Matrix method for eigenvalue assignment: The single input case
Abstract
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.
- Publication:
-
Journal of the Astronautical Sciences
- Pub Date:
- January 1994
- Bibcode:
- 1994JAnSc..42...91P
- Keywords:
-
- Control Systems Design;
- Controllers;
- Eigenvalues;
- Matrix Methods;
- Algorithms;
- Controllability;
- Dynamic Response;
- Feedback Control;
- Flexible Bodies;
- Libration;
- Matrices (Mathematics);
- Spacecraft Motion;
- Tethered Satellites;
- Spacecraft Design, Testing and Performance