YU P Z, LI M M, WANG C.Robust stabilization for singular vibration systems based on eigenstructure assignment[J].Journal of Henan Polytechnic University(Natural Science) ,2024,43(4):152-161.

doi:10.16186/j.cnki.1673-9787.2022040028

Received:2022/04/11

Revised:2023/08/09

Published:2024/07/05

Robust stabilization for singular vibration systems based on eigenstructure assignment

YU Peizhao, LI Mengmeng, WANG Chuang

College of Electrical and Information Engineering，Zhengzhou University of Light Industry，Zhengzhou 450002，Henan，China

Abstract:Due to infinite eigenstructure in singular vibration systems，the dynamic performance of systems is poor，which brings difficulties to practical application.  Objectives In order to improve the stability of singular vibration systems，  Methods robust stabilization for singular vibration systems based on eigenstructure assignment was presented using acceleration-velocity active control strategy.The stabilization problem was discussed in singular vibration systems based on eigenstructure assignment and singular value decomposition method.The parametric design method of stabilization controller was proposed.The robust eigenvalues stabilization problem and the design scheme of stabilization controller for singular vibration systems disturbed by parameters were discussed under random disturbance environment.A multivariate function based on perturbation displacement was constructed by introducing Lagrange multiplier.The robust stabilization problem was transformed into the eigenstructure optimization problem of descriptor systems.A new controller design method for robust stabilization in singular vibration systems was proposed by using the constructed disturbance function and Rayleigh theorem.  Results The design steps of corresponding controller were given by two algorithms.Simulations showed the feasibility of the algorithms.Numerical results revealed that the proposed methods could stabilize the singular vibration systems quickly，and the closed-loop systems had good steady state performance.  Conclusions The dynamic performance of the singular vibration systems was improved，and the anti-interference ability of the closed-loop systems was enhanced by using proposed new methods.The robustness of closed-loop systems was therefore improved.

Key words:vibration systems;eigenstructure assignment;stabilization;robustness