摘要：
Stability analysis and dominant eigenvalues computation for second-order linear systems with multiple time-delays are addressed by using a reduced characteristic function and the associated characteristic matrix comprised of measured open-loop receptances. This reduced characteristic function is derived from the original characteristic function of the second-order time delayed systems based on a reasonable assumption that eigenvalues of the closed-loop system are distinct from those of the open-loop system. Then a contour integral is used to test the stability and provide the stability chart with respect to different displacement and velocity feedback time-delays, and a Newton-type method to compute the dominant eigenvalues via this characteristic function. The proposed approach also utilizes the spectrum distribution features of the retarded time-delay systems. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach. (C) 2019 Elsevier Ltd. All rights reserved.
通讯机构：
[Zhang, Jia-Fan] W;[Zhang, Jia-Fan] H;Wuhan Polytech Univ, Sch Mech Engn, Wuhan 430023, Peoples R China.;Hubei Prov Engn Technol Res Ctr Fish Proc Equipme, Wuhan 430023, Peoples R China.
关键词：
second-order linear control system;retarded time-delay;dominant eigenvalue;receptance;contour integral method
摘要：
The computation of dominant eigenvalues of second-order linear control systems with multiple time-delays is tackled by using a contour integral method. The proposed approach depends on a reduced characteristic function and the associated characteristic matrix comprised of measured open-loop receptances. This reduced characteristic function is derived from the original characteristic function of the second-order time delayed systems based on the reasonable assumption that eigenvalues of the closed-loop system are distinct from those of the open-loop system, and has the same eigenvalues as those of the original. Then, the eigenvalues computation is equivalent to solve a nonlinear eigenvalue problem of the associated characteristic matrix by using a contour integral method. The proposed approach also utilizes the spectrum distribution features of the retarded time-delay systems. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach.
关键词：
Eigenvalues and eigenfunctions;Feedback control;Matrix algebra;Numerical methods;Damped vibrations;Displacement output;Eigenvalue assignment;Input and outputs;Matrix equations;Second-order systemss;Spectral decomposition;Static output feedback;Feedback
摘要：
This paper addresses the problem of the partial eigenvalue assignment for second-order damped vibration systems by static output feedback. The presented method uses the combined acceleration, velocity and displacement output feedback and works directly on second-order system models without the knowledge of the unassigned eigenpairs. It allows the input and output matrices to be prescribed beforehand in a simple form. The real-valued spectral decomposition of the symmetric quadratic pencil is adopted to derive a homogeneous matrix equation of output feedback gain matrices that assure the no spillover eigenvalue assignment. The method is validated by some illustrative numerical examples.
摘要：
A novel method for partial eigenstructure assignment of undamped vibration systems using acceleration and displacement output feedback is presented in this paper. It is based on modifications of mass and stiffness that preserve partial eigenstructure. A numerical algorithm for determining the required control gain matrices of acceleration and displacement output feedback, which assign the desired eigenstructure, is developed. This algorithm is easy to implement, and works directly on the second-order system model. More importantly, the algorithm allows the output matrix and the input matrix to be specified beforehand and also leads naturally to a small norm solution of the gain matrices. Finally, some numerical results are presented to demonstrate the effectiveness and accuracy of the proposed algorithm. (C) 2015 Elsevier Ltd. All rights reserved.
关键词：
Combinatorial optimization;Feedback;Linear systems;Optimization;Velocity;Algorithm for solving;Eigenvalue assignment;Eigenvalue assignment problem;Minimum norm;Second-order systemss;Unconstrained optimization;Velocity feedback;Vibrating systems;Eigenvalues and eigenfunctions
摘要：
The partial quadratic eigenvalue assignment problem (PQEVAP) is to shift a few undesired eigenvalues of a damped vibrating system to suitably chosen locations, while leaving the remaining eigenvalues and corresponding eigenvectors unchanged. In this paper, an algorithm for solving PQEVAPs and the minimum norm PQEVAP (MNPQEVAP) using acceleration and velocity feedback is proposed. It is shown that solving the PQEVAP here is transformed into solving an eigenvalue assignment of a linear system of a much lower order. Furthermore, the MNPQEVAP here can be efficiently solved by a gradient-based unconstrained optimization method with the derived gradient formula. This algorithm works directly on the second-order system model, and requires the knowledge of only the open-loop eigenvalues to be replaced and their corresponding eigenvectors. Lastly, through two numerical examples, the results of solving the MNPQEVAP under two different combined feedback signals, velocity and displacement signals, and acceleration and velocity signals, are compared from two points of view, i.e. the F-norms of their feedback matrices and the active control energy required from the actuators.
摘要：
A new approach for the partial eigenvalue and eigenstructure assignment of undamped vibrating systems is developed. This approach deals with the constant output feedback control with the collocated actuator and sensor configuration, and the output matrix is also considered as a design parameter. It only needs those few eigenpairs to be assigned as well as mass and stiffness matrices of the open-loop vibration system and is easy to implement. In addition, this approach preserves symmetry of the systems. Numerical example demonstrates the effectiveness and accuracy of the proposed approach.
会议名称：
The 3rd International Conference on Frontiers of Manufacturing Science and Measuring Technology
关键词：
Mass and stiffness modification;Partially prescribed spectral information;Structure dynamic modification;Undamped vibration system
摘要：
A necessary and sufficient condition is proposed for the incremental mass and stiffness matrices that modify some eigenpairs while keeping other eigenpairs unchanged, which requires the knowledge of only the few eigenpairs to be modified of the original undamped vibration system. The application prospects are proposed based on this formulation.
摘要：
A rigid-flexible coupling dynamic model is established for the grinding roller system of an Horomill. Two coordinates are chosen to describe the grinding roller motion, namely the linear displacement of the roller at the center of mass and its rotation around the centroid on the applied plane of the grinding forces. The grinding forces applied on the roller are simplified to be a force and a torque, acting respectively on the direction of two coordinates. The frequency response function (FRF) matrices, with the two grinding force components as input and the vibration acceleration responses of two measuring points on the roller as output, are obtained respectively by using multibody dynamics computational software. The auto-PSD and cross-PSD of the vibration response on two measuring points are known. An inverse pseudo excitation method (IPEM) is then used for solving the grinding dynamic load spectrum. The obtained load spectrum would be helpful for the Horomill dynamic design and the fatigue calculation.
作者机构：
[张家凡; 易启伟] Department of Mechanical Engineering, Wuhan Polytechnic University, Wuhan 430023, China;[李季] The Tramcar Research Institute, Shenyang Heavy Equipment Corporation, Shenyang 110025, China
通讯机构：
Department of Mechanical Engineering, Wuhan Polytechnic University, China
摘要：
Model parameters are identifiable if there exists a unique relationship between its input-output behaviour and the parameter values. The concept and approaches of analyzing the identifiability of parameters in mathematical models of nonlinear mechanical systems are presented in this paper. Since a global identifiability test using the analytical approach is intractable for even the simplest models, some numerical approaches to the local identifiability test are developed. It is proposed via the case study that one had better check the local identifiability of the model at the identified parameter point using the numerical approach, when the parameter identification procedure has been finished.
