Modeling and robust analysis of a liquid rocket engine

Abstract

Stability and dynamic performance of liquid-propellant rocket engines (LPRE) are two of the fundamental issues in the enginevehicle integration process. This analysis requires the construction of a detailed model, trying to capture the most realistic phenomena involved, which generally include several sources of uncertainties. In this paper, a methodology for robust modeling and stability analysis is presented. Firstly, the linear models of the LPRE components are obtained by modeling the various physical processes, at a nominal regime of operation. Afterwards, the Laplace transform is applied to derive a block diagram representation of the linear LPRE. The stability study and dynamic analysis are carried out taking in account the uncertainties in parameters of the plant. The robust stability is assured via the Generalized Kharitonov's Theorem; and the robust frequency and step responses are obtained with the use of specialized MATLAB toolboxes. The robust performance of the system in the time domain is obtained in terms of the response to step function input, while taking into account the plant uncertainties, also known as robust step response. A practical application is illustrated by analyzing a simple pressurefed LPRE system. Copyright © 2000 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. INTRODUCTION During the engine-vehicle integration phase, the knowledge of the engine dynamics can avoid serious instability problems, caused by the dynamic coupling of the propellant feed system, the rocket engine, and the vehicle structure. The dynamic analysis helps to characterize many aspects of the engine system operation. It requires the construction of a mathematical model to describe approximately the most important phenomena of the actual system. The engine itself contains several sources of intense pressure fluctuations due to turbulent flow in feed lines, fluttering of pump wheel blades, vibrations of control valves, and unsteady motion in the combustion chamber and gas generator. The coupling of these oscillations with the natural frequencies of the system structure represents often a source of instability, sometimes observed with catastrophic consequences. In general, solving the dynamic equations is not a simple task, since the more realistic models are time-variant, non-linear and of high order, and include uncertainties used to represent imprecise physical parameters or unknown operating conditions. Even for linear time-invariant models, this problem can become quite difficult to solve when the parameters deviate from the nominal values in a known rated regime. Traditional numerical methods of analysis are not suited for these uncertain models since they require a great amount of computational effort. Besides, the direct approach of solving the coupled differential