COBEM99

S9 Fenômenos Não-Lineares e Caóticos em Engenharia

Title:

CONTROL OF STRUCTURES WITH CUBIC AND QUADRATIC NON-LINEARITIES WITH TIME DELAY CONSIDERATION

Summary :

ABSTRACT. THIS PAPER STUDIES THE EFFECT OF TIME DELAY ON THE ACTIVE NON-LINEAR CONTROL OF DYNAMICALLY LOADED FLEXIBLE STRUCTURES. THE BEHAVIOR OF NON-LINEAR SYSTEMS UNDER STATE FEEDBACK CONTROL, CONSIDERING A FIXED TIME DELAY FOR THE CONTROL FORCE, IS INVESTIGATED. A CONTROL METHOD BASED ON NON-LINEAR OPTIMAL CONTROL, USING A TENSORIAL FORMULATION AND STATE FEEDBACK CONTROL IS USED. THE STATE EQUATIONS AND THE CONTROL FORCES ARE EXPRESSED IN POLYNOMIAL FORM AND A PERFORMANCE INDEX, QUADRATIC IN BOTH STATE VECTOR AND CONTROL FORCES, IS USED. GENERAL POLYNOMIAL REPRESENTATIONS OF THE NON-LINEAR CONTROL LAW ARE OBTAINED AND IMPLEMENTED FOR CONTROL ALGORITHMS UP TO THE FIFTH ORDER. THIS METHODOLOGY IS APPLIED TO SYSTEMS WITH QUADRATIC AND CUBIC NON-LINEARITIES. STRONGLY NON-LINEAR SYSTEMS ARE TESTED AND THE EFFECTIVENESS OF THE CONTROL SYSTEM, INCLUDING A DELAY IN THE APPLICATION OF CONTROL FORCES IS DISCUSSED. NUMERICAL RESULTS INDICATE THAT THE CONTROL ADOPTED ALGORITHM CAN BE EFFICIENT FOR NON-LINEAR SYSTEMS, CHIEFLY IN THE PRESENCE OF STRONG NON-LINEARITIES. ON THE OTHER HAND INCREASING TIME DELAY REDUCES THE EFFICIENCY OF THE CONTROL SYSTEM. THIS EMPHASIZES THE IMPORTANCE OF CONSIDERING TIME DELAY IN THE DESIGN OF ACTIVE STRUCTURAL CONTROL SYSTEMS. KEY WORDS: TIME DELAY, NON-LINEAR OPTIMAL CONTROL, ACTIVE CONTROL SYSTEMS.

Author :

Gonçalves, Paulo Batista
Pinto, Osvaldo Casares

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