Open AccessControl of Structures with Cubic and Quadratic Non-Linearities with Time Delay Consideration
Author(s) -
Osvaldo C. Pinto,
Paulo B. Gonçalves
Publication year - 2002
Publication title -
revista brasileira de ciências mecânicas
Language(s) - English
Resource type - Journals
ISSN - 0100-7386
DOI - 10.1590/s0100-73862002000200003
Subject(s) - control theory (sociology) , quadratic equation , time complexity , linear quadratic gaussian control , control (management) , state vector , state (computer science) , control system , linear system , optimal control , computer science , polynomial , mathematics , mathematical optimization , engineering , algorithm , mathematical analysis , physics , geometry , classical mechanics , artificial intelligence , electrical engineering
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 for the application of control forces is discussed. Numerical results indicate that the adopted control algorithm can be efficient for non-linear systems, chiefly in the presence of strong non-linearities but increasing time delay reduces the efficiency of the control system. Numerical results emphasize the importance of considering time delay in the project of active structural control systems