{"id":83942,"date":"2020-06-04T07:42:41","date_gmt":"2020-06-04T05:42:41","guid":{"rendered":"https:\/\/prohoster.info\/blog\/administrirovanie\/vvedenie-v-teoriyu-avtomaticheskogo-upravleniya-osnovnye-ponyatiya-teorii-upravleniya-tehnicheskim-sistemami"},"modified":"2020-06-04T07:42:41","modified_gmt":"2020-06-04T05:42:41","slug":"vvedenie-v-teoriyu-avtomaticheskogo-upravleniya-osnovnye-ponyatiya-teorii-upravleniya-tehnicheskim-sistemami","status":"publish","type":"post","link":"https:\/\/prohoster.info\/sk\/blog\/administrirovanie\/vvedenie-v-teoriyu-avtomaticheskogo-upravleniya-osnovnye-ponyatiya-teorii-upravleniya-tehnicheskim-sistemami","title":{"rendered":"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"<p>Zverej\u0148ujem prv\u00fa kapitolu predn\u00e1\u0161ok o te\u00f3rii automatizovan\u00e9ho riadenia, po ktor\u00fdch u\u017e v\u00e1\u0161 \u017eivot nikdy nebude rovnak\u00fd. <\/p>\n<p><\/p>\n<p>Predn\u00e1\u0161ky o kurze 'Riadenie technick\u00fdch syst\u00e9mov' vedie Oleg Stepanovi\u010d Kozlov na katedre 'Jadrov\u00e9 reaktory a energetick\u00e9 zariadenia' na Fakulte 'Energetick\u00e9ho stroj\u00e1rstva' MGTU im. N.E. Bauman. Za \u010do mu patr\u00ed ve\u013ek\u00e1 v\u010faka. <\/p>\n<p><\/p>\n<p>Tieto predn\u00e1\u0161ky s\u00fa len pripraven\u00e9 na publikovanie vo forme knihy, a ke\u010f\u017ee tu s\u00fa odborn\u00edci na TAU, \u0161tudenti a jednoducho zauj\u00edmaj\u00faci sa o predmet, ak\u00e1ko\u013evek kritika je v\u00edtan\u00e1. <\/p>\n<p>\n<img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/51ec35e261067ae210b961e3a4259d87.jpg\" style=\"display:block;margin: 0 auto;\" \/><noindex><a rel=\"nofollow\" name=\"habracut\"><\/a><\/noindex><\/p>\n<h1>1. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov<\/h1>\n<p><\/p>\n<h2>1.1. Ciele, princ\u00edpy riadenia, druhy riadenia, z\u00e1kladn\u00e9 defin\u00edcie, pr\u00edklady<\/h2>\n<p><\/p>\n<p>Rozvoj a zdokona\u013eovanie priemyselnej v\u00fdroby (energetiky, dopravy, stroj\u00e1rstva, kozmickej techniky at\u010f.) vy\u017eaduje neust\u00e1le zvy\u0161ovanie produktivity strojov a agreg\u00e1tov, zvy\u0161ovanie kvality v\u00fdroby, zni\u017eovanie n\u00e1kladov a najm\u00e4 v oblasti jadrovej energetiky, dramatick\u00e9 zv\u00fd\u0161enie bezpe\u010dnosti (jadrovej, radia\u010dnej at\u010f.) prev\u00e1dzky jadrov\u00fdch elektr\u00e1rn\u00ed a jadrov\u00fdch zariaden\u00ed.<\/p>\n<p><\/p>\n<p>Realiz\u00e1cia stanoven\u00fdch cie\u013eov nie je mo\u017en\u00e1 bez zavedenia modern\u00fdch riadiacich syst\u00e9mov, vr\u00e1tane automatizovan\u00fdch (s \u00fa\u010das\u0165ou \u010dloveka-oper\u00e1tora) aj automatick\u00fdch (bez \u00fa\u010dasti \u010dloveka-oper\u00e1tora) riadiacich syst\u00e9mov (RS).<\/p>\n<p><\/p>\n<p><b>Defin\u00edcia: <\/b><i>Riadenie je tak\u00e1 organiz\u00e1cia ur\u010dit\u00e9ho technologick\u00e9ho procesu, ktor\u00e1 zabezpe\u010duje dosiahnutie stanoven\u00e9ho cie\u013ea.<\/i><\/p>\n<p><\/p>\n<p><i>Te\u00f3ria riadenia<\/i> je odvetv\u00edm modernej vedy a techniky. Z\u00e1klad\u00e1 sa (vych\u00e1dza) ako na fundament\u00e1lnych (v\u0161eobecne vedeck\u00fdch) discipl\u00ednach (napr. matematika, fyzika, ch\u00e9mia at\u010f.), tak i na aplikovan\u00fdch discipl\u00ednach (elektronika, mikropo\u010d\u00edta\u010dov\u00e1 technika, programovanie at\u010f.).<\/p>\n<p><\/p>\n<p>Ka\u017ed\u00fd proces riadenia (automatick\u00e9ho) pozost\u00e1va z nasleduj\u00facich z\u00e1kladn\u00fdch et\u00e1p (prvkov):<\/p>\n<p><\/p>\n<ul>\n<li> z\u00edskanie inform\u00e1ci\u00ed o \u00falohe riadenia;<\/li>\n<li> z\u00edskanie inform\u00e1ci\u00ed o v\u00fdsledku riadenia;<\/li>\n<li> anal\u00fdza z\u00edskan\u00fdch inform\u00e1ci\u00ed;<\/li>\n<li> vykonanie rozhodnutia (z\u00e1sah do riaden\u00e9ho objektu). <\/li>\n<\/ul>\n<p><\/p>\n<p>Na realiz\u00e1ciu procesu riadenia mus\u00ed riadiaci syst\u00e9m (RS) disponova\u0165:<\/p>\n<p><\/p>\n<ul>\n<li> zdrojmi inform\u00e1ci\u00ed o \u00falohe riadenia;<\/li>\n<li> zdroje inform\u00e1ci\u00ed o v\u00fdsledkoch riadenia (r\u00f4zne senzory, meracie zariadenia, detektory at\u010f.);<\/li>\n<li> zariadenia na anal\u00fdzu z\u00edskan\u00fdch inform\u00e1ci\u00ed a na formulovanie rie\u0161en\u00ed;<\/li>\n<li> vykon\u00e1vacie zariadenia p\u00f4sobiace na riaden\u00fd objekt, obsahuj\u00face: regul\u00e1tor, motory, zosil\u0148ova\u010de a in\u00e9.<\/li>\n<\/ul>\n<p><\/p>\n<p><b>Defin\u00edcia:<\/b><i> Ak riadiaci syst\u00e9m (RS) obsahuje v\u0161etky vy\u0161\u0161ie uveden\u00e9 \u010dasti, je to uzavret\u00fd syst\u00e9m.<\/i><\/p>\n<p><\/p>\n<p><b>Defin\u00edcia:<\/b> <i>Riadenie technick\u00e9ho objektu vyu\u017e\u00edvaj\u00face inform\u00e1cie o v\u00fdsledkoch riadenia sa naz\u00fdva princ\u00edp sp\u00e4tnej v\u00e4zby.<\/i><\/p>\n<p><\/p>\n<p>Schematicky m\u00f4\u017ee by\u0165 tak\u00fdto riadiaci syst\u00e9m zobrazen\u00fd ako:<\/p>\n<p><\/p>\n<p><img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/8c48f4621773bbe8620934de7b1c2e16.jpg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<i>Obr. 1.1.1 \u2014 \u0160trukt\u00fara riadiaceho syst\u00e9mu (RS) <\/i><\/p>\n<p><\/p>\n<p> Ak riadiaci syst\u00e9m (RS) m\u00e1 \u0161trukt\u00farny diagram, ktor\u00e9ho vzh\u013ead zodpoved\u00e1 obr. 1.1.1, a funguje (pracuje) bez \u00fa\u010dasti \u010dloveka (oper\u00e1tora), naz\u00fdva sa <u>syst\u00e9m automatick\u00e9ho riadenia (SAR)<\/u>.<\/p>\n<p><\/p>\n<p> Ak RS funguje s \u00fa\u010dast\u00ed \u010dloveka (oper\u00e1tora), naz\u00fdva sa <u>automatizovan\u00fd RS<\/u>.<\/p>\n<p><\/p>\n<p> Ak riadenie zabezpe\u010duje stanoven\u00fd z\u00e1kon zmien objektu v \u010dase nez\u00e1visle od v\u00fdsledkov riadenia, potom tak\u00e9to riadenie prebieha v otvorenom cykle a samotn\u00e9 riadenie sa naz\u00fdva <u>programov\u00fdm riaden\u00edm<\/u>.<\/p>\n<p><\/p>\n<p> Medzi syst\u00e9my pracuj\u00face v otvorenom cykle patr\u00ed priemyseln\u00e1 automatika (dopravn\u00e9 linky, rota\u010dn\u00e9 linky at\u010f.), stroje s numerick\u00fdm programov\u00fdm riaden\u00edm (CNC): pozri pr\u00edklad na obr. 1.1.2.<\/p>\n<p><\/p>\n<p><img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/20c14fed7423b8be82da94b8e0eceae7.jpg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<i>Obr. 1.1.2 \u2014 Pr\u00edklad programov\u00e9ho riadenia<\/i><\/p>\n<p><\/p>\n<p>Poh\u00e1\u0148acie zariadenie m\u00f4\u017ee by\u0165 napr\u00edklad aj \u201ekop\u00edrovac\u00ed stroj\u201c.<\/p>\n<p><\/p>\n<p>Ke\u010f\u017ee v tomto pr\u00edklade nie s\u00fa senzory (meracie pr\u00edstroje), ktor\u00e9 by kontrolovali vyr\u00e1ban\u00fa s\u00fa\u010diastku, ak bol napr\u00edklad n\u00f4\u017e nespr\u00e1vne nastaven\u00fd alebo sa zlomen\u00fd, dosiahnutie stanoven\u00e9ho cie\u013ea (vyrobenie s\u00fa\u010diastky) nie je mo\u017en\u00e9 (realizovate\u013en\u00e9). Zvy\u010dajne v syst\u00e9moch tohto typu je potrebn\u00e1 v\u00fdstupn\u00e1 kontrola, ktor\u00e1 iba zaznamen\u00e1va odch\u00fdlky ve\u013ekosti a tvaru s\u00fa\u010diastky od po\u017eadovanej.<\/p>\n<p><\/p>\n<p> Automatick\u00e9 riadiace syst\u00e9my sa delia na 3 typy: <\/p>\n<p><\/p>\n<ul>\n<li> syst\u00e9my automatick\u00e9ho riadenia (SAR); <\/li>\n<li> syst\u00e9my automatick\u00e9ho regulovania (SAR);<\/li>\n<li> sledovacie syst\u00e9my (SS). <\/li>\n<\/ul>\n<p><\/p>\n<p>SAR a SS s\u00fa podmno\u017einami SAR ==&gt; <img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/21f340c84febe0f6ab25cc5c9256dfb1.jpg\" style=\"display:block;margin: 0 auto;\" \/>.<\/p>\n<p><\/p>\n<p>Defin\u00edcia: Automatizovan\u00fd riadiaci syst\u00e9m, ktor\u00fd zabezpe\u010duje st\u00e1lu hodnotu nejakej fyzik\u00e1lnej veli\u010diny (alebo skupiny veli\u010d\u00edn) v regulovanom objekte, sa naz\u00fdva syst\u00e9m automatick\u00e9ho riadenia (SAR).<\/p>\n<p><\/p>\n<p> Syst\u00e9my automatick\u00e9ho riadenia (SAR) s\u00fa najroz\u0161\u00edrenej\u0161\u00edm typom syst\u00e9mov automatizovan\u00e9ho riadenia.<\/p>\n<p><\/p>\n<p> Prv\u00fd na svete automatick\u00fd regul\u00e1tor (18. storo\u010die) \u2013 regul\u00e1tor Watt. T\u00e1to sch\u00e9ma (pozri obr. 1.1.3) bola implementovan\u00e1 Wattom v Anglicku na udr\u017eanie kon\u0161tantnej r\u00fdchlosti ot\u00e1\u010dania kolesa parn\u00e9ho stroja a t\u00fdm aj na udr\u017eanie st\u00e1losti r\u00fdchlosti ot\u00e1\u010dania (pohybu) remena prevodu.<\/p>\n<p><\/p>\n<p> V tejto sch\u00e9me <i>senzorov\u00fdmi prvkami<\/i> (merac\u00edmi senzormi) s\u00fa \"z\u00e1va\u017eia\" (gule). \"Z\u00e1va\u017eia\" (gule) taktie\u017e \"poh\u00e1\u0148aj\u00fa\" p\u00e1ku a n\u00e1sledne ventil. Preto je tento syst\u00e9m mo\u017en\u00e9 pova\u017eova\u0165 za syst\u00e9m priameho riadenia, a regul\u00e1tor je <u>regul\u00e1tor priameho \u00fa\u010dinku<\/u>, preto\u017ee s\u00fa\u010dasne pln\u00ed funkcie \"meradla\" a \"regul\u00e1tora.\" <\/p>\n<p>\nV regul\u00e1toroch priameho \u00fa\u010dinku <i>\u010fal\u0161\u00ed zdroj<\/i> energie na pohyb regula\u010dn\u00e9ho org\u00e1nu nie je potrebn\u00fd. <\/p>\n<p><img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/95d2c1901c2cc5e962a5c5c23643f155.jpg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<i>Obr. 1.1.3 \u2013 Sch\u00e9ma automatick\u00e9ho regul\u00e1tora Watta<\/i><\/p>\n<p>V syst\u00e9moch nepriameho riadenia je nevyhnutn\u00e1 pr\u00edtomnos\u0165 (existencia) zosil\u0148ova\u010da (napr\u00edklad v\u00fdkonov\u00e9ho), dodato\u010dn\u00e9ho vykon\u00e1vacieho mechanizmu, ktor\u00fd obsahuje, napr\u00edklad, elektromotor, servomotor, hydraulick\u00fd pohon a pod.<\/p>\n<p><\/p>\n<p> Pr\u00edkladom SAU (syst\u00e9m automatick\u00e9ho riadenia), v plnom zmysle tohto pojmu, m\u00f4\u017ee by\u0165 riadiaci syst\u00e9m, ktor\u00fd zabezpe\u010duje vypustenie rakety na orbitu, kde regulovanou veli\u010dinou m\u00f4\u017ee by\u0165, napr\u00edklad, uhol medzi osou rakety a norm\u00e1lou k Zemi ==&gt; pozri obr. 1.1.4.a a obr. 1.1.4.b <\/p>\n<p><\/p>\n<p><img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/e524a79caac45ea0e624938463f7b48e.jpg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<i>Obr. 1.1.4 (a)<\/i><br \/>\n<img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/a1f4ec58f29971dc866627f3cd5f8f44.jpg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<i>Obr. 1.1.4 (b)<\/i><\/p>\n<p><\/p>\n<h2>1.2. \u0160trukt\u00fara riadiacich syst\u00e9mov: jednoduch\u00e9 a viacrozmern\u00e9 syst\u00e9my<\/h2>\n<p><\/p>\n<p>V te\u00f3rii riadenia technick\u00fdch syst\u00e9mov sa ak\u00fdko\u013evek syst\u00e9m spravidla del\u00ed na s\u00fabor \u010dl\u00e1nkov spojen\u00fdch do sie\u0165ov\u00fdch \u0161trukt\u00far. V najjednoduch\u0161om pr\u00edpade syst\u00e9m obsahuje jeden \u010dl\u00e1nok, na ktor\u00fd je aplikovan\u00fd vstupn\u00fd vplyv (vstup), na v\u00fdstupe sa z\u00edskava odozva syst\u00e9mu (v\u00fdstup).<\/p>\n<p><\/p>\n<p>V te\u00f3rii riadenia technick\u00fdch syst\u00e9mov sa pou\u017e\u00edvaj\u00fa 2 z\u00e1kladn\u00e9 sp\u00f4soby zn\u00e1zornenia \u010dl\u00e1nkov riadiacich syst\u00e9mov:<\/p>\n<p><\/p>\n<p> \u2014 v premenn\u00fdch \"vstup-v\u00fdstup\";<\/p>\n<p><\/p>\n<p> \u2014 v stavov\u00fdch premenn\u00fdch (viac inform\u00e1ci\u00ed pozri v oddieloch 6\u20267). <\/p>\n<p><\/p>\n<p>Predstavenie v stavov\u00fdch premenn\u00fdch sa zvy\u010dajne pou\u017e\u00edva na opis relat\u00edvne jednoduch\u00fdch syst\u00e9mov, ktor\u00e9 maj\u00fa jeden \"vstup\" (jednu riadiacu intervenciu) a jeden \"v\u00fdstup\" (jednu regulovan\u00fa veli\u010dinu, pozri obr\u00e1zok 1.2.1).<\/p>\n<p><\/p>\n<p><img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/5771bf37f683d56890681a739ec80416.jpg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<i>Obr. 1.2.1 \u2013 Sch\u00e9matick\u00e9 zn\u00e1zornenie jednoduchej riadiacej s\u00fastavy<\/i><\/p>\n<p><\/p>\n<p>Zvy\u010dajne sa tak\u00e9to op\u00edsanie pou\u017e\u00edva pre technicky nen\u00e1ro\u010dn\u00e9 S\u00c1U (s\u00fastavy automatick\u00e9ho riadenia).<\/p>\n<p><\/p>\n<p>V poslednej dobe sa roz\u0161\u00edrilo predstavenie v stavov\u00fdch premenn\u00fdch, najm\u00e4 pre technicky zlo\u017eit\u00e9 syst\u00e9my, vr\u00e1tane mnohorozmern\u00fdch S\u00c1U. Na obr. 1.2.2 je zobrazen\u00e9 sch\u00e9matick\u00e9 zn\u00e1zornenie mnohorozmernej syst\u00e9mu automatick\u00e9ho riadenia, kde <b><i>u1(t)\u2026um(t)<\/i><\/b> \u2014 riadiace z\u00e1sahy (vektor riadenia), <i><b>y1(t)\u2026yp(t)<\/b><\/i> \u2014 regulovan\u00e9 parametre S\u00c1U (vektor v\u00fdstupu). <\/p>\n<p><\/p>\n<p><img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/d0025fbc783222e6f87a5a9f56945785.jpg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<i>Obr. 1.2.2 \u2014 Sch\u00e9matick\u00e9 zn\u00e1zornenie mnohorozmernej riadiacej s\u00fastavy<\/i><\/p>\n<p>Po\u010fme podrobnej\u0161ie presk\u00fama\u0165 \u0161trukt\u00faru S\u00c1U, prezentovan\u00fa v premenn\u00fdch \"vstup-v\u00fdstup\" a m\u00e1j\u00facou jeden vstup (vstupn\u00e9 alebo nastavovacie, alebo riadiace z\u00e1sahy) a jeden v\u00fdstup (v\u00fdstupn\u00fd z\u00e1sah alebo riaden\u00e1 (alebo regulovan\u00e1) veli\u010dina).<\/p>\n<p><\/p>\n<p>Predpokladajme, \u017ee \u0161truktur\u00e1lna sch\u00e9ma takej S\u00c1U sa sklad\u00e1 z nieko\u013ek\u00fdch prvkov (\u010dast\u00ed). Zoskupen\u00edm \u010dast\u00ed pod\u013ea funk\u010dn\u00e9ho princ\u00edpu (\u010do \u010dasti robia) sa \u0161truktur\u00e1lna sch\u00e9ma S\u00c1U m\u00f4\u017ee uvies\u0165 do nasleduj\u00faceho typick\u00e9ho tvaru: <\/p>\n<p><\/p>\n<p><img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/21b4fe1c08c1a168d1d68c0f47c3c186.jpg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<i>Obr. 1.2.3 \u2014 \u0160truktur\u00e1lna sch\u00e9ma syst\u00e9mu automatick\u00e9ho riadenia<\/i><\/p>\n<p><\/p>\n<p>Symbolom <b><i>\u03b5(t)<\/i><\/b> alebo premennou<b> <i>\u03b5(t)<\/i><\/b> ozna\u010duje sa nes\u00falad (chyba) na v\u00fdstupe porovn\u00e1vacieho zariadenia, ktor\u00e9 m\u00f4\u017ee \"pracova\u0165\" v re\u017eime jednoduch\u00fdch porovn\u00e1vac\u00edch aritmetick\u00fdch oper\u00e1ci\u00ed (\u010dastej\u0161ie od\u010d\u00edtanie, zriedkavej\u0161ie s\u010d\u00edtanie), ako aj v re\u017eimoch zlo\u017eitej\u0161\u00edch porovn\u00e1vac\u00edch oper\u00e1ci\u00ed (proced\u00far).<\/p>\n<p><\/p>\n<p>Ke\u010f\u017ee<i> <b>y1(t) = y(t)*k1<\/b><\/i>, kde <i><b>k1<\/b><\/i> \u2014 koeficient zosilnenia, teda ==&gt; <br \/>\n<b><i>\u03b5(t) = x(t) \u2014 y1(t) = x(t) \u2014 k1*y(t)<\/i><\/b><\/p>\n<p><\/p>\n<p>\u00dalohou riadiaceho syst\u00e9mu je v tom (ak je stabiln\u00fd), aby \"pracoval\" na elimin\u00e1ciu nes\u00faladov (ch\u00fdb) <b><i>\u03b5(t)<\/i><\/b>, t.j. ==&gt;<b> <i>\u03b5(t) \u2192 0<\/i><\/b>.<\/p>\n<p><\/p>\n<p>Je d\u00f4le\u017eit\u00e9 poznamena\u0165, \u017ee na riadiaci syst\u00e9m p\u00f4sobia ako vonkaj\u0161ie vplyvy (riadiace, nar\u00fa\u0161aj\u00face, ru\u0161iace), tak aj vn\u00fatorn\u00e9 ru\u0161enia. Ru\u0161enie sa od vplyvu odli\u0161uje stochastickos\u0165ou (n\u00e1hodnos\u0165ou) svojho existovania, zatia\u013e \u010do vplyv je takmer v\u017edy determinovan\u00fd.<\/p>\n<p><\/p>\n<p>Na ozna\u010denie riadiaceho (ur\u010duj\u00faceho vplyvu) budeme pou\u017e\u00edva\u0165 bu\u010f<i><b> x(t)<\/b><\/i>, alebo <i><b>u(t)<\/b><\/i>.<\/p>\n<p><\/p>\n<h2>1.3. Z\u00e1kladn\u00e9 z\u00e1kony riadenia<\/h2>\n<p><\/p>\n<p>Ak sa vr\u00e1time k posledn\u00e9mu obr\u00e1zku (\u0161truktur\u00e1lna sch\u00e9ma SAU na obr. 1.2.3), je potrebn\u00e9 \"de\u0161ifrova\u0165\" \u00falohu, ktor\u00fa hr\u00e1 zosil\u0148ovacie-prevodn\u00e9 zariadenie (ak\u00e9 funkcie vykon\u00e1va).<\/p>\n<p><\/p>\n<p>Ak zosil\u0148ovacie-prevodn\u00e9 zariadenie (ZPU) vykon\u00e1va iba zosilnenie (alebo oslabenie) sign\u00e1lu nes\u00fahlasu \u03b5(t), a to konkr\u00e9tne: <b><img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/0c09aa2ad2d14cb6d2f5666e33441afa.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/b>, kde <img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/be9dd549e8715f43c40c581217f29e3b.jpg\" style=\"display:block;margin: 0 auto;\" \/>\u2013 koeficient proporcionality (v osobitnom pr\u00edpade <img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/e16fccbb0217b69120081cd963525f6e.jpg\" style=\"display:block;margin: 0 auto;\" \/> = Const), tak\u00fdto re\u017eim riadenia uzavret\u00e9ho SAU sa naz\u00fdva re\u017eim <u>proporcionalneho riadenia <\/u>(P-riadenie).<\/p>\n<p><\/p>\n<p>Ak ZPU vykon\u00e1va tvorbu v\u00fdstupn\u00e9ho sign\u00e1lu \u03b51(t), ktor\u00fd je proporcion\u00e1lny chybe \u03b5(t) a integr\u00e1lu z \u03b5(t), t.j. <img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/6e6dbb0b4de0d9aaa3f6f788e61a3830.jpg\" style=\"display:block;margin: 0 auto;\" \/>, tak\u00fdto re\u017eim riadenia sa naz\u00fdva <u>proporcionalne-integruj\u00facim<\/u> (PI-riadenie). ==&gt; <img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/9dd1d2b339c33e975225d3438d39bc6c.jpg\" style=\"display:block;margin: 0 auto;\" \/>, kde <i>b<\/i> \u2013 koeficient proporcionality (v osobitnom pr\u00edpade <i>b = Const<\/i>). \n <\/p>\n<p><\/p>\n<p>Obvykle sa PI-riadenie pou\u017e\u00edva na zv\u00fd\u0161enie presnosti riadenia (regul\u00e1cie).<\/p>\n<p><\/p>\n<p>Ak ZPU tvor\u00ed v\u00fdstupn\u00fd sign\u00e1l \u03b51(t), ktor\u00fd je proporcion\u00e1lny chybe \u03b5(t) a jej deriv\u00e1cii, tak\u00fdto re\u017eim sa naz\u00fdva<u> proporcionalne-diferencuj\u00facim<\/u> (PD-riadenie): ==&gt; <img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/53491162f89bb3eb6d3afe53f8499ef7.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p><\/p>\n<p>Obvykle pou\u017eitie PD-riadenia zvy\u0161uje v\u00fdkonnos\u0165 SAU<\/p>\n<p><\/p>\n<p>Ak ZPU tvor\u00ed v\u00fdstupn\u00fd sign\u00e1l \u03b51(t), ktor\u00fd je proporcion\u00e1lny chybe \u03b5(t), jej deriv\u00e1cii a integr\u00e1lu z chyby ==&gt; <img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/8ebae93d72b03b5c107a1246c077c348.jpg\" style=\"display:block;margin: 0 auto;\" \/>, tak\u00fdto re\u017eim riadenia sa naz\u00fdva <u>proporcionalne-integr\u00e1lno-diferencuj\u00facim re\u017eimom riadenia<\/u> (PID-riadenie).<\/p>\n<p><\/p>\n<p>PID-riadenie umo\u017e\u0148uje \u010dasto zabezpe\u010di\u0165 \"dobr\u00fa\" presnos\u0165 riadenia pri \"dobrej\" v\u00fdkonnosti <\/p>\n<p><\/p>\n<h2>1.4. Klasifik\u00e1cia syst\u00e9mov automatick\u00e9ho riadenia <\/h2>\n<p><\/p>\n<h3>1.4.1. Klasifik\u00e1cia pod\u013ea druhu matematick\u00e9ho opisu<\/h3>\n<p><\/p>\n<p>Pod\u013ea druhu matematick\u00e9ho opisu (rovnice dynamiky a statiky) sa syst\u00e9my automatick\u00e9ho riadenia (SAU) delia na <u>line\u00e1rne<\/u> a <u>nelin\u00e1rne<\/u> syst\u00e9my (SAU alebo SAR). <\/p>\n<p><\/p>\n<p>Ka\u017ed\u00fd \u201epodtried\u201c (line\u00e1rnych a neline\u00e1rnych) sa \u010falej del\u00ed na mno\u017estvo \u201epodtried\u201c. Napr\u00edklad, line\u00e1rne S\u00c1U (SAR) maj\u00fa rozdiely v type matematick\u00e9ho opisu. <br \/>\nKe\u010f\u017ee v tomto semestre sa bud\u00fa sk\u00fama\u0165 dynamick\u00e9 vlastnosti len line\u00e1rnych syst\u00e9mov automatick\u00e9ho riadenia (regul\u00e1cie), ni\u017e\u0161ie uv\u00e1dzame klasifik\u00e1ciu pod\u013ea typu matematick\u00e9ho opisu pre line\u00e1rne S\u00c1U (SAR): <\/p>\n<p><\/p>\n<p>1) Line\u00e1rne syst\u00e9my automatick\u00e9ho riadenia, opisovan\u00e9 v premenn\u00fdch \u201evstup-v\u00fdstup\u201c oby\u010dajn\u00fdmi diferenci\u00e1lnymi rovnicami (ODR) s <u>kon\u0161tantn\u00fdmi <\/u>koeficientmi:<\/p>\n<\/p>\n<p><img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/cb3af3b0b89fc1e74c2b8d6d2d7fdb22.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<\/p>\n<p><img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/58090b17da60d2b517d3c94501cd59a2.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>\nkde <i>x(t)<\/i> \u2013 vstupn\u00e9 p\u00f4sobenie; <i>y(t)<\/i> \u2013 v\u00fdstupn\u00e9 p\u00f4sobenie (regulovan\u00e1 veli\u010dina). <\/p>\n<p>Ak pou\u017eijeme oper\u00e1torov\u00fa (\u201ekompaktn\u00fa\u201c) formu z\u00e1znamu line\u00e1rneho ODR, potom rovnicu (1.4.1) m\u00f4\u017eeme predstavi\u0165 v nasleduj\u00facej forme: \n<\/p>\n<\/p>\n<p><img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/b1c5ee221af3668d5f176a70ed14418f.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p> kde, <i>p = d\/dt<\/i> \u2014 oper\u00e1tor diferenci\u00e1cie; <i>L(p), N(p)<\/i> \u2014 pr\u00edslu\u0161n\u00e9 line\u00e1rne diferenci\u00e1lne oper\u00e1tory, ktor\u00e9 s\u00fa rovn\u00e9:<\/p>\n<p><img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/d43a08bffa114c25041a2f0980042c51.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<\/p>\n<p><img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/42636426b82dce860e9e17987f50c057.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p><\/p>\n<p>2) Line\u00e1rne syst\u00e9my automatick\u00e9ho riadenia, opisovan\u00e9 line\u00e1rnymi oby\u010dajn\u00fdmi diferenci\u00e1lnymi rovnicami (ODR) s <u>premenn\u00fdmi <\/u>(v \u010dase) koeficientmi: \n<\/p>\n<\/p>\n<p><img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/6dbc99fe9b268fe6f6ff996975637e1c.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<\/p>\n<p><img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/829ce6f7e73bfb06b4b76d0d4eeeef34.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p><\/p>\n<p>Vo v\u0161eobecnosti tak\u00e9to syst\u00e9my m\u00f4\u017eeme zaradi\u0165 do triedy neline\u00e1rnych S\u00c1U (SAR).<\/p>\n<p><\/p>\n<p>3) Line\u00e1rne syst\u00e9my automatick\u00e9ho riadenia, opisovan\u00e9 line\u00e1rnymi rozdielov\u00fdmi rovnicami: <\/p>\n<\/p>\n<p><img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/3ff7a042761c218b77ac2263e548642c.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<\/p>\n<p><img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/1adb8b5de9da0717c1d8af58023709db.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p> kde <i>f(\u2026)<\/i> \u2013 line\u00e1rna funkcia argumentov;<i> k = 1, 2, 3\u2026<\/i> \u2014 cel\u00e9 \u010d\u00edsla; <i>\u0394t<\/i> \u2013 interval kvantovania (interval diskr\u00e9tnosti). <\/p>\n<p>Rovnicu (1.4.4) m\u00f4\u017eeme predstavi\u0165 v \u201ekompaktnej\u201c forme z\u00e1pisu:\n<\/p>\n<\/p>\n<p><img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/3a555933ea0689d2adee3746d6ddeaad.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p><\/p>\n<p>Zvy\u010dajne sa tak\u00e9to opisovanie line\u00e1rnych S\u00c1U (SAR) pou\u017e\u00edva v digit\u00e1lnych riadiacich syst\u00e9moch (s pou\u017eit\u00edm po\u010d\u00edta\u010dov). <\/p>\n<p><\/p>\n<p>4) Line\u00e1rne syst\u00e9my automatick\u00e9ho riadenia so zpo\u017ed\u011bn\u00edm:\n<\/p>\n<\/p>\n<p><img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/7feca1e387cb0c6a1689e22d95e28a63.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>\nkde <i>L(p), N(p)<\/i> \u2014 line\u00e1rne diferenci\u00e1lne oper\u00e1tory; <i>\u03c4<\/i> \u2014 doba zpo\u017ed\u011bn\u00ed alebo kon\u0161tantn\u00e1 zpo\u017ed\u011bn\u00ed. <\/p>\n<p>Ak oper\u00e1tory <i>L(p)<\/i> a <i>N(p)<\/i> s\u00fa degenerovan\u00e9 (<i>L(p) = 1; N(p) = 1<\/i>), potom rovnicu (1.4.6) zodpoved\u00e1 matematick\u00e9mu opisu dynamiky \u010dl\u00e1nku ide\u00e1lneho zpo\u017ed\u011bn\u00ed: \n<\/p>\n<\/p>\n<p><img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/f3906140de2cd69b5ececf8b527a11e7.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p> a grafick\u00e1 ilustr\u00e1cia jeho vlastnost\u00ed je zobrazen\u00e1 na obr. 1.4.1<\/p>\n<p><img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/862f0d412914840cf9f0722087ccfb50.jpg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<i>Obr. 1.4.1 \u2014 Grafy vstupu a v\u00fdstupu \u010dl\u00e1nku ide\u00e1lneho zpo\u017ed\u011bn\u00ed<\/i><\/p>\n<p>5) Line\u00e1rne syst\u00e9my automatick\u00e9ho riadenia, opisovan\u00e9 line\u00e1rnymi diferenci\u00e1lnymi rovnicami v <i>parci\u00e1lnych deriv\u00e1ci\u00e1ch.<\/i>Niekedy tieto S\u00c1U naz\u00fdvaj\u00fa <u>distribuovan\u00e9<\/u> riadiace syst\u00e9my. ==&gt; \u201eAbstraktn\u00fd\u201c pr\u00edklad tak\u00e9hoto opisu:<\/p>\n<\/p>\n<p><img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/669b5c3c53ba7845842b18e5928ce839.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p><\/p>\n<p>Syst\u00e9ma rovn\u00edc (1.4.7) popisuje dynamiku line\u00e1rne rozlo\u017eenej S\u013dA, t.j. regulovan\u00e1 veli\u010dina z\u00e1vis\u00ed nielen od \u010dasu, ale aj od jednej priestorovej koordin\u00e1ty. <br \/>\nAk syst\u00e9m riadenia predstavuje \u201epriestorov\u00fd\u201c objekt, potom ==&gt;<\/p>\n<\/p>\n<p><img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/3448a365047c1bab4de5e8f25546f50e.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p><\/p>\n<p>kde <img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/f9ff2f7da6ef14612bc7debb1a6b13df.jpg\" style=\"display:block;margin: 0 auto;\" \/> z\u00e1vis\u00ed od \u010dasu a priestorov\u00fdch koordin\u00e1t, definovan\u00fdch radiusom vektorom <img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/779241bc6119457bd084ae3b359be126.jpg\" style=\"display:block;margin: 0 auto;\" \/>\n<\/p>\n<p>6) S\u013dA, popisovan\u00e9 <u>syst\u00e9mami<\/u> ODU alebo syst\u00e9mami diferenci\u00e1lnych rovn\u00edc, alebo syst\u00e9mami rovn\u00edc s \u010diasto\u010dn\u00fdmi deriv\u00e1ciami ==&gt;, a tak \u010falej\u2026<\/p>\n<p><\/p>\n<p>Podobn\u00fa klasifik\u00e1ciu je mo\u017en\u00e9 navrhn\u00fa\u0165 aj pre neline\u00e1rne S\u013dA (SAR)\u2026<\/p>\n<p><\/p>\n<p>Pre line\u00e1rne syst\u00e9my platia nasleduj\u00face po\u017eiadavky:<\/p>\n<ul>\n<li> line\u00e1rnos\u0165 statickej charakteristiky S\u013dA; <\/li>\n<li> line\u00e1rnos\u0165 rovnice dynamiky, t.j. premenn\u00e9 v rovnice dynamiky vstupuj\u00fa <u>iba v line\u00e1rnej kombin\u00e1cii.<\/u> <\/li>\n<\/ul>\n<p><\/p>\n<p>Statickou charakteristikou sa ozna\u010duje z\u00e1vislos\u0165 v\u00fdstupu od hodnoty vstupn\u00e9ho p\u00f4sobenia v ust\u00e1lenom re\u017eime (ke\u010f v\u0161etky prechodn\u00e9 procesy ust\u00fapili). <\/p>\n<p><\/p>\n<p>Pre syst\u00e9my, ktor\u00e9 s\u00fa op\u00edsan\u00e9 line\u00e1rnymi oby\u010dajn\u00fdmi diferenci\u00e1lnymi rovnicami s kon\u0161tantn\u00fdmi koeficientmi, sa statick\u00e1 charakteristika z\u00edskava z rovnice dynamiky (1.4.1) prirovnan\u00edm v\u0161etk\u00fdch nestacion\u00e1rnych \u010dlenov k nule ==&gt;\n<\/p>\n<\/p>\n<p><img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/bf0c596f0264b56e910f26fb3572d495.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p><\/p>\n<p>Na obr. 1.4.2 s\u00fa uveden\u00e9 pr\u00edklady line\u00e1rnych a neline\u00e1rnych statick\u00fdch charakterist\u00edk syst\u00e9mov automatick\u00e9ho riadenia (regul\u00e1cie). <\/p>\n<p><\/p>\n<p><img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/492e67e54fc30c8ffc81dbd922d44d69.jpg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<i>Obr. 1.4.2 \u2014 Pr\u00edklady statick\u00fdch line\u00e1rnych a neline\u00e1rnych charakterist\u00edk<\/i><\/p>\n<p>Nelinearita \u010dlenov obsahuj\u00facich deriv\u00e1cie pod\u013ea \u010dasu v rovnic\u00e1ch dynamiky m\u00f4\u017ee vznikn\u00fa\u0165 pri pou\u017eit\u00ed neline\u00e1rnych matematik\u00fdch oper\u00e1ci\u00ed (*, \/, <img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/2cb392451693aaecdf1b0b3c9d893b64.jpg\" style=\"display:block;margin: 0 auto;\" \/>, <img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/9b1e329d4a85a2633bbbc4f4ab024200.jpg\" style=\"display:block;margin: 0 auto;\" \/>, sin, ln at\u010f.). Napr\u00edklad, pri zva\u017eovan\u00ed rovnice dynamiky ur\u010ditej \"abstraktnej\" S\u013dA<\/p>\n<\/p>\n<p><img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/dae16ed9af4777cc0574d633840de24b.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p><\/p>\n<p>si v\u0161imnime, \u017ee v tejto rovnici pri line\u00e1rnej statickej charakteristike <img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/ef499e876cf4b9835a61605b9155144c.jpg\" style=\"display:block;margin: 0 auto;\" \/> druh\u00fd a tret\u00ed \u010dlen (dynamick\u00e9 \u010dleny) na \u013eavej strane rovnice \u2014 <u>nelin\u00e1rne<\/u>, preto S\u013dA, popisovan\u00e1 podobnou rovnicou, je <u>neline\u00e1rna v <i>dynamickom<\/i> pl\u00e1ne<\/u>.<\/p>\n<p><\/p>\n<h3>1.4.2. Klasifik\u00e1cia pod\u013ea povahy pren\u00e1\u0161an\u00fdch sign\u00e1lov<\/h3>\n<p><\/p>\n<p>Pod\u013ea povahy pren\u00e1\u0161an\u00fdch sign\u00e1lov sa syst\u00e9my automatick\u00e9ho riadenia (alebo regul\u00e1cie) delia: <\/p>\n<ul>\n<li> nepretr\u017eit\u00e9 syst\u00e9my (syst\u00e9my nepretr\u017eit\u00e9ho p\u00f4sobenia);<\/li>\n<li> relejn\u00e9 syst\u00e9my (syst\u00e9my rel\u00e9ov\u00e9ho p\u00f4sobenia);<\/li>\n<li> syst\u00e9my diskr\u00e9tneho p\u00f4sobenia (impulzn\u00e9 a digit\u00e1lne).<\/li>\n<\/ul>\n<p><\/p>\n<p>Syst\u00e9mom <u>nepretr\u017eit\u00e9ho<\/u> syst\u00e9my sa naz\u00fdva tak\u00e1 SAA, v ktorej v ka\u017edom z \u010dl\u00e1nkov <u>nepreru\u0161en\u00e9mu<\/u> zmeneniu vstupn\u00e9ho sign\u00e1lu v \u010dase <u>zodpoved\u00e1 nepreru\u0161en\u00e9<\/u> menenie v\u00fdstupn\u00e9ho sign\u00e1lu, pri\u010dom z\u00e1kon zmeny v\u00fdstupn\u00e9ho sign\u00e1lu m\u00f4\u017ee by\u0165 \u013eubovo\u013en\u00fd. Aby bola SAA nepreru\u0161ovan\u00e1, je potrebn\u00e9, aby statick\u00e9 charakteristiky v\u0161etk\u00fdch <u>\u010dl\u00e1nkov boli nepreru\u0161ovan\u00e9.<\/u><\/p>\n<\/p>\n<p><img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/73b156157b5a43c62fdc848170722c2d.jpg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<i>Obr. 1.4.3 \u2014 Pr\u00edklad nepreru\u0161ovan\u00e9ho syst\u00e9mu<\/i><\/p>\n<p>Syst\u00e9mom <u>rel\u00e9ov\u00e9ho<\/u> syst\u00e9mu sa naz\u00fdva SAA, v ktorej aspo\u0148 v jednom \u010dl\u00e1nku pri nepreru\u0161ovanej zmene vstupnej veli\u010diny v\u00fdstupn\u00e1 veli\u010dina v niektor\u00fdch momentoch procesu riadenia men\u00ed \u201eskokom\u201c v z\u00e1vislosti od ve\u013ekosti vstupn\u00e9ho sign\u00e1lu. Statick\u00e1 charakteristika tak\u00e9ho \u010dl\u00e1nku m\u00e1 <u>miesta skoku<\/u> alebo <u>zlomu s preru\u0161en\u00edm<\/u>.<\/p>\n<p><\/p>\n<p><img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/edfc6a65398bb0f409297d40a3aee0e2.jpg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<i>Obr. 1.4.4 \u2014 Pr\u00edklady rel\u00e9ov\u00fdch statick\u00fdch charakterist\u00edk<\/i><\/p>\n<p>Syst\u00e9mom <u>diskr\u00e9tneho<\/u> syst\u00e9mu sa naz\u00fdva syst\u00e9m, v ktorom aspo\u0148 v jednom \u010dl\u00e1nku pri nepreru\u0161ovanej zmene vstupnej veli\u010diny v\u00fdstupn\u00e1 veli\u010dina m\u00e1 <u>podobu jednotliv\u00fdch impulzov<\/u>, ktor\u00e9 sa objavuj\u00fa po ur\u010ditom \u010dasovom intervale. <\/p>\n<p><\/p>\n<p>\u010cl\u00e1nok, ktor\u00fd prev\u00e1dza nepreru\u0161en\u00fd sign\u00e1l na diskr\u00e9tny sign\u00e1l, sa naz\u00fdva impulzn\u00fd. Tak\u00fdto typ pren\u00e1\u0161an\u00fdch sign\u00e1lov sa vyskytuje v SAA s EVM alebo kontrol\u00e9rom. <\/p>\n<p><\/p>\n<p>Naj\u010dastej\u0161ie sa realizuj\u00fa nasleduj\u00face met\u00f3dy (algoritmy) prevodu nepreru\u0161en\u00e9ho vstupn\u00e9ho sign\u00e1lu na impulzn\u00fd v\u00fdstupn\u00fd sign\u00e1l: <\/p>\n<ul>\n<li> amplit\u00fadovo-impulzn\u00e1 modul\u00e1cia (AIM); <\/li>\n<li> \u0161\u00edrkov\u00e1-impulzn\u00e1 modul\u00e1cia (\u0160IM). <\/li>\n<\/ul>\n<p><\/p>\n<p>Na obr. 1.4.5 je grafick\u00e1 ilustr\u00e1cia algoritmu amplit\u00fadovo-impulznej modul\u00e1cie (AIM). V hornej \u010dasti obr. je zn\u00e1zornen\u00e1 \u010dasov\u00e1 z\u00e1vislos\u0165 <i>x(t)<\/i> \u2013 sign\u00e1lu <u>na vstupe<\/u> do impulzn\u00e9ho \u010dl\u00e1nku. V\u00fdstupn\u00fd sign\u00e1l impulzn\u00e9ho modulu (\u010dl\u00e1nku) <i>y(t)<\/i> \u2013 sekvencia obd\u013a\u017enikov\u00fdch impulzov, ktor\u00e9 sa objavuj\u00fa s <u>st\u00e1la<\/u> obdob\u00edm kvantovania \u0394t (pozri doln\u00fa \u010das\u0165 obr.). D\u013a\u017eka impulzov je rovnak\u00e1 a rovn\u00e1 \u0394. Amplit\u00fada impulzu na v\u00fdstupe modulu je \u00famern\u00e1 pr\u00edslu\u0161nej hodnote nepreru\u0161en\u00e9ho sign\u00e1lu x(t) na vstupe tohto modulu. <\/p>\n<p><\/p>\n<p><img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/c9a3c132c1ad71a56582f30d6d11f847.jpg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<i>Obr. 1.4.5 \u2014 Realiz\u00e1cia amplit\u00fadovo-impulznej modul\u00e1cie<\/i><\/p>\n<p>T\u00e1to met\u00f3da impulznej modul\u00e1cie bola ve\u013emi roz\u0161\u00edren\u00e1 v elektronick\u00fdch merac\u00edch pr\u00edstrojoch syst\u00e9mov riadenia a ochrany (S\u00daZ) jadrov\u00fdch energetick\u00fdch zariaden\u00ed (JAEZ) v 70. a 80. rokoch minul\u00e9ho storo\u010dia. <\/p>\n<p><\/p>\n<p>Na obr. 1.4.6 je zobrazen\u00e1 grafick\u00e1 ilustr\u00e1cia algoritmu \u0161\u00edrkovo-impulznej modul\u00e1cie (\u0160IM). V hornej \u010dasti obr. 1.14 je zn\u00e1zornen\u00e1 \u010dasov\u00e1 z\u00e1vislos\u0165 <i>x(t)<\/i> \u2013 sign\u00e1lu na vstupe do impulzn\u00e9ho prvku. V\u00fdstupn\u00fd sign\u00e1l impulzn\u00e9ho modulu (prvku) <i>y(t)<\/i> \u2013 s\u00e9ria obd\u013a\u017enikov\u00fdch impulzov, ktor\u00e9 sa objavuj\u00fa s kon\u0161tantn\u00fdm kvantiza\u010dn\u00fdm peri\u00f3dou <i>\u0394t <\/i>(pozri doln\u00fa \u010das\u0165 obr. 1.14). Amplit\u00fada v\u0161etk\u00fdch impulzov je rovnak\u00e1. D\u013a\u017eka impulzu <i>\u0394t<\/i> na v\u00fdstupe modulu je proporcion\u00e1lna zodpovedaj\u00facej hodnote kontinu\u00e1lneho sign\u00e1lu <i>x(t)<\/i> na vstupe impulzn\u00e9ho modulu.<\/p>\n<p><\/p>\n<p><img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/e9375a87c49f84b4b20891b024160264.jpg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<i>Obr. 1.4.6 \u2014 Implement\u00e1cia \u0161\u00edrkovo-impulznej modul\u00e1cie<\/i><\/p>\n<p>T\u00e1to met\u00f3da impulznej modul\u00e1cie je v s\u00fa\u010dasnosti najroz\u0161\u00edrenej\u0161ia v elektronick\u00fdch merac\u00edch pr\u00edstrojoch syst\u00e9mov riadenia a ochrany (S\u00daZ) jadrov\u00fdch energetick\u00fdch zariaden\u00ed (JEZ) a S\u00c1U in\u00fdch technick\u00fdch syst\u00e9mov.<\/p>\n<p><\/p>\n<p>Na z\u00e1ver tejto podkapitoly treba poznamena\u0165, \u017ee ak charakteristick\u00e9 kon\u0161tanty \u010dasu v in\u00fdch prvkoch S\u00c1U (SAR) <u>s\u00fa v\u00fdrazne v\u00e4\u010d\u0161ie<\/u> \u0394t (o poriadky), potom impulzn\u00fd syst\u00e9m <u>sa m\u00f4\u017ee pova\u017eova\u0165 za kontinu\u00e1lny syst\u00e9m automatick\u00e9ho riadenia (pri pou\u017eit\u00ed<\/u> ako AIM, tak aj \u0160IM). <\/p>\n<p><\/p>\n<h3>1.4.3. Klasifik\u00e1cia pod\u013ea charakteru riadenia<\/h3>\n<p><\/p>\n<p>Pod\u013ea charakteru procesov riadenia sa syst\u00e9my automatick\u00e9ho riadenia delia na nasleduj\u00face typy: <\/p>\n<ul>\n<li> deterministick\u00e9 S\u00c1U, v ktor\u00fdch m\u00f4\u017ee by\u0165 ka\u017ed\u00e9mu vstupn\u00e9mu sign\u00e1lu jednozna\u010dne priraden\u00fd v\u00fdstupn\u00fd sign\u00e1l (a naopak);<\/li>\n<li> stochastick\u00e9 S\u00c1U (\u0161tatistick\u00e9, pravdepodobnostn\u00e9), kde tento vstupn\u00fd sign\u00e1l S\u00c1U 'odpoved\u00e1' <u>n\u00e1hodn\u00fdm<\/u> (stochastick\u00fdm) v\u00fdstupn\u00fdm sign\u00e1lom. <\/li>\n<\/ul>\n<p><\/p>\n<p>V\u00fdstupn\u00fd stochastick\u00fd sign\u00e1l sa vyzna\u010duje: <\/p>\n<ul>\n<li>z\u00e1konom rozdelenia; <\/li>\n<li>matematick\u00fdm o\u010dak\u00e1van\u00edm (priemernou hodnotou); <\/li>\n<li>rozptylom (\u0161tandardn\u00fdm odch\u00fdlkou).<\/li>\n<\/ul>\n<p>\nStochastickos\u0165 charakteru procesu riadenia sa zvy\u010dajne pozoruje v <u>v\u00fdrazne neline\u00e1rnych SAR<\/u> \u010di u\u017e z poh\u013eadu statickej charakteristiky, alebo z poh\u013eadu (a\u017e v v\u00e4\u010d\u0161ej miere) nelinearity dynamick\u00fdch \u010dlenov v rovniciach dynamiky.<\/p>\n<p><\/p>\n<p><img decoding=\"async\" alt=\"\u00davod do te\u00f3rie automatick\u00e9ho riadenia. Z\u00e1kladn\u00e9 pojmy te\u00f3rie riadenia technick\u00fdch syst\u00e9mov\" src=\"\/wp-content\/uploads\/2020\/06\/30bfdc2e2b7df726f11ebfb859c8f094.jpg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<i>Obr. 1.4.7 \u2014 Rozdelenie v\u00fdstupnej veli\u010diny stochastickej S\u00c1U<\/i><\/p>\n<p>Okrem uveden\u00fdch z\u00e1kladn\u00fdch typov klasifik\u00e1cie riadiacich syst\u00e9mov existuj\u00fa aj in\u00e9 klasifik\u00e1cie. Napr\u00edklad klasifik\u00e1cia m\u00f4\u017ee by\u0165 vykonan\u00e1 pod\u013ea met\u00f3dy riadenia a zaklada\u0165 sa na interakcii s vonkaj\u0161\u00edm prostred\u00edm a mo\u017enosti adapt\u00e1cie SAU na zmenu parametrov okolia. Syst\u00e9my s\u00fa rozdelen\u00e9 do dvoch hlavn\u00fdch tried:<\/p>\n<p><\/p>\n<p>1) Obvykl\u00e9 (nesamostrukturuj\u00face) RI bez adapt\u00e1cie; tieto syst\u00e9my patr\u00ed do skupiny jednoduch\u00fdch, ktor\u00e9 nemenia svoju \u0161trukt\u00faru po\u010das riadenia. S\u00fa najviac vypracovan\u00e9 a \u0161iroko pou\u017e\u00edvan\u00e9. Obvykl\u00e9 RI sa delia na tri podtriedy: otvoren\u00e9, uzavret\u00e9 a kombinovan\u00e9 riadiace syst\u00e9my.<\/p>\n<p><\/p>\n<p>2) Samostr\u00e1vacie (adapt\u00edvne) RI. V t\u00fdchto syst\u00e9moch pri zmene vonkaj\u0161\u00edch podmienok alebo charakterist\u00edk regulovan\u00e9ho objektu doch\u00e1dza k automatickej (vopred nezadanej) zmene parametrov riadiaceho zariadenia v\u010faka zmene koeficientov RI, \u0161trukt\u00fary RI alebo dokonca zavedenia nov\u00fdch prvkov.<\/p>\n<p><\/p>\n<p>\u010eal\u0161\u00ed pr\u00edklad klasifik\u00e1cie: pod\u013ea hierarchick\u00e9ho znaku (jedno\u00farov\u0148ov\u00e9, dvoj\u00farov\u0148ov\u00e9, viac\u00farov\u0148ov\u00e9). <\/p>\n<p class=\"for_users_only_msg\">Len registrovan\u00ed pou\u017e\u00edvatelia sa m\u00f4\u017eu z\u00fa\u010dastni\u0165 prieskumu. <noindex><a rel=\"nofollow\" href=\"https:\/\/habr.com\/ru\/auth\/login\/\">Prihl\u00e1ste sa<\/a><\/noindex>, pros\u00edm.<\/p>\n<h2 class=\"default-block__polling-title\">Pokra\u010dova\u0165 v publikovan\u00ed predn\u00e1\u0161ok o UTS?<\/h2>\n<ul class=\"poll-result\">\n<li class=\"poll-result__item\">\n<p>                <strong class=\"poll-result__data-percent  poll-result__data-percent_winner\">88,7%<\/strong>\u00c1no118<\/p>\n<\/li>\n<li class=\"poll-result__item\">\n<p>                <strong class=\"poll-result__data-percent\">7,5%<\/strong>Nie10<\/p>\n<\/li>\n<li class=\"poll-result__item\">\n<p>                <strong class=\"poll-result__data-percent\">3,8%<\/strong>Neviem5<\/p>\n<\/li>\n<\/ul>\n<p>    Hlasovalo 133 pou\u017e\u00edvate\u013eov. Zdr\u017eali sa 10 pou\u017e\u00edvate\u013eov.<br \/>\n<br \/>Zdroj: <a content=\"nofollow\" rel=\"nofollow\" href=\"https:\/\/habr.com\/ru\/post\/503820\/\">habr.com<\/a> <\/p>","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"<p>\u041f\u0443\u0431\u043b\u0438\u043a\u0443\u044e \u043f\u0435\u0440\u0432\u0443\u044e \u0433\u043b\u0430\u0432\u0443 \u043b\u0435\u043a\u0446\u0438\u0439 \u043f\u043e \u0442\u0435\u043e\u0440\u0438\u0438 \u0430\u0432\u0442\u043e\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0443\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044f, \u043f\u043e\u0441\u043b\u0435 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u0432\u0430\u0448\u0430 \u0436\u0438\u0437\u043d\u044c \u0443\u0436\u0435 \u043d\u0438\u043a\u043e\u0433\u0434\u0430 \u043d\u0435 \u0431\u0443\u0434\u0435\u0442 \u043f\u0440\u0435\u0436\u043d\u0435\u0439. \u041b\u0435\u043a\u0446\u0438\u0438 \u043f\u043e \u043a\u0443\u0440\u0441\u0443 \u00ab\u0423\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0422\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u0438\u043c\u0438 \u0421\u0438\u0441\u0442\u0435\u043c\u0430\u043c\u0438\u00bb, \u0447\u0438\u0442\u0430\u0435\u0442 \u041a\u043e\u0437\u043b\u043e\u0432 \u041e\u043b\u0435\u0433 \u0421\u0442\u0435\u043f\u0430\u043d\u043e\u0432\u0438\u0447 \u043d\u0430 \u043a\u0430\u0444\u0435\u0434\u0440\u0435 \u00ab\u042f\u0434\u0435\u0440\u043d\u044b\u0435 \u0440\u0435\u0430\u043a\u0442\u043e\u0440\u044b \u0438 \u044d\u043d\u0435\u0440\u0433\u0435\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0443\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0438\u00bb, \u0444\u0430\u043a\u0443\u043b\u044c\u0442\u0435\u0442\u0430 \u00ab\u042d\u043d\u0435\u0440\u0433\u043e\u043c\u0430\u0448\u0438\u043d\u043e\u0441\u0442\u0440\u043e\u0435\u043d\u0438\u044f\u00bb \u041c\u0413\u0422\u0423 \u0438\u043c. \u041d.\u042d. \u0411\u0430\u0443\u043c\u0430\u043d\u0430. \u0417\u0430 \u0447\u0442\u043e \u0435\u043c\u0443 \u043e\u0433\u0440\u043e\u043c\u043d\u0430\u044f \u0431\u043b\u0430\u0433\u043e\u0434\u0430\u0440\u043d\u043e\u0441\u0442\u044c. \u0414\u0430\u043d\u043d\u044b\u0435 \u043b\u0435\u043a\u0446\u0438\u0438 \u0442\u043e\u043b\u044c\u043a\u043e \u0433\u043e\u0442\u043e\u0432\u044f\u0442\u0441\u044f \u043a \u043f\u0443\u0431\u043b\u0438\u043a\u0430\u0446\u0438\u0438 \u0432 \u0432\u0438\u0434\u0435 \u043a\u043d\u0438\u0433\u0438, \u0430 [&hellip;]<\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"author":1,"featured_media":83943,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[688],"tags":[],"class_list":["post-83942","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-administrirovanie"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.4 - 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