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Informačné Technológie Pre Modelovanie a Simuláciu

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Informačné Technológie Pre Modelovanie a Simuláciu MASARYKOVA UNIVERZITA FAKULTA INFORMATIKY Informačné technológie pre modelovanie a simuláciu DIPLOMOVÁ PRÁCA Bc. Tibor Káčerik Brno, jar 2014 Prehlásenie Prehlasujem, že táto diplomová práca je mojím pôvodným autorským dielom, ktoré som vypracoval samostatne. Všetky zdroje, pramene a literatúru, ktorú som používal alebo som z nich čerpal, v práci riadne citujem s uvedením úplného odkazu na príslušný zdroj. Vedúci práce: prof. RNDr. Jiří Hřebíček, CSc. ii Poďakovanie Touto cestou vyslovujem poďakovanie pánovi prof. RNDr. Jiřímu Hřebíčkovi, CSc. za pomoc, odborné vedenie, cenné rady a pripomienky pri vypracovávaní mojej diplomovej práce. iii Zhrnutie Cieľom diplomovej práce je zhodnotiť súčasný stav informačných a komunikačných technológií (vybraný softvér pre symbolické a numerické výpočty) pre modelovanie a simulácie procesov v praxi. Z týchto technológií budú konkrétnejšie opísané systémy počítačovej algebry Maple 18, vrátane jeho nadstavby, systému MapleSim 6.4. Pomocou spomenutých systémov bude riešený problém z oblasti mechatroniky a počítačovou simuláciou analyzujeme vlastnosti získaného riešenia. iv Kľúčové slová informačné a komunikačné technológie, systém počítačovej algebry, modelovanie, model, simulácia, Maple, MapleSim, Mathematica v Obsah Úvod ................................................................................................................................................ 1 1 Modelovanie a simulácia ........................................................................................................ 2 1.1 Model ............................................................................................................................... 2 1.1.1 Matematický model .................................................................................................. 3 1.2 Modelovanie ..................................................................................................................... 3 1.3 Simulácia .......................................................................................................................... 4 1.3.1 Dôvody využívania simulácií ................................................................................... 4 2 Systém počítačovej algebry .................................................................................................... 6 2.1 Vývoj CAS ....................................................................................................................... 6 2.2 Rozdelenie systémov ........................................................................................................ 6 2.3 Zoznam systémov počítačovej algebry ............................................................................ 7 3 Systém Maple 18................................................................................................................... 15 3.1 Základné informácie o systéme ...................................................................................... 15 3.2 Novinky v Maple 18 ....................................................................................................... 16 3.3 Užívateľské rozhranie .................................................................................................... 18 3.3.1 Hlavné menu systému ............................................................................................. 18 3.3.2 Menu pracovnej plochy 1........................................................................................ 19 3.3.3 Menu pracovnej plochy 2........................................................................................ 19 3.3.4 Menu paliet ............................................................................................................. 20 3.3.5 Kontextové menu .................................................................................................... 20 3.3.6 Pracovná plocha ...................................................................................................... 20 3.4 Ovládanie systému ......................................................................................................... 20 3.4.1 Vkladanie jednoduchých operácií a symbolov z paliet........................................... 21 vi 3.4.2 Vkladanie príkazov ................................................................................................. 21 3.4.3 Vyhodnocovanie výrazov, príkazov ....................................................................... 22 3.4.4 Základné programové konštrukcie .......................................................................... 23 3.5 Pomocníci v systéme Maple ........................................................................................... 24 3.5.1 Maple Help.............................................................................................................. 24 3.5.2 Maple Tour.............................................................................................................. 25 3.5.3 Maple Portal ............................................................................................................ 25 3.5.4 Quick Help .............................................................................................................. 25 3.5.5 Quick Reference...................................................................................................... 25 3.5.6 Assistants, Tutors (Asistenti, Inštruktori) ............................................................... 26 3.6 Porovnanie systémov Maple a Mathematica .................................................................. 26 3.6.1 Užívateľské rozhranie ............................................................................................. 27 3.6.2 Matematika ............................................................................................................. 27 3.6.3 Podpora pre študentov............................................................................................. 28 3.6.4 Programovanie ........................................................................................................ 28 3.6.5 Konektivita .............................................................................................................. 29 3.6.6 Otvorenosť .............................................................................................................. 29 4 Systém MapleSim 6.4 ........................................................................................................... 30 4.1 Základné informácie o systéme ...................................................................................... 30 4.1.1 Vlastnosti systému .................................................................................................. 30 4.2 Fyzikálne modelovanie v systéme MapleSim ................................................................ 31 4.2.1 Topologická/akauzálna reprezentácia systému ....................................................... 31 4.2.2 Matematická formulácia modelu a zjednodušovanie .............................................. 31 4.2.3 Algoritmy pre pokročilé diferenciálne algebrické rovnice ..................................... 32 4.2.4 Kauzálne, akauzuálne modelovanie ........................................................................ 32 vii 4.3 Novinky v MapleSim 6.4 ............................................................................................... 34 4.3.1 Novinky v MapleSim 6.3 ........................................................................................ 34 4.3.2 Výkonné nástroje pre vlastné komponenty ............................................................. 34 4.3.3 Vylepšenia výpočtov ............................................................................................... 35 4.3.4 Vylepšenia pre toolbox MapleSim Connector ........................................................ 35 4.3.5 Vylepšenia pre toolbox Control Design ................................................................. 35 4.4 Užívateľské rozhranie .................................................................................................... 36 4.4.1 Hlavné menu systému ............................................................................................. 36 4.4.2 Menu pracovnej plochy 1........................................................................................ 37 4.4.3 Menu pracovnej plochy 2........................................................................................ 37 4.4.4 Menu paliet ............................................................................................................. 38 4.4.5 Konzola, menu konzoly .......................................................................................... 38 4.4.6 Menu parametrov .................................................................................................... 38 4.4.7 Plocha 3-D vizualizácie, menu plochy 3-D ............................................................ 39 4.4.8 Pracovná plocha ...................................................................................................... 39 4.5 Ovládanie systému ......................................................................................................... 39 4.5.1 Práca s komponentmi .............................................................................................. 39 4.5.2 Prepájanie komponent do systému.......................................................................... 40 4.5.3 Práca so sondami....................................................................................................
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