The design of H2-optimal control with regional pole assignment via state feedback in linear time-invariant systems is investigated. The aim is to find a state feedback controller such that the closed-loop system has the desired eigenvalues lying in some desired stable regions and attenuates the disturbance between the output vector and the disturbance vector. Based on a proposed result of parametric eigenstructure assignment via state feedback in linear systems, the considered H2-optimal control problem is changed into a minimization problem with certain constraints, and a simple and effective algorithm is proposed for this considered problem. A numerical example and its simulation results show the simplicity and effectiveness of this proposed algorithm.

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H 2 -optimal Control with Regional Pole Assignment via State Feedback

In this paper, a partial eigenstructure assignment problem for the high-order linear time-invariant (LTI) systems via proportional plus derivative (PD) state feedback is considered. By partitioning the open-loop system into two parts (the altered part and the unchanged part) and utilizing the solutions to the high-order generalized Sylvester equation (HGSE), complete parametric expressions of the feedback gain matrices of the closed-loop system are established. Meanwhile, a group of arbitrary parameters representing the degrees of freedom of the proposed method is provided and optimized to satisfy the stability of the system and robustness criteria. Finally, a numerical example and a three-axis dynamic flight motion simulator system example with the simulation results are offered to illustrate the effectiveness and superiority of the proposed method.

A parametric approach of partial eigenstructure assignment for high-order linear systems via proportional plus derivative state feedback

In this paper eigenstructure assignment via proportional-plus-derivative feedback is investigated for a class of second-order descriptor linear systems. Under certain conditions, simple, general and complete parametric solutions of both finite closed-loop eigenvector matrices and feedback gain matrices are derived. The parametric approach utilizes directly original system data, involves manipulations only on n-dimensional matrices, and reveals all the design degrees of freedom which can be further utilized to achieve certain additional system specifications. A numerical example shows the effect of the proposed approach.

Eigenstructure assignment in a class of second-order descriptor linear systems: A complete parametric approach

The design problem of partial pole assignment (PPA) in two classes of frequency- domain MIMO models by constant gain feedback is investigated in this paper. Its aim is to design a constant gain feedback which changes only a subset of the open-loop eigenvalues, while the rest of them are kept unchanged in the closed-loop system. A near general parametric expression for the feedback gain matrix in term of a set of design parameter vectors and the set of the closed-loop poles, and a simple parametric approach for solving the proposed problem are presented. The set of poles do not need to be previously prescribed, and can be set undetermined and treated together with the set of parametric vectors as degrees of design freedom provided by the approach. An illustrative example shows that the proposed parametric method is simple and effective.

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Partial Pole Assignment via Constant Gain Feedback in Two Classes of Frequency-domain Models

Model reference asymptotically tracking for a class of second-order dynamical systems in matrix second-order framework is investigated in this paper. A controller is used, which is composed of two parts: one is a state plus derivative feedback stabilizing controller, the other is a compensator, which compensates the effect of the reference model state to the tracking error. Based on a complete parametric solution to a class of second-order Sylvester matrix equations, the controller gains are completely parameterized. The original system data is directly used in the approach, and physical insight of the original problem is preserved. In the end a numerical example is given, and the simulations show the effect of the proposed parametric method.

Asymptotically tracking in matrix second-order dynamical system framework

This paper investigates the problem of partial eigenstructure assignment (PESA) by state feedback in R-controllable, time-invariant descriptor linear systems. Simple, complete, parametric solutions to PESA are obtained. Two special cases are especially examined, one is replacing a single real eigenvalue and its corresponding eigenvector, the other is replacing a pair of conjugate eigenvalues together with their eigenvectors. Based one these results, a circulation method for PESA is developed, which does not involve inverses of matrices. The parameter vectors in the proposed solutions give all the degrees of design freedom which can be further utilized to achieve additional system specifications. A numerical example shows the effect of the proposed approach.

http://ieeexplore.ieee.org/iel5/8969/28456/01271670.pdf

Guo-Sheng Wang

Papers

Partial Eigenstructure assignment for descriptor linear systems: a complete parametric approach