偏微分控制系统的补偿设计与控制

项目名称： 偏微分控制系统的补偿设计与控制

项目编号： No.61273130

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 自动化技术、计算机技术

项目作者： 王军民

作者单位： 北京理工大学

项目金额： 79万元

中文摘要： 偏微分系统的补偿控制设计是分布参数系统控制新的研究热点和难点。在过去的三十年间，偏微分系统主要采用PID形式的反馈控制策略，研究表明PID的控制设计方案对保守系统的反馈设计是有效的，但当偏微分系统在右半平面有点谱时，系统能量不保守、非耗散，经典的PID控制设计不再适用，系统的控制设计变得非常困难。在本项目中，将采用Backstepping方法具体针对在右半平面有点谱的三类非稳定的偏微分控制系统设计补偿反馈控制策略，并进行严格的理论分析与证明：（i）控制输入带有时间延迟的非稳定波动系统的补偿控制设计；（ii）带有非稳定边界波动系统的补偿控制与设计；（iii）将热系统作为外部补偿输入源的非稳定反应扩散方程的补偿设计与控制。另外，在三类非稳定偏微分控制系统研究的基础上，拟研究更为一般的、复杂的、基于各类补偿控制输入源的非稳定系统的补偿设计与控制。

中文关键词： 偏微分控制系统；稳定性；补偿设计；Gevrey 正则性；耦合

英文摘要： Compensation design and control for the systems decrriging by partial differential equations (PDE) is a newly and hard research topics in distributed parameter control systems (DPCS). In past three decades, the PID control feedback strategy is the main control design for the PDE systems and it is found that PID method is effective for the conservative PDE systems. However, when there is some point spectrum of the system located in right half complex plane, the energy of the system is not conservative and dissipative yet. Under the situation, the classical PID control design does not apply to the unstable PDE systems and it is very hard to design the feedback controls to stabilize such PDE systems. In this project, the Backstepping approach is adopted investigation and three classes of unstable PDE control systems, which have the point spectrum located in right half complex plane, will be mainly considered to be compensated and to be stabilized for the control designs. The seriously theoretical analysis and stability proofs will be presented. Three PDE systems are: (i) Compensation and control design for unstable wave system with time delay; (ii) Compensation and control design for the wave equation with unstable boundaries; and (iii) Control design for an unstable reaction diffusion PDE compensated with a heat

英文关键词： Partial differential control systems；Stability；Compensation design；Gevrey regularity；Couple