Pole assignment in a specified circular region using a bilinear transformation onto the unit circle

An algorithm for pole assignment in a specified circular region using a bilinear transformation onto the unit circle is considered, A Lyapunov type test is developed to check that all the eigenvalues of a discrete system are within a circle in the complex plane. Pole placement in a circular region by LQ state feedback design is investigated for discrete linear systems. Perturbation bounds are derived, using bilinear transformation, for all closed-loop poles of a perturbed discrete system to remain inside a specified circular region. Illustrative examples are included     

二阶离散系统最优闭环极点配置

本文采用逆方法分析二阶离散系统最优闭环极点配置问题,只要所指定的闭环特征方程的系数满足文中推导出的条件式,就可以通过状态反馈法构成具有希望闭环极点配置的最优闭环系统,无需进一步验证其它最优条件。     

线性离散不确定系统区域极点配置的状态反馈实现方法

研究利用状态反馈对线性离散不确定系统进行区域极点配置的问题。导出了一个由离散代数Ｒｉｃａｔｉ方程表示的对线性离散不确定系统进行区域极点配置的充分条件,并给出了一个通过求解该方程来确定状态反馈增益矩阵的算法。     

不确定广义系统的圆形区域极点配置

考虑不确定连续或离散广义系统的圆形区域极点配置问题, 目的是设计状态反 馈控制律, 使得闭环系统正则, 无脉冲(连续广义系统情形)或因果(离散广义系统情形), 且 闭环极点位于一给定的圆形区域内. 给出了所期望的状态反馈控制律存在的充分条件及其解 析表达式.     

离散线性周期系统的模型匹配

考虑离散线性周期系统的模型匹配问题, 提出一种基于参数化极点配置的模型匹配方法. 该方法从时域的角度出发, 采用周期状态反馈, 使得闭环系统充分接近目标系统. 由于所采用的参数化极点配置算法提供了充分的自由度, 所提出的方法能够实现零误差匹配. 数值算例验证了所提出算法的有效性.

     

基于区域极点约束的鲁棒H2控制

考虑了在区域极点约束下状态反馈的鲁棒H2控制问题.分别对含多面体不确定性的连 续和离散系统进行了讨论.基于LMI,给出了存在参数相关的Lyapunov矩阵的充分条件.利用 LMI凸优化方法的解,所得静态反馈控制器,不仅保证闭环系统的极点在-给定区域内,而且还 使性能指标H2的一上界达到最小.     

区域极点约束下线性离散系统的Riccati鲁棒控制

讨论区域极点约束下,含结构参数扰动的不确定线性离散系统的鲁棒控制问题,即设计一 鲁棒状态反馈控制器,使线性离散系统在可允许的参数扰动下,闭环矩阵极点始终位于一预先 给定的圆形区域中,从而闭环系统具有期望的动态性能.上述控制目的可通过求解一含参数 的代数离散Riccati方程达到.     

Partial pole placement by LQ regulators: an inverse problemapproach

This paper gives a necessary and sufficient condition under which a state feedback control law places part of the closed-loop poles exactly at specified points and, at the same time, is linear quadratic optimal for some quadratic weightings. This is made possible by means of a solution to the inverse problem of optimal control. A design example is given to illustrate the result     

A Lyapunov approach to analysis of discrete singular systems

In this paper, a new type generalized Lyapunov equation for discrete singular systems is proposed. Then it is applied to study problems such as pole clustering, controllability and observability for discrete singular systems. First, some necessary and sufficient conditions for pole clustering are derived via the solution of this new type Lyapunov equation. Further, the relationship between the solution of the Lyapunov equation and structure properties of discrete singular systems will be investigated based on these results. Finally, a type of generalized Riccati equation is proposed and its solution is used to design state feedback law for discrete singular systems such that all the finite poles of the closed-loop systems are clustered into a specified disk.     

多变量系统固定状态反馈下的容错极点配置

本文研究了多变量系统对执行器故障的容错极点配置问题。基于n-线性特征系数系统理论及参数空间设计方法,提出了一种容错极点配置的方法。借助这一方法,对于给定的被控对象,可以设计出一个固定的状态反馈控制律,在执行器的各种故障模式下都将系统的闭环极点设置在预定的区域内。     

2-D奇异系统Roesser模型的鲁棒H∞控制

考虑具有参数不确定性的2-D奇异系统Roesser模型(简称2-D SRM)鲁棒H∞控制问题．在给出界实引理的另一等价形式的基础上,通过求解矩阵不等式,给出了不确定2-D奇异系统鲁棒H∞控制问题可解的充分条件及静态状态反馈控制律设计的代数表达式．最后通过一个仿真算例验证了方法的有效性．     

Linear periodic systems: eigenvalue assignment using discreteperiodic feedback

The eigenvalue assignment problem of a T-periodic linear system using discrete periodic state feedback gains is discussed. For controllable systems, an explicit formula for the feedback law is given that can be used for the arbitrary assignment of the eigenvalues of Φ_c1(T,0), the closed-loop state transition matrix from 0 to T. For the special case of periodic systems controllable over one period, this control law can be used to obtain any desired Φ_c1(T,0)     

线性区间离散时滞系统的区域镇定

针对线性离散时滞系统的区域镇定问题, 基于非奇异状态变换技术提出了区间不确定性系统区域可镇定的充分条件, 保证闭环系统的所有极点均位于给定的圆盘区域内. 所给条件可简化为LMI描述形式, 利用LMI工具求解非常方便. 所给实例表明了该方法用于判断线性区间离散时滞系统的区域可镇定性与设计区域镇定控制器的可行性.     

Pole assignment using dynamic compensators with prespecified poles

The paper describes a simple method for the design of physically realizable dynamic output feedback compensators with prespecified poles to achieve pole assignment in single-input, single-output and multivariable systems. In this method, the numerator parameters of the compensator transfer function are used to position the poles of the augmented closed-loop system consisting of the plant and the compensator at specified locations in the complex plane. It is shown that some or all poles of the closed-loop system can be positioned arbitrarily depending on the order of the compensator. The method is first developed for single-input systems. It is then shown to apply directly to single-output systems and is extended to multivariable systems by restricting the compensators to have unity rank. A number of illustrative numerical examples are given     

Robustness in partial pole placement

The robustness of state feedback solutions to the problem of partial pole placement obtained by a new projection procedure is examined. The projection procedure gives a reduced-order pole assignment problem. It is shown that the sensitivities of the assigned poles in the complete closed-loop system are bounded in terms of the sensitivities of the assigned reduced-order poles, and the sensitivities of the unaltered poles are bounded in terms of the sensitivities of the corresponding open-loop poles. If the assigned poles are well-separated from the unaltered poles, these bounds are expected to be tight. The projection procedure is described in [3], and techniques for finding robust (or insensitive) solutions to the reduced-order problem are given in [1], [2].     

An iterative algorithm for pole placement by output feedback

An iterative algorithm is proposed for solving the pole assignment by output feedback problem for an nth-order l-input m-output linear system. The algorithm uses a full rank feedback gain matrix and requires only linear equations of low dimension to be solved at each iteration. Application of the proposed algorithm allows all n closed-loop poles to be almost exactly assigned provided that the iterations converge so that deviations of the resulting closed-loop poles from the respective desired values become less than some user-specified tolerance, and m×t⩾n. Examples are provided to illustrate the applicability of the proposed method     

Spectrum assignability of parabolic distributed parameter systems

The pole assignment problem of a parabolic distributed parameter system with boundary or pointwise inputs is studied. The problem is solved under a weak restriction on the separation of the open-loop poles and the closed-loop ones. A characteristic equation whose roots are the poles of the closed-loop system is first given and it is shown that the infinite number of open-loop poles can be uniformly moved by means of a suitable linear feedback.     

离散非线性系统的鲁棒模糊协方差控制

针对T-S模糊模型描述的一类不确定非线性离散系统，研究使闭环系统的稳态方差小于某个给定上界，同时闭环极点位于给定圆盘中的状态反馈鲁棒协方差控制律设计问题，并导出以一组线性矩阵不等式表示的控制律的存在条件。     

Non-fragile robust optimal guaranteed cost control of uncertain 2-D discrete state-delayed systems

This paper is concerned with the problem of non-fragile robust optimal guaranteed cost control for a class of uncertain two-dimensional (2-D) discrete state-delayed systems described by the general model with norm-bounded uncertainties. Our attention is focused on the design of non-fragile state feedback controllers such that the resulting closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible parameter uncertainties and controller gain variations. A sufficient condition for the existence of such controllers is established under the linear matrix inequality framework. Moreover, a convex optimisation problem is proposed to select a non-fragile robust optimal guaranteed cost controller stabilising the 2-D discrete state-delayed system as well as achieving the least guaranteed cost for the resulting closed-loop system. The proposed method is compared with the previously reported criterion. Finally, illustrative examples are given to show the potential of the proposed technique.