分布参数系统源控制系统设计

Distributed Parameter Systems of Source Control

针对一类分布参数系统(Distributed parameter system,DPS),提出了源控制方法.将构成分布参数系统的空间分成若干分,每份为一个节点,在所有的节点中,将能产生量变源头的节点定义为源节点,跟随源节点变化的节点为跟随节点,以此构建分布参数系统模型.对于源节点,根据经验函数结合反馈偏差调节设计控制器,对跟随节点考虑源节点控制的逸散作用控制.利用Lyapunov稳定性理论并结合线性矩阵不等式(Linear matrix inequality,LMI)处理方法,得出了分布式参数系统稳定源控制器存在的充分条件.最后结合所给条件,给出一个数值仿真说明其有效性.

The stability problem of distributed parameter systems(DPSs)is investigated.For this purpose,a source controller is developed for such a system.The space is divided into several parts,and each part is considered a node.The source of the node that produces quantitative changes is defined as the source node.The nodes that follow the change of source nodes are defined as the subsequent nodes.On the basis of these definitions,the distributed parameter system model is constructed.The designed controller for the source nodes is the empirical function combined with the feedback adjustment and that for the subsequent nodes considers the diffusion control action of the source nodes.Numerous sufficient conditions with stable source controller for distributed parameter systems are derived using Lyapunovs stability theory and the method of linear matrix inequality(LMI).A numerical simulation illustrates the effectiveness of the method under given conditions.