混合H2/H∞鲁棒控制器设计

Design of mixed H2/H∞ controller

中文关键词  鲁棒控制  性能指标  不确定性  H₂/H_∞控制

英文关键词  robust control  performance  uncertain  H₂/H_∞ control

中文摘要

      在状态空间描述下,定义了混合H₂/H_∞控制的完整信息、完整控制、干扰顺馈、输出估计这4种典型情况.在二次稳定意义上,讨论了混合H₂/H_∞的性能指标,及这4种典型情况的混合H₂/H_∞线性反馈控制器设计,给出了充分必要条件.在典型情况分析的基础上,研究一般意义上的混合H₂/H_∞反馈控制器设计.H₂和H_∞的干扰输入阵及性能评价函数各不相同时的混合H₂/H_∞反馈控制器,与H₂和H_∞控制器设计相似,归结为解两个Riccati方程.但这两个Riccati方程含有参数,最优解要通过搜索这两个参数得到.结果包含了单纯的H₂和H_∞设计,可看作是H₂,H_∞和混合H₂/H_∞的统一设计方法.最后通过一个简单的例子,说明了控制器设计方法的可行性.

英文摘要

      In state space descriptions, four typical systems of mixed H-two／H-infinity control were defined. They are full information system, full control system, feedforward disturbance system and output estimation system. Their controllers were designed to optimize the performance based on a kind of quadratic stable. Mixed H-two／H-infinity control system was decomposed into an inner matrix and a mixed H-two／H-infinity output estimation system. The output feedback controller was deduced according to this decomposition. Mixed H-two／H-infinity controller delivered here are analog to H-two and H-infinity controller in that they have the same controller structure, the same number of Riccati equations and similar Riccati equations. The given controllers including the H-two and H-infinity cases, can be treated as unified controllers of H-two, H-infinity and mixed H-two／H-infinity control. Finally, a simple example was given to illustrate the proposed methods.