二维线性系统特征结构配置的两种新算法

本文提出了二维线性系统特征结构配置的两种新算法,并给出了状态反馈矩阵存在的充分条件。     

Eigenstructure assignment in a class of second-order descriptor linear systems: A complete parametric approach

1 Introduction Second-order linear systems capture the dynamic behaviour of many natural phenomena and have found wide applications[1～4] in robotics, vibration and structure analysis etc. Many results in second- order linear systems have focused on eigenstructure assignment[5～10] as an important design method. Most of the results relating to eigenstructure assignment are derived from conventional second-order linear systems. There have been few reported results produced from eigenstructure a…     

具有时变状态滞后2-D离散系统的稳定与镇定(英文)

针对一类由局部状态空间(LSS)Fornasini-Marchesini(FM)第二模型描述的,具有时变状态滞后的2-D离散系统,其中时变滞后项的上、下界均为正实数,研究了其稳定性和控制综合问题。首先,利用Lyapunov-Krasovski泛函方法,提出了系统的稳定性准则。再根据这一准则,分别设计状态反馈和动态输出反馈控制器保证系统的稳定性。状态反馈控制律和输出反馈矩阵可由线性矩阵不等式(LMI)求得。最后,通过数值算例说明所得结果的有效性。     

Augmented gradient flows for on-line robust pole assignment via state and output feedback

This paper is concerned with robust pole assignment in synthesis of linear control systems via state and output feedbacks. First, both the pole assignment and robustness requirements are appropriately formulated as two optimization problems. Then, gradient flow models are developed for the on-line computation of feedback gain matrices that result in robust pole assignment by solving these two optimization problems. A technique is introduced to facilitate the real-time matrix inverse involved for realizing the gradient flow models. The resulting augmented gradient flows have desired convergence properties. Simulation results are included to show the effectiveness of the proposed approach.     

切换时滞线性系统的状态反馈H∞控制

研究一类由任意有限个时滞线性子系统组成的切换系统的状态反馈 控制问题。利用Lyapunov函数方法和凸组合技术,给出由矩阵不等式表示的控制器存在的充分条件,设计相应的子控制器和切换规则。采用变量替代方法,将该矩阵不等式转化为一组线性矩阵不等式。给出一个求解状态反馈控制器增益矩阵的仿真算例。     

Eigenvalue assignment by minimal state-feedback gain in LTI multivariable systems

In this article, an improved method for eigenvalue assignment via state feedback in the linear time-invariant multivariable systems is proposed. This method is based on elementary similarity operations, and involves mainly utilisation of vector companion forms, and thus is very simple and easy to implement on a digital computer. In addition to the controllable systems, the proposed method can be applied for the stabilisable ones and also systems with linearly dependent inputs. Moreover, two types of state-feedback gain matrices can be achieved by this method: (1) the numerical one, which is unique, and (2) the parametric one, in which its parameters are determined in order to achieve a gain matrix with minimum Frobenius norm. The numerical examples are presented to demonstrate the advantages of the proposed method.     

一类非线性不确定时滞系统的混杂状态反馈H∞鲁棒控制

利用混杂状态反馈控制策略研究一类非线性不确定时滞系统的H∞鲁棒控制问题.假定在给定的控制器集合中有有限个备选的状态反馈控制器,并且每个单一的连续控制器都不能使系统具有鲁棒H∞性能.当控制器的增益矩阵已知时,基于单Lyapunov函数技术和凸组合条件给出控制器切换方案以确保非线性不确定时滞系统具有鲁棒H∞性能.当控制器的增益矩阵未知时,使用多Lyapunov函数技术得到了问题可解的另一个充分条件,同时还给出了混杂状态反馈H∞控制器的设计.     

利用位置和加速度反馈的矩阵二阶系统特征结构配置

考虑一类利用位置和加速度反馈二阶线性系统的特征结构配置问题．在允许闭环系统的特征值是未知的前提下,结合矩阵多项式的右互质分解提出二阶线性系统特征结构配置的参数化方法,建立反馈增益阵和特征向量矩阵的显示参数化表达式．本文涉及的参数化方法直接将二阶系统模型转化为一阶状态空间形式,从而降低了系统设计中的计算工作量,并且提出的算法简单,无“返回”步骤．最后,数值算例表明了该算法的有效性．     

线性时滞系统的耗散控制

从全新的二次型供给率的耗散角度,研究了线性时滞系统的二次稳定性和耗散控制问题,给出了线性矩阵不等式(LMI)形式的充分条件。而且,考虑了时滞系统在状态反馈控制器和动态输出反馈控制器作用下的闭环系统的二次稳定和耗散性问题,同样给出了LMI形式的充分条件,并通过线性矩阵不等式的可行解构造出耗散状态反馈控制律和动态输出反馈控制律。     

索-梁耦合结构的分岔反控制研究

斜拉索是斜拉桥主要的支撑单元,是斜拉桥的重要组成部分.本文研究了控制增益参数G对索-梁耦合结构的振动控制.利用文献已得到的索-梁耦合结构的面内非线性运动微分方程,根据离散法,对其进行分离变量法处理,进而得到索-梁耦合结构的单自由度和两自由度模态方程.不同于以往的研究,本文假设索(梁)的左支撑点即坐标原点处是可以沿纵向方向自由移动的,则索的动态应变会发生改变,进而改变其模态方程一次项系数,通过这一规律可以在理论上转换得到一套状态控制反馈准则,并根据Floquet稳定性理论,将上述方程转换为Hill方程形式.然后通过摄动法,得到运动微分方程的稳定解.最后对索-梁耦合结构的单自由度和两自由度系统进行了数值分析计算,通过改变反馈控制增益系数,可以实现系统的反控制.而设计者可以通过这些复杂现象的参数变化范围设计选择合适的参数,尽量使得系统能在工程师所能控制的安全范围内振动.这种控制策略保持了系统的平衡,并且可以应用于在期望位置处具有最优稳定性的退化倍周期分岔.研究表示,无论结构是单自由度还是两自由度系统,反馈控制增益系数的变化能明显有效地改变系统的共振情形下的幅值.通过适当调整控制参数,能在预先...     

Output regulation problem for a class of regular hyperbolic systems

This paper investigates the output regulation problem for a class of regular first-order hyperbolic partial differential equation (PDE) systems. A state feedback and an error feedback regulator are considered to force the output of the hyperbolic PDE plant to track a periodic reference trajectory generated by a neutrally stable exosystem. A new explanation is given to extend the results in the literature to solve the regulation problem associated with the first-order hyperbolic PDE systems. Moreover, in order to provide the closed-loop stability condition for the solvability of the regulator problems, the design of stabilising feedback gain and its dual problem design of stabilising output injection gain are considered in this paper. This paper develops an easy method to obtain an adjustable stabilising feedback gain and stabilising output injection gain with the aid of the operator Riccati equation.     

Decentralized compensation of controller uncertainty in the steady‐state bumpless transfer under the state/output feedback

The state/output feedback topology required for bumpless transfer under controller uncertainty is considered. A steady‐state diagonal dominance condition for a subsystem of this topology is derived, which is shown to be sufficient for the existence of the stabilizing decentralized mismatch compensator parameters. Recent results on the input/output steady‐state gain structure of the one‐degree‐of‐freedom and the two‐degrees‐of‐freedom infinite horizon LQ bumpless transfer topologies are used to show that the diagonal dominance condition applies to topologies generated by a broad class of controllers, thus completing the state/output feedback bumpless transfer technique. The topologies are also shown to be robust with respect to uncertainty in the mismatch compensator. Copyright © 2008 John Wiley & Sons, Ltd.     

A constructive method to static output stabilisation of Markov jump systems

This paper is concerned with the static output feedback stabilisation of Markov jump systems. Transition probabilities are assumed to be incomplete, namely, they may be known, uncertain with known lower and upper bounds and unknown. To linearise the nonlinearities induced by unknown transition probabilities, a linearisation is developed. To solve the static output feedback problem by means of linear matrix inequalities, a constructive method is proposed to separate the controller gain matrices from Lyapunov variables. Based on the linearisation and the separation, sufficient conditions are established to guarantee that the closed-loop system is stochastically stable by the designed static output feedback controller. The obtained results are further extended to deal with norm-bounded or polytopic uncertainties on system matrices. Numerical examples are given to demonstrate the effectiveness of the proposed method.     

一类不确定非线性系统的模糊动态输出反馈控制

利用模糊T－S模型对一类不确定非线性系统进行模糊建模,在此基础上研究基于观测器的模糊动态输出反馈控制,给出了模糊闭环系统二次稳定的充分条件及其反馈控制增益和观测器的求法,以及输出反馈控制器的设计方法,仿真结果证明所提出的控制方法是有效的。     

Robust stability analysis and stabilization for uncertain linear neutral delay systems

This paper considers the problem of robust stability analysis and robust stabilization for uncertain neutral delay systems. The system under consideration is subject to norm-bounded parameter uncertainty appearing in all the matrices of the state-space model. Both delay-dependent and -independent robust stability conditions are obtained in terms of linear matrix inequalities. Based on these, the corresponding conditions for the exsitence of robust stabilizing state feedback controllers are developed. When these conditions are feasible, the desired state feedback controller gain matrices can be obtained via convex optimization.     

Gain‐scheduled ℋ︁2 controller synthesis for linear parameter varying systems via parameter‐dependent Lyapunov functions

This paper deals with the problem of gain‐scheduled ??₂ control for linear parameter‐varying systems. The system state–space model matrices are affinely parameterized and the admissible values of the parameters and their rate of variation are supposed to belong to a given convex bounded polyhedral domain. Based on a parameter‐dependent Lyapunov function, a linear matrix inequality methodology is proposed for designing a gain‐scheduled state feedback ??₂ controller, where the feedback gain is a matrix fraction of polynomial matrices with quadratic dependence on the scheduling parameters. Copyright © 2005 John Wiley & Sons, Ltd.     

Control of slowly-varying linear systems

State feedback control of slowly varying linear continuous-time and discrete-time systems with bounded coefficient matrices is studied in terms of the frozen-time approach. This study centers on pointwise stabilizable systems. These are systems for which there exists a state feedback gain matrix placing the frozen-time closed-loop eigenvalues to the left of a line Re s=-γ<0 in the complex plane (or within a disk of radius ρ<1 in the discrete-time case). It is shown that if the entries of a pointwise stabilizing feedback gain matrix ar continuously differentiable functions of the entries of the system coefficient matrices, then the closed-loop system is uniformly asymptotically stable if the rate of time variation of the system coefficient matrices is sufficiently small. It is also shown that for pointwise stabilizable systems with a sufficiently slow rate of time variation in the system coefficients, a stabilizing feedback gain matrix can be computed from the positive definite solution of a frozen-time algebraic Riccati equation     

不确定离散广义系统的鲁棒H∞控制

考虑不确定离散广义系统的鲁棒H∞控制问题,目的是设计状态反馈控制律,使得对所有容许的不确定参数,闭环系统正则、因果、稳定且满足给定的H∞性能指标,本文给出了鲁棒H∞状态反馈控制律的存在条件及其代数表达式.     

状态时滞时变不确定系统的鲁棒H∞ 输出反馈控制器设计

主要研究了存在状态滞后的线性时变不确定时滞系统的鲁棒∞控制分析和综合问题,给出了对所有容许不确定性,被控对象可二次镇定和满足从干扰输入到控制输出的Ｈ∞范数界约束的动态输入出反馈鲁棒Ｈ∞控制分析结果,将不确定时滞系统的鲁棒Ｈ∞输出反馈控制器设问题等价对两个线性时不变系统的状态反馈标准Ｈ∞控制问题,并由此得到反馈阵和观测阵,了终得到鲁棒Ｈ∞控制器综合设计方法。