降阶正实控制器设计

基于线性矩阵不等式 (LMI)方法, 考虑了连续和离散对象的降阶正实控制器设计问题. 通过一阶对象的分析表明, 广义对象阶是最小阶正实控制器阶的可达上界, 因此降阶正实控制器的存在性依赖于具体对象参数. 给出了一个新的降阶正实控制器阶的上界, 该上界蕴涵了已有结果. 上界的估计是构造性的, 可以给出这种降阶正实控制器的设计算法. 文中给出了简单的算例, 说明本文方法的可行性.     

降阶正实控制器设计

基于线性矩阵不等式(LMI)方法,考虑了连续和离散对象的降阶正实控制器设计问题.通过一阶对象的分析表明,广义对象阶是最小阶正实控制器阶的可达上界,因此降阶正实控制器的存在性依赖于具体对象参数.给出了一个新的降阶正实控制器阶的上界,该上界蕴涵了已有结果.上界的估计是构造性的,可以给出这种降阶正实控制器的设计算法.文中给出了简单的算例,说明本文方法的可行性.     

离散对象的降阶H∞控制器设计

基于LMI方法,考虑了离散对象的阶数不超过广义对象阶的降阶H∞控制器存在性问题.通过3LMIs可解性条件的等价变换,给出了一个降阶控制器的上界.该上界可适用于奇异和非奇异对象两种情形,且在奇异情形不为已有结果蕴涵.证明是构造性的,当降阶控制器存在时,可以设计出这种控制器.最后给出了两个简单的算例,说明文中方法的可行性.     

离散对象的降阶H∞控制器设计

基于LMI方法, 考虑了离散对象的阶数不超过广义对象阶的降阶H_∞ 控制器存在性问题. 通过3LMIS可解性条件的等价变换, 给出了一个降阶控制器的上界. 该上界可适用于奇异和非奇异对象两种情形, 且在奇异情形不为已有结果蕴涵. 证明是构造性的, 当降阶控制器存在时, 可以设计出这种控制器. 最后给出了两个简单的算例, 说明文中方法的可行性.     

反馈控制器降阶的约束与聚集方法

根据线性随机系统的包含原理,研究系统状态反馈和输出反馈控制器的降阶问题,给出了系统控制器降阶的约束和聚集两类条件。以一个18阶系统降阶反馈控制器的设计为例,说明该方法既简化了控制器的结构,又不失全阶控制器的主要性能。     

基于线性矩阵不等式的奇异Ｈ∞控制问题的降阶控制器*

本文基于线性矩阵不等式方法研究了广义对象既具有无穷远零点又具有有限虚轴零点的奇异Ｈ∞问题的降阶控制器设计问题，对于所述广义对象，本文指出：若Ｈ∞控制问题可解，则它必存在降阶控制器。并给出了可行的降阶控制器设计方法。     

基于观测器的广义线性系统降阶H∞控制器设计

本文研究基于Luenberger观洲器的广义系统降阶H∞控制器的设计问题,并且该观测器是关于干扰解耦的。首先是提出了广义系统H∞状态反馈控制问题的一个充要条件,并利用线性矩阵不等式方法求解出广义系统的H∞状态反馈增益。然后对该H∞状态反馈增益进行渐进降阶观测,基于广义Sylvester矩阵方程的显式通解的参数化设计方法,实现了广义系统的降阶H∞控制。本文最主要的工作是给出了相应的广义线性系统降阶H∞控制器的设计算法。在文章的最后给出了一个例子,用来说明降阶算法的有效性。     

降阶的鲁棒分散自适应反推控制

针对一类含有未建模动态的关联系统,考虑了降阶的鲁棒分散自适应反推控制问题.首先通过一系列坐标变换,将原系统重新参数化,然后引入降阶观测器,得到一个误差系统.基于该系统,给出了一种降阶自适应反推控制器的设计方案.证明了自适应控制系统的所有信号全局一致有界,调节误差渐近收敛到零.控制器阶次的降低使得本文的设计方案更具应用价值.     

不确定广义系统的最优保性能控制

该文讨论不确定广义系统的最优保性能控制问题.给出了不确定广义系统保性能控 制器的两种设计方法:一是代数Riccati方程方法,给出了参数化的控制器;另一个是线性矩阵 不等式方法,给出了在使性能函数上界最小的意义下,最优控制器的设计算法,用实例演示了 该方法的有效性.     

线性不确定系统的给定阶最优控制器设计

为避免间接法设计降阶控制器的模型近似引起的性能下降,本文在静态输出反馈控制器设计的基础上,直接设计了线性不确定系统的给定阶混合H2/H∞动态反馈控制器.利用系统内外分解方法,得到了最优降阶状态观测器.通过求解降维状态观测器的静态输出反馈,可得到降阶控制的最优反馈增益阵.给定阶控制器由两个Ric cati方程和一个Lyapunov方程参数化表示.最后,通过一个例子,说明了本文提出的给定阶控制器设计方法.     

结构不确定离散系统的最优非脆弱保成本控制

讨论了一类不确定线性离散系统的最优非脆弱保成本控制问题.考虑的系统和状态反馈控制器均具有时变的结构化的不确定性.基于线性矩阵不等式的方法,给出了存在和设计非脆弱保成本控制律的一个充分条件,以及在使二次成本函数上界最小意义下,最优非脆弱保成本控制律的凸优化设计方法.并用数值例子说明该方法降低了成本函数上界的保守性.     

基于LMI的一类混合H2/H∞控制问题的降价控制器设计——连续情形

考虑连续系统的一类混合H2/H∞控制问题,对于含无穷远零点和有限虚轴零点的奇异 广义对象,引入线性矩阵不等式(LMI)方法研究了降价控制器存在判据和设计准则.文中指出,对 于所述对象,若混合H2/H∞控制问题可解,则它必存在降价控制器.存在准则和设计方法分别归 结到LMI的可解性及其凸优法解法.     

Structural analysis of fuzzy controllers with nonlinear input fuzzy sets in relation to nonlinear PID control with variable gains

The popular linear PID controller is mostly effective for linear or nearly linear control problems. Nonlinear PID controllers, however, are needed in order to satisfactorily control (highly) nonlinear plants, time-varying plants, or plants with significant time delay. This paper extends our previous papers in which we show rigorously that some fuzzy controllers are actually nonlinear PI, PD, and PID controllers with variable gains that can outperform their linear counterparts. In the present paper, we study the analytical structure of an important class of two- and three-dimensional fuzzy controllers. We link the entire class, as opposed to one controller at a time, to nonlinear PI, PD, and PID controllers with variable gains by establishing the conditions for the former to structurally become the latter. Unlike the results in the literature, which are exclusively for the fuzzy controllers using linear fuzzy sets for the input variables, this class of fuzzy controllers employs nonlinear input fuzzy sets of arbitrary types. Our structural results are thus more general and contain the existing ones as special cases. Two concrete examples are provided to illustrate the usefulness of the new results.     

Normalized H∞ controller reduction with a priorierror bounds

This paper describes an approach to the reduction of controllers for the normalized coprime factor robustness problem as well as the normalized H_∞ problem. It is shown that a relative error approximation of a coprime factor representation of any suboptimal controller leads to a stability guarantee and an upper bound on the performance degradation when the reduced order controller is implemented. When the approximation is performed on the controller generator, guaranteed a priori stability and performance bounds are obtained in terms of the synthesis Riccati equation solutions of the normalized H_∞ control problems     

Reduced-order controllers for the H∞ control problem with unstable invariant zeros

This paper addresses the existence and design methods of reduced-order controllers for the H_∞ control problem with unstable invariant zeros in the state-space realization of the transfer function matrix from the control input to the controlled error or from the exogenous input to the observation output, where the realization is induced from a stabilizable and detectable realization of the generalized plant. This paper presents a new controller degree bound for the H_∞ control problem in terms of the minimal rank of the system matrix pencils of these two transfer function matrices in the unstable region. When the unstable invariant zero exists, this paper shows that reduced-order controllers with orders strictly less than that of the generalized plant exist if the H_∞ control problem is solvable. Moreover, this paper shows that the computational problem of finding the controllers with the new degree bound is convex by providing two linear matrix inequality-based design methods (algorithms) for constructing the reduced-order controllers. The results developed in this paper are valid both for the continuous- and discrete-time H_∞ control problems.     

不确定离散系统的输出反馈保性能控制

对一类具有范数有界时变参数不确定性的离散时间系统，研究设计一个输出反馈保性能控制器，使得闭环系统对所有允许的不确定性渐近稳定，且闭环性能指标值不超过某个确定的上界。基于线性矩阵不等式处理方法，证明了保性能控制器的存在性等价于一个线性矩阵不等式的可行性，并用该线性矩阵不等式的可解给出了控制器的构造方法和闭环性能指标的上界。     

线性对象的正实控制问题

在时域中考虑线性对象的正实控制(PRC)问题.对于一般的广义对象,在状态空间 中提出了一个基于线性矩阵不等式(LMI)的统一处理PRC问题的方法,指出’PRC问题可解 的充分必要条件是与系统的实现有关的三个LMI可解,并可利用LMI的解构造出所有的正 则PR控制器.此外还提出了降价PR控制器的存在条件并讨论了可行的综合方法.     

Self‐triggered state‐feedback control of linear plants under bounded disturbances

This paper addresses the problem of self‐triggered state‐feedback control for linear plants under bounded disturbances. In a self‐triggered scenario, the controller is allowed to choose when the next sampling time should occur and does so based on the current sampled state and on a priori knowledge about the plant. Besides comparing some existing approaches to self‐triggered control available in the literature, we propose a new self‐triggered control strategy that allows for the consideration of model‐based controllers, a class of controllers that includes as a special case static controllers with a zero‐order hold of the last state measurement. We show that our proposed control strategy renders the solutions of the closed‐loop system globally uniformly ultimately bounded. We further show that there exists a minimum time interval between sampling times and provide a method for computing a lower bound for it. An illustrative example with numerical results is included in order to compare the existing strategies and the proposed one. Copyright © 2014 John Wiley & Sons, Ltd.