Eigenstructure assignment in a class of second-order dynamic systems

Eigenstructure assignment using the proportional-plus-derivative feedback controller in a class of secondorder dynamic system is investigated. Simple, general, complete parametric expressions for both the closed-loop eigenvector matrix and the feedback gains are established based on two simple Smith form reductions. The approach utilizes directly the original system data and involves manipulations only on n-dimensional matrices. Furthermore, it reveals all the degrees of freedom which can be further utilized to achieve additional system specifications. An example shows the effect of the proposed approach.

Eigenstructure Assignment in a Class of Second-order Descriptor Linear Systems: A Complete Parametric Approach

In this paper eigenstructure assignment via proportional-plus-derivative feedback is investigated for a class of second-order descriptor linear systems. Under certain conditions, simple, general and complete parametric solutions of both finite closed-loop eigenvector matrices and feedback gain matrices are derived. The parametric approach utilizes directly original system data, involves manipulations only on n-dimensional matrices, and reveals all the design degrees of freedom which can be further utilized to achieve certain additional system specifications. A numerical example shows the effect of the proposed approach.

Two parametric approaches for eigenstructure assignment in second-order linear systems

This paper considers eigenstructure assignment in second-order linear systems via proportional plus derivative feedback. It is shown that the problem is closely related to a type of so-called second-order Sylvester matrix equations. Through establishing two general parametric solutions to this type of matrix equations, two complete parametric methods for the proposed eigenstructure assignment problem are presented. Both methods give simple complete parametric expressions for the feedback gains and the closed-loop eigenvector matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the right factorization of the system, and allows the closed-loop eigenvalues to be set undetermined and sought via certain optimization procedures. An example shows the effectiveness of the proposed approaches. Keywords Second-order linear systems - Eigenstructure assignment - Proportional plus derivative feedback - Parametric solution - Singular value decompoition - Right factorization This work was supported in part by the Chinese Outstanding Youth Foundation (No.69504002).

An explicit solution to right factorization with applicationin eigenstructure assignment

Based on the well-known Leverrier algorithm, a simple explicit solution to right factorization of a linear system is established. This solution is expressed by the controllability matrix of the given system and a symmetric operator matrix. Applications of this solution to a type of generalized Sylvester matrix equatiorls and the problem of parametric eigenstructure assignment by state feedback are investigated,and general complete parametric solutions to these two problems are deduced. These new solutions are simple, and possess desirable structural properties which render the solutions readily implementable. An example demonstrates the effect of the proposed results.

Updating Mass and Stiffness Matrices Using Eigenstructure Assignment Methods

A novel numerical method is presented to update mass and stiffness matrices simultaneously with measured vibration data by means of the combined acceleration and displacement output feedback.By the method,the required displacement and acceleration output feedback gain matrices are determined,and thus the optimal approximation mass matrix and stiffness matrix which satisfy the required orthogonality relation and eigenvalue equation are found.The proposed method is computationally efficient and the updated mass and stiffness matrices are also symmetric and have the compact expressions.The numerical example shows that the proposed method is reliable and attractive.

An explicit solution to polynomial matrix right coprime factorization with application in eigenstructure assignment

在这篇论文，输入状态转移功能的多项式矩阵权利 coprimefactorization 的一个明确的答案以 Krylov 矩阵和系数矩阵的对的 thePseudo 可控制性索引被获得。建议途径仅仅需要解决一系列线性方程。generalizedSylvester 矩阵方程和由州的反馈的参量的 eigenstructure 赋值的问题的一种类型的这个答案的应用程序被调查。这些新答案简单，他们拥有更好结构的性质和方便的空想使用。一个例子显示出建议结果的效果。

Eigenstructure assignment of lower-order dynamical compensatorsfor linear systems with unknown inputs

Presents a systematic design method of reduced order dynamical compensator via the parametric representations of eigenstructure assignment for linear system, which provides maximum degree of freedom, and can be easily used for the design of a linear system with unknown inputs under some conditions. Even when these conditions are not satisfied, the lower order dynamical compensator can also be designed under some relaxed conditions. Some examples illustrate that the method is neat, simple and effective.

Three-axis coupled flight control law design forflying wing aircraft using eigenstructure assignment method

Due to elimination of horizontal and vertical tails,flying wing aircraft has poor longitudinal and directional dynamic characteristics.In addition,flying wing aircraft uses drag rudders for yaw control,which tends to generate strong three-axis control coupling.To overcome these problems,a flight control law design method that couples the longitudinal axis with the lateraldirectional axes is proposed.First,the three-axis coupled control augmentation structure is specified.In the structure,a‘‘soft/hard"cross-connection method is developed for three-axis dynamic decoupling and longitudinal control response decoupling from the drag rudders;maneuvering turn angular rate estimation and subtraction are used in the yaw axis to improve the directional damping.Besides,feedforward control is adopted to improve the maneuverability and control decoupling performance.Then,detailed design methods for feedback and feedforward control parameters are established using eigenstructure assignment and model following technique.Finally,the proposed design method is evaluated and compared with conventional method by numeric simulations.The influences of control derivatives variation of drag rudders on the method are also analyzed.It is demonstrated that the method can effectively improve the dynamic characteristics of flying wing aircraft,especially the directional damping characteristics,and decouple the longitudinal responses from the drag rudders.

EIGENSTRUCTURE ASSIGNMENT VIA DYNAMICOUTPUT FEEDBACK

In this papers the problem of eigenstructure assignment via dynamic output feedback is studied. First, the necessary and sufficient assignability conditions via dynamic output feedback are given. Then, an approach to determine the structure and the minimal order of the dynamic output feedback based on the assigned eigenstructure is proposed.Finally, the controllability and the observability of the compensated system are analyzed.

EIGENSTRUCTURE ASSIGNMENT FOR TIME-VARYING LINEAR SYSTEMS

The problem of eigenstructure assignment via output feedback for time-varying linearsystems is treated, and the sufficient and necessary condition and two simple effective algorithmsare presented. Two forms of parametric representations of the set of closed loop eigenvectormatrices and the set of feedback gains with respect to the closed loop eigenvalues and twogroups of parameter vectors are established. Without any constraint to the closed loop poles,the obtained results have generalized many previous results even in the constant case, andhave also overcome their defects.

EIGENSTRUCTURE ASSIGNMENT PROBLEM

There have been many discussions about the eigenstructure assignment problem of linear multivariable time-invariant system in the past years. In [1], we studied the problem by polynomial matrix theory for state feedback case and gave two ways to find the state feedback matrix K. But there was a presumption that the given eigenstructure is assignable.

Conditions for Robust D-Stability of Discrete-Delay Perturbed Singular Systems

In this paper, a sufficient condition of robust D-stability for discrete-delay perturbed singular systems is presented, and the robust stability sufficient condition is independent of the delay. Two classes of perturbations for systems are discussed: (1) highly structured parametric perturbations; (2) unstructured parametric perturbations. An useful technique for robust pole-assignment in a specified circular region is also proposed, the criterion is tested easily, and convenient for the application in the engineering. Two examples have been given to validate the proposed method.

基于特征结构配置的电磁轴承-刚性转子系统动态补偿器的设计

由于电磁轴承-转子系统的动力学特性与控制器的结构和参数密切相关,若要使系统安全、稳定及可靠地运行,控制器的设计尤为重要。针对电磁轴承-刚性转子系统,提出一种基于特征结构配置的动态补偿器的设计方法。首先,通过模态解耦,将平动和锥动运动相互耦合的四自由度电磁轴承-刚性转子系统解耦为2个单自由度平动子系统和2个单自由度锥动子系统。然后,基于特征结构配置,建立引入动态补偿器后的闭环系统的特征值和特征向量与补偿器参数之间的关系。之后,限定特征值的变化范围,以使系统具备稳定性和良好的动态性能,构造优化目标函数,以同时抑制转子系统的不平衡位移和不平衡控制电流,从而使系统具备所需的动力特性。最后,通过数值仿真和试验,验证所设计的动态补偿器的有效性。

导向钻井稳定平台精确线性化控制

针对导向钻井稳定平台的强非线性、强扰动,致使传统控制算法难以实现高稳定性的角度输出问题,提出了一种基于反馈线性化的极点配置控制策略。首先,根据已知的平台非线性动力学方程,采用反馈线性化理论对该系统中的非线性因素进行精确线性化。其次,通过极点配置法设计期望极点,使系统动态性能达到期望效果。最后,在Matlab/Simulink环境中,搭建平台角度控制系统模型,对提出的控制算法进行仿真验证。仿真结果表明,上述控制算法相对传统PID算法有效的改善了系统角度稳定控制问题,并且在强扰动的作用下具有较强的鲁棒性,提高了系统的控制精度。

基于特征结构配置的奇异振动系统鲁棒镇定

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。

Global stabilizing controller design for linear time-varying systems and its application on BTT missiles

A parametric method for the gain-scheduled controller design of a linear time-varying system is given. According to the proposed scheduling method, the performance between adjacent characteristic points is preserved by the invariant eigenvalues and the gradually varying eigenvectors. A sufficient stability criterion is given by constructing a series of Lyapunov functions based on the selected discrete characteristic points. An important contribution is that it provides a simple and feasible approach for the design of gain-scheduled controllers for linear time-varying systems, which can guarantee both the global stability and the desired closed-loop performance of the resulted system. The method is applied to the design of a BTT missile autopilot and the simulation results show that the method is superior to the traditional one in sense of either global stability or system performance.

飞行控制系统设计的特征结构配置法

阐述了特征结构配置法在飞行控制系统设计中的应用问题 .根据对飞行控制系统动态响应的分析 ,从理论上探讨了特征结构配置的概念和根据设计指标确定特征结构的方法 .应用这种方法 ,可设计出结构简单的多输入多输出飞行控制器 ;能同时考虑鲁棒性和系统动态性能要求 ,满足解耦与鲁棒性等高性能飞行控制系统的设计要求 ;能像经典设计那样 ,预知系统输出和期望控制输入 .该方法的主要缺点是 ,当系统存在不确定模态时 。

一类非线性系统的观测器设计

本文针对一类广泛存在的非线性系统，给出了状态观测器的形式，证明了观测器误差渐进收敛的条件，并利用线性系统的特征结构配置理论，给出了简便而切实可行的观测器的设计方法．

线性系统的状态反馈特征结构配置

一、引言关于线性系统状态反馈特征结构配置问题的研究,现已有一些结果,但这些结果或者要求了闭环极点互异,闭环极点异于开环极点等条件,或者在开、闭环公有极点存在的情况下,要求验证一系列的附加条件约束.本文给出了线性系统状态反馈特征结构配置的一种新方法,克服了文[1—4]的缺点.