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.

Keywords

Improved Rubin's model non-singular assembly method nonlinear simulation Pogo

Get full access to this article

View all access options for this article.

References

Rubin

. Longitudinal instability of liquid rockets due to propulsion feedback. J Spacecr Rockets 1966; 3: 1188–1195.

Rose RG. Dynamic analysis of longitudinal instability in liquid rockets. In: 4th aerospace science meeting, Los Angeles, California, 27–29 June 1966, paper no. 66-472, pp.1–24. New York: AIAA.

Ryan

Papadopoulos

Kiefling

et al.

A study of Saturn As-502 coupling longitudinal structural vibration and lateral bending response during boost. J Spacecr Rockets 1970; 7: 113–118.

Coppolino RN, Lock MH and Rubin S. Space shuttle pogo studies (systems stability). Report, NASA, NASA-CR-151596, US, October 1977.

Ordonneau G. A new numerical method for pogo analysis. In: 30th joint propulsion conference and exhibit, Indianapolis, Indiana, 27–29 June 1994, paper no. AIAA-94-2884, pp.1–10. New York: AIAA.

Oppenheim

Rubin

. Advanced Pogo stability analysis for liquid rockets. J Spacecr Rockets 1993; 30: 360–373.

Rubin S. An interpretation of transfer function data for a cavitating pump. In: The 40th AIAA/ASME/SAE/ASEE joint propulsion conference, Fort Lauderdale, Florida, 11–14 July 2004, paper no. AIAA 2004-4025, pp.1–13. New York: AIAA.

Rong

Zhang

et al.

Research on POGO problem for CZ-2F rocket. Manned Spacefl 2011; 4: 8–18.

Dordain

Lourme

Estoueig

. Study on POGO effect on launchers Europa-2 and diamond-B. Acta Astrona 1974; 1: 1357–1384.

10.

Wagner RG and Rubin S. Detection of titan POGO characteristics by analysis of random data. In: ASME symposium on stochastic processes in dynamical problems, Los Angeles, 1969.

11.

Larsen EC. NASA experience with Pogo in human spaceflight vehicles. In: The NATO RTO symposium ATV-152 on limit-cycle oscillations and other amplitude-limited, self-excited vibrations, Norway, May 2008, pp.1–23.

12.

Zhao

Ren

et al.

Parameter study on Pogo stability of liquid rockets. J Spacecr Rockets 2011; 48: 537–541.

13.

Hao

Tang

. New Pogo analysis method using rational fitting and three-dimensional tank modeling. AIAA J 2015; 53: 405–412.

14.

Peng

Zhao

et al.

Optimal periodic controller for formation flying on libration point orbits. Acta Astron 2011; 67: 537–550.

15.

Peng

Gao

et al.

Optimal guidance based on receding horizon control for low-thrust transfer to libration point orbits. Adv Space Res 2013; 51: 2093–2111.

16.

Dotson

Rubin

Sako

. Mission-specific Pogo stability analysis with correlated pump parameters. J Propul Power 2005; 21: 619–626.

17.

Wang

Tan

et al.

Improved modeling method of Pogo analysis and simulation for liquid rockets. Acta Astron 2015; 107: 262–273.

18.

Ren

Rong

et al.

A nonlinear model on the simulation of Pogo vibrations in liquid rocket. Struct Environ Eng 2006; 3: 1–6.