高阶系统方法——I全驱系统与参数化设计  

High-order System Approaches:I.Fully-actuated Systems and Parametric Designs

作　　者：段广仁[1] DUAN Guang-Ren(Center for Control Theory and Guidance Technology,Harbin Institute of Technology,Harbin 150001)

机构地区：[1]哈尔滨工业大学控制理论与制导技术研究中心,哈尔滨150001

出　　处：《自动化学报》2020年第7期1333-1345,共13页Acta Automatica Sinica

基　　金：国家自然科学基金重大项目(61690210,61690212);国家自然科学基金(61333003);机器人与系统国家重点实验室自主计划任务(HIT)(SKLRS201716A)资助。

摘　　要：本文首先指出了控制领域中普遍使用的增广一阶系统方法的弊端,介绍了高阶全驱系统的概念及其在控制器设计方面的优势,并通过一些基础物理定律、串联系统、严反馈系统和可反馈线性化系统等例子说明了高阶全驱系统的普遍性,进而指出高阶全驱系统是动态系统的一种描述形式,是面向控制的模型.然后介绍了一类高阶全驱系统的一种参数化设计方法.通过适当选取一类非线性状态反馈控制律,可获得一个具有希望特征结构的线性定常闭环系统,并给出了闭环系统特征向量和反馈控制律的完全参数化表示,讨论了解的存在性条件以及设计参数集合的稠密性等相关问题.最后对高阶全驱系统方法的后续问题做了说明和展望.In this paper, the drawback of the first-order system approaches which are widely used in the field of control systems is firstly pointed out, meanwhile the concept of high-order fully-actuated systems and, in particular, its advantage in controller design are introduced. The type of systems is demonstrated to be of wide existence by examining a number of basic physical laws and a few examples, including the common cascaded systems, the well-known strict-feedback systems,and those which can be linearized through feedback, and thus can be taken as a description of dynamical systems,more precisely, as a model for control. Then, a parametric design approach for the type of high-order fully-actuated systems is presented. With a proper nonlinear state feedback controller, a linear constant closed-loop system with desired eigenstructure can be derived, and complete parametric presentations for the closed-loop eigenvectors and the feedback law are given. Conditions of existence of solutions as well as the density of the set of design parameters are discussed.Finally, some further comments are made about future problems existing in the field of high-order fully-actuated systems.

关 键 词：高阶系统 全驱系统 参数化方法 特征结构 设计自由度 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]