A Simple Approach for Stabilization of Linear Second-Order Asymmetric Systems
Phelippe de Aguiar Lima1; Eduardo Telmo Fonseca Santos1; João Batista da Paz Carvalho2; José Mário Araújo1
1 IFBA; 2 UFRGS
doi:10.20906/CPS/CILAMCE2017-1143
Resumo
Linear second-order systems with an asymmetric structure on the damping and stiffness matrices arise from the modeling of dynamic vibrating systems with aeroelastic or friction-induced phenomena, such as flutter in wings of spacecraft, attrition in belt conveyors, among others [1]. Asymmetry can induce complex eigenvalues in the RHP, that is, unstable, dangerous vibrations appear with crescent amplitude. Very often, this unwanted set of eigenvalues is small, then, the central goal of feedback control in such systems is stabilizing these undesired eigenpairs. Meanwhile, the others can be kept unchanged. This last property is known as no spillover, and several researchers have devoted attention on this in the last two decades, e.g. [2]. The solution of no spillover is consolidated for systems with symmetric matrices, but for that with the asymmetric ones, the contributions on the problem solution are seldom [3]. Using some recent advances in the no spillover for asymmetric systems by the well-known receptance approach [4,5], we proposed in this work a technique for stabilization of unstable eigenpairs with a single control input and fixed influence matrix, using state or derivative feedbacks [6]. To provide extra degree-of-freedom for the feedback gains and then incorporating other performance criteria, as small norm gains or robustness, a set of 2k-1 out of 2k unstable complex eigenvalues is reassigned in the LHP, with a single one constrained to be real. The feedback gains are computed to minimize a given objective function, with a constraint on the eigenvalues product that assures closed-loop stability. Two numerical experiments based on real-world models borrowed from the literature are given [1,7], to illustrate the merits of the proposed approach. References 1. H. Ouyang, Journal of Sound and Vibration, Volume 329, Issue 11, 2010, Pages 1985-1991. 2. J. Carvalho, B. N. Datta, A. Gupta, M. Lagadapati, Mechanical Systems and Signal Processing, Volume 21, Issue 7, 2007, Pages 2715-2731. 3. J. F. Zhang, Jou
Palavras-chave: Eigenvalue assignment; Stabilization; Second-order systems; Asymmetric systems; Optimization