矩阵二阶系统误差反馈调节问题的解

Solvability and complete parametric approach for output regulation problems of matrix second-order systems via error feedback

在二阶系统的框架下,考虑了输出与要调节的向量相一致的矩阵二阶系统的输出调节问题,得出了矩阵二阶系统误差反馈调节问题的可解性等价于调节方程MΠS2+DΠS+KΠ=BΓ+P和RΠS+CΠ+Q=0的可解性.通过对调节方程适当的变换,利用求解线性方程组的方法给出了反馈增益矩阵的完全参数化表达,给求解多目标设计问题带来极大便利.数值例子证明了本文的方法简便有效.

We consider the output regulation problem for matrix second-order systems and identify an important case of the general regulation problem where the measurement output is identical to the vector to be regulated directly in the matrix second frame work. It is given that the solvability of output regulation problem equals to the solvability of regulation equations MΠS^2＋DΠS＋KΠ=BΓ＋P and RΠS＋CΠ＋Q=0. Moreover, complete parametric expressions for feedback gain matrices are established by the method of solving linear equations. A numerical example demonstrates the effect of the proposed method.