year=1942\|series=Transactions of the ASME\|volume=64\|pages=759–768\|url=http://www2.eie.ucr.ac.cr/~valfaro/docs/Ziegler%26Nichols.pdf}}</ref>
			\|-----
			\| align="center" \| '''Control Type'''
			\| align="center" \| <math>K_p</math>
			\| align="center" \| <math>K_i</math>
			\| align="center" \| <math>K_d</math>
			\|-----
			\| align="center" \| ''P''
			\| align="center" \| <math>0.5 K_u</math>
			\| align="center" \| -
			\| align="center" \| -
			\|-----
			\| align="center" \| ''PI''
			\| align="center" \| <math>0.45 K_u</math>
			\| align="center" \| <math>K_p/T_u/1.2</math>
			\| align="center" \| -
			\|-----
			\| align="center" \| ''PD''
			\| align="center" \| <math>0.8 K_u</math>
			\| align="center" \| -
			\| align="center" \| <math>K_p T_u/8</math>
			\|-----
			\| align="center" \| ''classic PID''<ref name="microstar">[http://www.mstarlabs.com/control/znrule.html Ziegler-Nichols Tuning Rules for PID], Microstar Laboratories</ref>
			\| align="center" \| <math>0.60 K_u</math>
			\| align="center" \| <math>2K_p/T_u</math>
			\| align="center" \| <math>K_p T_u/8</math>
			\|-----
			\| align="center" \| ''Pessen Integral Rule''<ref name="microstar"/>
			\| align="center" \| <math>0.7 K_u</math>
			\| align="center" \| <math>2.5K_p/T_u</math>
			\| align="center" \| <math>0.15K_p T_u</math>
			\|-----
			\| align="center" \| ''some overshoot''<ref name="microstar"/>
			\| align="center" \| <math>0.33 K_u</math>
			\| align="center" \| <math>2K_p/T_u</math>
			\| align="center" \| <math>K_pT_u/3</math>
			\|-----
			\| align="center" \| ''no overshoot''<ref name="microstar"/>
			\| align="center" \| <math>0.2 K_u</math>
			\| align="center" \| <math>2K_p/T_u</math>
			\| align="center" \| <math>K_pT_u/3</math>
			\|}

			== Evaluation ==
			Z–N tuning creates a "quarter wave decay". This is an acceptable result for some purposes, but not optimal for all applications.

			* "The Ziegler-Nichols tuning rule is meant to give PID loops best disturbance rejection <ref name="microstar"/>
			Z–N yields an aggressive gain and [[overshoot (signal)\|overshoot]]<ref name="microstar"/> – some applications wish to instead minimize or eliminate overshoot, and for these Z–N is inappropriate.

			==References==
			{{reflist}}

			* {{cite web
			\| last =Co
			\| first =Tomas
			\| authorlink =
			\| coauthors =Michigan Technological University
			\| title =Ziegler-Nichols Closed Loop Tuning
			\| work =
			\| publisher =
			\| date = February 13, 2004
			\| url =http://www.chem.mtu.edu/~tbco/cm416/zn.html
			\| doi =
			\| accessdate = 2007-06-24}}
			{{refend}}

			==External links==
			* http://controls.engin.umich.edu/wiki/index.php/PIDTuningClassical#Ziegler-Nichols_Method

			{{DEFAULTSORT:Ziegler-Nichols method}}
			[[Category:Control devices]]


			{{Engineering-stub}}

en>R. J. Mathar: /* Two parameters case */ oeis tag added

2012-08-08T15:46:27Z

Two parameters case: oeis tag added

New page

La crainte n'a pas sa place ici car les erreurs font partie du jeu. L'agent est mandataire c'est -dire qu'il agit au nom pour le compte et aux risques de l'entreprise mandante.<br><br>Also visit my web page: [http://www.gagnerdelargent.tv/ bourse binaire en ligne]

Multiple zeta function - Revision history

en>Rjwilmsi: /* The sum and duality conjectures */Journal cites:, added 1 DOI using AWB (10473)

en>Pinazza: /* Other results */ added some derivate formulas (ref in note 3)

en>R. J. Mathar: /* Two parameters case */ oeis tag added