混合H_2/H_∞鲁棒控制器设计

Design of mixed H_2/H_∞ controller

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.

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.