摘要：
The partial eigenvalue (or natural frequency) assignment or placement, only by the stiffness matrix perturbation, of an undamped vibrating system is addressed in this paper. A novel and explicit formula of determining the perturbating stiffness matrix is deduced from the eigenvalues perturbation theorem for a low-rank perturbed matrix. This formula is then utilized to solve the partial eigenvalue (or natural frequency) assignment via the static output feedback. The control matrix, output matrix and feedback gain matrix can be explicitly expressed and easily constructed.
关键词：
Partial eigenvalue assignment;static output feedback;second-order system;acceleration;velocity and displacement 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.
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.
关键词：
acceleration and velocity feedback;partial quadratic eigenvalue assignment;vibrating system;minimum norm;70J50;65F18;93B52
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 method for partial eigenstructure assignment using acceleration and displacement feedback for undamped vibration systems is presented in this paper. Firstly, a necessary and sufficient condition is proposed for the incremental mass and stiffness matrices that modify some eigenpairs while keeping other eigenpairs unchanged. Secondly, based on this condition, an algorithm for determining the required control gain matrices of acceleration and displacement feedback, which assign the desired eigenstructure, is developed. This algorithm is easy to implement, and works directly on the dsecond-order system model. More importantly, the algorithm allows the control matrix to be specified beforehand and also leads naturally to a small norm solution of the feedback gain matrices. Finally, some numerical examples are given to demonstrate the effectiveness and accuracy of the proposed algorithm. (C) 2013 Elsevier Ltd. All rights reserved.
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.
摘要：
Model parameters of a nonlinear mechanical system are identifiable if a unique relationship exists between its input-output behavior and the parameter values. The identifiability analysis of the parameters is one of the most important steps in the parametric model identification of nonlinear mechanical systems. The concept and two numerical approaches of analyzing the identifiability are presented in this paper. We propose that, via case studies, one had better check of the local identifiability of a parametric model at the identified parameter point using the numerical approach, when the parameter identification procedure has been finished. [DOI: 10.1115/1.4004062]
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.
关键词：
nonlinear systems;fault diagnosis;differential elimination;algebraic observability and diagnosability
摘要：
The differential elimination algorithm is used to eliminate the non-observed variables of the nonlinear systems. By incorporating the algebraic observability and diagnosability concepts and using numerical differentiation algorithms, another approach to the certain classes of nonlinear systems fault diagnosis problem is presented.
关键词：
uncertain structural system;semidefinite programming;linear fractional representation;finite element method
摘要：
A semidefinite programming (SDP) approach is presented to estimate bounds on static responses of structural systems with uncertain material and geometric parameters that are described as interval numbers. Under the constraint of static governing equations of the structural system, an ellipsoid of minimal size in the sense that minimizes the sum of squares of semi-axis lengths is sought to contain the exact solution set of the displacement responses. The computation is formulated as a (convex) SDP problem based on the results from semidefinite relaxation techniques, which can be solved very efficiently using interior-point algorithms. The approach presented here considers the modeling of the structural stiffness matrix containing uncertain structural parameters using linear fractional representation (LFR). We present a procedure to formulate the LFR of the structural stiffness matrix, combining with the finite-element method. It is shown by numerical examples that the approach can give reasonable estimates on the solution intervals, and tends to overestimate the bounds of some response quantities with the increasing number of the uncertain parameters. Using an interval-truncation procedure, more accurate results can be obtained. Keywords: uncertain structural system, semidefinite programming, linear fractional representation, finite element method.
