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Matrix method for eigenvalue assignment: The single input case

Pradhan, S and Modi, VJ and Bhat, MS (1994) Matrix method for eigenvalue assignment: The single input case. In: Journal of the Astronautical Sciences, 42 (1). 91 -111 .

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The eigenvalue assignment/pole placement procedure has found application in a wide variety of control problems. The associated literature is rather extensive with a number of techniques discussed to that end. In this paper a method for assigning eigenvalues to a Linear Time Invariant (LTI) single input system is proposed. The algorithm determines a matrix, which has eigenvalues at the desired locations. It is obtained from the knowledge of the open-loop system and the desired eigenvalues. Solution of the matrix equation, involving unknown controller gains, open-loop system matrices and desired eigenvalues, results in the state feedback controller. The proposed algorithm requires the closed-loop eigenvalues to be different from those of the open-loop case. This apparent constraint is easily overcome by a negligible shift in the values. Two examples are considered to verify the proposed algorithm. The first one pertains to the in-plane libration of a Tethered Satellite System (TSS) while the second is concerned with control of the short period dynamics of a flexible airplane. Finally, the method is extended to determine the Controllability Grammian, corresponding to the specified closed-loop eigenvalues, without computing the controller gains.

Item Type: Journal Article
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Additional Information: Copyright of this article belongs to American astronautical society.
Department/Centre: Others
Date Deposited: 18 Apr 2011 07:10
Last Modified: 19 Apr 2011 08:50
URI: http://eprints.iisc.ernet.in/id/eprint/36632

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