Pole shifting for families of systems: The dimension one case

We prove that ifR is a one-dimensional ring, then each basic submodule of a freeR-moduleE contains a rank one projective summand ofE. As it is known that this property implies the pole assignability property for rings, it follows that any one-dimensional ring has the pole assignability property. Applications to systems over rings are briefly explained. The authors were partially supported by NSF grants.     

Pole assignment for systems over rings

A very simple proof of the pole assignment theorem for systems over a principal ideal domain (and other rings) is given. Furthermore, an algorithm is presented. Extensions are also indicated.     

Pole assignment by output feedback: A solution for 2 × 2 plants

The problem of pole assignment by static output feedback is solved in this paper for 2 × 2 plants. It is shown that the problem solvability is equivalent to the solvability of some quadratic equation and the latter can be checked through the affine transformation of quadratic functions. All solutions are given in a parametric form if a solution exists. An example is provided to illustrate the method.     

一种多变量隐式极点配置自校正控制器及其应用A

本文提出了一种极点配置自校正控制器.该控制器不仅能控制开环不稳定或非最小相位 系统,而且能控制具有任意、未知或变化传输延时结构的多变量系统.该控制器采用隐式方式 来实现即利用输入输出数据直接辨识控制器的参数.这样不仅避免在线解矩阵方程,而且增 加算法的鲁棒性.仿真和实时控制多变量电加热系统的结果表明该控制器具有好的控制性能.     

全局收敛的鲁棒极点配置自校正控制算法

提出了一种可消除确定性扰动影响的鲁棒极点配置自适应控制器的设计方法.这种方法可以直接获得控制器参数,无需求解Diophantine方程,也不需要辨识多余的辅助参数和进行参数分离,而且根据内模原理可以消除未知确定性扰动的影响,实现对参考输入的稳态无误差跟踪.给出了所提算法的全局收敛性证明,并通过仿真实验验证了算法的有效性.     

A continuation approach to eigenvalue assignment

This paper describes a continuation approach to eigenvalue assignment. The method is a homotopy technique which embeds the control problem into a parameterized family of control problems. This parameterization describes a continuous deformation of a system with the desired spectrum into the original system. Based on this deformation, a differential equation is constructed whose solution trajectory has an end-point which is a constant output feedback matrix assigning the desired spectrum to the original system. The derivation of this differential equation and conditions which guarantee the existence of a solution are given. Also, two examples of its numerical implementation are detailed.     

Pole assignment for multi-input multi-output systems using output feedback

In this paper the problem of pole assignment using constant gain output feedback is studied for MIMO system with system order n > m + l − 1, where m and l are the number of inputs and outputs, respectively. A new procedure is presented to design a constant gain output feedback matrix which assigns (m + l − 2) poles exactly to the desired locations and shifts all the unassigned poles to suitable locations using root locus techniques.     

An algorithm for inverting rational matrices

We propose an algorithm for computing the inverses of rational matrices and in particular the inverses of polynomial matrices. The algorithm is based on minimal state space realizations of proper rational matrices and the matrix inverse lemma and is implemented as a MATLAB¹ function. Experiments show that the algorithm gives accurate results for typical rational matrices that arise in analysis and design of linear multivariable control systems. Illustrative examples are given.     

一种鲁棒自适应极点配置预估控制器

本文提出一种鲁棒自适应极点配置预估控制新方法。它有效地克服了因对象模型与史密斯预估模型不同而引起的系统不稳定现象。     

基于极点配置的网络流量控制研究

应用极点配置方法,讨论了根据网络的现实状态将极点配置在不同区域,使链路具有较高的利用率且解决网络拥塞的问题.由于利用前面时刻的信息,提前通知源端网络的使用情况,从而避免了时延对其性能的破坏性影响.此算法不仅保证了网络缓冲器的不溢出及带宽的公平分配和充分利用,而且使信源速率能快速、动态地响应网络状态的变化.仿真结果验证了极点配置算法能使网络具有良好的动态性能.     

配置极点的约束方差设计

在随机控制问题中,性能指标常常表现为系统的状态方差或其上界的形式.本文研究了使闭环系统满足给定的状态方差约束、且具有预期闭环极点的线性反馈控制器的存在条件,给出具体的设计方法,并举例说明该设计方法具有简单、直接的特点.     

一类不确定离散系统的严格正实分析和设计

考虑了一类不确定离散多变量系统严格正实分析和控制问题,其中不确定参数具有非负性.分析了系统鲁棒稳定且严格正实的条件,讨论了状态反馈、输出反馈使闭环系统鲁棒稳定且严格正实的问题.将不确定系统的鲁棒严格正实分析和设计转化为确定系统的严格正实分析和控制,得到了系统鲁棒稳定且严格正实的充分必要条件.最后给出了鲁棒严格正实控制问题的可解条件及控制器的综合方法.     

实现输出反馈极点配置的数值方法

本文讨论了用数值方法实现输出反馈极点配置的问题.求解反馈阵的矩阵方程被等效成非线性向量方程,用牛顿迭代法可求得反馈阵.本文推导了牛顿迭代法所需的导数公式,并给出有关算例.还可将非线性向量方程化作性能指标,用寻优的方法求得所需的输出反馈阵.     

超空泡航行器极点配置变结构控制方法研究

超空泡航行器在航行过程中，尾部会周期性拍打空泡壁而表现出强烈的“尾拍”现象，尾部空泡是由空化器经历的历史位置形成，呈现强烈的时滞特性，动力学建模和稳定控制是制约其发展的核心难题。针对泡体耦合问题，建立了空泡/刚体相对几何关系一体化实时解算的动力学模型。针对后体非线性特性，采用分段线性化方法，在保留后体尾拍非线性特性的基础上，建立了面向控制的简化模型。为了解决超空泡航行器非线性时滞控制问题，针对弹体运动极其敏感、操纵效率高等特点，采用极点配置的方式将控制模型配置到理想状态。针对尾拍过程非线性和不确定极大的特点，建立了面向扰动的变结构控制器，实现超空泡航行器扰动运动控制。采用极点配置变结构控制方法，分别设计了滚转通道和俯仰通道控制律。利用泡体耦合动力学模型进行6DOF控制闭环轨迹仿真，稳定巡航过程中深度控制误差小于0.1m，滚转角控制误差小于4°，表明该控制方法能够对航行器滚转角和深度实现稳定控制，控制效果较好，能够满足超空泡航行器航行要求。     

Generic eigenvalue assignment by memoryless real output feedback

By extensive use of methods from algebraic geometry, X. Wang proved that arbitrary pole placement by static output feedback is generically possible for strictly proper plants with n states, m inputs, and p outputs, if n < mp. Here we show the same result using no more of algebraic geometry than the definition of genericity.     

基于多模型切换的多变量直接自适应极点配置控制器

提出一种基于多模型切换的多变量直接自适应控制器,控制器参数模型集可由系统参数模型集直接得到,不但仍为一紧集并且被其模型子集完全覆盖.该多模型控制器不仅改善了控制系统的暂态响应,而且可以实现极点配置,最后给出了全局收敛性分析.     

A unified method for optimal arbitrary pole placement

We consider the classic problem of pole placement by state feedback. We offer an eigenstructure assignment algorithm to obtain a novel parametric form for the pole-placing feedback matrix that can deliver any set of desired closed-loop eigenvalues, with any desired multiplicities. This parametric formula is then exploited to introduce an unconstrained nonlinear optimisation algorithm to obtain a feedback matrix that delivers the desired pole placement with optimal robustness and minimum gain. Lastly we compare the performance of our method against several others from the recent literature.     

鲁棒性指标分析及其在多变量控制系统极点配置中的应用

本文详细分析了文献[3,4,6]中采用的鲁棒性指标的优缺点,进而提出了一种改进的鲁棒极点配置方法.其收敛性比文[8]的结果好,计算复杂性明显优于文献[4,6,11]的方法.     

多变量极点配置自校正Smith控制器及其应用

本文根据许多工业被控过程具有大纯滞后的特点,将自校正调节器与Smith预估器相结合,给出一种多变量极点配置自校正Smith控制算法.该算法结构简单,不仅能对输出进行预报和无偏跟踪,而且适用于非最小相位系统.该算法已成功地应用于太原钢铁公司轧辊罩式退火炉微机自适应群控系统,实际运行结果表明控温精度和炉内温度场均匀度均在±3℃以内,远比常规PID仪表的控温效果好.