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 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.

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 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.

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 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.

Design of Luenberger function observer with disturbance decoupling for matrix second-order linear systems-a parametric approach

A simple method for disturbance decoupling for matrix second-order linear systems is proposed directly in matrix second-order framework via Luenberger function observers based on complete parametric eigenstructure assignment. By introducing the H2 norm of the transfer function from disturbance to estimation error, sufficient and necessary conditions for disturbance decoupling in matrix second-order linear systems are established and are arranged into constraints on the design parameters via Luenberger function observers in terms of the closed-loop eigenvalues and the group of design parameters provided by the eigenstructure assignment approach. Therefore, the disturbance decoupling problem is converted into an eigenstructure assignment problem with extra parameter constraints. A simple example is investigated to show the effect and simplicity of the approach.

Robust parametric approach for tracking control of an air-breathing hypersonic cruise vehicle

To realize the stabilization and the tracking of flight control for an air-breathing hypersonic cruise vehicle, the linearization of the longitudinal model under trimmed cruise condition is processed firstly. Furthermore, the flight control problem is formulated as a robust model tracking control problem. And then, based on the robust parametric approach, eigenstructure assignment and reference model tracking theory, a parametric optimization method for robust controller design is presented. The simulation results show the effectiveness of the proposed approach.

Explicit Determination of State Feedback Matrices

Methods which calculate state feedback matrices explicitly for uncontrollable systems are considered in this paper. They are based on the well-known method of the entire eigenstructure assignment. The use of a particular similarity transformation exposes certain intrinsic properties of the closed loop w-eigenvectors together with their companion z-vectors. The methods are extended further to deal with multi-input control systems. Existence of eigenvectors solution is established. A differentiation property of the z-vectors is proved for the repeated eigenvalues assignment case. Two examples are worked out in detail.

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。

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。

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 。

导弹三维制导控制一体化设计

针对导弹的三维制导控制一体化设计问题,给出了基于微分几何和特征结构配置的一体化设计方法,以保证导弹能够垂直命中目标。综合考虑制导回路与控制回路之间的耦合关系、纵向通道与侧向通道之间的耦合关系,给出了导弹的三维制导控制一体化模型,使用微分几何方法对一体化模型进行了反馈线性化,基于特征结构配置方法根据期望性能设计三维制导控制系统的结构。仿真结果表明,针对不同的仿真算例脱靶量都小于0.5m,同时弹道倾角都大于83.5°、弹道偏角都小于5.5°,说明该方法满足制导控制精确度要求,而且在命中目标的同时能够满足对攻击角的约束。

基于特征结构配置的结构主动控制及仿真

考虑了具有最优控制的结构主动控制问题,目的是在系统满足闭环特性的前提下,设计状态反馈控制器使得系统性能泛函极小化。利用特征结构配置方法提供的自由度,给出了性能泛函的显示参数化表示,从而该问题转化为带有约束条件的优化问题,参与优化的变量仅为一组参量。并给出了求解该优化问题的算法,该算法直接基于结构系统矩阵,故其简单性为工程应用提供方便。地震作用下对三层剪切结构建筑模型进行仿真分析,结果表明所提结构主动控制方法的有效性。