Active damping of vibration in large space structures using a Karhunen-Loeve reduced order model
Grogan, Terence M.
Burl, Jeff B.
Titus, Harold A.
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Large space structures are difficult to control because of the high order of their mathematical models. The high order mathematical model makes the use of a reduced order model to control the structure desirable. The Karhunen-Loeve expansion along with Galerkin's method is used to generate a reduced order model. A control algorithm is achieved by applying linear quadratic regulator theory to the reduced order model. The Karhunen-Loeve basis functions or mode shapes must first be found to identify the reduced order model. Previous results have shown that in the limit as the structural damping approaches zero the Karhunen-Loeve mode shapes and natural mode shapes converge. Numerical techniques are applied to evaluate the structural damping required for convergence. Once the Karhunen-Loeve mode shapes are determined, the reduced order control model is applied to the full order system. The performance of various Karhunen-Loeve models is compared by measuring the modal energies in the controlled and uncontrolled modes.
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