利用稳定零点构造降阶H_∞控制器的方法

Constructing a reduced-order H-infinity controller using stable invariant zeros

现有的针对奇异情形的H∞降阶控制器的基于线性矩阵不等式(LMI)的构造算法仅利用了系统不稳定的不变零点,而没有利用系统的稳定零点.本论文试图通过对系统矩阵A引入不确定性来利用这些稳定零点,即将奇异系统矩阵A变为A0+αI(α<0),以A0代替A和系统的其它部分构成新系统,从而使得原来系统的稳定零点成为新系统的不稳定零点,进而使用降阶控制器算法得到低阶控制器.一个简单的算例表明了该方法的有效性.

Unstable invariant zeros have been used in constructing reduced order controllers based on linear matrix inequalities for H-infinity control problem of singular case while stable invariant zeros have not been used. These zeros have been used by adding uncertainty to the system matrix A in this paper. The system matrix A of the original system is changed to A0 ＋ αI（a 〈 0）. A new system that is made up of A0 and other system matrixes of the original system is constructed, then stable zeros of the original system become unstable in the new system and the algorithm for constructing the reduced order controllers can be used to obtain a reduced order controller. The effectiveness of this method is shown by a simple example.