鲁棒比例与部分状态导数反馈控制系统设计

基于广义线性系统比例与部分状态导数反馈参数化特征结构配置结果和矩阵对广义特征值灵敏度结果, 得到了关于开环系统矩阵中摄动元素的闭环特征值灵敏度的参数表达式, 并在此基础上提出了广义线性系统比例与部分状态导数反馈最小灵敏度特征值配置的有效算法. 该算法不含有"返回"过程, 允许闭环特征值在希望的区域内方便地参与优化. 一个算例说明了算法的简单性和有效性.     

A gradient flow approach to on-line robust pole assignment for synthesizing output feedback control systems

Pole assignment is a basic design method for synthesis of feedback control systems. In this paper, a gradient flow approach is presented for robust pole assignment in synthesizing output feedback control systems. The proposed approach is shown to be capable of synthesizing linear output feedback control systems via on-line robust pole assignment. Convergence of the gradient flow can be guaranteed. Moreover, with appropriate design parameters the gradient flow converges exponentially to an optimal solution to the robust pole assignment problem and the closed-loop control system based on the gradient flow is globally exponentially stable. These desired properties make it possible to apply the proposed approach to slowly time-varying linear control systems. Simulation results are shown to demonstrate the effectiveness and advantages 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.     

基于特征结构配置的二阶线性系统鲁棒容错控制设计

研究基于特征结构配置的二阶线性系统鲁棒容错控制设计问题,目的是重新设计状态反馈控制律,使得故障闭环系统和正常闭环系统具有相同的特征值.两闭环系统的特征向量依最小二乘法接近,而且能通过极小化灵敏度指标提高系统的鲁棒性.基于状态反馈特征结构配置的参数化结果,将系统灵敏度指标优化问题转化为含有约束条件的优化问题,并提出了鲁棒容错控制设计方法.数值算例及其仿真结果验证了所提出设计方法的有效性.     

矩阵二阶系统的鲁棒极点配置

直接在矩阵二阶框架下,利用特征结构配置参数化方法,研究矩阵二阶线性系统的鲁棒极点配置问题.将两种测量闭环特征值灵敏度方法有机地结合起来,给出一个新的优化性能指标,此指标的优化过程完全依赖于特征结构配置中的设计自由度.为进一步提高闭环系统的鲁棒稳定性,闭环极点也作为设计自由度的一部分参与优化.数值例子分析结果表明了该方法的有效性.     

Parametric state feedback design of linear distributed-parameter systems

The parametric approach for the design of state feedback controllers has been formulated so far only for linear lumped-parameter systems. It yields an explicit parametric expression for the state feedback gain given the closed-loop eigenvalues and the set of corresponding parameter vectors. This contribution presents a parameterisation of state feedback controllers for linear distributed-parameter systems with scalar state and distributed control. By introducing the closed-loop eigenvalues and the parameter vectors as design parameters, an explicit expression for the state feedback is obtained. In contrast to the pure eigenvalue assignment, the parameterisation allows the assignment not only of the closed-loop eigenvalues but also of the closed-loop eigenfunctions. The usefulness of the proposed parametric approach is demonstrated by decoupling the transfer behaviour of a MIMO diffusion system with respect to its dominant modes.     

A note on robust pole assignment for periodic systems

In this note a robust pole assignment algorithm is proposed for linear periodic discrete-time systems with time-varying dimensions of the state and/or input spaces. The algorithm deduces a periodic state feedback law by the minimization of the condition numbers of the eigenvector matrices of the closed-loop system. Numerical examples are provided to show the performances of the algorithm     

A robust periodic pole assignment algorithm

In this note a robust periodic pole assignment algorithm is proposed for linear, time-invariant, discrete-time systems. The condition numbers of the eigenvector matrices of the closed-loop system are assumed as a robustness measure and a periodic state-feedback law is deduced by the minimization of the condition numbers associated to the eigenvectors of the monodromy matrix of the closed-loop system. The proposed periodic pole assignment algorithm has been tested on a number of examples, giving satisfactory results