Mixture Ratio and Thrust Control of a Liquid-Propellant Rocket Engine Aerospace Engineering

104 Pages·2016·3.02 MB·English

by  Andre C. Marta

Mixture Ratio and Thrust Control of a Liquid-Propellant
Rocket Engine
Henrique Coxinho TomØ Raposo
Thesis to obtain the Master of Science Degree in
Aerospace Engineering
Supervisor: Eng. Elisa Cliquet Moreno
Dr. Ant(cid:243)nio Manuel dos Santos Pascoal
Examination Committee
Chairperson: Dr. Joªo Manuel Lage de Miranda Lemos
Supervisor: Dr. Ant(cid:243)nio Manuel dos Santos Pascoal
Member of the Committee: Dr. Lu(cid:237)s Manuel Braga da Costa Campos
November 2016
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Resumo
Atualmente a maioria dos motores de foguet˜oes europeus funcionam em anel aberto. Para obter
uma determinada for¸ca propulsiva e r´acio de consumo de combust´ıveis ´e necess´ario ajustar a sec¸c˜ao das
v´alvulas que controlam o caudal dos combust´ıveis antes de cada voo. Na pr´atica, este procedimento
limita o desempenho porque existem um conjunto de perturbac¸˜oes externas que atuam sobre o motor
ao longo do voo, o que se traduz na deriva do ponto de equil´ıbrio. A dispers˜ao e a imprevisibilidade
associada a esta deriva tˆem um impacto negativo sobre a quantidade de combust´ıveis embarcados para
assegurar o sucesso da miss˜ao. O presente trabalho implementa um controlador em anel fechado para
o motor VINCI, tendo por objetivo assegurar a manutenc¸˜ao de um ponto de equil´ıbrio ´otimo nominal
assimcomoatransi¸c˜aoparaumregimea70%daforc¸apropulsivanominal. Primeiramente,obt´em-seum
modelo linear reduzido a cinco estados do ciclo termodinˆamico expander, combinando uma abordagem
anal´ıtica de lineariza¸c˜ao e um m´etodo de identifica¸c˜ao de m´ınimos quadrados. Dois controladores PID
s˜ao ajustados com base nos pares input-output que minimizam os efeitos de acoplagem. Modificac¸˜oes
tais como feed-forward, anti-windup e tratamento das medidas dos sensores s˜ao realizadas de forma a
respeitarasespecifica¸c˜oes. Simulac¸˜oesefetuadasnomodelon˜ao-linearindicamqueumu´nicocontrolador
´esuficientementerobustopararealizaratransic¸˜aoentreregimes. Estetrabalhoconfirmaaaplicabilidade
de um controlador PID modificado a um motor naturalmente est´avel e estabelece a base para o estudo
da dinˆamica dominante de outros ciclos termodinˆamicos.
Palavras-chave:
VINCI, Ciclo termodinˆamico expander, Controlo de for¸ca propulsiva, Con-
trolo de r´acio de mistura, PID
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Abstract
Presently, most European launchers’ engines work in open-loop. Not only does this oblige the valves
which regulate the mass flow-rates to be calibrated before flight in order to obtain a desired thrust and
mixture ratio, but it also limits performance. Varying operating conditions translate into a drifting
equilibrium point. The associated dispersion forces us to carry extra propellants to ensure mission
success. The present work implements a closed-loop controller on the VINCI engine, which aims to
maintain an optimal nominal equilibrium point despite external perturbations, and also to transition to
a 70% thrust regime. To meet these objectives, a reduced linear model of the expander thermodynamic
cycle of the engine is obtained through a combination of an analytic linearization approach and a least-
squaresidentificationmethod. Asensitivitystudyconfirmsthat5statessufficetodescribethedominant
dynamics. Two PID controllers are tuned based on the input-output pairings that minimize coupling
within the 2×2 MIMO system. Modifications such as feed-forward, anti-windup and measurements
filtering are made in order to match the control specifications. Simulations on the non-linear model
indicate a single controller to be both capable of maintaining an operating point and of transitioning
to the low-thrust regime, all while attenuating perturbations. Robustness to parameter uncertainty is
assessed and preliminary results indicate actuator saturation before the controller displays any signs of
instability. This work confirms the applicability of a modified PID controller to a naturally stable engine
and lays the foundation to the study of other thermodynamic cycles.
Keywords:
VINCI,Expanderthermodynamiccycle,Thrustcontrol,Mixture-ratiocontrol,PID
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Contents
Resumo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix
1 Introduction 1
1.1 Historical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Controlled Engines and Reusable Rockets . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.5 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 Liquid-propellant Engines 9
2.1 Propulsion Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Engine Work Principle and Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.1 Liquid Propellants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3 Elements of Control Theory 17
3.1 State-space Model Linearization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2 Model Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2.1 Least-squares Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.3 Reduction Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.3.1 Matched DC Gain Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.4 Controllability and Observability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.4.1 Controllability and Observability Matrices . . . . . . . . . . . . . . . . . . . . . . . 21
3.5 Singular Values and Modulus Margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.6 Robustness Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
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4 VINCI Engine 27
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.2 Thermodynamic Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.3 Mixture Ratio and Thrust Control Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.4 VINCI Governing Equations Linearization . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.4.1 State-space Model Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5 Model Implementation 35
5.1 Analytical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
5.1.1 Complete Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
5.1.2 Reduced Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
5.2 Identified Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.2.1 Complete Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5.2.2 Reduced Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5.2.3 Controllability and Observability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.3 Model Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.4 Model Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.4.1 Turbo-pump Moment of Inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.4.2 Regenerative Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.4.3 Hydrogen Injection Cavity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.4.4 Mode Analysis Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
6 Control Specifications 51
6.1 Transient and Steady-State Time-Response . . . . . . . . . . . . . . . . . . . . . . . . . . 51
6.2 Stability margins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
6.3 Discretization Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
6.4 Sensor’s Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
6.5 Parameter Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
6.6 Domain Variation of the Input Perturbations . . . . . . . . . . . . . . . . . . . . . . . . . 53
6.7 Mechanical and Thermal Bounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
6.8 Failure Events. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
6.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
7 Control Law Design and Implementation 55
7.1 PID Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
7.2 PID Controller Design with the Reduced Linear Model . . . . . . . . . . . . . . . . . . . . 58
7.3 Effect of the Valve’s Dynamic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
7.4 Performance Evaluation on the Complete Linear Model and Measurement Noise Effect . . 60
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7.4.1 Simulink Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
7.4.2 Closed-loop Poles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
7.4.3 Modulus Margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
7.4.4 Frequency Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
7.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
8 Results 67
8.1 Flight Simulation on the CARINS Non-linear Model . . . . . . . . . . . . . . . . . . . . . 67
8.1.1 Energy Consumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
8.2 Robustness to Parameter Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
8.2.1 Complete Linear Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
8.2.2 Non-Linear Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
8.2.3 Failure cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
8.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
9 Conclusion and Future Work 79
9.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
9.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Bibliography 81
A Engine State Admissible Bounds 83
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