二阶线性系统高阶PI观测器的参数化设计

Parameterization of high order PI observers for second-order linear systems

考虑了二阶线性系统的高阶比例积分观测器设计问题。基于一类广义Sylvester矩阵方程的解,提出了二阶线性系统的高阶比例积分观测器设计参数化方法。该方法给出了该类观测器的增益矩阵和左特征向量矩阵的参数化表达式,其所含参数除了满足两个约束条件之外是完全自由的。这些参数为控制系统设计提供了全部自由度,可通过优化等手段适当选择这些参数来满足某些性能要求,如干扰解耦、LTR和鲁棒性等。此外,该观测器设计的参数化直接基于二阶线性系统的参数矩阵,不涉及二阶线性系统的变换或增广,表明了所提方法的简单有效性。

The design of high-order proportional plus integral (PI) observers in second-order linear systems is investigated. Based on the solutions to a so-called generalized Sylvester equation, a parametric method to solve this design problem is proposed. This method presents the parametric expressions for the gain matrices and the left eigenvector matrix of the high-order PI observers. These parameters included in this method offer all the design degrees of freedom, which can be further utilized to satisfy certain specified performances, such as disturbance decoupling, LTR and robustness. In addition, this method utilizes directly the original system data and involves manipulations only on n-dimensional matrices. An illustrative example shows the effect and simpleness of the proposed method.