Symmetry preserving partial eigenvalue assignment for undamped structural systems

In this paper, the partial eigenvalue assignment problem for undamped structural systems by output feedback control where the output matrix is also a designing parameter is considered. We propose a method to solve this problem in which the unwanted eigenvalues are move to desired values and all other eigenpairs remain unchanged. In addition, our method can preserve symmetry of the systems. Numerical example shows that the proposed method is effective.     

A multi-step hybrid method for multi-input partial quadratic eigenvalue assignment with time delay

A hybrid method was given by Ram et al. (2011) [15] for solving the partial quadratic eigenvalue assignment problem of single-input vibratory systems. In this paper, we consider the partial quadratic eigenvalue assignment problem of multi-input vibratory systems. We solve the multi-input partial quadratic eigenvalue assignment problem by a multi-step hybrid method using both the system matrices and the receptance measurements. Our method can assign the partial expected eigenvalues and keep the no spillover property. We also extend our method to the case when there exists time delay between measurements of state and actuation of control. Numerical tests show the effectiveness of our method.     

Decentralized iterative learning control for a class of large scale interconnected dynamical systems

The problem of decentralized iterative learning control for a class of large scale interconnected dynamical systems is considered. In this paper, it is assumed that the considered large scale dynamical systems are linear time-varying, and the interconnections between each subsystem are unknown. For such a class of uncertain large scale interconnected dynamical systems, a method is presented whereby a class of decentralized local iterative learning control schemes is constructed. It is also shown that under some given conditions, the constructed decentralized local iterative learning controllers can guarantee the asymptotic convergence of the local output error between the given desired local output and the actual local output of each subsystem through the iterative learning process. Finally, as a numerical example, the system coupled by two inverted pendulums is given to illustrate the application of the proposed decentralized iterative learning control schemes.     

Partial pole placement with time delay in structures using the receptance and the system matrices

Datta et al. solved the partial pole placement problem for the symmetric definite quadratic eigenvalue problem where part of the spectrum is relocated to predetermined locations and the rest of the spectrum remains unchanged. In this paper, the problem is solved by a hybrid combination of this result and the method of receptances. This allows for the partial assignment of desired poles with no spillover when there is time delay between the measured or estimated state and actuation of the control.     

Eigenstructure assignment for linear parameter-varying systems with applications

The aim of this paper is to show that a recently proposed technique for eigenstructure assignment of linear time-invariant systems can be extended to solve the corresponding eigenstructure assignment problem for linear parameter-varying systems, whose state-space matrices depend on a set of time-varying parameters that are bounded and available online. In particular, the design of eigenstructure assignment is performed without requiring any conditions on the closed-loop eigenvalues, and provides a simple, complete and analytical parametric approach as well as the most degrees of design freedom for the eigenstructure assignment problem of linear parameter-varying systems. A parameter-varying attitude control system of refueling spacecraft in-orbit is used to demonstrate the usefulness and practicality of the proposed approach.     

线性系统的输出反馈特征结构配置——具有不可控不可观模态的情形

本文考虑具有不可控不可观模态的线性系统的输出反馈特征结构配置问题。根据文中给出的矩阵方程AV＋BW＝VF的一种显式参数解，得到了线性系统的输出反馈特征结构配置的一种参数化方法，本文没有对系统附加能控能观条件，在[AB]能控的条件下，本文得到的矩阵方程的解是文[5]中定理2的结果，在[AB]能控且[AC]能观的条件下，本文得到的输出反馈特征结构配置方法是文[6]在系统为定常时算法Ⅱ的结果。     

Pole placement problem for singular systems

In this paper the pole placement problem for singular systems via state feedback is studied. We give a complete solution to this problem for systems without row minimal indices. As a corollary, the eigenvalue assignment problem is solved for singular systems in the case they are regularizable. Copyright © 2009 John Wiley & Sons, Ltd.     

Robust dynamical compensator design for discrete-time linear periodic systems

This paper considers dynamical compensators design for purpose of pole assignment for discrete-time linear periodic systems. Similar to linear time-invariant systems, it is pointed out that the design of a periodic dynamical compensator can be converted into the design of a periodic output feedback controller for an augmented system. Utilizing the recent result on output feedback pole assignment, parametric solutions for this problem are obtained. The design approach can be used as a basis for the robust dynamical compensator design for this type of systems. Combined with a robustness index presented in this paper, robust dynamical compensator design problem is converted into a constrainted optimization problem. A numerical example is employed to illustrate the validity and feasibility of the methods.     

The formulation and numerical method for partial quadratic eigenvalue assignment problems

In this paper, we consider the minimum norm and robust partial quadratic eigenvalue assignment problems (PQEVAP). A complete theory on the existence of solutions for the PQEVAP is established. It is shown that solving the PQEVAP is essentially solving an eigenvalue assignment for a linear system of a much lower order, and the minimum norm and robust PQEVAPs are then concerning the minimum norm and robust eigenvalue assignment problems associated with this linear system. Based on this theory, an algorithm for solving the minimum norm and robust PQEVAPs is proposed, and its efficient behaviors are illustrated by some numerical examples. Copyright © 2010 John Wiley & Sons, Ltd.     

Structure preserving eigenvalue embedding for undamped gyroscopic systems

This paper concerns the eigenvalue embedding problem of undamped gyroscopic systems. Based on a low-rank correction form, the approach moves the unwanted eigenvalues to desired values and the remaining large number eigenvalues and eigenvectors of the original system do not change. In addition, the symmetric structure of mass and stiffness matrices and the skew-symmetric structure of gyroscopic matrix are all preserved. By utilizing the freedom of the eigenvectors, an expression of parameterized solutions to the eigenvalue embedding problem is derived. Finally, a minimum modification algorithm is proposed to solve the eigenvalue embedding problem. Numerical examples are given to show the application of the proposed method.     

Solution of large scale parametric eigenvalue problems arising from brake squeal modeling

We present a proper orthogonal decomposition (POD) based approach for the accurate solution of parametric eigenvalue problems arising from brake squeal modeling. We compare this approach to a traditional method based on modal decomposition which is very popular in industry. The proposed approach is more accurate than the traditional method especially for parametric studies and for studying non-proportionally damped systems. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

一类离散事件动态系统极点分配的优化问题

应用极大代数作为数学工具,用系统矩阵的特征值法讨论了m × n-型离散事件动态系统极点分配的优化问题.给出了系统取得优化的条件.并证明了至少存在,n个具有最优极点分配的优化系统.     

Some computational issues in optimal control by nonlinear programming

The Roppenecker [11] parameterization of multi-input eigenvalue assignment, which allows for common open- and closed-loop eigenvalues, provides a platform for the investigation of several issues of current interest in robust control. Based on this parameterization, a numerical optimization method for designing a constant gain feedback matrix which assigns the closed-loop eigenvalues to desired locations such that these eigenvalues have low sensitivity to variations in the open-loop state space model was presented in Owens and O'Reilly [8]. In the present paper, two closely related numerical optimization methods are presented. The methods utilize standard (NAG library) unconstrained optimization routines. The first is for designing a minimum gain state feedback matrix which assigns the closed-loop eigenvalues to desired locations, where the measure of gain taken is the Frobenius norm. The second is for designing a state feedback matrix which results in the closed-loop system state matrix having minimum condition number. These algorithms have been shown to give results which are comparable to other available algorithms of far greater conceptual complexity.     

具有输入时滞的时滞关联不确定系统的鲁棒分散控制

研究了一类同时具有输入时滞以及不确定参数的时滞关联大系统的稳定性问题.基于所谓的还原法,给出一种新的状态反馈控制器的设计方法,这种方法的不同之处在于利用了时延的大小以及反馈控制的历史信息.根据Lyapunov稳定性理论得到了系统在控制器作用下稳定的充分条件,所有条件都化成可解的标准LMIs(Linear matrix inequalities)形式.文章最后给出了一个数值例子说明本文结果的可行性.     

Controlling Hopf bifurcations of discrete-time systems in resonance

Resonance in Hopf bifurcation causes complicated bifurcation behaviors. To design with certain desired Hopf bifurcation characteristics in the resonance cases of discrete-time systems, a feedback control method is developed. The controller is designed with the aid of discrete-time washout filters. The control law is constructed according to the criticality and stability conditions of Hopf bifurcations as well as resonance constraints. The control gains associated with linear control terms insure the creation of a Hopf bifurcation in resonance cases and the control gains associated with nonlinear control terms determine the type and stability of bifurcated solutions. To derive the former, we propose the implicit criteria of eigenvalue assignment and transversality condition for creating the bifurcation in a desired parameter location. To derive the latter, the technique of the center manifold reduction, Iooss’s Hopf bifurcation theory and Wan’s Hopf bifurcation theory for resonance cases are employed. In numerical experiments, we show the Hopf circles and fixed points from the created Hopf bifurcations in the strong and weak resonance cases for a four-dimensional control system.     

一类含参数的分块对称矩阵的正定性及应用

首先给出一种判断分块对称矩阵正定的方法,提供了确定一组尽可能小的参数,使一类含参数的分块对称矩阵正定的简单算法,然后,将其结果用于研究线性定常大系统的分散镇定性,得到了一类可分散镇定的线性大系统,并给出了相应的分散镇定算法,同文献中提供的方法相比,该算法不仅扩大了所考虑的系统范围,而且不会引起过高的反馈增益,同时还简单易算。     

Design of an optimal tuned mass damper for a system with parametric uncertainty

Structural control is becoming an attractive alternative for enhanced performance of civil engineering structures subject to seismic and wind loads. However, in order to guarantee stability and performance of structures when implemented with a passive or active control technique, there is a need to include information of uncertainty in the structural models due to the fact that civil engineering structures are time variant and nonlinear. These variations in the structure are often due to parameters such as variable live loads and inelastic behavior and, in cases, may be modeled as parametric uncertainty. The design of an optimal tuned mass damper (TMD) for a one degree-of-freedom (SDOF) system with parametric uncertainty is presented in this paper. The optimization of the connection between the absorber and the primary structure is cast as a constant feedback problem which is solved using structured singular value, μ, synthesis with D-K iteration and decentralized H _∞ design. Results are presented of the TMD that minimize the harmonic response of the primary structure represented by a set of systems within an uncertainty set.     

Decentralized event-based control: Stability analysis and experimental evaluation

Event-based control aims at reducing the amount of information which is communicated between sensors, actuators and controllers in a networked control system. The feedback link is only closed at times at which an event indicates the need for an information update to retain a desired performance. Between consecutive event times the control loop acts as a continuous system, whereas at the event times it performs a state jump. Thus, the event-based control loop belongs to the class of hybrid dynamical systems. In this paper a new method for decentralized event-based control is proposed. Two methods are presented for the stability analysis of the decentralized event-based state feedback control of physically interconnected systems. The comparison principle leads to a stability criterion that provides an upper bound for the coupling strength for which the stability of the uncoupled event-based control loops implies ultimate boundedness of the interconnected event-based system. It is shown that ultimate boundedness of the event-based state-feedback loop is implied by the asymptotic stability of the continuous state-feedback system. Furthermore, it is explained how the number of events can be reduced by estimating the interconnection signals between the subsystems and two different estimation methods are proposed. The derived methods are demonstrated for a thermofluid process by simulation and experiments.     

Hierarchical multi-objective decision systems for general resource allocation problems

We consider optimization methods for hierarchical power-decentralized systems composed of a coordinating central system and plural semi-autonomous local systems in the lower level, each of which possesses a decision making unit. Such a decentralized system where both central and local systems possess their own objective function and decision variables is a multi-objective system. The central system allocates resources so as to optimize its own objective, while the local systems optimize their own objectives using the given resources. The lower level composes a multi-objective programming problem, where local decision makers minimize a vector objective function in cooperation. Thus, the lower level generates a set of noninferior solutions, parametric with respect to the given resources. The central decision maker, then, parametric with respect to the given resources. The central decision maker, then, chooses an optimal resource allocation and the best corresponding noninferior solution from among a set of resource-parametric noninferior solutions. A computational method is obtained based on parametric nonlinear mathematical programming using directional derivatives. This paper is concerned with a combined theory for the multi-objective decision problem and the general resource allocation problem.The authors are indebted to Professor G. Leitmann for his valuable comments and suggestions.