Eigenvalue assignment via uncertain state feedback controllers

Abstract

In this paper, we propose a method for eigenvalue assignment using linear control systems containing uncertain elements. Uncertain systems are systems described by state equations which depend on uncertain parameters. In this paper, uncertainty is modeled with interval numbers. The proposed method assigns prescribed eigenvalues to a state feedback control system. Also, we introduce two interval operations to be used in our method use them. Some numerical experiments are presented to illustrate the effectiveness of the proposed method.

State feedback control for stabilization of PMSM ‐based servo‐drive with parametric uncertainty using interval analysis

“…where, K c ∈ K c I is the gain (r  n) interval matrix. The closed loop for the ICCF (19), by using the state feedback control (20), is given as follow…”

“…Computing of the gain interval matrix K c ∈ K c I from the reduced form of the ICCF (see Equations [19], [21], and [22]). Thus, we consider the following matrices…”

“…The control design that we will develop is based on an interval analysis, which is achieved by placing all coefficients of the system characteristic polynomial within assigned intervals. [17][18][19][20] Indeed, the uncertain dynamical system is modeled by using an interval system in state-space representation, which is described as a set of column interval vectors. 21 The developed approach is applied to a linearized model of PMSM servo-drive; for position control.…”

“…The ICCF in open loop using the new change of coordinate P I From the change of coordinate (A5), the interval matrices of the ICCF(19) in open loop are given as follows: 8A ∈ A I and 8P ∈ P I andB c ∈ B c I ¼ B c _ ∈ B and8P ∈ P I :ðA7ÞCalculation of the gain interval matrixK c ∈ K c I of the state feedback control u t ð Þ ¼ K c x c t ð Þþ v t ð Þ 1. Closed-loopICCF using the transformation interval matrix P I Using the asymptotically stable interval polynomial (51) of the desired closed-loop behavior allows us to have the following interval state matrix A f c I in closed loop, based on Equation (24): Reduced ICCF for the calculation of the gain interval matrix K c I The calculation of the r  n ð Þgain interval matrix K c I is obtained by using the reduced open-loop ICCF as described by the interval matrices A c I and B c I of Equations (A6) and (A7), respectively, and the reduced closed-loop ICCF as…”

Partial eigenstructure assignment problem for vibration system via feedback control

“…The dynamic performances of vibration systems can be improved by using eigenstructure assignment approach [8,10]. Both eigenvalues and corresponding eigenvectors are concerned in eigenstructure assignment problems which evolved from poles/eigenvalues assignment problems [11][12][13]. Decoupling problems, impulse elimination problems, and feedback stabilization problems can be transformed into solving eigenstructure assignment problems [4,12,14].…”