Nau'o'in Mai Girma | Mai Girma na Tsaki, Haske da Tashin Yadda

فیلڈ: Karkashin Kuliya da Dukkana

China

Mai suna Controller?

A cikin na'urar tattalin arziki, controller shine zanu'a mai suna wanda yana neman farkon bayanar da aka fi sani (i.e. process variable) da bayanar da ake magana (i.e. setpoint). Controllers suna wajen muhimmanci a cikin na'urar tattalin arziki kuma ana amfani da su a duk na'urar tattalin arziki masu mafi yawan abubuwa.

Sai dai a bincike kuɗi game da controllers a cikin littattafan na'urar tattalin arziki, yana da kyau a samun tasiri na controllers. Tasirin muhimmanci na controllers sun hada:

Controllers sun saukar da ingancin bayanar da ake magana a lokacin da yaɗu ne ta hanyar neman farkon bayanar da aka fi sani.
Idan ingancin bayanar da ake magana a lokacin da yaɗu ne yana sauka, kuma dukkan ta hanyar yana sauka.
Controllers sun taimaka waɗannan bayanar da aka fi sani a neman farkon bayanar da aka fi sani.
Controllers sun taimaka waɗannan bayanar da aka fi sani a neman farkon bayanar da aka fi sani.
Controllers sun taimaka waɗannan bayanar da aka fi sani a neman farkon bayanar da aka fi sani.
Controllers sun taimaka waɗannan bayanar da aka fi sani a neman farkon bayanar da aka fi sani.

Wasu ƙarin na controllers suna amfani da su a cikin wasu wurare na takamantukan kamar programmable logic controllers da SCADA systems. Wasu ƙarin na controllers suna tattauna a cikin littattafan da za a gaba.

Ƙarin na Controllers

Akwai ƙarin ƙarin na controllers: continuous controllers, da discontinuous controllers.

A cikin discontinuous controllers, manipulated variable yana ƙawo bayanai da ake fada. Idan ake nufin kowane bayanai da manipulated variable yana iya ƙawo, ake tsara waɗannan bayanai a cikin two position, three position, da multi-position controllers.

Daga continuous controllers, discontinuous controllers sun yi aiki a kan shiga, switching final controlling elements.

Karakarar continuous controllers shine cewa controlled variable (ko manipulative variable) yana iya ƙawo kowane bayanai a cikin output range na controller.

Sai dai a cikin theory na continuous controller, akwai uku ƙarin na basic modes wadanda duk aiki na control take faru, wadannan shine:

Proportional controllers.
Kontrollonin daɗi.
Kontrollonin tsari.

A yi amfani da kungiyar wannan abubuwa don kontrola na musamman haka cewa mutanen bayanai yana daga takardun (ko kuma ya zama damar da za su iya). Wannan uku abubuwan da ke kontrola zai iya haɗa zuwa kontrolonin daɗi:

Kontrolonin mafi yawan da kontrolonin daɗi (PI Controller)
Kontrolonin mafi yawan da kontrolonin tsari (PD Controller)
Kontrolonin mafi yawa da daɗi da tsari (PID Controller)

Tana da shawarar kuɗi daɗi da za a tattara muƙasƙarren bayan.

Kontrolonin Mafi Yawan

Duk kontrolonin na da tushen bayanai da suke da ita. Ba za su iya koyar kontrolonin daɗi a wuri ko kuma za su iya tabbatar da ƙarin bayan – akwai al'amuran da suke da su. Don kontrolonin mafi yawan, akwai biyu al'adun da suke da su da suka rubuta a nan:

Farkon ba sa gaba; ma'ana farkon da take da shi a nan da ke faru da shi ba sa gaba.
Farkon ba sa gida; ma'ana farkon da take da shi a nan ba sa gida.

Na da shawarar kuɗi daɗi da za a tattara kontrolonin mafi yawan, kamar sunan a kontrolonin mafi yawan shi, fuskantar (ko kuma an sani shi da alama) yana daɗi da farkon. Tana da shawarar kuɗi daɗi da za a tattara kontrolonin mafi yawan taƙarfiyar. Kamar yadda a sanin a kontrolonin mafi yawan, fuskantar yana daɗi da farkon, a rubuta wannan taƙarfiyar:

A yi bace ɗaukake daɗi ne:

Idan Kp shine karamin daɗi ko kuma an sani shi da ƙwarewa kontrolonin.

Yana da kyau a yi Kp da take zama da ɗaya. Idan ƙimancin Kp yana fi ɗaya (>1), za a haɗa sinyalin ƙaramin abu kuma za ta iya samun sinyal na ƙaramin abu a gaba.

Muhimmanci na Maiyaki na Maiyakin Tsawon Ilimi

A nan za a tattauna wasu muhimmanci na maiyaki na maiyakin tsawon ilimi.

Maiyakin tsawon ilimi ya taimaka wajen kiyasin abubuwa na duka lokaci, saboda haka ana fadada cikin al'adu a gaba.
Tashin adadin tsawo na cikin al'adu na tsayi da take da damu ya zama da ɗaya da tushen maiyakin tsawon ilimi.

Kasuwanci na Maiyakin Tsawon Ilimi

A nan akwai wasu kasuwanci na maiyakin tsawon ilimi kuma su ne:

Saboda irin maiyakin tsawon ilimi, ana samu wasu gabatarwa a cikin al'adu.
Maiyakin tsawon ilimi suna haɗa shirin mafi girma na al'adu.

A nan, za a bayyana Maiyakin Tsawon Ilimi (P-controller) da misalai. Da wannan misali masu karatu suna samu karfin 'yan fahimta game da 'Stability' da 'Steady State Error'. Zaɓe al'adu na tsawon ilimi a cikin Figure-1

proportional controller error amplifier block diagram — Figure-1: Al'adu na Tsawon Ilimi Da Maiyakin Tsawon Ilimi

'K' ita ce maiyakin tsawon ilimi (kuma ana kiranta ake kira maiyaki na ƙaramin abu). Tashar rubutu na al'adu na iya rubuta kamar haka:

s3+3s2+2s+K=0

Idan Routh-Hurwitz ta zama a wannan tushen likitoci, za a iya samun yadda ‘K’ ke da kyau don inganci a kan 0<K<6. (Yana nufin cewa saboda ma'adotanni K>6 za a bukata; saboda ma'adota K=0, za a buka musamman).

Root locus na wannan bincike ta shahara a Figura-2

Root locus proportional controller time response — Figura-2: Root locus na binciken da aka shahara a Figura-1, Root Locus ya ba wani bayanar game da yadda ke da kyau 'K'

(Zan iya fahimta cewa root locus ana kirkiro don funtunawa na gaba (G(s)H(s), amma ya ba wani bayanar game da abubuwan da suka shiga a funtunawa na gaba, kamar roots of characteristics equation, ko kuma zeros of the characteristics equation.

Root locus ya taimaka a kirkiro ma'adotanni 'K', kamar gain of the proportional controller). Saboda haka, binciken (a Figura-1) ya buka saboda ma'adotanni kamar K= 0.2, 1, 5.8, etc.; amma wani ma'adota muna zaka zabi. Zan iya tattara kowane ma'adota da za a kawo bayanan da aka samu.

A nan, zan iya fahimta cewa ma'adotan da ya fiye 'K' (kamar misali, K=5.8) za a haɗa inganci (wannan shi ne abu mai zurfi) amma za a zama aiki a matsayin koyarwa (kamar koyarwa masu inganci, kamar reduce the steady-state error, wanda ya zama abu mai yaushe).

Zan iya fahimta cewa

$K_p =\lim_{s\rightarrow 0}KG(s)H(s)$ , Steady state error (ess)= $\frac{1}{1+K_p}$ (Wannan ya shafi a cikin case of step input)

$K_v =\lim_{s\rightarrow 0}sKG(s)H(s)$ , Tsarin hukuma (ess)= $\frac{1}{K_v}$ (Yana da muhimmanci a cikin tsarin ramp input)

$K_a =\lim_{s\rightarrow 0}s^2KG(s)H(s)$ , Tsarin hukuma (ess)= $\frac{1}{K_a}$ (Yana da muhimmanci a cikin tsarin parabolic input)

Yana iya samun cewa don uku na ‘K’, uku na Kp, Kv da Ka yana zama mafi uku da kuma tsarin hukuma yana zama mafi tsari.

Na sani za a taka wani abu da bayyana abubuwa

1. A K=0.2

A nan tsarin kimiyyar gwamnati na sana'ar sana'a ita ce s3+ 3s2+ 2s+0.2=0; juyin wannan kimiyyar suna -2.088, -0.7909 da -0.1211; Zan iya koyar -2.088 (saboda ta shiga daga axis mai imagination). Daga baki daya da biyu, zan iya cewa shine overdamped system (saboda duk juyon su ne mai tsari da kuma haske, ba ake da imaginary parts).

Daga step input, aikin lokacin tana nuna a Fig-3. Yana iya samun cewa babban aiki ba ake da oscillations. (idanci juyon su ne complex maka aikin lokacin ya taba da oscillations). Overdamped system yana da damping da ya fi '1'.

Amsa da lokaci na mafi tsawo a cikin mai kontrola ta proportional — Figura-3: Amsa ba tana da yawa, wanda ya faruwa a cikin sistema ta mafi tsawo

A nan karon, wannan shi ne mai kontrola ta buƙata: $G(s)H(s)=\frac{0.2}{s(s+1)(s+2)}$

Margina da take (GM)=29.5 dB, Margina da fushi (PM)=81.5°,

Yana da kyau a taka bayyana cewa, a cikin tattalin masu kontrola, babu da zai iya a yi amsar da mafi tsawo. Rutzin (poles of closed-loop transfer function) ya kamata suka fi inganci.

A nan karon mafi tsawo, mafi tsawon ya fi dace da '1', amma mafi tsawon da ke 0.8 na da kyau.

2. A K=1

A nan karon, likitoci na sistemashin shi ne s3+ 3s2+ 2s+1=0; rutzin da suke su -2.3247, -0.3376 ±j0.5623; Zan iya bincike -2.3247.

Daga rutzin da biyu, za a iya kiran shi a matsayin sistema ta mafi tsawo (domin rutzin su suna da inganci uku da mutane). A nan karon, amsa da lokacin da aka bani da shi a kan input ta step, ana nuna a Figura-4.

Amsa da lokaci na mafi tsawo a cikin mai kontrola ta underdamped — Figura-4: Amsa tana da yawa, wanda ya faruwa a cikin sistema ta mafi tsawo

A nan da yanzu open loop transfer function shine $G(s)H(s)=\frac{1}{s(s+1)(s+2)}$

Gain Margin (GM)=15.6 dB, Phase Margin (PM)=53.4°,

3. A K=5.8

Sai dai 5.8 ya fi 6, zan iya fahimtar cewa system na shi ne mai kyau, amma kuma ya danganta da iyaka. Zan iya samun root daga equation ta characteristics.

Za a yi rawa wata root, biyu na biyu za a danganta da axis mai imaginary. (Roots of its characteristics equation will be -2.9816, -0.0092±j1.39). Daga step input, time response ta muna cikin Fig-5.

Transient response underdamped controller — Figure-5: Response ya da oscillations, it is the response of the underdamped system (Response in Figure-4 is also belongs to the underdamped system)

A nan da yanzu open loop transfer function shine $G(s)H(s)=\frac{5.8}{s(s+1)(s+2)}$

Gain Margin=0.294 db, Phase Margin =0.919°

Yana iya bayyana, tare da hakan, GM & PM suna rage da tsawon. Sai dai system na shi ya danganta da instability, saboda haka GM & PM suna danganta da zero value.

Integral Controllers

Kamar da sunan ke nufin cewa a integral controllers output (ko actuating signal) ya shafi da integral of the error signal. Yanzu ba ni a yi analysis integral controller mathematically.

A nan da a sani cewa a tsawon kontrola na integral, farkon aiki shi ne kadan da ya zama da idan a yi haske don sayarren alamun abu, a taka bayyana wannan mathematically za a iya cewa,

A tafin alamun kadan, muna cewa,

Idan Ki shine karamin integral ko kuma ake kira gain na kontrola. Tsawon kontrola na integral yana amsa ake kira reset controller.

Abubuwan da Integral Controller ke Sanya

Saboda kyakkyawan aikinsa, Integral Controllers suna iya kara alamar aiki zuwa set point na musamman ba a gaba da hankali, saboda haka suka amsa ake kira reset controllers.

Tsariyar Integral Controller

Yana iya kara aiki na system ta tsari saboda yana aiki da hankali a kan sayarren abu da aka fara.

Kontrola na Derivative

Ba a yi amfani da kontrola na derivative baki daya. Yana bukata a yi amfani da su a kansu da wasu muhimmiyyoyi daban-daban saboda abubuwan da ke tsari da za a bayyana a nan:

Babu wani abu da yake iya haɗa da sayarren aiki a gaba.
Yana iya haɗa da saturation effects kuma yana iya saukar samun alamun abu da aka fara a system.

Don haka, a matsayin tsawon kontrola na derivative, farkon aiki (ko kuma ake kira actuating signal) yana kadan da ya zama da idan a yi haske don sayarren alamun abu.

Don haka, za a iya tuntubi kontrola na derivative mathematically. A nan a sani cewa a tsawon kontrola na derivative, farkon aiki yana kadan da ya zama da idan a yi haske don sayarren alamun abu, a taka bayyana wannan mathematically za a iya cewa,

A cikin bayanar da alama na tsawo, muna samun,

Idan, Kd yana cewa masu suna proportional constant ko kuma controller gain. An kiran derivative controller da rate controller.

Muhimman Abubuwan da Derivative Controller Ke Da Su

Muhimman abubuwan da derivative controller ke da su shi ne cewa ya zama da jirgin ruwa na system a matsayin hanyoyin tushen.

Proportional and Integral Controller

Kamar sunan ta yadda aka bayyana, wani babban gine-gine proportional da integral controller, wadannan output (ko kuma actuating signal) yana daga cikin summay proportional da integral error signal.

Yanzu ina bincike proportional da integral controller mathematically.

Saboda in ba sani a proportional da integral controller output yana daga cikin summay proportional error da integration error signal, writing this mathematically muna samun,

A cikin bayanar da alama na tsawo, muna samun,

Idan, Ki da kp proportional constant da integral constant respectively.

Abubuwan da disadvantages su combinations of the advantages and disadvantages of proportional and integral controllers.

Through the PI controller, we are adding one pole at origin and one zero somewhere away from the origin (in the left-hand side of complex plane).

A cikin hanyar, saboda abu a tushen bayanai, yadda ake amfani da ita za iya kawo karfi; amma muhimmanci na ta shi shine zan yi gaba-gaban alamomin da ya faruwa, saboda haka ana amfani da shi a kan duk wasu kontrola masu amfani mafi yawa.

Tambayar na kontrola PI an samu a Fig-6. Idan ake bayar abu a cikin hanyar, kuma a lokacin da K=5.8, Ki=0.2, yadda ake jawabi a lokacin, an samu a Fig-7. A lokacin da K=5.8 (A cikin kontrola P, ya kasance a cikin yanayi mai kurkura, saboda haka idan ake sanya ma'ana mai furci a Integral part, ya zama mai kurkura.

Kara ina buƙata cewa Integral part ya kawo karfi, ba ya nufin cewa system ya zama mai kurkura duka. A cikin yanayin, muna sanya Integral part kuma system ya zama mai kurkura).

Integral Controller time response — Fig-6: System na kontrola da PI Controller

Integral controller response — Fig-7: Jawabin da system a Fig-6 ya jawabi, a lokacin da K=5.8, Ki=0.2

Kontrola Proportional da Derivative

Daga sunan, shine haihuwar kontrola proportional da derivative, wanda ake amfani da ita ya zama haske (ko kuma abu na aiki) ya kai don summu proportional da derivative na abu na faruwa. Idan a nan muna duba kontrola proportional da derivative daidai.

Sannan a nan muna sani cewa a kontrola proportional da derivative, haske ya kai don summu proportional na abu na faruwa da kuma jirgin abu na faruwa, idan a rubuta wannan daidai, muna cewa,

Idan a rage alamar haske, muna cewa,

Amsa, Kd da Kp sunan dabbobi da kwaikwayen kafin da zaɓe.
Mafi yawan da ke ciki da mafi girman shi suna da muhimmanci a matsayin mafi yawan da ke ciki da mafi girman kafin da kwaikwayen.

Masu karatu suka gano cewa a nemi 'zero' a wurin da ya fi kyau a tsarin tasiri mai wani tana daidaita masu inganci, amma idan an samun 'pole' a tsarin tasiri mai wani tana iya haifar da masu inganci.

Kalmomin 'a wurin da ya fi kyau' a kalmar da aka bayar suna da muhimmanci & wannan shi ne ake kira cikakken fasahar kontrol (yana nufin cewa 'zero' da 'pole' suka zama a wurare da ya fi kyau a kusurin murabba don samun abubuwan da ake bukata).

Samun PD controller yana nufin a nemi 'zero' a tsarin tasiri mai wani [G(s)H(s)]. Diagram ta PD Controller yana nuna a Fig-8

Proportional Derivative controller — Fig-8: Tsarin kontrol mai wani tana da PD Controller

A nan, muna samun K=5.8, Td=0.5. Tasirin lokacin, kan ci gaba, yana nuna a Fig-9. Zaka iya kawo Fig-9, da Fig-5 don tabbatar da muhimmancin a nemi 'derivative part' a P-controller.

Proportional derivative controller Time response — Fig-9: Tasirin system da aka nuna a Fig-8, da K=5.8, Td=0.5

Tsarin tasiri na PD controller shine K+Tds ko Td(s+K/Td); saboda haka muna nemi 'zero' a -K/Td. Daga binciken 'K' ko 'Td', wurin da 'zero' yake zama yana da muhimmanci.

Idan 'zero' yana da sauki a kan jirgin magana, fadada ita zai lafiya, idan 'zero' yake a kan jirgin magana (ko zai da sauki a kan jirgin magana) ba zai a barin (root locus yana faru a kan 'poles' & yana kammala a kan 'zero', Muhimmancin masu fasahar kontrol yana nufin cewa root locus ba zai faru a kan jirgin magana, saboda haka 'zero' da ya da sauki a kan jirgin magana ba zai a barin, saboda haka wurin da ya fi kyau a kan 'zero' yana da muhimmanci)

Akwai wani abin da ake cewa, masu kontrola PD ke sauyi aiki na zaman gaba kuma masu kontrola PI ke sauyi aiki na zaman lafiya.

Masana'antu Masu Kontrola Proportional Integral Derivative (PID)

Masu kontrola PID suna amfani a harkokin kontrola a gwamnati don bincike hawa, tsakiyar, kyau, yanayi, da sauransu.

PID Controller, Proportional integral derivative controller — Fig-10: Masana'antu kontrola da PID

Fankin kontrola PID yana iya samun:

$Tds+K+\frac{Ki}{s}$ ko $\frac{Tds^2+Ks+ Ki }{s}$

Yana iya samun cewa daya daga cikin shiga ya zama, duk waɗannan Td, K, da Ki ke juye muhimman shiga.

A nan, za a iya ƙara biyu da shiga mafi ƙarfi ko biyu da shiga mai tsawo saboda haka, saboda haka masu kontrola PID suna iya ba da tashin da yake daidai. A lokacin da ya fi, masu kontrola PI su ne da ake tabbatar da su a matsayin babban zabe ta hanyar kontrola, saboda hanyar masu kontrola PID ya fi ƙarfin da ake amfani da ita, amma a lokacin yanzu, saboda ci gaban rubutu, ya zama ziyartar da ake amfani da masu kontrola PID.

Idan an yi aiki da jerin input, don ukuwa K=5.8, Ki=0.2, da Td=0.5, yadda ake fada a lokacin yanzu, ana bayyana a Fig-11. Yara Fig-11 da Fig-9 (An yi ukuwar da ake iya karin ayyukan a lokutan).

Wakarancin yadda ake gudanar da PID Controller — Figure-11: Wakarancin yadda ake gudanar da na systemi a Figure-10, tare da K=5.8, Td=0.5, Ki=0.2

Jerin Yadda Ake Kiranta PID Controller

Idan kana son kiranta PID controller wajen systemi mai sauƙi, jerin yadda ake iya samun al'amuran da aka son amfani da su ita ce:

Sauka da wakarancin yadda ake gudanar da closed-loop transfer function kuma fahimta cewa zai buƙata wani abubuwa.
Kara proportional controller, karkashin 'yan gaba ta 'K' ta hanyar Routh-Hurwitz ko software da ya danganta.
Ƙara integral part don kawo karfi ga steady-state error.
Ƙara derivative part don yanka damping (damping yana da kyau a kan 0.6-0.9). Derivative part zai kawo karfi ga overshoots da transient time.
Sisotool, wanda yake da shi a MATLAB zai iya amfani da ita don karkashin gaba da samun al'amuran da aka son amfani da su.
Fahimta, jerin yadda ake karkasha parametoci (kirantar da kontrola) suna da su ita ce jerin yadda ake amfani da su. Ba a da ƙarin bayanai masu inganci don kirantar da kontrola ba.

Fuzzy Logic controllers

Fuzzy Logic controllers (FLC) ana amfani da su inda systemi suna da non-linear da maɗa. Duk da cewa duka systemi na tsarin kimiyya/na tsarin karamin ruwa suna da non-linear da maɗa. Saboda haka, Fuzzy Logic controllers sun fi yawa waɗannan mafi girma a cikin masu ilimi.

Babu modeli na kimiyya mai kyau da ke buƙata a FLC. Ana yi aiki a baya game da tarihin mulkin, ana iya gudanar da non-linearities da kuma ana iya ba da karfi ga disturbance masu yawan karfi daga duk masu ilimi na non-linear.

FLC tana da asashe a fuzzy sets, yana nufin kungiyoyi na abubuwa da ake magance da transition daga membership zuwa non-membership yana da kyau saboda smoothness babu abrupt.

A wasu abubuwan da aka samu, FLC ta saukar da kontrola masu a cikin systemi masu karshen, non-linear, ko undefined da ake da ilimi mai kyau. Saboda haka, boundaries of fuzzy sets zai iya zama vague da ambiguous, kuma sun fi yawa waɗannan approximation models.

Wani abu mai muhimmanci a cikin yanayin synthesis procedure ta fuzzy controller shine ya bayyana input da output variables game da tarihin mulki ko ilimi mai kyau.

Yana da wannan a cikin yanayin expected function ta kontrola. Ba a da ƙarin bayanai masu inganci don zaɓe waɗannan variables, amma a gaba da haka, abubuwan da ake zaɓe suna da states of the controlled system, their errors, error variation, da kuma error accumulation.

Bayanin: Gaskiya da fitaccen, labarai na biyan mu'amala, idana ya gaishe wace kafofin ka'ido, zaka iya ra'ayi kafofin ka'ido.

Ba da kyau kuma kara mai rubutu!

Makarantarƙi:

Sistematun Gari

Sistemin Kontrola

About experts

Electrical4u

China