区域极点约束下不确定系统鲁棒非脆弱H_∞控制  

Robust and non-fragile H-infinity control for uncertain systems with regional pole constraints

作　　者：王宏强[1] 王道波[1] 段海滨[2] 马国梁[1] 

机构地区：[1]南京航空航天大学自动化学院,南京210016 [2]北京航空航天大学自动化科学与电气工程学院,北京100083

出　　处：《南京大学学报（自然科学版）》2009年第4期499-507,共9页Journal of Nanjing University（Natural Science）

基　　金：国家自然科学基金(60604009);航空科学基金(2006ZC51039);中国博士后科学基金

摘　　要：多目标控制是控制系统工程领域近年来的研究热点问题,用于解决在若干个相互矛盾的目标存在的情况下如何得到一个能够满足多方面要求的解决方案.考虑到对闭环系统的鲁棒性、非脆弱性、干扰抑制性能以及动态响应特性等多方面控制目标要求,针对一类含有范数有界参数不确定性的线性系统,研究了其在干扰抑制指标约束以及闭环极点区域共同约束下的鲁棒非脆弱H∞控制问题.以有限能量扰动输入信号到性能评价输出信号之间的L2增益来衡量系统的抗干扰性能,以极点区域约束来改善闭环系统的动态响应特性,控制目标要求在对象和控制器同时存在参数不确定性的情况下,所设计的控制器能够使不确定性系统鲁棒稳定,闭环系统干扰抑制性能指标小于给定上界,并且闭环极点配置于复平面上指定的圆盘区域内.针对控制器增益具有加法式摄动和乘法式摄动的情况,分别以一个线性矩阵不等式(LMI)形式给出了满足设计要求的非脆弱鲁棒H∞控制器的可解性条件.通过数值算例进行控制器设计并对结果进行了深入讨论,分析结果表明了所提方法的有效性.6 The problem of control design for uncertain systems with multiple control objectives is a hotspot in the field of control system engineering,which is referred to as multi-objective control.Multi-objective control focuses on the design of controllers that can meet diverse control criteria in order to make closed-loop system behave in the desired manner.Taking into account multiple control objectives for closed-loop system,such as robustness,non-fragililty,diturbance attenuation performance and dynamical response characteristics,the problem of robust and non-fragile H-infinity state feedback control with regional pole constraint in a disk is investigated,for a class of uncertain systems with norm bounded parametric uncertainties.Disturbance attenuation performance is evaluated by L2 gain from energy-bounded disturbance input to regulated output signal.Dynamical response characteristics is improved by placing closed-loop poles in a prescribed disk region in the complex plane.The resulting design is such that the closed-loop system is robustly stable and has an H-infinity disturbance attenuation upper bound.At the same time the closed-loop poles are assigned in a specific disk region in the complex plane,with respect to system uncertainty and controller gain perturbations.Two classes of controller perturbations are considered,i.e.,additive and multiplicative.Solvability condition for the existence of robust and non-fragile H-infinity controller is derived in the form of linear matrix inequality（LMI）.An illustrative numerical example is utilized to demonstrate the design procedure and the design results are discussed comprehensively.Analytical results show the validity of the proposed design method.

关 键 词：鲁棒控制 非脆弱控制 干扰抑制 区域极点配置 线性矩阵不等式 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]