Abstract
The problem of state feedback optimal pole assignment is to design a feedback gain such that the closed-loop system has desired eigenvalues and such that certain quadratic performance index is minimized. Optimal pole assignment controller can guarantee both good dynamic response and well robustness properties of the closed-loop system. With the help of a class of linear matrix equations, necessary and sufficient conditions for the existence of a solution to the optimal pole assignment problem are proposed in this paper. By properly choosing the free parameters in the parametric solutions to this class of linear matrix equations, complete solutions to the optimal pole assignment problem can be obtained. A numerical example is used to illustrate the effectiveness of the proposed approach.
Highlights
Introduction and Problem FormulationThe linear quadratic optimal control problem for linear systems is to design a linear state feedback controller such that a quadratic performance index function is minimized
We present a new method for the optimal pole assignment problem
Just remember that it is well known that the analytical solutions of the algebraic Riccati equations are generally not available
Summary
The linear quadratic optimal control problem for linear systems is to design a linear state feedback controller such that a quadratic performance index function is minimized. The poles of closed-loop system resulting from the quadratic optimal controller are still not clear; that is, if the weighting matrices Q and R are prescribed, the feedback gain matrix is uniquely determined, while the locations of the poles of the closedloop systems can not be determined by specifying Q and R in advance. If we can combine the linear quadratic optimal control approach and the pole placement technique together to design the feedback gain, such gain can place the poles of the closed-loop systems to the desired position, and minimize certain quadratic performance index functions. By choosing appropriate free parameters in the parametric solutions of a class of linear matrix equations, the resulting feedback gain matrix can simultaneously minimize some quadratic performance index and assign the poles of the closed-loop systems to the desired locations. Just remember that it is well known that the analytical solutions of the algebraic Riccati equations are generally not available
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