,
Global Control of a Life Support System
Flow control and optimisation BENJAMIN THIRON
KTH ROYAL INSTITUTE OF TECHNOLOGY
SCHOOL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE
Abstract
The subject of study of this degree project is the MELiSSA (Micro-Ecological Life Support System Alternative) Life Support System (LSS) developed by the European Space Agency (ESA). The MELiSSA LSS aims to recycle human wastes into O
2, water and food for the crew of a spacecraft. The purpose of this project is to model and study the MELiSSA LSS, in order to design a global control system that ensures the survival of the crew while minimizing the resources needed. The MELiSSA LSS is composed of 4 biochemical reactors, called the compartments, controlled locally. A model of all the possible critical flows exchanged by the compartments is built from a functional point of view. These flows are controlled using the Predictive Functional Control (PFC) method.
This study confirms that the MELiSSA LSS can function properly but requires external resources. In addition, the study shows that by using the right external resources, the MELiSSA LSS can achieve its goal. The objective of the MELiSSA LSS is to produce 100% of the O
2, 90% of the water and about 40% of the food the crew needs to survive. With an additional amount of ammonia (NH
3), nitric acid (HNO
3) and carbon dioxide (CO
2), the LSS reaches a production of 100% of the O
2, more than 100% of the water and between 45 and 50% of the food the crew needs. Moreover, when its operation is optimized, it reduces the mass to carry per astronaut per day to less than 50% of the mass needed without optimization. This is about 12% of the mass needed when there is no recycling system. The model built for this study can also be used as a dimensioning model or an environment and contextualization model for the development and testing of the different compartments.
Sammanfattning
Amnet f¨or det h¨ar examensprojektet ¨ar MELiSSA (Micro-Ecological Life Support System Alternative) Life Support System ¨ (LSS) som utvecklats av Europeiska rymdorganisationen (ESA). MELiSSA LSS ¨amnar att ˚atervinna m¨anskligt avfall till syre (O
2), vatten och mat f¨or en rymdbes¨attning. Examensarbetet syftar att modellera och studera MELiSSA LSS f¨or att utforma ett globalt kontrollsystem som s¨akerst¨aller bes¨attningens ¨overlevnad samtidigt som de n¨odv¨andiga resurserna minimeras. MELiSSA LSS best˚ar av fyra biokemiska reaktorer, kallat “utrymmena”, som kontrolleras lokalt. En modell av all t¨ankbara kritiska fl¨oden som utbyts mellan utrymmena ¨ar byggd utifr˚an ett funtionellt perspektiv. Fl¨odena kontrolleras med Predictive Functional Control (PFC) metoden.
Studien bekr¨aftar att MELiSSA LSS kan fungera korrekt men kr¨aver externa resurser. Dessutom visar studien att MELiSSA LSS kan upfylla sitt m˚al givet r¨att externa resurser. M˚alet med MELiSSA LSSS ¨ar att producera 100% av O
2, mer ¨an 90% av vattnet och 40% av maten som bes¨attningen beh¨over f¨or att ¨overleva. Med en ytterligare m¨angd ammoniak (NH
3), salpetersyra (HNO
3) och koldioxid (CO
2), n˚ar LSS en produktion p˚a 100% av O
2, mer ¨an 100% av vattnet samt mellan 45 och 50% av maten som bes¨attningen beh¨over. Vid optimering reduceras massan som beh¨over b¨aras per astronaut per dag till mindre ¨an 50%
av massan som beh¨ovs utan optimering. Det motsvarar ungef¨ar 12% av massan som beh¨ovs utan ett ˚atervinningssystem. Modellen
som har byggts f¨or denna studie kan ¨aven anv¨andas som dimensioneringsmodell eller som en milj¨o och kontextualiseringsmodell
f¨or utveckling och testning av de olika utrymmena.
A CKNOWLEDGEMENTS
I would like to thank first Christophe Lasseur who introduced me to the MELiSSA project and helped me to get the internship.
I would then like to thank Elling W. Jacobsen, my examiner and coordinator at KTH, who helped me to define a clear and precise framework for my work and guided me throughout this project.
I would especially like to thank Philippe Fiani, my supervisor at SHERPA Engineering, for trusting me and his always pertinent advice and remarks which guided my work. His knowledge of the world of systems engineering was invaluable.
Finally, I would like to thank Olivier Gerbi, Jean-Luc Estival and Baptiste Boyer
from SHERPA Engineering for our conversations which allowed me to enrich both
my work and my personal knowledge.
C ONTENTS
Acronyms 6
Chemical Elements 6
I Introduction 7
II System and Problem Description 8
II-A Life Support System description . . . . 8
II-A1 Compartments . . . . 8
II-A2 LSS efficiency analysis . . . . 10
II-B Requirements . . . . 11
III Methods 13 III-A Model-Based System Engineering . . . . 13
III-A1 Method description . . . . 13
III-A2 Choice motivation . . . . 13
III-B Functional Energy-Based Modelling method . . . . 13
III-B1 Functional Energy-Based Modelling principle . . . . 14
III-B2 Types of components . . . . 14
III-B3 Communication . . . . 14
III-B4 Components internal structure . . . . 15
III-B5 Simulink-based Phi-EMI software . . . . 16
III-B6 Motive . . . . 16
III-C Predictive Functional Control . . . . 17
III-C1 PFC principle . . . . 17
III-C2 PFC equations . . . . 18
III-C3 Choice of the parameters . . . . 20
III-C4 Systems with constraints on the control action . . . . 20
III-C5 Delay system case . . . . 21
III-C6 Non-minimum phase system case . . . . 21
III-C7 Decomposition principle . . . . 21
III-C8 Motive . . . . 22
III-D First study of the MELiSSA loop by UCA . . . . 23
III-D1 Model description . . . . 23
III-D2 Results . . . . 23
III-E First models of the MELiSSA loop by SHERPA Engineering . . . . 23
III-E1 Phi-System model . . . . 24
III-E2 First Phi-EMI model . . . . 24
IV Results 26
IV-A Modelling approach . . . . 26
IV-B LSS and crew model . . . . 26
IV-B1 States . . . . 26
IV-B2 Stoichiometric Model . . . . 27
IV-B3 Dynamic Model . . . . 28
IV-B4 Assumptions . . . . 28
IV-C First static study . . . . 29
IV-C1 Natural production . . . . 29
IV-C2 Boosted production . . . . 30
IV-D Dynamic model . . . . 31
IV-D1 Description . . . . 31
IV-D2 Functional Energy-Based Modelling adaptation . . . . 33
IV-D3 First results . . . . 33
IV-E Model evolution . . . . 33
IV-E1 Cabin air control . . . . 35
IV-E2 CIV air control . . . . 35
IV-E3 O 2 production using NH 3 and CO 2 . . . . 35
IV-E4 Optimization criterion . . . . 37
IV-F Final model and control system results . . . . 37
IV-F1 Scenario 1 . . . . 39
IV-F2 Scenario 2 . . . . 40
IV-F3 Scenario 3 . . . . 41
IV-F4 Scenario 4 . . . . 42
IV-F5 Scenario 5 . . . . 43
IV-F6 Scenario 6 . . . . 44
IV-F7 Scenario 7 . . . . 45
V Discussion 46 V-A Final model results analysis . . . . 46
V-A1 Mass consumption . . . . 46
V-A2 Food supply . . . . 46
V-A3 Water supply . . . . 46
V-A4 Cabin atmosphere . . . . 46
V-A5 CIV atmosphere . . . . 47
V-A6 Coverage . . . . 47
V-A7 Control validation . . . . 48
V-B Modelling method discussion . . . . 48
V-B1 FEBM discussion . . . . 48
V-B2 Model discussion . . . . 48
V-C Possible evolution of the system . . . . 49
VI Conclusion 50
References 51
Appendix 52
A CRONYMS
CHON Carbon-Hydrogen-Oxygen-Nitrogen CI Compartment 1
CII Compartment 2 CIII Compartment 3 CIV Compartment 4 CIVa Compartment 4a CIVb Compartment 4b CV Compartment 5
ESA European Space Agency
FEBM Functional Energy-Based Modelling ISS International Space Station
LSS Life Support System LTI Linear Time-Invariant
MBSE Model-Based System Engineering
MELiSSA Micro-Ecological Life Support System Alternative MIMO Multi-Input Multi-Output
MPC Model Predictive Control MPP MELiSSA Pilot Plant PFC Predictive Functional Control PID Proportional-Integral-Derivative RHP Right Half Plan
SISO Single-Input Single-Output VFA Volatile Fatty Acid
C HEMICAL E LEMENTS T ABLE
C carbon
C 2 H 4 O 2 acetic acid C 3 H 6 O 2 propionic acid C 4 H 8 O 2 butyric acid C 5 H 10 O 2 valeric acid C 6 H 12 O 2 caproic acid CH 4 ON 2 urea
CH 1.273 O 0.71 N 0.393 nucleid acids CH 1.554 O 0.284 N 0.268 proteins
CH 1.627 O 0.364 N 0.199 nitri bacteria (from CIII) CH 1.649 O 0.15 N 0.106 faeces
CH 1.65 O 0.95 fibres
CH 1.667 O 0.833 carbohydrates
CH 1.6 O 0.324 N 0.209 rhodo bacteria (from CII) CH 1.895 O 0.528 N 0.07 food
CH 2 O 0.125 lipids CO 2 carbon dioxide H hydrogen
H 2 dihydrogen
H 2 O water
HNO 2 nitrous acid
HNO 3 nitric acid
N nitrogen
N 2 dinitrogen
NH 3 ammonia
O oxygen
O 2 dioxygen
P phosphorus
S sulfur
I. I NTRODUCTION
The space industry is today in full swing. After national agencies such as NASA or ESA began to conquer space in the 60s and opened the first doors, it is now the turn of private companies such as SpaceX, Blue Origin or RocketLab, or new countries national agencies such as the China National Space Administration, to launch their activities. Many projects are being developed to go further in space exploration. Some focus on the design of super-precise GPS systems or new scientific tools to detect gravitational waves, and others are planning to return to the Moon and further explore other planets such as Mars, Venus or Saturn.
A burning question in the middle of all this activity is the return of Man into space. This is a controversial issue but almost all major players already have manned missions to other celestial bodies on their agenda. NASA is planning on setting up a space station orbiting the Moon, SpaceX is developing its long-duration cargo- and passenger-carrying spacecraft “Starship”
to go to Mars, and ESA is studying the influence of potential long-term stays on Mars on the human body and mind.
These long-term manned space missions away from Earth pose many problems, such as protection against interstellar radiation or the effects of microgravity on the human body. One of them is the resources needed for the survival of a crew.
Missions to Mars as today planned will last between 500 and 1 000 days. An astronaut consumes about 5 kg of supplies per day excluding hygiene items, 22 kg per day including hygiene items. A 6-member crew would therefore require 66 000 kg of resources for a 500-day mission, 132 000 kg of resources for a 1 000-day mission. Knowing that current launchers can only drop 9 000 kg to the Moon and that the cost of sending a payload into space increases exponentially with its mass, it is impossible to send that many resources. Instead of sending all the resources that are going to be consumed, one solution is to recycle part of the local waste into additional resources.
To this end, ESA launched the Micro-Ecological Life Support System Alternative (MELiSSA) project. MELiSSA aims to develop a microbiological and regenerative Life Support System (LSS) for long term space missions. A Life Support System is a system that provides all or part of the elements necessary for the survival of a human or group of humans in a hostile environment. Microbiological and regenerative means that it produces the elements to be supplied using microorganisms. In other words, the MELiSSA project aims to develop a system for recycling the waste of a spacecraft crew into resources. Since the project was launched in 1989, the study of such a system is now well under way and its structure is known. There are still some problems to be solved, although many technological solutions have already been found. Three questions in particular remains unresolved, that of the ability of the system to fulfil its mission, to reject disturbances and to be optimised. This is the subject of this degree project.
The main objective of this master thesis is to design and implement a global control system of the MELiSSA LSS. The study focuses on the overall behaviour of the system, not the precise functioning of individual components. It is carried out at SHERPA Engineering, which is in charge of the development of the whole MELiSSA control. The control system to develop must satisfy two major points:
1) to dynamically control the LSS in order to ensure a viable environment for the crew,
2) to optimize the operation of the system in order to minimize the mass that will necessarily be sent into space.
This second point reflects the fact that the recycling rate of the LSS must be high enough to significantly reduce the mass to be launched into space, and thus the cost of missions, to offset the cost of developing the MELiSSA technology.
A first study of the global LSS operation has been carried out by Laurent Poughon and the Universit´e Clermont-Auvergne (UCA) in France. They built a first static model of the MELiSSA LSS to analyse the mass balance between the resources consumed and produced.[18] Following this first study, SHERPA Engineering, the receiving company, developed a first dynamic model of the whole system. This dynamic model is the basis for the work presented in this report.
This master thesis is part of the Model-Based System Engineering methodology applied to the MELiSSA project. This methodology consists in designing products based on models. [7, 4, 19, 25] A full dynamic model of the LSS is developed using the Functional Energy-Based Modelling method. [6, 15, 16, 17] This method was developed by SHERPA Engineering, the receiving company. A secondary objective of the degree project is to adapt it to matter flows. The global controller of the system is then built following the Predictive Functional Control, which is part of the Model Predictive Control methods. [14, 3, 22, 23]
This report presents the work carried out during this degree project. The MELiSSA Life Support System is first described
as well as the requirements it should meet. The methods used to build the full dynamic model and its global control system
are then presented, followed by the first static and dynamic models from UCA and SHERPA Engineering. The results are
then presented, firstly the model and the modelling approach, followed by the conclusions of a first static study, the dynamic
model presentation and its evolution, and the results of the final global control system. These results are then analysed, and
the modeling method is discussed. Possible future developments of the model are finally presented.
II. S YSTEM AND P ROBLEM D ESCRIPTION
This section aims at presenting the MELiSSA Life Support System, its operation and the context of its study. The LSS is first described, decomposed into its 4 compartments. A rapid qualitative analyse of its effectiveness is carried out and questions to be answered are raised. The requirements it must meet in terms of quantity produced and quality of the environment are then presented.
A. Life Support System description
Figure 1: Description of the MELiSSA ecosystem. (source: https://www.melissafoundation.org/)
The principle of the MELiSSA Life Support System (LSS) is to recycle human wastes (faeces, urea and CO 2 ). Its goal is to create the necessary resources for the survival of a spacecraft crew. It means that it should transform the wastes of this crew into edible nutrients, drinking water and O 2 . To do so, LSS transforms gradually faeces and urea into fertilizer, and uses it with CO 2 and water to grow plants and produce food and oxygen.
1) Compartments
The MELiSSA LSS is composed of 4 main elements (see figure 1). These elements are biochemical reactors, where chemical transformations take place. They are called the “Compartments”. Each compartment has a precise role in the system.
The Compartment 1 (CI) is the compost compartment (see figure 2). It retrieves all the organic wastes (faeces, urine, bacteria, non-edible parts of plants, etc.) and decompose them. During this decomposition, bacteria transform the wastes into ammonia (NH 3 ), carbon dioxide (CO 2 ), dihydrogen (H 2 ), water (H 2 O) and Volatile Fatty Acid (VFA) (organic matter). Part of the organic wastes cannot be recycled. They are considered as the “residual biomass”. This residual biomass, as well as an excess of bacteria produced during decomposition, is lost.
The Compartment 2 (CII) transforms the VFA and H 2 from CI into CO 2 using a small quantity of NH 3 and another type of
bacteria, “rhodo bacteria” (see figure 3). The goal of this compartment is to increase the global system efficiency by recycling
VFA and H 2 . The excess of rhodo bacteria that proliferate there is thrown into CI as organic waste.
Organic wastes → CI CO 2 + NH 3 + VFA
+ H 2 + water + residual wastes
Residual wastes
CO 2 + H 2
Urine
Water + NH 3 +
VFA Faeces edible Non-
food Bacteria
Figure 2: Scheme of the Compartment 1
VFA + H CII 2 + NH 3 + CO 2 → CO 2 + water + rhodo bacteria
CO 2 + H 2
CO 2
Water + NH 3 +
VFA
Water + NH 3
Rhodo bacteria
Figure 3: Scheme of the Compartment 2
The Compartment 3 (CIII) is the nitrification compartment (see figure 4). It transforms NH 3 into nitric acid (HNO 3 ) and water using O 2 , a small quantity of CO 2 and a third type of bacteria, called “nitri bacteria”. The HNO 3 produced here is the fertilizer that is going to allow plants to grow. The excess of nitri bacteria that proliferate there is also thrown into CI as organic waste.
NH 3 + O CIII 2 + CO 2 → HNO 3 + water +
nitri bacteria
Air + O 2
Air
Water + NH 3
Water + HNO 3
Nitri bacteria
Figure 4: Scheme of the Compartment 3
The Compartment 4 (CIV) is a greenhouse (see figure 5). It is in fact composed of two sub-compartments, Compartment 4a (CIVa) and Compartment 4b (CIVb). In CIVa, Spirulina grows. In CIVb, edible plants such as tomatoes, beans, wheat and others grow. In both case, they grow using CO 2 , water and HNO 3 while producing O 2 . When they are ripe, they are collected.
The edible part of the plants and the Spirulina are eaten by the crew, and the non-edible parts of plants (leaves, roots, etc.)
are thrown into CI as organic waste. Spirulina is very responsive to light. The oxygen it produces depends quite reactively on
the light it receives (the response time is about 30 minutes). The advantage of having Spirulina and plants growing into two
separate sub-compartments is that short-term variations in oxygen production can be monitored by controlling light in CIVa.
Spirulina is meant to produce 5% of the oxygen the crew needs, the remaining 95% being produced by the plants.
HNO 3 CIV + CO 2 + water → food + O 2
Food Water Air + O 2
Air + CO 2
Water + HNO 3
edible Non- food
Figure 5: Scheme of the Compartment 4
With these 4 compartments, the MELiSSA Life Support System and the crew form a loop of material exchanges. The LSS gradually transforms the crew wastes into plants and O 2 , and they are transformed back into human wastes by the crew. Figure 6 summarizes all the exchanges between compartments and the crew. Light green arrows represent breathing air flows, with a good O 2 level and a low CO 2 level in accordance with the standards. Dark green arrows represent non-breathing air flows. The blue arrow represents the drinking water flow. Yellow arrows represent non-drinking liquid flows. The orange arrow represents the food flow. Grey arrows represent recyclable wastes flows. The black arrow represents the non-recyclable wastes flow, which is lost.
In the ideal case of 100% waste recycling, the ecosystem thus formed would not need any external resources to survive and ensure its stability. However, the waste recycling rate does not reach 100%.
2) LSS efficiency analysis
To have 100% waste recycling, every atom of waste must be recycled into food, water or O 2 , which is not the case.
First, CII does not work as it should. It is supposed to transform the VFA and H 2 from CI into additional CO 2 and water to increase the loop efficiency. In practice, it does not produce the desired amount of CO 2 . The VFA and H 2 are lost in unusable elements. CII has been removed from the loop, until another compartment that fulfils this function is designed. An ideal functioning version is kept in this study in order to model the LSS in its working version.
Then, part of the wastes thrown into CI cannot be decomposed and recycled. Fibers, nucleid acids, and a small part of the proteins and lipids contained in the organic wastes cannot be transformed. This is the “residual biomass” and it is lost, it cannot be used. And the organic wastes thrown into CI are nutrients for the bacteria that decompose them. They proliferate inside. Their population grows and may become excessive. The excess of bacteria must be removed, and is then considered as lost matter too.
These various losses therefore prevent the loop from achieving 100% recycling. But there is also a question of proportion. The proportion of each element naturally produced by the LSS depends on the chemical reactions occurring in the compartments and what they produce. It depends also on the proportion of each waste generated by the crew. These proportions are fixed, determined solely by the chemical reactions in question and the metabolism of the crew. This means that the proportion of each element naturally produced by the LSS is also fixed. However, the proportion of each element produced has to meet the proportion of each element consumed. For example, if for 1 kg of food and 1 kg of O 2 consumed by the crew, 0.5 kg of food and 1.5 kg of O 2 are produced by the LSS, the crew is going to run out of food and have an excess of O 2 . The excess of O 2
will be lost and lack of food will starve the crew.
The question of the efficiency of the LSS is therefore not a trivial one. One can already say that it will not naturally produce the desired elements in the right proportions. But it has to be modelled and analysed in order to determine: 1) how much does it lose in unusable wastes? 2) what are the proportions of the different elements produced naturally? 3) how can we influence and control its operation so that its production meets the crew consumption?
These questions are investigated in a first static study of the MELiSSA loop in section IV-C. A dynamic study of the system
follows then with the objective to dynamically ensure its operation. It should be however reminded that the motivation for
Crew
CI
CII
CIII CIV
Wastes Air +
O 2
Air + O 2
Air + CO 2
CO 2
Air
CO 2 + H 2
Water
Food Urine
Water + VFA +
NH 3
Water + NH 3
Water + HNO 3
Faeces
edible Non- food
Rhodo bacteria Nitri
bacteria
Figure 6: Scheme of the MELiSSA loop. The rectangles represent the compartments. (light green: breathing air - blue: drinking water - orange: food - dark green: non breathing air - yellow: non drinking liquid - grey: recyclable waste - black: non recyclable waste)
the development of the MELiSSA project is to reduce the mass to be launched into space for long-term manned missions. It should therefore be borne in mind that the total mass of the system and the resources needed for its proper functioning will have to be significantly lower than the mass of resources that would have to be sent if no recycling system were used.
B. Requirements
The primary objective of the MELiSSA Loop is to create the resources necessary for the survival of a spacecraft crew. This means measuring the needs and waste of such a crew. They depend on the metabolism of the crew members and their activity.
However, an average metabolism can be identified.
The different space agencies have characterized the human metabolism in different studies and give different results. In this project, data from the European Space Agency (ESA) is used. Tables I and II give the ESA estimation of the astronauts daily needs and daily waste production [8].
Table I: Consumption per astronaut.
Elements needed Kg/astr./day Mol/astr/h
Food 0.5809 1.038
Oxygen 0.8923 1.162
Water 1.500 3.472
Table II: Waste production per astronaut.
Elements produced Kg/astr./day Mol/astr/h
Faeces 0.01332 3.167 ×10
−2Urea 0.04973 3.452 ×10
−2CO
21.026 9.719 ×10
−1Water 1.884 4.361
These values give a general trend. They will be used to model and analyse the operation of the MELiSSA loop, and build its control system. The actual metabolism of the crew members will be more or less different from this average metabolism. The LSS will have to be able to adapt to the differences between this theoretical metabolism of the astronauts and their real one.
It will have to be ”robust” to this uncertainty. Providing this robustness is part of the role of the loop global control system.
In addition to providing the necessary resources to the crew, the LSS must ensure them a viable environment that meets certain standards. Some of these standards, such as those concerning water, are not considered in this project because they relate to a single compartment in particular, or an auxiliary module, and do not influence the operation of the overall loop.
It should be reminded that the main objective of this project is to control the global behaviour of the MELiSSA loop. The standards to be taken into account are the air composition standards in terms of O 2 and CO 2 . The composition of the air in the cabin directly depends on the balance between the quantities of resources produced and consumed.
In the MELiSSA project, O 2 level should stay above 18% in the cabin and under 25% everywhere, with a nominal value of 20.9% in the cabin. Under 18%, the crew suffocates. It corresponds to the minimum volume percentage of O 2 at sea level before hypoxia [13]. And the higher the O2 level, the greater the risk of fire [1]. For fire safety reason, the upper O 2 level limit is set at 25%. O 2 level should not rise above this limit. The nominal value is taken equal to the nominal O 2 level at sea level, i.e. 20.9% .
About the CO 2 level standards, they depend on which compartment is considered. In general, there is no lower value. The crew does not need CO 2 to live. But it is necessary for the plants and Spirulina to grow in CIV. It is necessary therefore to keep a minimum quantity of CO 2 in the loop. There is no upper limit for the plants. In the cabin however, it can be toxic for the crew. The maximal CO 2 level depends on how long the crew is exposed to it. But it should not rise above 15 000 ppm (1.5%) for short-term exposure (1 day), 7 500 ppm (0.75%) for mid-term exposure (7-180 days), and NASA recommends not more than 5 000 ppm (0.5%) for long-term exposure (1 000 days) [13].
Table III summarizes the O 2 and CO 2 level standards to take into account. The lower limit of CO 2 level in CIV is set at
“x” since the CO 2 quantity depends on the wanted O 2 production and is calculated by the CIV controller.
Table III: Air composition standards.
Limits Upper Lower O
2Overall 25% /
CIV 25% /
Cabin 25% 18%
CO
2Overall / /
CIV / x
Cabin 1.5% /
III. M ETHODS
This section aims at presenting the methods used to carry this study and build the model of the Life Support System (LSS). Three methods are first presented: the Model-Based System Engineering (MBSE) method, the Functional Energy-Based Modelling (FEBM) method and the Predictive Functional Control (PFC) method. The first one is a product design method based on models. This is the method followed all along this project. FEBM is the modelling method used, imposed by SHERPA Engineering. PFC is the control design method used to develop the global control system of the LSS. The choice of these methods is motivated. The first study of the MELiSSA loop by Laurent Poughon and the Universit´e Clermont-Auvergne (UCA) is then presented. And follows the work done so far by SHERPA Engineering and the first dynamic model the company built.
A. Model-Based System Engineering 1) Method description
The first method, Model-Based System Engineering (MBSE) is a product design and project management method. It focuses on models in order to design a product [7]. A model is a simplified representation of a concept, a phenomenon, a relationship, a structure or a system [4]. It is an abstraction of the reality as it does not include unnecessary components. “A model (the term “model” derives from the Latin word modulus, which means measure, rule, pattern, example to be followed) is a representation of a selected part of the world, the domain of interest, that captures the important aspects, from a certain point of view, simplifying or omitting the irrelevant features.”[19]
The MBSE method uses models in order to support the system requirements, design, analysis, verification and validation activities. Models are used during the whole designing process, from the conceptual design phase and continuing throughout development and later in the product life-cycle phases. “MBSE is part of a long-term trend toward model-centric approaches adopted by other engineering disciplines, including mechanical, electrical and software. In particular, MBSE is expected to replace the document-centric approach that has been practiced by systems engineers in the past and to influence the future practice of systems engineering by being fully integrated into the definition of systems engineering processes.”[7]
Within the framework of this project, this method results in the establishment of models to represent the requirements and specifications of the MELiSSA loop, to study the multi-physical behaviour of each compartment, to simulate the overall behaviour of the loop and control it, and to build a common environment for all compartments.
A model to graphically represent the system requirements and specifications has already been developed by SHERPA Engineering (see section III-E1). And multi-physical models of certain compartments have been built by the company that designed them. This project focuses on developing a simulation model to study the overall behaviour of the loop, identify the problems it encounters, and find solutions in order to meet the specifications. Moreover, the model built during this project may serve as a common environment for the design and test of the compartments.
2) Choice motivation
This master thesis is part of the MBSE method already implemented in the MELiSSA project. In addition to providing a control system of the loop, the built model will provide data on the overall functioning of the loop, and bring the complex information of an environment to the companies developing the MELiSSA compartments.
An alternative would be to transmit all this information, requirements and specifications through documents and reports. But it is a tough work and significantly less effective. The advantage of the MBSE approach is to enhance communications between the stakeholders and team members “as well as a true shared understanding of the domain, improved knowledge capture, design precision and integrity” [19]. Models are a big advantage in a project such as the MELiSSA project that involves many fields of study and stakeholders. It allows them to focus on their domain while having a fixed and common context of study. Wilkiens [25] says in his book “The modeling language allows me to move on different abstraction levels. The more abstract I get the simpler the system appears to be. This is the art of being concrete on an abstract level.”.
B. Functional Energy-Based Modelling method
The second approach of this master thesis is the Functional Energy-Based Modelling (FEBM) method. This is the modelling
approach that has been followed during this study. Its particularity is that it has been developed by SHERPA Engineering
during two PHD [6, 15] and is still under development. The degree project presented here is part of its development process,
as the secondary objective of this study is to adapt it.
1) Functional Energy-Based Modelling principle
The FEBM method is a modelling approach designed for systems of systems. The term “Systems of Systems” describes systems that are composed of different independent sub-systems, which are joined together and work toward a common goal, the overall objective of the system [17]. The principle of FEBM is to study the flows involved within a system of systems by modelling each sub-system by its “functional” use, i.e. the action it has been designed for. Each one is modelled from a simplified point of view, using as few equations as possible [16]. Its precise operation is not represented. And each sub-system is autonomous, working on its own. It communicates with its direct upstream and downstream neighbors, thus forming a chain (see figure 7). This independence of the sub-systems makes the method modular.
System
system Sub- n − 1
system Sub- n
system Sub- n + 1
downstream upstream
Figure 7: FEBM modularity representation.
FEBM has been developed only for energetic systems so far. It was meant to be used for the energy optimisation of electric and hybrid vehicles.
2) Types of components
Each sub-system, or component, is modelled by its functional block. In his thesis report, Mert Mokukcu[15] defines the 5 types of functional block of the Functional Energy-Based Modelling method:
• Source: Component that provides a flow (energy, matter or others) to the upstream component without any quantity limitation.
• Storage: Component that can receive a flow (energy, matter or others) from the downstream component, store it, and send it to the upstream component when needed. It is equivalent to a finite source that can be recharged.
• Distributor: Component that can distribute flows from several downstream elements to several upstream elements depending on their request (Need).
• Transformer: Component that transforms a flow into another (energy conversion, chemical transformation, flow mixture, others) with some efficiency (for example an electrical engine that converts electrical energy into mechanical energy).
• Effector: Component that requests a flow to the downstream component and consumes it in order to fulfill a mission.
These 5 components are supposed to be generic enough to model every possible functional component [15].
Let’s take the example of the power train of an electric car. It can be broken down into 4 elements: the battery, the electrical engine, the vehicle motion (the mission) and the power grid. The battery can be modelled as a Storage, the engine as a Transformer, the power grid as a Source that is sometimes activated (when the vehicle is connected to the charging station) and the vehicle motion as a Consumer with a mission (for example a velocity profile). The power grid (Source) is the downstream component, then the battery (Storage) follows, then the engine (Transformer) and then the vehicle motion is the upstream component (Consumer). To represent the consumption of the internal equipment of the car (car radio, heating etc.), this model can be enriched with a power distributor (Distributor) and the equipment (Consumer). Figure 8 gives the model of an electric car power train made with the FEBM method.
3) Communication
Clement Fauvel [6] and Mert Mokukcu [15] laid the foundations for communication between the components in their two thesis reports. The components exchange “Needs” and “Supplies” with a “Disponibility” and an “Acceptance”.
Figure 9 presents this communication process. A component n gets a Need of flow from the upstream component n + 1. It
processes it (in different way depending on the type of component) and sends a Need of flow to the downstream component
n −1. The downstream component n−1 replies with a Supply of flow. This Supply may or may not comply with the Need. The
component n processes this Supply depending on its functionality. It sends then a Supply of flow to the upstream component
n + 1. (the Supply may or may not comply with the initial Need).
Figure 8: Model of the power train of an electric car, made with the Functional Energy-Based Modelling method.
System
system Sub- n − 1
system Sub- n
system Sub- n + 1
Need
Disp/Acc
Need
Disp/Acc
Supply
Disp/Acc
Supply
Disp/Acc
downstream upstream
Figure 9: FEBM communication process.
Needs and Supplies are accompanied with an Acceptance and a Disponibility. They represent the maximum or minimum flow rate a component can accept/provide (It depends on its physical limit for example, and/or its state of charge for a Storage, or the characteristics of the upstream/downstream components for a Distributor etc.). They are the boundaries that limit the flow exchanges. In the case of a Need, the Acceptance is the upper boundary and the Disponibility is the lower boundary. In the case of a Supply, the Disponibility is the lower boundary and the Acceptance is the upper boundary. These Acceptances and Disponibilities will help the sub-systems to chose the best strategy.
The goal of such a communication process is to satisfy as far as possible the Needs of the different components and to find the appropriate strategy when the Need is too big to be satisfied. Let’s take again the example of the electric car power train (see figure 8). The vehicle motion and the electrical auxiliary will send Needs to their downstream components all the way to the Distributor. The Distributor will sum these Needs and send a Need of energy to the Storage. The Storage will then provide a Supply of energy, depending on the Need and on its state of charge. If the state of charge is high enough, the Supply will match the Need. If not, it will be lower. The Distributor will then have to split this Supply of energy between the electric engine and the electrical auxiliary. If the Supply is lower than the Need, it will have to split it depending on the strategy and the priorities that have been defined. The Supplies are then forwarded respectively to the vehicle motion Consumer and the electrical auxiliary Consumer. [6, 15, 16]
4) Components internal structure
Each block is composed of a “Control Part” and an “Operation Part” (see figure 10). The Control Part is meant to ensure
the proper operation of the block. It can be just a planning algorithm, or a dynamic controller, or a combination of both
depending on the case. It processes the Need received from the upstream component and calculates the best Need to send
to the downstream component (depending on its functionality, the Acceptances and Disponibilities etc.). The Operation Part
System
n − 1 n n + 1
Control Part Control Part Control Part
Operation Part
Operation Part
Operation Part Need
Disp/Acc
Need
Disp/Acc
Supply
Disp/Acc
Supply
Disp/Acc
downstream upstream
Figure 10: FEBM internal structure of the components.
is the operating part of the system. It represents the functional action of the block. It processes the Supply of flow from the downstream component and send a Supply of flow to the upstream component with the right Disponibility and Acceptance.
Both Control Part and Operation Part communicate with each other. The first one gives instructions to the second one, and the second one sends measurements to the first one. [6, 15, 16]
5) Simulink-based Phi-EMI software
The framework of the Functional Energy-Based Modelling method is therefore already laid down and defined. An internal structure common to all components has been designed, and they have a precise communication process. SHERPA Engineering has implemented these components into the Simulink-based Phi-EMI software. The model presented on figure 8 is made with Phi-EMI.
They have been implemented in different ways relatively to their functionality:
• Source: The source receives Needs and sends Supplies. The Supply always satisfies the Need as long as it corresponds to its field of Disponibility and Acceptance.
• Storage: The storage is a pure integrator. It sends a Need of charge, receives a Supply of charge, receives a Need of discharge and sends a Supply of discharge. It integrates the difference between both Supplies. The Supply sent always meet the received Need as long as it corresponds to its field of Disponibility and Acceptance and its state of charge is high enough.
• Distributor: The distributor is connected to several upstream and downstream components. It distributes the Needs and Supplies depending on their demand, Disponibility and Acceptance. It can follow different algorithms with a different distribution logic.
• Transformer: The transformer is the less generic component. It transforms the Supplies depending on coefficients. This may take the form of matrices, or efficiency variables, or stoichiometric coefficients, or others.
• Effector: The effector only sends the Need corresponding to the mission it has to fulfil.
The main benefit of Phi-EMI is that it allows the user to build models really quickly. All components are cooperative and compatible. And their internal structure and communication process form a first control system implicitly integrated in the model. A global control system can be added to modify the components behaviour and optimize the system operation.
This entire method has been developed for energy flows and optimization. A secondary objective of this degree project is to adapt it to matter flows.
6) Motive
The main advantage of the FEBM method is its simplicity and the speed with which it is possible to build and simulate a model. Although it does not describe the precise behaviour of the system, it allows to quickly size components, evaluate architecture solutions and efficiently define a resource management strategy [15]. The last two points correspond perfectly to the work to be carried out in this study.
Within the framework of the MBSE approach, this method should not be used alone. A multi-physical study of complex
systems such as the MELiSSA loop is still necessary. The FEBM method greatly simplifies the components. It is possible
that important behaviours may have been neglected or appear during the actual connection of the compartments. Once the
functional model has been designed, it can be very interesting to connect it to a multi-physics model. The multi-physics model
then takes the place of the ”Operation Part” in the components.
C. Predictive Functional Control
As explained in the previous section, it might be necessary to add a global control system to models built from the FEBM approach. The implicit control system included in the method sometimes leads to unwanted or sub-optimal behaviours, e.g.
in the case of saturated systems or feedback loops. The MELiSSA loop in a certain configuration, for example, contains a non-minimum phase feedback loop (see section IV-E3). This non-minimum phase behaviour is dangerous as it can lead to a lack of dioxygen for the crew. It must then be controlled and adapted by means of an external control system.
The method chosen to design a control system depends on the system and on the performances expected. An open-loop filter can be sufficient to control a simple system with low performance expectations. But, in the case of the MELiSSA loop, the system must fulfil strong requirements in term of atmosphere quality (see section II-B). Besides, disturbances such as variations in the metabolism of the crew members, changes in the plants grown in CIV or variation of the number of crew members may occur. They must be canceled as they can lead to an non-viable envionment. And the storages as described in section III-B2 are implemented in Phi-EMI as pure integrators (see section III-B5). Pure integrating systems are quasi-stable, so they can be unstable. In this case, an open-loop filter is not a sufficient control system. It cannot cancel disturbances and control unstable systems.
Closed-loop feedback controllers are necessary in the case of the MELiSSA Life Support System. Several methods can be considered to design them. In this master thesis, it has been chosen to follow the Predictive Functional Control (PFC) method, which is part of the Model Predictive Control (MPC) methods. Its principle and equations are first presented. Its choice is motivated last.
1) PFC principle
The Predictive Functional Control (PFC) method is one of the Model Predictive Control (MPC) methods. [9] The MPC approach consists in predicting the behaviour of the system to be controlled with the help of an explicit model of the plant (the internal model), and to choose the best control action to fulfil its mission. [9] It has been developed in the 60s and 70s, with the PFC method presented by Jacques Richalet in the journal “Automatica” in 1978 [21], and the Dynamic Matrix Control method presented by Cutler and Ramaker in 1979. [5, 9] The whole following section presents the PFC as Jacques Richalet wrote it it in his book “Predictive functional control practice”. [22]
Figure 11: PFC principle. (source: Control Course PFC base - SHERPA Engineering PFC training presentation).
PFC is a discrete control method. Figure 11 presents its basic principle. At time n, the process output y p is measured.
It must reach a setpoint c. To do so, a reference trajectory y r is calculated from this measured point y p (n) to the setpoint
c. The process output must closely follow this reference trajectory. To do so, the controller calculates the optimal value of
the Manipulated Variable (MV) (which is the system input, also known as the optimal control action u ∗ (n)) that makes the
predicted process output correspond to the reference trajectory at least at some preset coincidence points. The Manipulated Variable optimal value, which is the optimal control action u ∗ (n), is applied until time n + 1, when the process output is measured. The calculation starts then again and a new optimal control action u ∗ (n + 1) is applied. (This strategy of applying the first value of the control action and start again the calculation at time n + 1 is called the “receding-horizon strategy”). [22]
The optimal control action u ∗ is calculated by putting this problem into equation.[22] The equations and solution are presented bellow for linear Single-Input Single-Output (SISO) systems, as PFC method will not be used for non-linear of Multi-Input Multi-Output (MIMO) systems in this degree project.
2) PFC equations
Let’s consider a linear SISO system. It is described by its state-space equation model (1).
x M (n) = F M x M (n − 1) + G M u(n − 1)
y M (n) = C M T x M (n) (1)
with x M its state vector, u its input and y M its output. A SISO system means that there is a single input u and a single output y, but the system can have multiple states.
The whole PFC calculation consists in minimizing the criteria D(n):
D(n) =
n
hX
j=1
{ˆy p (n + h j ) − y r (n + h j ) } 2 (2)
where y r is the reference trajectory, y ˆ p is the estimated process output, h j is the coincidence point number j and n h is the number of coincidence points. Minimizing D(n) means then to find the optimal control action u ∗ that minimizes the difference between the estimated process output and the reference trajectory at the coincidence points h 1 ... h n
B. These coincidence points are preset by the control engineer. [22]
In order to estimate the future process output, a model of the system is used in the controller. It does not need to perfectly represent the process but must be more or less close to it. [22]
The reference trajectory y r is first set. Any choice is possible to define it. The simplest one, and the one chosen in this degree project, is a first-order dynamic for the difference between c and y r , as described in equation (3). [22]
c(n + i) − y r (n + i) = α i (c(n) − y r (n)) (3)
where α = e
CLRT−3Te, T e being the sampling time and CLRT the desired closed-loop response time. Since the reference trajectory is set from the measured process output at time n:
y r (n) = y p (n) (4)
control action functions are then chosen. [22] In PFC, the future control action u is structured as a linear combination of pre-selected functions called “base functions”. A polynomial base is usually used as base functions, as described in equation (5).
u(n + i) =
n
BX
k=1
µ k (n)i k −1 (5)
n B is the number of base functions and µ k is the coefficient of the base function k. The polynomial base is used in this degree project. The parameters to be calculated are then the base functions coefficients {µ k (n) } k at time n. [22]
The estimated process output y ˆ p (n) is then calculated. A strength of the PFC method is the “self-compensation”. The controller is built so that it analyses the error between the model output y M (n) and the process output y p (n) at time n, and takes this error into account for the estimation of the future process output y ˆ p (n + i). Equation (6) gives the estimated process output at time n + i. [22]
ˆ
y p (n + i) = y M (n + i) + ˆ e(n + i) (6)
ˆ
e(n + i) is the error compensation term. It is often taken as the difference between the model and the process, plus a degree d e polynomial estimate of the evolution of this difference , as given by equation (7). [22]
ˆ
e(n + i) = y p (n) − y M (n) +
d
eX
m=1
e m (n)i m (7)
Coefficients {e m (n) } m are calculated by the self-compensation method. It allows to correct systems where the error is divergent.
In this degree project, there is no system with a divergent error. Coefficients {e m (n) } m are set to zero. The self-compensation is said to be of degree 0 (d e = 0). The estimated process output is then given by equation (8). [22]
ˆ
y p (n + i) = y M (n + i) + y p (n) − y M (n) (8)
The model output y M (n + i) at time n + i breaks down into a forced response y F (n + i) and a free response y L (n + i).
The free response is the natural evolution of the system from the state x M (n) (see equation (10)). The forced response is its evolution on the application of the control action u(n) (see equation (11)).
y M (n + i) = y L (n + i) + y F (n + i) (9)
y L (n + i) = C M T F M i x M (n) (10)
y F (n + i) = µ(n) T y B (i) µ(n) = (µ 1 µ 2 ... µ n
B) T y B = (y B1 y B2 ... y Bn
B) T
(11)
y Bk is here the response to the base function u Bk = i k −1 . [22]
Using (2), (3), (4) (8), (9), (10) and (11) the criteria D(n) becomes then: [22]
D(n) =
n
hX
j=1
µ(n) T y B (i) − d(n + h j ) 2
(12) with
d(n + h j ) = c(n + h j ) − α h
j(c(n) − y p (n)) − y p (n) − (C M T F M h
j− I)x M (n) (13)
The minimization of D(n) is obtained by cancelling its gradient ∂D/∂µ. It gives the optimal control action coefficients: [22]
µ ∗ (n) = R d(n) (14)
with
R =
n
hX
j=1
y B (h j )y B (h j ) T
−1
[y B (h 1 ) y B (h 2 ) ... y B (h n
h)] (15)
and
d(n) = [d(n + h 1 ) d(n + h 2 ) ... d(n + h n
h)] T (16) The receding-horizon strategy, which consists in applying the first value of the optimal control action u ∗ sequence, gives that:
u ∗ (n) = µ ∗ (n) T u B (0) (17)
with u B = (u B1 u B2 ... u Bn
B) T and {u Bk } the base functions. [22] Knowing that, within the framework of this degree project, u Bk = i k −1 , and using (14) and (17), it gives: [22]
u ∗ (n) = d(n) T v (18)
with v = R T (u B1 (0) u B2 (0) ... u Bn
B(0)) T
= R T (1 0 ... 0) T (19)
The last step before determining the optimal control action equation is to estimate the setpoint c(n + h j ) at time n + h j . Its evolution depends on the problem. One way to write it is to present it in polynomial form. [22] Equation (20) gives the setpoint c at time n + h j in polynomial form.
c(n + i) = c(n) +
d
cX
m=1
c m (n)i m (20)
d c is the degree of the polynomial and {c m } m its coefficients. [22] Coefficients {c m } m are either known or determined by a method akin to the self-compensation method.[22] In this degree project, the control action is always estimated as constant, and the degree of the polynomial is null (d c = 0).
Equations (13), (16), (18), (19) and (20) give then the final optimal control action equation (21). [22]
u ∗ (n) = k 0 {c(n) − y p (n) } + v T x x M (n) (21) where
k 0 = v T
1 − α h
11 − α h
2...
1 − α h
nh
(22)
and
v x = −
C M T (F M h
1− I) C M T (F M h
2− I)
...
C M T (F M h
nh− I)
T
v (23)
The PFC controller has finally a structure as described in figure 12. The block called “Model” is the internal model, a state-space representation of the process with the matrix v x instead of the matrix C M and with u as input. [22]
Figure 12: Block diagram of an PFC controller.
3) Choice of the parameters
The choice of the parameters is decisive for the robustness, the stability and the precision of the controller. [22]
The base functions must be chosen so that the process can reach and follow the setpoint. Their maximal degree should be higher than or equal to the maximal degree of the setpoint or the disturbance to reject, minus the number of pure integrator in the system. For example, if a system with one integrator has to follow a parabolla as setpoint, the base functions should be at least of a degree 1. [22]
The number of coincidence points should be chosen higher than or equal to the number of base functions. They are also decisive for the dynamic and the robustness. They must be chosen at an appropriate position. Coincidence points should be after any delay but before the closed-loop response time. In systems with overshoots or exotic behaviour, they have to be chosen so that the unwanted behaviour is controlled. [22]
The Closed-Loop Response Time CLRT has a great influence on the dynamic. In theory, any CLRT can be chosen.
However, the faster the response time, the lower the robustness. And the control action becomes more extreme with a short response time. A longer response time softens the optimal control action u ∗ and increases the robustness of the system. It’s a question of balance between speed and respect for constraints and robustness. [22]
Table IV presents the influence of each parameter on the system characteristics. 2 means a strong influence, 0 means no influence.
Table IV: Influence of the controller parameters on the characteristics of the system. [22]
Precision Dynamic Robustness
Base functions 2 0 0
Reference trajectory 0 2 1
Coincidence points 0 1 2
4) Systems with constraints on the control action
It is common for the control action u to be constrained. In the case it is saturated, the PFC controller has to know it.
Otherwise, it risks diverging, having an integrator effect. [22]
To do so, in the case of SISO systems, a simple and quasi-optimal solution is to update the internal model not with the control action u but with the control action constrained u c as described in figure 13. [22]
In the case of constraints on the output y p , the controller should also be informed of the saturation. An output constraint
is manageable by using two PFC controllers in parallel, connected differently, and a decision system that will choose either
the first or the second depending on the saturation. [10] The case of output constraints is however not present in this degree
project. This solution is therefore not further explained.
Figure 13: Block diagram of an PFC controller with constraints on the control action.
5) Delay system case
The PFC method excels in the control of non-trivial systems, [23] and in particular delay systems. In the case of a delay system, the measured process output y p is corrected with a delay compensation calculated using the model. The result is given by equations (24) and (25) where r M is the delay and k 0 and v x are given by equations (22) and (23). [22]
u ∗ (n) = k 0 {c(n) − ˆy p (n) } + v T x x M (n) (24) ˆ
y p (n) = y p (n) + y M (n) − y M (n − r M ) (25)
The coincidence points have to be chosen after the delay. [22]
6) Non-minimum phase system case
Non-minimum phase systems are systems with zeros in the RHP. On a step solicitation, their response first goes in the opposite direction before converging. This behaviour might be misleading for a controller. In the case of PFC, a solution is to model these systems as a delay systems. The delay is set as approximately equal to the time during which the system has a negative response on a positive step solicitation (see figure 14). [22]
0 0.5 1 1.5 2 2.5
-0.2 0 0.2 0.4 0.6 0.8 1
non-minimum phase system delay system
