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'''Quantitative feedback theory''' (QFT), developed by [[Isaac Horowitz]] (Horowitz, 1963; Horowitz and Sidi, 1972), is a [[frequency domain]] technique utilising the [[Nichols plot | Nichols chart]] (NC) in order to achieve a desired robust design over a specified region of plant uncertainty. Desired [[time domain|time-domain]] responses are translated into frequency domain tolerances, which lead to bounds (or constraints) on the loop transmission function. The design process is highly transparent, allowing a designer to see what trade-offs are necessary to achieve a desired performance level.
== 'Xiao Yan little brother is not the Central Plains people ==


==Plant templates==
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[[Image:Qftsystem.jpeg|thumb|320px|QFT Feedback System]]
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Usually any system can be represented by its Transfer Function ([[Laplace transform|Laplace]] in continuous time domain), after getting the model of a system.
== is gradually calmed down ==


As a result of experimental measurement, values of coefficients in the Transform Function have a range of uncertainty. Therefore, in QFT every parameter of this function is included into an interval of possible values, and the system may be represented by a family of plants rather than by a standalone expression.  
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<math>\mathcal{P}(s) = \left \lbrace \dfrac{\prod_{i} (s + z_i)}{\prod_{j} (s + p_j)}, \forall z_i \in [z_{i,min}, z_{i,max}], p_j \in [p_{j,min}, p_{j,max}] \right \rbrace </math>
== the former even stronger ==


A frequency analysis is performed for a finite number of representative frequencies and a set of ''templates'' are obtained in the NC diagram which encloses the behaviour of the open loop system at each frequency.
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==Frequency bounds==
== ' Last time the old gentleman would have said ==
<!-- Image with unknown copyright status removed: [[Image:Qft feq constraints.PNG|thumb|300px|QFT Templates on the NC]] -->


Usually system performance is described as robustness to '''instability''' (phase and gain margins), '''rejection to input and output noise disturbances''' and reference '''tracking'''. In the QFT design methodology these requirements on the system are represented as frequency constraints, conditions that the compensated system loop (controller and plant) could not break.
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With these considerations and the selection of the same set of frequencies used for the templates, the frequency constraints for the behaviour of the system loop are computed and represented on the [[Nichols plot|Nichols Chart]] (NC) as curves.
== ' Shen Yun wrinkled ==


To achieve the problem requirements, a set of rules on the Open Loop Transfer Function, for the nominal plant <math>L_0(s) = G(s)P_0(s)</math> may be found. That means the nominal loop is not allowed to have its frequency value below the constraint for the same frequency, and at high frequencies the loop should not cross the ''Ultra High Frequency Boundary'' (UHFB), which has an oval shape in the center of the NC.
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==Loop shaping==
<ul>
The controller design is undertaken on the NC considering the frequency constraints and the ''nominal loop'' <math>L_0(s)</math> of the system. At this point, the designer begins to introduce controller functions (<math>G(s)</math>) and tune their parameters, a process called '''Loop Shaping''', until the best possible controller is reached without violation of the frequency constraints.
 
 
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The experience of the designer is an important factor in finding a satisfactory controller that not only complies with the frequency restrictions but with the possible realization, complexity, and quality.
 
 
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For this stage there currently exist different CAD (''Computer Aided Design'') packages to make the controller tuning easier.
 
 
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==Prefilter design==
 
Finally, the QFT design may be completed with a pre-filter (<math>F(s)</math>) design when it is required. In the case of tracking conditions a shaping on the Bode diagram may be used. Post design analysis is then performed to ensure the system response is satisfactory according with the problem requirements.
</ul>
 
The QFT design methodology was originally developed for ''Single-Input Single-Output'' (SISO) and ''Linear Time Invariant Systems'' (LTI), with the design process being as described above. However, it has since been extended to weakly nonlinear systems, time varying systems, distributed parameter systems, multi-input multi-output (MIMO) systems (Horowitz, 1991), discrete systems (these using the [[z-transform|Z-Transform]] as transfer function), and non minimum phase systems. The development of [[computer aided design|CAD]] tools has been an important, more recent development, which simplifies and automates much of the design procedure (Borghesani et al., 1994).
 
==References==
*  Horowitz, I., 1963, Synthesis of Feedback Systems, Academic Press, New York, 1963.
*  Horowitz, I., and Sidi, M., 1972, “Synthesis of feedback systems with large plant ignorance for prescribed time-domain tolerances,” International Journal of Control, 16(2), pp. 287–309.
*  Horowitz, I., 1991, “Survey of Quantitative Feedback Theory (QFT),” International Journal of Control, 53(2), pp. 255–291.
*  Borghesani, C., Chait, Y., and Yaniv, O., 1994, Quantitative Feedback Theory Toolbox Users Guide, The Math Works Inc., Natick, MA.
*  Zolotas, A. (2005, June 8). ''[http://cnx.rice.edu/content/m11109/latest/ QFT - Quantitative Feedback Theory]''. Connexions.
 
==See also==
* [[Control engineering]]
* [[Feedback]]
* [[Process control]]
* [[Robotic unicycle]]
* [[H infinity]]
* [[Optimal control]]
* [[Servomechanism]]
* [[Nonlinear control]]
* [[Adaptive control]]
* [[Robust control]]
* [[Intelligent control]]
* [[State space (controls)]]
 
==External links==
* [http://ftp.rta.nato.int/public/PubFullText/RTO/EN/RTO-EN-SCI-166/EN-SCI-166-01.pdf Mario Garcia-Sanz, Quantitative Robust Control Engineering:Theory and Applications]
 
 
[[Category:Control theory]]

Latest revision as of 00:09, 3 June 2014

'Xiao Yan little brother is not the Central Plains people

And 'medicine' division of the benefits of it, beat to death a rival, is the most frightening.

'Yes, カシオ レディース 電波ソーラー腕時計 Han Chong brother, to ask, here is what the Central Plains?' Xiao Yan hesitated, suddenly asked, he did not want pains through space channels, the results had him give Hu 'chaos' lost in the Continental somewhere to go.

'ah, here is カシオ gps 時計 the Northern Plains domain.' Han Chong nodded, immediately some surprised and said: 'Xiao Yan little brother is not the Central Plains people?'

Xiao Yan smile a cry, fell not conceal the space wormhole briefly say something again.

'space storm turned casio 腕時計 説明書 out to be met, no wonder that the injury would be so heavy, but this, too, good luck, I met a storm in space wormhole in space, few people can escape カシオ 時計 プロトレック Han year we have 時計 カシオ once a guard wearing When the storm had all the space wormhole is swallowed. 'Heard, Han Chong had just suddenly, immediately breathtaking smack smack 相关的主题文章：

is gradually calmed down

Amount, and in this world, no one did not want to have this power ...

retreat with fire snake, riots casio 時計 magma to 'cave', is gradually calmed down, but to be safe, 'Xiao Yan' did not immediately set カシオの時計 off to find different fire trail, but standing http://alleganycountyfair.org/sitemap.xml in the air waiting for a Nearly ten minutes, confirmed that the snake is true retreat after the fire, just a sigh of relief, the two front-channel arbitrary direction and shook casio 腕時計 メンズ his hand, and then pick up the wings, magma began slowly to 'cave' Search among them.

'Teacher, this カシオ gps 時計 will have a different fire traces of it exist?' repulsed the fire snake, Xiao Yan is gradually re-mastered the body, the moment softly inquired.

'look at the environment and the extent of violent energy here, and then there is the other end of the previous fire snake and animals, there should be a lot of differences there may be fire ...' 'medicine' old smiled and replied. 相关的主题文章：

the former even stronger

Different atmosphere, but also カシオ腕時計 g-shock slowly between this piece appeared in the world.

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'This nothingness swallow inflammation, turned out to form a cross-fire of the Spirit,' 'medicine' old looked at Xiao Yan, a dry mouth, inflammation of this nothingness swallow fire with fire demon demon Joren space is the same existence, even, compared to net lotus fire demon, the former even stronger!

'good atmosphere of terror 相关的主题文章：

' Last time the old gentleman would have said

Slender Yu Zhi tap in the table, for a moment, and shoved meal, whispered: 'It seems that the old gentleman, it seems very xiaojia care ah ...'

frowned, Valley Nepal face surprise: '? casio 腕時計 ゴールド Are you saying that he wanted to give Xiao 電波時計 casio Lian healing' medicine

'I recently heard that added to the family invited a one product refining' medicine 'division, cheap' rejuvenation casual 'has been snatched from the Crescent City's most popular city, if we do not take measures xiaojia probably have to drop a workshop in . unmanned embarrassing situation of the casio 腕時計 'Ya-Fei wavefront flow, faint smiles:' Last time the old gentleman would have said, if given the opportunity, will and xiaojia cooperation, gps 腕時計 カシオ but at this time he was buying so much healing 'medicine' material, its purpose, it seems self-evident. '

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' Shen Yun wrinkled

Looking over all the way to the line, but so long time, but still no results.

'That kid does not know what method to use my blood left in his body imprint to wipe except mine.' Shen Yun gloomy road, indeed, his mind this is extremely consternation, blood Ray カシオ ソーラー電波腕時計 imprint is how difficult get カシオ 腕時計 バンド rid of, he most clearly, however, less than half of this effort, however, is actually completely fade away to go, this is the first time he encountered so many years.

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'What roar roar? you catch? Well, if you were not afraid of the hands of the boy casio 腕時計 ゴールド puppet, not earlier to catch up to it?' Shen Yun wrinkled, but also some impatience Road.

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