Partial Pole Assignment Problem Research Articles

Active aeroelastic control with time delay for targeted flutter modes

The dynamic behavior of aeroelastic systems is characterized by multiple numbers of modes. Aeroelastic instability, such as flutter, associated with a certain mode can be stabilized by active control through pole placement. However, the controller can influence or may destabilize other aeroelastic modes due to spillover. In this paper, flutter suppression and flutter boundary extension by partial pole placement in an aeroelastic system is presented by active state feedback having a single time delay in the control loop. This allows the control of the desired mode of interest without influencing any other modes. A quadratic partial pole assignment problem with constant time delay is generalized here for the case of asymmetric system matrices. It is shown with a numerical example that with this approach poles associated with a targeted flutter mode can be stabilized without affecting the other aeroelastic modes. The effect of time delay on control gains and incorporation of actuator dynamics in the proposed framework are demonstrated. Posterior stability analysis is briefly presented for estimating the critical time delays for the controlled system.

Robust partial pole assignment problem for high order control systems

In this paper, we consider the partial pole assignment problem (PPAP) for high order control systems. It is shown that solving the PPAP is essentially solving a pole assignment for a linear system of a much lower order, and the robust PPAP is then concerning the robust pole assignment problem for this linear system. Based on this theory, a rather simple algorithm for solving the robust PPAP is proposed, and numerical examples show that this algorithm does lead to comparable results with earlier algorithms, but at much lower computational cost.

Partial pole assignment for the quadratic pencil by output feedback control with feedback designs

In this paper we study the partial pole assignment problem for the quadratic pencil by output feedback control where the output matrix is also a designing parameter. In addition, the input matrix is set to be the transpose of the output matrix. Under certain assumption, we give a solution to this partial pole assignment problem in which the unwanted eigenvalues are moved to desired values and all other eigenpairs remain unchanged. Copyright © 2005 John Wiley & Sons, Ltd.

POLE ASSIGNMENT FOR SECOND-ORDER SYSTEMS

This paper contains some results for pole assignment problems for the second-order system Mẍ(t)+Dẋ(t)+Kx (t)=Bu (t). Specifically, Algorithm 0 constructs feedback matrices F1 and F2 such that the closed-loop quadratic pencil Pc(λ)=λ2M+λ (D+BF2)+(K+BF1) has a desired set of eigenvalues and the associated eigenvectors are well-conditioned. The method is a modification of the SVD-based method proposed by Juang and Maghami [1, 2] which is a second-order adaptation of the well-known robust eigenvalue assignment method by Kautsky et al. [3] for first-order systems. Robustness is achieved by minimising some not-so-well-known condition numbers of the eigenvalues of the closed-loop second-order pencil. We next consider the partial pole assignment problem. In 1997, Datta, Elhay and Ram proposed three biorthogonality relations for eigenvectors of symmetric definite quadratic pencils [4]. One of these relations was used to derive an explicit solution to the partial pole assignment problem by state feedback for the related single-input symmetric definite second-order control system. The solution shed new light on the stabilisation and control of large flexible space structures, for which only one small subset of the spectrum needs to be reassigned while retaining the complementary part of the spectrum. In this paper, the method has been generalised for multi-input and non-symmetric quadratic pencils. Finally, we discuss briefly the output feedback pole assignment problem.

POLE ASSIGNMENT IN VIBRATORY SYSTEMS BY MULTI-INPUT CONTROL

The problem of reassigning some poles of a vibratory system, while keeping the other poles unchanged, is considered. The problem may be solved uniquely by single-input state feedback control. A family of solutions to the partial pole assignment problem may be obtained by applying multi-input control forces. An algorithm for determining a multi-input control which is small in some sense is presented. The non-iterative algorithm proposed, defines a closed-form solution to the partial pole assignment problem in its natural second order form, and no first order realization is used. The reduction in the control effort achieved by the proposed method is demonstrated by numerical examples.

Pole assignment for the vibrating rod

Relocating some poles of an axially vibrating rod by feedback leads to a certain integro-differential eigenvalue problem. An explicit solution to the problem of determining the force needed to assign part of the spectrum while leaving the remaining spectrum unchanged is presented, and the conditions under which this solution is unique are determined. The results are then used to determine a certain self-adjoint control, analogous to symmetric rank-one update in finite-dimensional systems, which solves the partial pole assignment problem with a control which satisfies the reciprocity law relating displacement and force. The results obtained may be used in practical engineering applications of reducing the forced vibration response of harmonically excited systems.

An algorithm for the single-input partial pole assignment problem

An algorithm for translating unstable eigenvalues of single-input partial pole assignment problems based on rank-one transformations is suggested. Special attention is paid to the practical case where translations are constructed using inexact spectral information provided by the Arnoldi procedure. Estimates of the resulting perturbations of stable and translated poles are derived. These estimates depend on the accuracy of spectral information about the unstable poles. The algorithm proposed is illustrated with numerical examples. Bibliography: 11 titles.

Orthogonality and partial pole assignment for the symmetric definite quadratic pencil

The eigenvectors of a symmetric matrix can be chosen to form an orthogonal set with respect to the identity and to the matrix itself. Similarly, the eigenvectors of a symmetric definite linear pencil can be chosen to be orthogonal with respect to the pair. This paper presents the three sets of matrix weights with respect to which the eigenvectors of the symmetric definite quadratic pencil are orthogonal. One of these is used to derive an explicit solution of the partial pole assignment problem by state feedback control for a control system modeled by a system of second order differential equations. The solution may be of particular interest in the stabilization and control of flexible, large space structures where only a small part of the spectrum is to be reassigned and the rest of the spectrum is required to remain unchanged.

Arnoldi methods for large Sylvester-like observer matrix equations, and an associated algorithm for partial spectrum assignment

We propose an Arnoldi-based numerical method for solving a Sylvester-type equation arising in the construction of the Luenberger observer. Given an N× N matrix A and an N× m matrix G, the method simultaneously constructs an m× m Hessenberg matrix H with a preassigned spectrum and an N× m orthonormal matrix X such that AX− XH= G. We consider the case when A is large and sparse, so that the standard techniques such as the well-known Hessenberg-Schur method for solving a Sylvester equation cannot be easily applied. As a byproduct, we propose an algorithm for the partial pole-assignment problem for large matrices.