H_∞与H_2优化控制系统的比较

COMPARISON OF H_∞ AND H_2 OPTIMAL CONTROL SYSTEMS

分析和研究了Ｈ∞优化控制理论在结构主动控制系统中的应用．根据简单的状态方程求解Ｈ∞优化控制器，即对给定的γ（＞０），计算Ｈ∞优化控制器，使系统闭环传递函数的无穷大模量小于γ．当γ→∞时，Ｈ∞优化控制问题转化为著名的Ｈ２（ＬＱＧ）优化控制问题，Ｈ∞优化控制是对最坏情况下功率的优化控制．而Ｈ２（ＬＱＧ）优化控制是对总能量的优化控制．为了便于比较分析，本文同时给出了Ｈ∞和Ｈ２的优化控制计算方法，井在算例中进行了比较．

The analysis results of H∞ optimal active control of structure are presented inthis paper. Simple state-space formulas are applied for controllers by solvingstandard H. problems in struCture active control: for a given- number γ>0, to findthe controller such that the H∞ norm of closed-loop transfer function is less thany. As γ→ ∞, the problems are just well-known LQG or H2 control problems. H∞optimal control design is used for'worst case', but LoG or H2 for 'average' or'total'. Both H. and H2 optimal control algorithms are presented and theircomparisons are carried out in example in this paper.