Derivation and Analysis of a State-Space Model for Transient Control of Liquid-Propellant Rocket Engines

A dynamic model of a liquid-propellant rocket engine has been developed in this paper, with the future purpose of meeting the more demanding requirements of rocket-engines control forced by the new reusability scenarios. This transientrepresentative modelling approach has been carried out in two phases: initially the purely thermodynamic modelling and subsequently its adaptation to the control framework. The former was tackled by building first a representative simulator of the well-known Vulcain engine. The differential equations considered come from mass, momentum and energy conservation equations and from turbo-pump dynamics. In general, macroscopic behavior at component and system levels is considered. Once this simulator started to provide satisfactory results, it was translated into a state-space model for control by symbolically joining all components' equations, which led to a set of differential equations capturing system's global behaviour. Its states consist in mass flows, pressures, temperatures and shaft rotational speeds. The available actuators are five continuously-controllable valves, one binary igniter and one binary starter. That combination of continuous and discrete features forces the definition of a hybrid system in the control sense. The analysis of its dynamic characteristics points to a good controllability of thrust via the gas-generator injection valves, and of mixture ratio via the turbines' flow-distribution valve.