串联弦系统的控制器和补偿器的设计及其Riesz基  

Design of controllers and compensators for a serially connected string system and its Riesz basis

作　　者：刘东毅[1,2] 尚英锋[1,2] 许跟起[1] 

机构地区：[1]天津大学理学院数学系,天津300072 [2]天津大学电气与自动化工程学院自动化系,天津300072

出　　处：《控制理论与应用》2008年第5期815-818,共4页Control Theory & Applications

基　　金：国家自然科学基金资助项目(NSFC-60474017);国家自然科学青年基金资助项目(NSFC-60704015).

摘　　要：针对一类串联弦系统,在两端自由,内部连接点处力连续而位移不连续的条件下,论文先在内部连接点处构造补偿器对位移进行补偿,然后在两端设计控制器对系统进行控制.于是得到一个闭环控制系统.利用半群理论证明了这一系统的适定性.通过算子的谱分析,推出了该系统的谱由重数有限的孤立本征值构成并且谱分布在左半复平面,平行于虚轴的一个带域内.因此该系统存在Riesz基,满足谱确定增长条件并且是渐近稳定的.Under free boundary conditions, for a serially connected string system with continuity of vertical force and discontinuity of displacement at the interior nodes, compensators are designed at the interior nodes to compensate the displacement, and controllers are placed on both endpoints to control the system. Thus, a closed loop control system is established. Its well-posedness is then shown via the semigroup theory. From spectrum analysis of operators, it is known that the spectrum of the system is composed of isolated eigenvalues with finite multiplicity, and its spectrum is located in a strip parallel to the imaginary axis in the left half complex plane. Hence, the existence of the Riesz basis is derived and the spectrum-determined growth condition is concluded. The asymptotic stability of the system is thus proved.

关 键 词：闭环控制系统 弦系统 反馈 控制设备 谱分析 RIESZ基 渐近稳定性 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]