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<sup>[[{{TALKPAGENAME}}#With Respect to What|[With Respect to What?] ]]</sup> {{-}} {{Citation needed|date=July 2009}} {{-}} {{compu-hardware-stub}} {{-}} {{disambig}}

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Hybrid PI

What is hybrid about this?

u(t_{\text{k}})=K_{\text{p}}e(t_{\text{k}})+K_{\text{i}}\sum _{i=1}^{k}e(t_{i})\,\Delta t

All practical controllers have limited outputs; in the case where the control output is PWM Duty, these general limits are

0% ≤ minimum duty limit ≤

u(t_{\text{k}})

≤ maximum duty limit ≤ 100%

That is, as all controllers saturate at their limits, so too does our PWM controller "saturate" at either minimum or maximum duty limit.

All practical controllers with integral terms experience integral windup at saturation unless anti-windup techniques are applied.

So, the only possible "hybridization" in our PWM controller is this: the integral term is constrained to never wind up, that is, never drive the control output into saturation, in other words, never further than the minimum or maximum duty limits.

To prevent integrator wind up in our PWM controller, our controller implements the following standard' overlapping techniques:

"Disabling the integral function until the to-be-controlled process variable (PV) has entered the controllable region"
"Preventing the integral term from accumulating above or below pre-determined bounds"
"Back-calculating the integral term to constrain the process output within feasible bounds"

First: the proportional and integral terms are separated:

P_{\text{k}}=K_{\text{P}}e(t_{\text{k}})

I_{\text{k}}=K_{\text{I}}\sum _{i=1}^{k}e(t_{i})\,\Delta t

So:

u(t_{\text{k}})=P_{\text{k}}+I_{\text{k}}

To prevent windup, the proportional term $P_{\text{k}}$ is constrained first:

Error is computed: $e(t_{k})=r(t_{k})-y(y_{k})$ ,

but then is constrained to the reciprocal gain, a.k.a. proportional band ("the controllable region"), beyond which the output is saturated, full-"off" or full-"on" at the duty limits

and the proportional term is then computed from this constrained error.

The integral term is then updated, but with the constraint that the integral term may not place the control output outside of its limits.

Given

MinDty<P_{\text{k}}<MaxDty

MinDty<u(t_{\text{k}})=P_{\text{k}}+I_{\text{k}}<MaxDty

So:

MinDty<P_{\text{k}}+I_{\text{k}}<MaxDty

(MinDty-P_{\text{k}})<I_{\text{k}}<(MaxDty-P_{\text{k}})

0<I_{\text{k}}<(MaxDty-P_{\text{k}})

ISO 26262

**Comparison of Hazard Effects Level**
ASIL	Severity Classifications	DAL	Failure condition	Passenger threats	Crew threats	Airplane capability or safety margin
-	-	A	Catastrophic	Loss of the airplane and death of all aboard	Fatality or incapacity	Hull loss
D	Life-threatening (survival uncertain) to fatal injuries
		B	Hazardous	Serious or fatal injuries	Impared abilty	Large reduction
C	Severe to life-threatening (survival probable) injuries
		C	Major	Distress or minor injuries	Distraction	Significant reduction
B	Light to moderate injuries
A
		D	Minor	Physical discomfort	Flight change or emergency procedures	Slight reduction
QM	No Injuries	E	No Effect	Inconvenience	No Effect	No Effect

Modern

In particular, Russia and North America are the homes of great mechanized granaries, known separately and more conventionally as grain elevators.

Planet of the Apes

In a background subcontext, television and newspaper media report the launch and subsequent loss of the Icarrus mission to Mars. Ceasar's parable with the sticks refers to the Roman and Italian symbology of the Facsise Rise makes several references to the Bright eyes was both the name of Ceasar's mother and Dr. 's ... name for Taylor The general layout of the ape cages in Rise reflect the layout in PotA Both Ceasar and Taylor are hosed down in punishment. Ceasar's first word is "No" in both Rise and PotA 's line "its a mad house! It's a mad house"

B9

B9 was originally defined by its neutritional effects, tha tis if there is not enough B9 factor tissue that depends on rapid cell devision fail. Such tissues include skin, hair, blood cells, intestinal linings and cancerous tumors) Vitamin B9 refers to a particular essential nutritional factor. Absence or suppression of the B9 factor results notably in slowing or failure of rapidly dividing cells (e.g., blood, skin, hair, intestines, or cancers), but also results in elevation of homocystine ^[1] and problems with nerve function.^[2] Chemically, all B9 vitamers have the same parent structure, which is named pterolymonoglutamic acid (PMGA). Plants and bacteria are able to form this stucture de novo from pterin, p-aminobenzoate (PABA), and glutamate moieties [Biosynthesis of Folates] but vertebrates lack a complete folate synthesis pathway and so need a dietary supply.^[3]^[4]^[5]

The terms Folic Acid and Folates are both used interchangably to refer to all natural and syntheric compounds that function as B9. However, there are situations where either term is used more narrorwly. Folic Acid can be used to refer generally to all compounds based on PMGA; but it can also refer specifically or implicitly to the manufactured "crystaline" form of PMGA, particularly as used in supplementation. Folate can also be used to refer generally to all compounds based on PMGA; but it is also used to refer specifically to PMGA-based compounds arrising through biological processes, especially the folate metabolism. The distinction between "crystaline" PMGA and bological folates is important because the to forms have different biochemical properties and effects.

FA prefered syn FA all PGMA FA food supplement F prefered syn F all natural

however, The prefered synonym for pterolymonoglutamic acid is folic acid, however there is some difficulty here because in some literature folic acid refers specifically or implicitly to the manufactured "crystaline" form of PMGA while other literaure applies the term equally to any metabolic compound, natural or synthetic, having pterolyglutamate as a parent structure.

^ "Folate: Evidence". Health Information - Drugs and Supplements. Mayo Clinic.
^ Stahl, Stephan M., M.D. Ph.D (2008). "L-Methylfolate: A Vitamin for Your Monoamines". Journal For Clinical Psychiatry. 5. 70: 767, author reply 767-9. PMID 19193337. {{cite journal}}: Unknown parameter |month= ignored (help)CS1 maint: multiple names: authors list (link)
^ Goyer, Aymeric (2004). "Folate Biosynthesis in Higher Plants. cDNA Cloning, Heterologous Expression, and Characterization of Dihydroneopterin Aldolases". Plant Physiology. 135:103-111. PMID PMC429337. {{cite journal}}: Check |pmid= value (help); Unknown parameter |coauthors= ignored (|author= suggested) (help)
^ Bauer, Stefanie (2004). "Biosynthesis of Tetrahydrofolate in Plants: Crystal Structure of 7,8-Dihydroneopterin Aldolase from Arabidopsis thaliana Reveals a Novel Adolase Class". Journal of Molecular Biology. 339 (4): 967–979. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help); Unknown parameter |month= ignored (help)
^ Fischer, Markus. "Biosynthesis of Folates". flavins.info.

[1] "Folate: Evidence". Health Information - Drugs and Supplements. Mayo Clinic.

[2] Stahl, Stephan M., M.D. Ph.D (2008). "L-Methylfolate: A Vitamin for Your Monoamines". Journal For Clinical Psychiatry. 5. 70: 767, author reply 767-9. PMID 19193337. {{cite journal}}: Unknown parameter |month= ignored (help)CS1 maint: multiple names: authors list (link)

[3] Goyer, Aymeric (2004). "Folate Biosynthesis in Higher Plants. cDNA Cloning, Heterologous Expression, and Characterization of Dihydroneopterin Aldolases". Plant Physiology. 135:103-111. PMID PMC429337. {{cite journal}}: Check |pmid= value (help); Unknown parameter |coauthors= ignored (|author= suggested) (help)

[4] Bauer, Stefanie (2004). "Biosynthesis of Tetrahydrofolate in Plants: Crystal Structure of 7,8-Dihydroneopterin Aldolase from Arabidopsis thaliana Reveals a Novel Adolase Class". Journal of Molecular Biology. 339 (4): 967–979. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help); Unknown parameter |month= ignored (help)

[5] Fischer, Markus. "Biosynthesis of Folates". flavins.info.

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