互联大系统分散鲁棒控制器设计的BMI方法

讨论具有重叠结构互联大系统的分解及分散鲁棒Ｈ∞控制器的设计问题，首先利用包含原理的约束和聚类条件（１，２）对系统进行重叠结构分解，然后对扩展空间中已解耦的互联系统，用ＢＭＩ方法设计分解的鲁棒Ｈ∞控制器作为原系统的一个次优控制。     

互联大系统动态输出反馈多重叠鲁棒分散关联镇定

针对一类具有网型拓扑结构的互联大系统,提出一种动态输出反馈多重叠鲁棒分散关联镇定方法.该方法将系统状态空间加以扩展,在扩展空间中将其分解为按循环逆序排列的一系列两两子系统对,并为每个子系统对分别设计使其关联稳定的鲁棒分散动态输出反馈控制器,将这些多重叠设计的控制器再收缩回原空间,实现控制律的协调.将该方法应用到一个四区域网型电力系统控制设计中,仿真结果验证了所提出方法的可行性和优越性.     

多区域重叠互联电力系统的H∞控制

研究多区域重叠互联电力系统的鲁棒控制问题。利用包含原理的约束条件和ＬＭＩ算法,提出以两两区域互联子系统控制为基础的多区域系统分散鲁棒Ｈ∞控制器的设计方法。以两区域重叠互联电力系统为例,对系统进行负载阶跃扰动响应仿真,结果表明了该设计方法的有效性。     

具有输入时滞的不确定采样系统的鲁棒控制北大核心CSCD

针对具有输入时滞的结构不确定采样系统,研究了该类系统基于离散化模型的鲁棒控制器设计问题。通过将采样系统的连续的结构不确定对象离散化得到其近似模型,使具有输入时滞不确定采样系统的鲁棒控制器设计问题转换为讨论具有输入时滞的离散系统的鲁棒稳定性问题。利用Lyapunov函数的构造及解析技巧,给出了基于线性矩阵不等式(LMI)的输入时滞离散系统的鲁棒稳定性条件,并在此基础上将控制器参数化,得到了一个通过求解线性矩阵不等式(LMI)来获得采样系统鲁棒控制器的设计方法,所设计的控制器保证了系统的鲁棒稳定性,对结构摄动有着较好的鲁棒性能。最后,通过数值计算仿真验证了本文方法的可行性。     

具有输入时滞的不确定采样系统的鲁棒控制

针对具有输入时滞的结构不确定采样系统,研究了该类系统基于离散化模型的鲁棒控制器设计问题。通过将采样系统的连续的结构不确定对象离散化得到其近似模型,使具有输入时滞不确定采样系统的鲁棒控制器设计问题转换为讨论具有输入时滞的离散系统的鲁棒稳定性问题。利用Lyapunov函数的构造及解析技巧,给出了基于线性矩阵不等式(LMI)的输入时滞离散系统的鲁棒稳定性条件,并在此基础上将控制器参数化,得到了一个通过求解线性矩阵不等式(LMI)来获得采样系统鲁棒控制器的设计方法,所设计的控制器保证了系统的鲁棒稳定性,对结构摄动有着较好的鲁棒性能。最后,通过数值计算仿真验证了本文方法的可行性。     

电力市场条件下互联电力系统的分散H_∞控制

根据分散的自动发电控制AGC(AutomaticGenerationControl)的控制要求和电力市场的条件,研究了互联电力系统分散的鲁棒控制问题。采用虚拟控制区域的概念修正原互联电力系统的状态空间模型;利用大系统包含原理的约束和聚集条件将修正后的互联电力系统模型分解为各个子系统;根据LMI算法来设计可随时满足区域间功率交换合同的分散H∞自动发电控制器。此方法应用到受负载阶跃扰动的两区域互联电力系统中,结果表明了该方法的有效性,并且满足了电力市场条件下自动发电控制的要求。     

一类互联电力系统的鲁棒联结稳定性分析

研究一类互联电力系统在不确定结构扰动下的鲁棒联结稳定问题．基于系统中互联矩阵的不确定性给出了鲁棒联结稳定的定义,利用向量Lyapunov函数方法及范数、特征值的性质推导了此类系统鲁棒联结稳定的两个充分条件．对系统在不确定结构扰动下联结稳定的鲁棒程度进行分析,得到了不确定参数的鲁棒界．两区域互联电力系统的仿真实例说明了所推导条件的有效性．     

反标架规范化控制器的鲁棒性能

研究反标架规范化控制器的鲁棒性能问题,以结构奇异值SSV(Structured Singular Value)为工具,将对象、系统开环传递函数和控制器以奇异值分解形式参数化,就方向性 和耦合性引起的困难分别进行了讨论,得到了使系统保持鲁棒性能所需要的关于开环传递函 数和控制器参数的充分条件,为反标架规范化结构鲁棒控制器设计提供了理论依据.     

基于LMI的μ方法及其在电力系统中的应用

提出了一个新的基于linear matrix inequality(LMI)的混合结构奇异值(μ)分析与综合 方法,通过采用S-过程,将Robust LMI形式的判据简化,得到了可验证的基于LMI的μ分析综 合判据.该判据是基于状态空间描述的,从而消除了频率扫描过程和频率响应曲线拟合过程并 具有更好的数值性态.将该方法应用于典型电力系统励磁控制的鲁棒稳定性分析和鲁棒控制器 的设计中,数值仿真结果同现有AVR+PSS控制器的结果所做比较表明该方法的有效性.     

Delta算子系统具有极点约束的鲁棒非脆弱方差控制

研究Delta算子描述的线性不确定系统具有圆形区域极点约束的鲁棒非脆弱方差控制问题. 针对系统参数范数有界不确定性和控制器的乘性增益不确定性, 运用线性矩阵不等式(LMI)方法, 提出具有圆形区域极点约束的状态反馈鲁棒非脆弱方差控制器存在的条件和设计方法. 数值算例表明设计方法的可行性.     

Robust Overlapping Guaranteed Cost Control of Uncertain State-Delay Discrete-Time Systems

This note presents a new extension of the inclusion principle to cope with the problem of designing robust overlapping controllers for state-delayed discrete-time systems with norm bounded uncertainties using the concept of guaranteed cost control. Expansion-contraction relations for systems and contractibility conditions for output guaranteed cost memoryless controllers are proved, including conditions on the equality of guaranteed performance bounds. The controllers are designed in the expanded space using a linear matrix inequality (LMI) delay independent procedure specifically adapted to this class of problems. The designed controllers are then contracted and implemented into the original system. The results are specialized for the overlapping decentralized control design. The method enables an effective construction of block tridiagonal controllers. A numerical illustrative example is supplied     

LMI optimization approach to robust decentralized controller design

A new approach for design of robust decentralized controllers for continuous linear time‐invariant systems is proposed using linear matrix inequalities (LMIs). The proposed method is based on closed‐loop diagonal dominance. Sufficient conditions for closed‐loop stability and closed‐loop block‐diagonal dominance are obtained. Satisfying the obtained conditions is formulated as an optimization problem with a system of LMI constraints. By adding an extra LMI constraint to the system of LMI constraints in the optimization problem, the robust control is addressed as well. Accordingly, the decentralized robust control problem for a multivariable system is reduced to an optimization problem for a system of LMI constraints to be feasible. An example is given to show the effectiveness of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

一类不确定非线性切换系统的鲁棒容错控制

研究一类不确定非线性切换系统的鲁棒容错控制问题,当执行器失效或部分失效时,利用Lyapunov函数法建立切换闭环系统混杂状态反馈容错控制器存在的充分条件;然后运用线性矩阵不等式将鲁棒容错控制器设计问题转化为一组线性矩阵不等式的可行解问题,从而借助Matlab中线性矩阵不等式工具箱求解;最后通过数值算倒验证了所提出设计方法的有效性.     

Design Of Robust Pid Controllers

In this paper, a new method is proposed to design the robust PID controllers for uncertain linear time‐invariant systems. We describe a simple and programming procedure for designing PID controllers by applying Kharitonov's theorem and LMI method. Such a controller enables the resulting control system to achieve robust stability as well as asymptotic tracking.     

基于LMI的输出反馈鲁棒完整性控制器设计

完整性是容错控制的一个重要研究方向,不确定系统的鲁棒完整性研究具有很强的实际意义.本文基于[0,σ]故障模型和线性矩阵不等式(LMI)方法,提出了参数不确定系统的输出反馈鲁棒完整性控制器存在的充分条件,通过求解两个矩阵不等式获得控制器,使闭环系统在传感器发生故障时仍然保持二次稳定,并对参数不确定性具有鲁棒性.数值示例说明了该方法的有效性.     

一类离散车组偏差系统的分散鲁棒控制

研究一类具有结构不确定性的离散车组偏差系统的分散鲁棒控制问题。应用大系统包含原理的约束条件扩展系统的信息重叠结构;兼顾系统的结构不确定性、数据传输时延及丢包,将扩展后的模型离散化;采用求解线性矩阵不等式（LMIs）的方法设计出系统存在外界干扰情况下的[H∞]次优状态反馈分散鲁棒控制器。数例仿真检验了结果的有效性。     

Overlapping decentralized approach to automation generation control of multi-area power systems

An overlapping decentralized control scheme is presented and applied to automatic generation control (AGC) for multi-area power systems. Based on the inclusion principle, the system is first decomposed in the expanded space as a group of pair-wise subsystems (areas). Then, the decentralized controllers designed, by standard linear quadratic (LQ) control laws are implemented in each pair-wise subsystem. Finally, the overlapping decentralized controller is obtained by coordinating and contracting the pair-wise decentralized controllers from the expanded space to the original space, preserving the inclusion conditions. When applied to AGC of a four-area power system, the proposed methodology not only guarantees AGC qualities, but also increases the system reliability with respect to a wide variety of structured perturbations. Simulation results illustrate the effectiveness of the presented approach both in the general case of information structure constraints and in the cases when some pairs of subsystems are disconnected by unpredicted faults.     

Robust control of polytopic systems by convex optimization

Robust control synthesis of linear time-invariant SISO polytopic systems is investigated using the polynomial approach. A convex set of all stabilizing controllers for a polytopic system is given over an infinite-dimensional space. A finite-dimensional approximation of this set is obtained using the orthonormal basis functions and represented by a set of LMIs thanks to the KYP lemma. Then, an LMI based convex optimization problem for robust pole placement with sensitivity function shaping in two- and infinity-norm is proposed. The simulation results show the effectiveness of the proposed method.     

Robust non-fragile guaranteed cost control of uncertain large-scale systems with time-delays in subsystem interconnections

In this paper, the robust non-fragile guaranteed cost-control problem is studied for a class of uncertain linear large-scale systems with time-delays in subsystem interconnections and given quadratic cost functions. The uncertainty in the system is assumed to be norm-bounded and time-varying. Also, the state-feedback gains for subsystems of the large-scale system are assumed to have norm-bounded controller gain variations. The problem is to design a state feedback control law such that the closed-loop system is asymptotically stable, and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. Sufficient conditions for the existence of such controllers are derived based on the linear matrix inequality (LMI) approach combined with the Lyapunov method. A parameterized characterization of the robust non-fragile guaranteed cost controllers is given in terms of the feasible solutions to a certain LMI. A numerical example is given to illustrate the proposed method.