余培照, 李孟孟, 王闯.基于特征结构配置的奇异振动系统鲁棒镇定[J].河南理工大学学报（自然科学版）,2024,43(4):152-161.

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.

基于特征结构配置的奇异振动系统鲁棒镇定

余培照, 李孟孟, 王闯

郑州轻工业大学 电气信息工程学院，河南 郑州 450002

摘要:奇异振动系统由于存在无穷远特征结构，导致系统的动态性能较差，这给实际应用带来了困难。  目的  为了改善奇异振动系统的稳定性， 方法 采用加速度-速度主动控制策略，提出基于特征结构配置的奇异振动系统鲁棒镇定。基于特征结构配置及奇异值分解方法讨论奇异振动系统的镇定问题，提出镇定控制器的参数化设计方法。在随机扰动环境下，讨论奇异振动系统受参数扰动时的鲁棒特征值镇定问题和镇定控制器设计方案。通过引入拉格朗日乘子，构造基于扰动位移的多元函数，将鲁棒镇定问题转化为广义系统特征结构优化问题。利用构造的扰动函数及Rayleigh定理，提出奇异振动系统鲁棒镇定控制器设计的新方法。 结果 通过两个算法制定了相应控制器设计步骤，仿真验证了算法的可行性。数值结果表明，本文方法能快速镇定奇异振动系统，且使闭环系统具有很好的稳态性能。 结论 提出的新方法改善了奇异振动系统动态性能的同时，也增强了闭环系统的抗干扰能力，从而提高了系统的鲁棒性。

关键词:振动系统;特征结构配置;镇定;鲁棒性

doi:10.16186/j.cnki.1673-9787.2022040028

基金项目:国家自然科学基金资助项目（61903342）；河南省科技攻关计划项目（232102210086）

收稿日期:2022/04/11

修回日期:2023/08/09

出版日期:2024/07/15

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