A method for deriving a non-singular state-space formulation based on Rubin's model for Pogo analysis

Abstract

A method for deriving a non-singular state-space formulation based on Rubin's model for Pogo analysis is presented in this study. Because of the non-singularity, the state-space model can be directly used in frequency-domain analyses and time-domain simulations. To describe the assembly method concisely, the dynamic equations of the nine types of independent elements are described in a standard manner. The nine types of elements are divided into two classes according to characteristics of the dynamic equations. The mapping relationship between the local and global numbers of elements and nodes is obtained by numbering all of the elements and nodes. By integrating the element stiffness matrixes to obtain the total stiffness matrix used in the finite element method, the coefficient matrixes of the improved Rubin's model are assembled from the coefficient matrixes of all of the elements according to the mapping relationship. Based on the non-singular model, the time-varying simulation with the nonlinear property of the accumulator can be done conveniently by revising the state-space model. The successful application of this method to a Pogo analysis of a certain type of CZ rocket used in China verifies the correctness and efficiency of the method of this study.