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Optimierung Linearer Regelsysteme Mit Quadratischer Zielfunktion: Habilitationsschrift an Der Abteilung Für Elektrotechnik Der Eidgenössischen Technis by H. a. Nour Eldin

Optimierung Linearer Regelsysteme Mit Quadratischer Zielfunktion: Habilitationsschrift an Der Abteilung Für Elektrotechnik Der Eidgenössischen Technis

by H. a. Nour Eldin
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Book cover type: Paperback
  • ISBN13: 9783540054658
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 168
  • Original Price: EUR 46.72
  • Language: German
  • Edition: N/A
  • Item Weight: 323 grams
  • BISAC Subject(s): General

Diese Arbeit befasst sich mit der Steuerung (bzw. Regelung) von linear en Regelsystemen mit quadratischer Zielfunktion. Das lineare Regelsystem kann durch gewehnliche Differential- gleichung, Differential-Differenzengleichungen, Differenzen- gleichung oder partielle Differentialgleichungen beschrieben werden. Der Zustandsvektor oder der Steuervektor kann be- schrankt sein. Mit einer direkten Optimierungsmehtode, welche einen stufen- fermigen Steuervektor verwendet, wurde gezeigt, dass die Lesung fur Betragsbeschrankungen eine quadratische Program- mierungsaufgabe ist. Fur andere Formen der Restriktionen wird die Lesung eine nichtlin2are Programmierungsaufgabe sein. Falls keine Restriktionen vorhanden sind, wird die Lesung eine lineare Ruckflihrung mit variablen Ruckfuhrungs- koeffizienten sein. Die Vorteile der vorgeschlagenen Optimierungsmethode werden hier kurz zusammengefasst: 1. Die Optimierung fur Zielfunktionen mit R(t) = 0 kann durchgefuhrt werden. Dies bedeutet, dass man eine gressere Klasse von Regelungsproblemen behandeln kann als dies bis jetzt der Fall ist. In vielen praktischen Anwendungen war die Einfuhrung einer Gewichtsfunktion fur die Steuergresse nur eine mathematische Notwendig- keit, damit die Variationsmethoden verwendet werden. Die Befrehmg von solchem "Zwang" bedeutet eine bes- sere Anpassung des mathematischen Modells an die Wirklichkeit. 2. Die Matrizen, welche in der Programmierungsaufgabe vorhanden sind, kennen direkt aus der Regelstrecke gemessen werden. Man ist damit in der Lage, die Opti- mierung von Regelstrecken, welche nicht explizit - 15- durch Differentialgleichungen beschrieben sind, durch- zuftihren. Mit den vorherigen Methoden war man immer gezwungen, die Regelstrecke zuerst zu identifizieren. Das ist aber ein schwieriges Problem, welches oft nicht losbar ist. Aus- serdem wissen wir keine brauchbare Methode zur Identi- fizierung von Regelstrecken mit Totzeiten oder gemisch- ten Differentialgleichungen.

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