Partial eigenvalue assignment for structural damage mitigation

Abstract In partial eigenvalue assignment, not all eigenvalues of the open loop system matrix are modified through a multiple input state or output feedback controller. This freedom available to assign selected eigenvalues of the closed loop system matrix has been widely used in design contexts such as to eliminate spillover effects in structural control problems. Similar approach is also required to modify damping and/or stiffness characteristics in selected eigenmodes of a damaged structure. When an external force acts on the damaged structure, partial eigenvalue assignment in this fashion will attempt to use minimal control effort and keep the structure active with safe operation. In this paper, a new approach to partial eigenvalue assignment and its application to structural damage mitigation are presented. A three mass spring–damper model with damage in one of the springs is illustrated with damping modifications at specific eigenmodes. The procedure is repeated for a second example, which is a cantilever beam modeled using two inputs and 10 state variables.

[1]  Charles R Farrar,et al.  Damage prognosis: the future of structural health monitoring , 2007, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[2]  Mohamed A. Ramadan,et al.  Partial eigenvalue assignment problem of high order control systems using orthogonality relations , 2010, Comput. Math. Appl..

[3]  Jason L. Speyer,et al.  Application of a fault detection filter to structural health monitoring , 2006, Autom..

[4]  J. T. Weissenburger.  Effect of Local Modifications on the Vibration Characteristics of Linear Systems , 1968 .

[5]  Jiang Qian,et al.  Orthogonal basis selection method for robust partial eigenvalue assignment problem in second-order control systems , 2008 .

[6]  B.N. Datta,et al.  Multi-input partial eigenvalue assignment for the symmetric quadratic pencil , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[7]  Virgil W. Snyder,et al.  Local Modifications of Damped Linear Systems , 1971 .

[8]  Biswa Nath Datta,et al.  Robust and minimum norm partial quadratic eigenvalue assignment in vibrating systems: A new optimization approach , 2010 .

[9]  Li Zhou,et al.  Experimental Study of an Adaptive Extended Kalman Filter for Structural Damage Identification , 2008 .

[10]  Jiang Qian,et al.  Robust partial eigenvalue assignment problem for the second-order system , 2005 .

[11]  Sathya Hanagud,et al.  OPTIMAL VIBRATION CONTROL BY THE USE OF PIEZOCERAMIC SENSORS AND ACTUATORS , 1992 .

[12]  J.G. Chase,et al.  LMS-based structural health monitoring methods for the ASCE benchmark problem , 2004, Proceedings of the 2004 American Control Conference.

[13]  Biswa Nath Datta,et al.  Feedback Control in Distributed Parameter Gyroscopic Systems: A Solution of the Partial Eigenvalue A , 2001 .

[14]  Sathya Hanagud,et al.  An integral equation for changes in the structural dynamics characteristics of damaged structures , 1997 .

[15]  Jann N. Yang,et al.  Identification of Parametric Variations of Structures Based on Least Squares Estimation and Adaptive Tracking Technique , 2005 .