Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana

Ke paʻi nei au i ka mokuna mua o nā haʻiʻōlelo e pili ana i ke kumumanaʻo o ka mana ʻakomi, a ma hope o ka like ʻole o kou ola.

Hāʻawi ʻia nā haʻawina ma ka papa "Management of Technical Systems" e Oleg Stepanovich Kozlov ma ke Keʻena o "Nuclear Reactors and Power Plants", Faculty of "Power Mechanical Engineering" o MSTU. N.E. Bauman. Mahalo nui wau iā ia.

Ke hoʻomākaukau ʻia nei kēia mau haʻiʻōlelo no ka paʻi ʻana ma ke ʻano puke, a no ka mea aia nā loea TAU, nā haumāna, a me ka poʻe hoihoi i ke kumuhana, ʻae ʻia nā ʻōlelo hoʻohewa.

Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana

1. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana

1.1. Nā pahuhopu, nā loina o ka hoʻokele, nā ʻano ʻōnaehana hoʻokele, nā wehewehe kumu, nā laʻana

ʻO ka hoʻomohala ʻana a me ka hoʻomaikaʻi ʻana i ka hana ʻoihana (ka ikehu, ka lawe ʻana, ka ʻenekinia mechanical, ka ʻenehana ākea, a me nā mea ʻē aʻe) pono ka hoʻonui mau ʻana i ka huahana o nā mīkini a me nā ʻāpana, hoʻomaikaʻi i ka maikaʻi o ka huahana, hoʻemi i nā kumukūʻai a, ʻoi aku hoʻi i ka ikehu nuklea, kahi piʻi nui o ka. palekana (nukelea, radiation, etc.) .d.) hana o na mea kanu nukili a me na mea hookuonoono.

ʻAʻole hiki ke hoʻokō i nā pahuhopu i hoʻonohonoho ʻia me ka ʻole o ka hoʻokomo ʻia ʻana o nā ʻōnaehana hoʻomalu hou, me nā ʻōnaehana hoʻokele (me ke komo ʻana o kahi mea hoʻohana kanaka) a me ka ʻōnaehana (CS).

Wehewehe: ʻO ka hoʻokele kahi hui o kahi kaʻina hana ʻenehana e hōʻoia i ka hoʻokō ʻana i kahi pahuhopu i hoʻonohonoho ʻia.

Manaʻo hoʻomalu he lālā o ka ʻepekema a me ka ʻenehana hou. Hoʻokumu ʻia (ma muli) ma luna o nā kumu aʻoaʻo ʻelua (e like me ka makemakika, physics, chemistry, etc.) a me nā hoʻopaʻi ʻana (electronics, microprocessor technology, programming, etc.).

ʻO kēlā me kēia kaʻina hana hoʻomalu (akomi) aia nā pae nui aʻe (nā ʻeleʻele):

  • ka loaʻa ʻana o ka ʻike e pili ana i ka hana hoʻomalu;
  • ka loaʻa ʻana o ka ʻike e pili ana i ka hopena o ka hoʻokele;
  • ka nānā 'ana i ka 'ike i loa'a;
  • ka hoʻokō ʻana i ka hoʻoholo (impact on the control object).

No ka hoʻokō ʻana i ke Kaʻina Hoʻokele, pono e loaʻa i ka ʻōnaehana hoʻokele (CS):

  • nā kumu ʻike e pili ana i ka hana hoʻokele;
  • nā kumu o ka ʻike e pili ana i nā hopena hoʻomalu (nā ʻike like ʻole, nā mea ana, nā mea ʻike, a me nā mea ʻē aʻe);
  • nā mea hana no ka nānā ʻana i ka ʻike i loaʻa a me ka hoʻomohala ʻana i nā haʻina;
  • nā mea hana e hana ana ma ka Mana Mana, aia: regulator, motors, amplification-converting device, etc.

Wehewehe: Inā loaʻa i ka ʻōnaehana mana (CS) nā ʻāpana āpau i luna, a laila ua pani ʻia.

Wehewehe: ʻO ka hoʻomalu ʻana i kahi mea ʻenehana me ka hoʻohana ʻana i ka ʻike e pili ana i nā hopena hoʻomalu i kapa ʻia ʻo ka manaʻo pane.

Schematically, hiki ke hōʻike ʻia kahi ʻōnaehana mana e like me:

Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana
Laiki. 1.1.1 — Hoʻonohonoho o ka ʻōnaehana hoʻomalu (MS)

Inā loaʻa i ka ʻōnaehana hoʻomalu (CS) kahi kiʻi poloka, ʻo ke ʻano o ia mea e like me ka Fig. 1.1.1, a me nā hana (hana) me ke komo ʻole o ke kanaka (operator), a laila ua kapa ʻia ʻōnaehana mana ʻakomi (ACS).

Inā hana ka ʻōnaehana hoʻomalu me ke komo ʻana o kahi kanaka (operator), a laila kapa ʻia ia ʻōnaehana hoʻokele automated.

Inā hāʻawi ka Mana Mana i ke kānāwai i hāʻawi ʻia no ka hoʻololi ʻana o kahi mea i ka manawa, me ka nānā ʻole i nā hopena o ka mana, a laila e hana ʻia ia mana ma kahi puka hāmama, a ua kapa ʻia ka mana ponoʻī. polokalamu hoʻomalu.

Loaʻa nā ʻōnaehana open-loop i nā mīkini ʻenehana (nā laina conveyor, nā laina rotary, a me nā mea ʻē aʻe), nā mīkini helu kamepiula (CNC): e ʻike i ka laʻana ma Fig. 1.1.2.

Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana
Fig.1.1.2 - Ka laʻana o ka mana polokalamu

Hiki i ka mea haku ke lilo, no ka laʻana, he "copier".

No ka mea ma kēia hiʻohiʻona ʻaʻohe mea ʻike (mika) e nānā ana i ka ʻāpana i hana ʻia, inā, no ka laʻana, ua hoʻokomo pololei ʻia ka mea ʻoki a haki paha, a laila ʻaʻole hiki ke hoʻokō ʻia ka pahuhopu i hoʻonohonoho ʻia (ka hana ʻana o ka ʻāpana). ʻO ka maʻamau, i nā ʻōnaehana o kēia ʻano, koi ʻia ka mana hoʻopuka, e hoʻopaʻa wale i ka deviation o nā ana a me ke ʻano o ka ʻāpana mai ka mea i makemake ʻia.

Hoʻokaʻawale ʻia nā ʻōnaehana mana aunoa i 3 mau ʻano:

  • nā ʻōnaehana hoʻomalu aunoa (ACS);
  • nā ʻōnaehana hoʻomalu aunoa (ACS);
  • ʻōnaehana hahai (SS).

ʻO SAR a me SS nā ʻāpana o SPG ==> Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana.

Wehewehe: ʻO kahi ʻōnaehana hoʻomalu aunoa e hōʻoiaʻiʻo i ka paʻa o kekahi nui kino (hui o nā nui) i loko o ka mea hoʻomalu i kapa ʻia he ʻōnaehana hoʻokele aunoa (ACS).

ʻO nā ʻōnaehana hoʻokele aunoa (ACS) ka ʻano maʻamau o nā ʻōnaehana mana aunoa.

ʻO ka mea hoʻoponopono ʻakomi mua o ka honua (18th century) ʻo ia ka Watt regulator. ʻO kēia papahana (e nānā i ka Fig. 1.1.3) ua hoʻokō ʻia e Watt ma ʻEnelani e mālama i ka wikiwiki o ka hoʻololi ʻana o ka huila o kahi mīkini mahu a, no laila, e mālama i ka wikiwiki mau o ka rotation (motion) o ka pulley transmission (belt. ).

Ma kēia papahana nā mea maʻalahi (nā mea ʻike ana) he "kaumaha" (nā pōʻai). "Nā Weights" (spheres) "hoʻoikaika" i ka lima pōhaku a laila e neʻe ka valve. No laila, hiki ke hoʻokaʻawale ʻia kēia ʻōnaehana ma ke ʻano he ʻōnaehana hoʻokele pololei, a hiki ke helu ʻia ka mea hoʻoponopono mea hooponopono pololei, no ka mea, hana ia i ka manawa like i nā hana o ka "mika" a me ka "regulator".

Ma nā mea hoʻoponopono pololei kumu hou ʻaʻole koi ʻia ka ikehu e hoʻoneʻe i ka mea hoʻoponopono.

Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana
Laiki. 1.1.3 — Watt kaapuni mea hooponopono

Pono nā ʻōnaehana hoʻokele indirect i ka hele ʻana (ke alo) o kahi amplifier (no ka laʻana, ka mana), kahi mea hana hou i loaʻa, no ka laʻana, kahi kaʻa uila, servomotor, hydraulic drive, etc.

ʻO kahi hiʻohiʻona o kahi ʻōnaehana hoʻokele aunoa (ʻōnaehana hoʻokele aunoa), ma ke ʻano piha o kēia wehewehe ʻana, he ʻōnaehana hoʻokele e hōʻoia i ka hoʻomaka ʻana o kahi rocket i loko o ka orbit, kahi e hiki ai ke hoʻololi ʻia, no ka laʻana, ke kihi ma waena o ka rocket. axis a me ka mea maʻamau i ka Honua ==> nānā Fig. 1.1.4.a a me fig. 1.1.4.b

Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana
Laiki. 1.1.4(a)
Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana
Laiki. 1.1.4 (b)

1.2. Ka hoʻonohonoho o nā ʻōnaehana hoʻomalu: nā ʻōnaehana maʻalahi a me nā multidimensional

Ma ke kumumanaʻo o Technical Systems Management, hoʻokaʻawale pinepine ʻia kekahi ʻōnaehana i kahi pūʻulu o nā loulou i hoʻopili ʻia i nā hale pūnaewele. Ma ka hihia maʻalahi, aia ka pūnaewele i hoʻokahi loulou, ua hoʻolako ʻia ka mea hoʻokomo me kahi hana hoʻokomo (input), a loaʻa ka pane o ka ʻōnaehana (output) ma ka hoʻokomo.

Ma ke kumumanaʻo o ka Manawa Pūnaehana ʻenehana, hoʻohana ʻia 2 mau ala nui e hōʻike ai i nā loulou o nā ʻōnaehana mana:

- ma nā ʻano hoʻololi "hoʻokomo-puka";

— ma nā ʻano hoʻololi mokuʻāina (no nā kikoʻī hou aku, e ʻike i nā pauku 6...7).

Hoʻohana mau ʻia ka hōʻike ʻana i nā mea hoʻololi hoʻokomo-huaʻo no ka wehewehe ʻana i nā ʻōnaehana maʻalahi i loaʻa hoʻokahi "hoʻokomo" (hoʻokahi hana hoʻomalu) a me hoʻokahi "hoʻopuka" (hoʻokahi hoʻololi hoʻomalu, e nānā i ke Kiʻi 1.2.1).

Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana
Laiki. 1.2.1 – Hōʻike manaʻo o kahi ʻōnaehana mana maʻalahi

ʻO ka mea maʻamau, hoʻohana ʻia kēia wehewehe no nā ʻōnaehana hoʻokele maʻalahi maʻalahi.

I kēia mau lā, ua laha nui ka hōʻike ʻana i nā ʻano hoʻololi mokuʻāina, ʻoi aku hoʻi no nā ʻōnaehana paʻakikī ʻenehana, me nā ʻōnaehana hoʻomalu aunoa multidimensional. Ma Fig. 1.2.2 hōʻike i ka schematic representation o ka multidimensional 'akomi mana'ōnaehana, kahi u1(t)…um(t) — nā hana hoʻomalu (control vector), y1(t)…yp(t) — nā ʻāpana hoʻololi o ka ACS (vector output).

Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana
Laiki. 1.2.2 — Hōʻike manaʻo o kahi ʻōnaehana mana multidimensional

E noʻonoʻo pono kākou i ke ʻano o ka ACS, i hōʻike ʻia ma nā ʻano hoʻololi "input-output" a loaʻa i hoʻokahi mea hoʻokomo (hoʻokomo a haku a hana hoʻomalu paha) a me hoʻokahi mea hoʻopuka (hana hoʻopuka a i ʻole hoʻololi ʻia (a hiki ke hoʻololi ʻia).

E noʻonoʻo kākou ʻo ke kiʻikuhi poloka o ia ACS aia kekahi helu o nā mea (nā loulou). Ma ka hui pū ʻana i nā loulou e like me ke kumu hana (nā mea e hana ai nā loulou), hiki ke hoʻemi ʻia ke kiʻikuhi hoʻolālā o ka ACS i kēia ʻano maʻamau:

Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana
Laiki. 1.2.3 — Hoʻopaʻa kiʻi o ka ʻōnaehana hoʻomalu aunoa

hōʻailona ε(t) a i ʻole ka loli ε(t) hōʻike i ka like ʻole (hewa) ma ka hoʻopuka ʻana o ka mea hoʻohālikelike, hiki ke "hana" ma ke ʻano o nā hana helu helu maʻalahi (ka unuhi pinepine, hoʻohui pinepine ʻia) a me nā hana hoʻohālikelike paʻakikī (nā kaʻina hana).

mai y1(t) = y(t)*k1kahi k1 ʻo ia ka waiwai, a laila ==>
ε(t) = x(t) - y1(t) = x(t) - k1*y(t)

ʻO ka hana o ka ʻōnaehana hoʻomalu (inā paʻa ia) e "hana" e hoʻopau i ka mismatch (hewa) ε(t), i.e. ==> ε(t) → 0.

Pono e hoʻomaopopo ʻia ua hoʻopili ʻia ka ʻōnaehana hoʻomalu e nā mana o waho (ka hoʻomalu, hoʻopilikia, keakea) a me ka hoʻopili i loko. 'Oko'a ka ho'opili 'ana mai ka hopena ma muli o ka stochasticity (randomness) o kona noho 'ana, a'o ka hopena e aneane mau loa.

No ka koho ʻana i ka mana (hana hoʻonohonoho) e hoʻohana mākou i kekahi x(t), aiʻole u(t).

1.3. Nā kānāwai kumu o ka mana

Inā hoʻi mākou i ke kiʻi hope (block diagram o ka ACS ma Fig. 1.2.3), a laila pono e "decipher" i ka hana i hoʻokani ʻia e ka mea hoʻololi hoʻonui (he aha nā hana e hana ai).

Inā hoʻonui wale ka mea hoʻololi hoʻonui (ACD) i ka hōʻailona like ʻole ε(t), ʻo ia hoʻi: Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehanakahi Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana- ka helu kaulike (ma ka hihia Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana = Const), a laila ua kapa ʻia kēlā ʻano mana o ka ʻōnaehana hoʻokele maʻalahi i pani ʻia he mode mana kūlike (P-mana).

Inā hoʻopuka ka pūʻulu mana i kahi hōʻailona hoʻopuka ε1(t), e like me ka hewa ε(t) a me ka hoʻohui o ε(t), ʻo ia hoʻi. Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana, a laila kapa ʻia kēia ʻano mana proportionally-integrating (ka mana PI). ==> Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehanakahi b - ka helu kaulike (ma ka hihia b = Const).

ʻO ka maʻamau, hoʻohana ʻia ka mana PI e hoʻomaikaʻi i ka pololei o ka mana (ka hoʻoponopono).

Inā hoʻopuka ka pūʻulu mana i kahi hōʻailona hoʻopuka ε1(t), e like me ka hewa ε(t) a me kāna kumu, a laila ua kapa ʻia kēia ʻano. hoʻokaʻawale like ʻole (PD mana): ==> Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana

ʻO ka maʻamau, hoʻonui ka hoʻohana ʻana i ka mana PD i ka hana o ka ACS

Inā hoʻopuka ka pūʻulu mana i kahi hōʻailona hoʻopuka ε1(t), e like me ka hewa ε(t), kāna kumu, a me ka hui pū o ka hewa ==> Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana, a laila kapa ʻia kēia ʻano a laila kapa ʻia kēia ʻano mana proportional-integral-differentiating control mode (PID mana).

Hāʻawi pinepine ka mana PID iā ʻoe e hāʻawi i ka pololei mana "maikaʻi" me ka wikiwiki "maikaʻi".

1.4. Hoʻokaʻawale i nā ʻōnaehana hoʻokele aunoa

1.4.1. Hoʻokaʻawale ma ke ʻano o ka wehewehe makemakika

Ma muli o ke ʻano o ka wehewehe makemakika (equations of dynamics and statics), ua māhele ʻia nā ʻōnaehana mana aunoa (ACS) i loko. laina laina и laina laina ʻole nā ʻōnaehana (nā pū hoʻoneʻe ponoʻī a i ʻole SAR).

Hoʻokaʻawale ʻia kēlā me kēia "subclass" (linear a me nonlinear) i kekahi mau "subclasses". No ka laʻana, he ʻokoʻa nā pū kī ponoʻī linear (SAP) i ke ʻano o ka wehewehe makemakika.
No ka mea e noʻonoʻo ana kēia kau i nā waiwai hoʻoikaika o nā ʻōnaehana hoʻokele otometi linear (regulation) wale nō, ma lalo mākou e hāʻawi i kahi hoʻohālikelike e like me ke ʻano o ka wehewehe makemakika no nā ʻōnaehana hoʻokele laina laina (ACS):

1) ʻO nā ʻōnaehana hoʻokele ʻakomi laina i wehewehe ʻia i nā mea hoʻololi hoʻokomo-puka e nā hoʻohālikelike ʻokoʻa maʻamau (ODE) me mau loa coefficients:

Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana

Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana

kahi x(t) - ka mana hoʻokomo; y(t) - ka mana hoʻopuka (waiwai hiki ke hoʻololi).

Inā mākou e hoʻohana i ke ʻano o ka mea hoʻohana ("compact") o ke kākau ʻana i kahi ODE laina, a laila hiki ke hōʻike ʻia ka hoohalike (1.4.1) ma kēia ʻano:

Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana

ma hea, p = d/dt — mea hana hoʻokaʻawale; L(p), N(p) ʻo ia nā mea hoʻohana ʻokoʻa linear pili, e like me:

Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana

Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana

2) Nā ʻōnaehana hoʻomalu ʻakomi laina i wehewehe ʻia e nā hoʻohālikelike ʻokoʻa maʻamau (ODE) me nā mea hoʻololi (i ka manawa) coefficients:

Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana

Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana

Ma ka hihia maʻamau, hiki ke hoʻokaʻawale ʻia ia mau ʻōnaehana ma ke ʻano he nonlinear automatic control system (NSA).

3) Nā ʻōnaehana hoʻokele ʻakomi laina i wehewehe ʻia e nā hoʻohālikelike ʻokoʻa laina:

Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana

Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana

kahi f(…) - ka hana laina o nā manaʻo; k = 1, 2, 3… - nā helu holoʻokoʻa; Δt – ka helu helu (sampling interval).

Hiki ke hōʻike ʻia ka hoʻohālikelike (1.4.4) ma kahi hōʻailona “compact”:

Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana

ʻO ka mea maʻamau, hoʻohana ʻia kēia wehewehe ʻana o nā ʻōnaehana hoʻokele linear (ACS) i nā ʻōnaehana hoʻokele kikohoʻe (me ka hoʻohana ʻana i ke kamepiula).

4) Nā ʻōnaehana hoʻokele ʻakomi laina me ka lohi:

Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana

kahi L(p), N(p) - nā mea hoʻohana ʻokoʻa laina; τ - ka manawa lag a i ʻole lag mau.

Inā nā mea hoʻohana L(p) и N(p) degenerate (L(p) = 1; N(p) = 1), a laila pili ka hoohalike (1.4.6) i ka wehewehe makemakika o ka dynamics o ka loulou lohi maikai:

Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana

a ua hōʻike ʻia kahi kiʻi kiʻi o kona mau waiwai ma Fig. 1.4.1

Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana
Laiki. 1.4.1 — Nā kiʻi o ka hoʻokomo a me ka hoʻopuka ʻana o ka loulou lohi kūpono

5) Nā ʻōnaehana hoʻomalu ʻokoʻa laina i wehewehe ʻia e nā hoʻohālikelike ʻokoʻa laina ma nā mea hoʻopuka hapa. Ua kapa pinepine ia ia mau pu hookui puunaueia ʻōnaehana hoʻomalu. ==> He laʻana "abstract" o ia wehewehe:

Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana

ʻO ka ʻōnaehana hoʻohālikelike (1.4.7) e wehewehe ana i ka dynamics o kahi ʻōnaehana hoʻokele ʻakomi i puʻunaue ʻia, ʻo ia hoʻi. ʻAʻole pili ka nui i ka manawa wale nō, akā ma kahi hoʻonohonoho spatial hoʻokahi.
Inā he mea "spatial" ka ʻōnaehana, a laila ==>

Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana

kahi Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana pili i ka manawa a me nā hoʻonohonoho spatial i hoʻoholo ʻia e ka radius vector Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana

6) Hōʻike ʻia nā pū kīwī ponoʻī ʻōnaehana Nā ODE, a i ʻole nā ​​ʻōnaehana o ka hoʻohālikelike ʻokoʻa, a i ʻole nā ​​ʻōnaehana o nā hoʻohālikelike ʻokoʻa ʻāpana ==> a pēlā aku...

Hiki ke hāʻawi ʻia kahi hoʻohālikelike like no nā ʻōnaehana hoʻokele nonlinear aunoa (SAP)…

No nā ʻōnaehana linear ua hoʻokō ʻia nā koi penei:

  • linearity o nā hiʻohiʻona static o ka ACS;
  • linearity o ka dynamics equation, i.e. Hoʻokomo ʻia nā mea hoʻololi i ka hoʻohālikelike dynamics ma ka hui laina wale.

ʻO ka hiʻohiʻona static ka hilinaʻi o ka puka ma ka nui o ka mana hoʻokomo i ke kūlana paʻa (ke pau nā kaʻina hana transient a pau).

No nā ʻōnaehana i wehewehe ʻia e nā hoʻohālikelike ʻokoʻa maʻamau maʻamau me nā coefficient mau, loaʻa ke ʻano paʻa mai ka hoʻohālikelike dynamic (1.4.1) ma ka hoʻonohonoho ʻana i nā huaʻōlelo paʻa ʻole i ka zero ==>

Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana

Hōʻike ka Figure 1.4.2 i nā hiʻohiʻona o nā hiʻohiʻona linear a me nonlinear static o nā ʻōnaehana hoʻokele aunoa (ka hoʻoponopono).

Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana
Laiki. 1.4.2 - Nā hiʻohiʻona o nā hiʻohiʻona static linear a me nonlinear

Hiki ke ala mai ka linearity o nā huaʻōlelo i loaʻa nā derivatives manawa i nā hoʻohālikelike ikaika ke hoʻohana i nā hana makemakika nonlinear (*, /, Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana, Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana, hewa, ln, etc.). No ka laʻana, e noʻonoʻo ana i ka hoʻohālikelike dynamics o kekahi pū "abstract" ponoʻī

Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana

E hoʻomanaʻo i loko o kēia hoohalike, me kahi hiʻohiʻona static linear Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana ʻo nā huaʻōlelo ʻelua a me ke kolu (mau huaʻōlelo hoʻoikaika) ma ka ʻaoʻao hema o ka hoohalike laina laina ʻole, no laila ka ACS i ho'ākāka 'ia e ka hoohalike like nonlinear in hoʻoikaika kino hoʻolālā.

1.4.2. Hoʻokaʻawale e like me ke ʻano o nā hōʻailona i hoʻouna ʻia

Ma muli o ke ʻano o nā hōʻailona i hoʻouna ʻia, hoʻokaʻawale ʻia nā ʻōnaehana hoʻokele (a i ʻole hoʻoponopono) i:

  • ʻōnaehana mau (continuous systems);
  • ʻōnaehana hoʻokuʻu (relay action systems);
  • nā ʻōnaehana hana discrete (pulse and digital).

Pūnaehana mau kapa ʻia ka hana he ACS, ma kēlā me kēia loulou o ia mea mau hoʻololi i ka hōʻailona hoʻokomo i ka manawa pili me ka hoomau hoʻololi i ka hōʻailona hoʻopuka, ʻoiai ke kānāwai o ka hoʻololi ʻana i ka hōʻailona puka hiki ke hoʻololi. No ka hoʻomau ʻana i ka pū paʻa ponoʻī, pono ia i nā ʻano static o nā mea āpau mau loulou.

Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana
Laiki. 1.4.3 - Laʻana o kahi ʻōnaehana mau

Pūnaehana hoʻolele Ua kapa ʻia ka hana he ʻōnaehana hoʻokele ma kahi liʻiliʻi ma ka loulou hoʻokahi, me ka hoʻololi mau ʻana i ka waiwai hoʻokomo, ʻo ka waiwai hoʻopuka i kekahi mau manawa o ke kaʻina hana e hoʻololi i ka "lele" ma muli o ka waiwai o ka hōʻailona hoʻokomo. Loaʻa ka ʻano paʻa o ia loulou nā wahi haki ai ole ia, haʻihaʻi me ka haki.

Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana
Laiki. 1.4.4 - Nā laʻana o nā hiʻohiʻona static relay

Pūnaehana ʻokoʻa ʻO ka hana he ʻōnaehana kahi ma ka liʻiliʻi ma hoʻokahi loulou, me ka hoʻololi mau ʻana i ka nui hoʻokomo, ua loaʻa ka nui o ka puka. ʻano hoʻoikaika kino, ʻike ʻia ma hope o kekahi manawa.

ʻO ka loulou e hoʻololi i kahi hōʻailona mau i kahi hōʻailona discrete i kapa ʻia he loulou pulse. Hiki ke ʻano like o nā hōʻailona hoʻouna ʻia i loko o kahi ʻōnaehana hoʻokele aunoa me kahi kamepiula a i ʻole mea hoʻokele.

ʻO nā ʻano hana maʻamau (algorithms) no ka hoʻololi ʻana i kahi hōʻailona hoʻokomo mau i kahi hōʻailona puka pulsed:

  • pulse amplitude modulation (PAM);
  • Pulse laula hoʻololi (PWM).

Ma Fig. Hōʻike ka 1.4.5 i kahi kiʻi kiʻi o ka pulse amplitude modulation (PAM) algorithm. Ma ka piko o Fig. hōʻike ʻia ka hilinaʻi manawa x(t) - hōʻailona ma ka puka komo i loko o ka pauku impulse. ʻO ka hōʻailona puka o ka pulupulu poloka (loulou) y(t) - he kaʻina o nā puʻupuʻu rectangular e ʻike ʻia ana me mau loa manawa quantization Δt (e nānā i ka hapa haʻahaʻa o ke kiʻi). Ua like ka lōʻihi o nā pulupulu a ua like me Δ. ʻO ka amplitude pulse ma ka puka o ka poloka e like me ka waiwai kūpono o ka hōʻailona hoʻomau x (t) ma ka hoʻokomo o kēia poloka.

Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana
Laiki. 1.4.5 - Hoʻokō i ka modulation amplitude pulse

He mea maʻamau kēia ʻano o ka hoʻololi ʻana i ka pulse i nā lako ana uila o ka mana a me nā ʻōnaehana pale (CPS) o nā mea kanu mana nuklea (NPP) i nā 70s...80s o ke kenekulia hope.

Ma Fig. Hōʻike ka Figure 1.4.6 i kahi kiʻi kiʻi o ka pulse width modulation (PWM) algorithm. Ma ka piko o Fig. Hōʻike ka 1.14 i ka hilinaʻi manawa x(t) - hōʻailona ma ka hoʻokomo i ka loulou pulse. Hōʻailona hoʻopuka o ka poloka pulse (loulou) y(t) - he kaʻina o nā pulupulu ʻāpana ʻehā e ʻike ʻia me kahi manawa quantization mau Δt (e nānā i lalo o ke kiʻi 1.14). Ua like ka amplitude o nā pulupulu a pau. Ka lōʻihi o ka pulupulu Δt ma ka puka ana o ka poloka e like me ka waiwai pili o ka hoailona mau x(t) ma ka hookomo o ka pulupulu poloka.

Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana
Laiki. 1.4.6 - Hoʻokō i ka modulation ākea pulse

ʻO kēia ʻano o ka pulse modulation ka mea maʻamau i nā lako ana uila o ka mana a me nā ʻōnaehana pale (CPS) o nā mea kanu nuklea (NPP) a me ACS o nā ʻōnaehana ʻenehana ʻē aʻe.

Ke hoʻopau nei i kēia ʻāpana, pono e hoʻomaopopo ʻia inā e hoʻomau ka manawa maʻamau i nā loulou ʻē aʻe o nā pū hoʻokele ponoʻī (SAP) ʻoi aku ka nui Δt (ma nā kauoha o ka nui), a laila ka ʻōnaehana pulse hiki ke noʻonoʻo ʻia he ʻōnaehana hoʻomau mau (i ka wā e hoʻohana ai ʻO AIM a me PWM).

1.4.3. Hoʻokaʻawale ma ke ʻano o ka mana

Ma muli o ke ʻano o nā kaʻina hana hoʻomalu, ua hoʻokaʻawale ʻia nā ʻōnaehana mana aunoa i nā ʻano aʻe:

  • deterministic auto control system, kahi e hiki ai ke hoʻopili pono ʻia ka hōʻailona hoʻokomo me ka hōʻailona hoʻopuka (a me ka hope);
  • stochastic ACS (statistical, probabilistic), kahi i "pane" ai ka ACS i kahi hōʻailona hoʻokomo. kūʻokoʻa (stochastic) hōʻailona puka.

Hōʻike ʻia ka hōʻailona stochastic e:

  • kanawai o ka mahele;
  • manaʻo makemakika (waiwai maʻamau);
  • hoʻopuehu (standard deviation).

ʻIke pinepine ʻia ke ʻano stochastic o ke kaʻina hoʻomalu ʻAʻole laina ʻole ACS ʻelua mai ka manaʻo o nā hiʻohiʻona paʻa a mai ka manaʻo (ʻoi aku ka nui) o ka nonlinearity o nā huaʻōlelo hoʻoikaika i nā hoʻohālikelike dynamics.

Introduction to theory of automatic control. Nā manaʻo kumu o ke kumumanaʻo o ka mana o nā ʻōnaehana ʻenehana
Laiki. 1.4.7 — Ka mahele ʻana i ka waiwai hoʻopuka o kahi ʻōnaehana hoʻokele stochastic

Ma waho aʻe o nā ʻano nui o ka hoʻokaʻawale ʻana o nā ʻōnaehana hoʻokele, aia kekahi mau hoʻohālikelike ʻē aʻe. No ka laʻana, hiki ke hoʻokō ʻia ka hoʻokaʻawale ʻana e like me ke ʻano kaohi a hoʻokumu ʻia ma ka launa pū ʻana me ke kaiapuni o waho a me ka hiki ke hoʻololi i ka ACS i nā loli i nā ʻāpana kaiapuni. Hoʻokaʻawale ʻia nā ʻōnaehana i ʻelua mau papa nui:

1) Nā ʻōnaehana maʻamau (hoʻoponopono ʻole) me ka hoʻololi ʻole; Aia kēia mau ʻōnaehana i ka ʻāpana o nā mea maʻalahi ʻaʻole e hoʻololi i ko lākou ʻano i ka wā o ke kaʻina hoʻokele. ʻO lākou ka mea i kūkulu ʻia a hoʻohana nui ʻia. Hoʻokaʻawale ʻia nā ʻōnaehana hoʻomalu maʻamau i ʻekolu subclasses: open-loop, closed-loop a me nā ʻōnaehana mana hui.

2) Nā ʻōnaehana hoʻoponopono ponoʻī (adaptive). I kēia mau ʻōnaehana, i ka wā e hoʻololi ai nā kūlana o waho a i ʻole nā ​​hiʻohiʻona o ka mea i hoʻomalu ʻia, hoʻololi ʻia (ʻaʻole i koho mua ʻia) i nā ʻāpana o ka mea hoʻokele ma muli o ka hoʻololi ʻana i nā coefficients system control, ʻōnaehana ʻōnaehana mana, a i ʻole ka hoʻokomo ʻana i nā mea hou. .

ʻO kekahi laʻana o ka hoʻokaʻawale ʻana: e like me ke kumu hierarchical (hoʻokahi pae, ʻelua-pae, multi-level).

Hiki i nā mea hoʻohana i hoʻopaʻa inoa ʻia ke komo i ka noiʻi. Eʻe, e 'oluʻolu.

E hoʻomau i ka hoʻopuka ʻana i nā haʻiʻōlelo ma UTS?

  • 88,7%ʻAe118

  • 7,5%ʻAʻole10

  • 3,8%ʻAʻole maopopo iaʻu5

133 mea hoʻohana i koho. Ua hōʻole nā ​​mea hoʻohana 10.

Source: www.habr.com

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