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Structral–control optimization with H 2 ‐ and H ∞ ‐norm bounds
Author(s) -
Khot N. S.,
Öz H.
Publication year - 1997
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/(sici)1099-1514(199707/08)18:4<297::aid-oca604>3.0.co;2-a
Subject(s) - control theory (sociology) , linear quadratic gaussian control , norm (philosophy) , truss , singular value , optimal control , upper and lower bounds , actuator , quadratic equation , robust control , mathematics , linear quadratic regulator , control system , computer science , mathematical optimization , engineering , control (management) , mathematical analysis , physics , eigenvalues and eigenvectors , geometry , structural engineering , electrical engineering , quantum mechanics , artificial intelligence , political science , law
An integrated approach to minimum weight structural design and robust control system design is presented. The controller is designed to tolerate both the structured real parameter uncertainty in the structural natural frequencies and the unstructured unmodelled dynamics due to model truncation. The control approach utilizes a mixed H 2 – H ∞ LQG compensator with an H ∞ ‐norm bound on the disturbance to the output transfer matrix in the closed‐loop system and an upper bound on the H 2 ‐norm signifying the maximum value of the quadratic control performance index for the uncertain system. In structural–control optimization problems, constraints are imposed on the fundamental structural frequency and on the dB gain separation between the open‐loop and closed‐loop singular values at prescribed frequencies. The method is demonstrated on a 48‐state structural truth model of a three‐dimensional tapered box truss with collocated actuators and sensors in which the control design model is eighth‐order including the compensator dynamics. © 1997 John Wiley & Sons, Ltd.