MELISSA: Global control strategy of the artificial ecosystem by using first principles models of the compartments

MELISSA: Global control strategy of the artificial ecosystem by using first principles models of the compartments

Adv.SpaceRes.Vol. 24, No. 3, pp. 397405,1999 0 1999COSPAR. Published by Elsevier Science Ltd. All rights reserved Pergamon www.elsevier.nl/~ocate~asr...

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Adv.SpaceRes.Vol. 24, No. 3, pp. 397405,1999 0 1999COSPAR. Published by Elsevier Science Ltd. All rights reserved

Pergamon www.elsevier.nl/~ocate~asr

Printed in Great Britain 0273- 1177199$20.00 + 0.00 PII: 50273-l 177(99)00490-l

MELISSA : GLOBAL CONTROL STRATEGY OF THE ARTIFICIAL ECOSYSTEM BY USING FIRST PRINCIPLES MODELS OF THE COMPARTMENTS N. Fulget ’ , L. Poughon 2, J. Richalet ’ , Ch. Lasseur3

I

ADERSA - 7, Bd du Mar.&ha1 Juin-BP 52-91371 Verrit;res-le-B&on

Cedex (France). ’ LGCB - Universite’Blaise Pascal -

63177 Aubi&e (France). 3 ESA-ESTEC - Keperlaan I - 2201 AG Noordwijk (The Netherlands)

ABSTRACT

MELISSA is a micro-organisms based ecosystem conceived as a tool for understanding the behaviour of artificial ecosystems, and developing the technology for a future biological life support system for long term space mission. The driving element of MELISSA is the recovering of oxygen and edible biomass from waste (faeces, urea). Due to its intrinsic instability and the safety requirements of manned missions, an important control strategy is developed to pilot this system and to optimize its recycling performance. This is a hierarchical control strategy. Each MELISSA compa~~nt has its local control system, and taking into account the states of other compa~ments and a global desired functioning point, the upper level determines the setpoints for each compartment. The developed approach is based on first principles models of each compartment (physic0 chemical equations, stoichiometries, kinetic rates, ...). Those models are used to develop a global simulator of the system (in order to study the global functioning}. They are also used in the control strategy, which is a non linear predictive model based strategy. This paper presents the general approach of the control strategy of the loop from the compartment level up to the overall loop. At the end, some simulation and experimental results are presented. 0 1999 COSPAR.Published by Elsevier Science Ltd. INTRODUCTION

To use Regenerative Life Support Systems for manned space missions requires serious considerations to study its safety and reliability, moreover the well known space requirements of efficiency and optimisation in terms of energy, volume and weight will have to be satisfied. In view of the current state of the art, there is little doubt that the holistic ecosystem approach is by far the most simple and efficient way of constituting Life Support systems for extended periods of time. It has been suggested (Sezer and Siljak, 1981) that if a global system could be divided into interconnects subsystems representing physical entities (i.e. a compa~ment), its stability could be considered as the stabilization of all the smaller subsystems. The main advantage of this approach is that each functional subsystem can be handled by conventional engineering approach: mathematical modeling, simulation, optimisation and robust control. For these reasons the compartmentalized ecosystem MELISSA has been selected by ESA for the p~li~n~ development of a Regenerative Life Support System (Mergeay et al., 1988, Lasseur and Binot, 1991). This paper presents our approach of mathematics modeling, from the mass balance evaluation of the loop in steady state, up to the dynamic control of the complete MELISSA loop. Based on this approach, preliminary control results are presented. 397

N. Fulget et al.

398

MATHEMATICAL COMPARTMENTS Modellinp

MODELLING

:

MASS

BALANCE

AND

DYNAMIC

MODELS

OF

THE

of the Mass Balance of the Loou

In a preliminary approach, the compartments within the MELISSA loop were analysed separately. Due to the lack of knowledge at the time of the study it was not possible to directly define a process design for all the compartments. So, a preliminary analysis of the complete loop was carried out for equilibrium conditions. This analysis of the complete loop, as well as the development of dynamic models was carried out by the Laboratoire de Genie Chimique Biologique (Universitt B. Pascal, Clermont-Ferrand, France). Each compartment was described by one (or more) stoichiometric equations derived from the knowledge of the cell metabolic pathway specific of the microorganism colonizing the compartment (Dussap et al., 1993), or, for the crew derived from human metabolic needs (Binot 1991), and from experiments leaded by the MELiSSA partners. As an example, the nitrification process, was represented by the following stoichiometry, when nitrites are assumed to be completely transformed : CO, CH

+ 0.0089 0

1.6147

0 3906

H,PO,

+ 0.0035

N 0.1994S 0.0035 P 0.0089

H,SO, +

+ 28.3838

JJ 14.7295

(NO,,H+)

O2 + 14.9289 + 6.8733

NH, H,O

For each stoichiometric equation, a key substrate entering the compartment is assumed to be completely exhausted at the outlet, table 1, which provides the limit for each compartment and consequently for the system. In the static approach, process kinetics, such as rates of biological reactions described by stoichiometries, and mass transfer were ignored. However some stoichiometries depend on the cultures conditions, as for Spirulina where the stoichiometric coefficients and the biomass quality are functions of the radiant light input energy (Comet et al., 1995). MELiSSA was simulated using the chemical process simulator ProSim (ProSim SA, Toulouse, France). Each unit operation or unit process was modeled by a unit module chosen from the software library of unit models or a new user programmed unit. Each module was treated separately with its own inputs and outputs, and the outlet state vector was determined from the inlet one. The entire system was described using unit operation models i.e. reactors modules, flash modules, separators modules, streams dividers and stream mixer modules (Figure 1). To the modules describing the biological reactions were associated the stoichiometries characterizing the microorganism colonizing the reactor. The complete system of stoichiometric equations (8 stoichiometries) was made up of 17 compounds.

Liquid

Fo Fig. 1. Modular representation

Fresh biomass

of the Spirulina compartment

For equilibrium simulations, MELISSA was considered as a semi-closed system, as outlined in Figure 2. For simplicity the totality of the gas and liquid streams within the compartments and the detailed representation of compartments (Figures 1) are not shown in Figure 2. The external inputs on the loop and the constraints (food management, water management and gas management) are shown. The food management deals with the nutritional constraints for human (proteins, carbohydrate, fats). The gas management deals with the atmosphere requirement for the crew (ventilation, gas composition). The water management deals with potable water and humidity (linked to gas management). A total of 6 compounds in inputs and 6 compounds in output streams were defined. With the 4 elements (C.H.O.N.) mass balance and the constraints applied on the loop by management modules, 2 degrees of freedom appeared on the loop. These two degrees were noted Z (fraction of Spirulina biomass recycled in the loop) and Y (fraction of Rhodobacter recycled in the loop). This model does not take into account transient, upset and start up or shutdown conditions, but it served as a basis for the development of the dynamic model.

399

MELISSA:Global Control Strategy

Simulation of the Loop. By varying the values of the degrees of freedom Y and 2, different behaviours of the MELISSA loop were simulated in equilib~um conditions. - For &l and Y=l (i.e. the totality of the edible biomass produced is consumed by the crew), the recycling performances of the loop are 96% for N recycling, 26% for 02 recycling and 29% for CO2 recycling.- For m-35 and Y=O. (i.e. only 35% of the spirulina biomass produced is consumed by the crew), the recycling pe~o~~ces of the loop are 32% for N recycling, 90% for 02 recycling and 92% for CO2 recycling. In the first case, the MELISSA loop acts as a food (N element) supplier, while in the second case it acts as an atmosphere regenerator. For other values of Z and Y, intermediates behaviours are obtained. Models of the Dynamics of the Comnartments. Following this preliminary approach of modelling (Mass balances), a detailed model was developed for the photosynthetic reactor Spirulina plurensis (Comet et al., 1992a). It enables to take into account the limitations, i.e. light, nutrients, inside the photobioreactor and its coupling with growth kinetics. This model leads to inde~ndant calculation of the mean volumetric growth rate and biomass quality. By coupling with mass balances, this enables dynamic or steady state simulations of the photosynthetic compartment. This approach is currently extended to the phototrophs compartment and the validation of the model parameters for As. rubrum is under investigation. A nitrifying fixed bed reactor is as well under consideration, It involves physical constraints (mass transfer between the different phases, acid-base equilib~a), biological constraints (i.e. bioiogical kinetics for each org~ism) and the process working design (column design, flow rates...). Table 1. Compounds involved in the MELiSSA steady-state simulations. Compounds

Liquid phase

Gas phase Compartmentfor which compound is a key substrate

Food (Proteins, Glucose, Palmitic acid) NH3 (ammonia) HN03 (nitrate) Urea Faeces VFA (Acetate, Butyrate) H2 (hydrogen) (-32 02 N2 H20 {water) Spirufina biomass Phototrophs biomass Nitrifyers biomass

MATHEMATICAL

+ + f f c + + + + f c 4 + +

f

c + + + + +

Crew Njtrifying Spiruline Liquefying Liquefying Phototrophs Phototrophs

MODEL, SIMULATION, ANALYSIS, AND CONTROL LAW SYNTHESIS

The steady state simulator described in the preceding section is very useful to validate, predict, improve and optimize the behaviour of the MELISSA loop, but it cannot be used to build and test a robust control strategy. The development of a dynamic simulator was necessary to analyse the behaviour of the MELISSA loop with different control strategies. This simulator has been developed on MATLAB-SIMULINK software. It consists of the five compa~ments of the loop, their local control blocks, and an upper control level, which allows to control the global loop, and to transfer informations from one compartment to another. First of all the physical interactions between the compartments have been taking into account and are described hereafter.

N. Fulget ef al.

400

Food

I

Glucose (carbohydrates) Palmitic acid (fat) Proteins

I

0~N2

I

I-

I

-

+

G

crew: f stoichiometry

4

Water

I I

I

I

I

(variable with mputs)

Liquefying: 2 stoichiometric equations Phototrophs: 3 stoichiometric equations Nitrifying: 1 stoichiometric equation Spindines: I stoichiometric equation (variable with light radiant input energy)

I

I

I

I

I

1

I

:‘:! Y

Sipndina biomass

Phototrophs biomass

Nitrjfying biomass

V co2 (N2)

Waste

Fig. 2. Simplified representation of the MELiSSA loop for steady state simulations Gas, Liquid and Biomass Flowsheet The physical exchanges and interactjons between the compa~~nts biomass flows (Figure 3).

3.a. : Gas flow

biomass ueliminatedn

3-b. : Biomass flow

are separated in three parts: gas, liquid and

MELISSA: Global

401

Control Strategy

Water tank

‘I

I

w

.

.

Waste water tank AC.: Liquid flow

Fig. 3. Gas, Biomass and liquid flowsheet In the simulator, the flows are separated in two parts only: the gas and the liquid flows. The solid flows are considered diluted in the liquid flow. This is considered as a good representation of the reality. Indeed the biomass will effectively be mixed with all the liquid components. In the final ~nctioning, the MELISSA loop will be closed but, in the current studied version, the loop is supposed open before the crew comp~ment. The crew comp~ment is then considered as the first one of the system. Stoichiometric and kinetic equations As explained previously, the recycling is characterised in each compartment by some stoichiometric equations. They are written regarding the elements C, II, 0 and N (the elements S and P will be added in the future). They have been determined by the MELISSA partners, according to literature and to experimental results. They are not de~nitively fixed at one time and can evolute according to the culture conditions (i.e njtrogen and light ligation). Concerning the kinetic laws, the researches have been firstly focused on the photosynthetic reactors. Kinetic laws have been established in function of the light and nutrient limiting factor, for 5 different compounds of the produced biomass (carbohydrate, fat, proteins, nucleic acids and exopolysaccharide) (Comet et al., 1992b, 1994, 1995). The biomass growth rate, based on Monod’s model structure (Comet et al., 1992a), is expressed as: rx =

CN

* f(C,bd

hJ+CN

(1)

(rx : biomass growth rate, CN : nitrate concentration, Cx : biomass concentration FB : radiant flux, KN : half saturation coefficient) In each compartment, a differential equation is written for each species contained in the compartment, according to the mass conservation principle: y

= $J Cie - q0Ut

JdL+ VOl Vol

where: Mi : mass of the species in the compartment qjn : input flOW

(g)

gout : output flow Vol : total volume Cie : input flow concentration : growth rate

(fi) (1) (gll)

(Yh)

(gW

The growth rate is deduced from the kinetic and stoichiometric equations (I). It is negative if the species is consumed, and positive if we have a production.

402

N. Fulget ef at.

Simulator Structure Taking into account the study of the flow sheeting, the stoichiometric equations, and &hekinetic laws, a dynamic simulator has been built. This simulator is represented in Figure 4. It is composed of the five comp~~nts of MELISSA, and of the hierarchical control system. In the current version, the architecture of the hierarchical control system is completely designed but the control laws in each block are not totally defined. These blocks witI be completed in due course with the obtaining of the new results.

Fig. 4. Globai simulator HIERARCHICAL

CONTROL STRATEGY

The MELISSA control system is composed of 3 main levels, a global control for the optimization of the functioning point (level 2), a local control for each comp~ment (level I), and a basic control loop (level 0). Global ControI: Functioning Ontimization The global control level is in charge of the management and optimisation of the complete MELISSA loop. It calculates set-points for each compartment in order to satisfy criteria. Those general criteria are not strictly defined yet. However, the general concept remains to optimize the waste processing and not to produce a determined amount of food or oxygen. At this level its appears clearly that the mass balance m~eling will be of a real importance. Local Control of Each Comuartment : Analvsis of Functions In order to define the local control strategy for each compartment, an analysis of functions was done. It consists of dete~ning the possible actions, the manipulated variables, the disturbance variables, and the measured variables. If some non-measurable parameters are necessary to drive the comp~ments correctly, an estimator of this parameter will have to be developed. The main actions and the main controlled variables are summarized in the table 2.

MELISSA:

Table 2. Classification

Liquefying

compartment

of the parameters

Rhodobacter

compartment

Global Control Strategy

(mv: manipulated

variables, cv : controlled

Nitrifying compartment

variables)

Spirulina compartment

Non linear predictive control strategy As an example, we will present the Spirulina production control. The simulator is based on nonlinear first principles models. Those models are dynamic and can be used as the internal model in the control laws. As they are non linear, a predictive control law named scenario strategy has been proposed. It is based on conventional predictive control principles (Richalet, 1993), but with a non linearity. The principles of Predictive Functional Control (PFC) are: - internal model : a dynamic model between the action also named Manipulated Variable (MV) and the Controlled Variable (CV) is used to predict the process output on a future horizon ; - reference trajectory : a trajectory is defined on the future horizon, to reach the set-point. This trajectory is initialized on the current measured process output, and is considered as the future control objective. This trajectory is chosen as a first order trajectory. The dynamics of this trajectory is fixed according to specifications on the closed loop desired dynamics; - structuration of manipulated variable : a future manipulated variable projection is established in order to minimize the distance between the reference trajectory and the predicted process output, on a certain number of points of the future horizon. Those chosen points are named co’incidence points. This future manipulated variable protocol is structured as a linear combination of polynomial base functions. The choice of the degree of those base functions is done in function of the precision specifications. - auto-compensation procedure : as the future horizon is very close, the model can be considered as linear, its incremental behaviour doesn’t depend on its initial state. Due to state or structural perturbations, the model output can be different from the process output. This error is taken into account for the expression of predicted process output, but the model is independent. The state of the model is not set to the state of the process. As the behaviour of a nonlinear system depends on its initial state, this independent approach is not available in a non linear case, In the linear case, the superposition principle allows to express the predicted process output as a linear function of the manipulated variable, and then to obtain a linear controller whose coefficients are calculated off line. When the model is nonlinear, it is no more possible to use this superposition principle. Then, the scenario strategy methods should be applied. Scenario strategy The control method presented hereafter is based on the Model Based Predictive Control principles with the use of a nonlinear model. It consists of the application of several input protocols on the non linear model, to calculate the prediction of the process output on the coincidence point, and to determine the input protocol which gives a predicted process output equal to the reference trajectory. This determination is done with a non linear solver using the secant method. In the presented case, the future manipulated variable is supposed constant on the prediction horizon. A first step scenario (MV 1(n+i) = MV 1(n)) is applied to the model during the prediction horizon, and gives a model output equal to YMI (n+h,) on the cdincidence point. A second scenario (MV2(n+i) = MV2(n) = MVl(n) + DMV(n)) is applied to the model during the prediction horizon, and gives a model output equal to YM2(n+h,). Then the manipulated

variable is expressed according to secant method by equation (3).

N. Fulget

404

et al.

YR(n+ h,) - YMl(n+ h,) YM2(n+ h,) - YMl(n+ h,)

&IV*(n) = MVl(n) +

l

AMV(n)

13)

As the model is non linear, the step scenario solution MV* won’t give exactly a model output equal to the reference trajectory YR(n+h,) at coincidence point. It is then possible to do one or two additional iterations if necessary, but in fact, as this calculation is done on a sliding horizon, at each contro1 period, the convergence It is not necessary to obtain the exact solution at each control period.

E C

: _______________~_-----_-__

0.06 -

:

‘CI

0.06

1

10

500

will be progressive,

20

t

30

L AI



t

40

20

30

I

50

I

10

L

40

#

60

1

50

70

I

60

60

,

70

,

f

90

100



60

90

100

time tn hours

Fig. 5. Experimental of the reactor

resuh~. C,,, 1, the Biomass concentration

inside the reactor, EB the light intensity at the center

MELISSA: Global Control Strategy

405

Example of the Snirulina growth control This control strategy has been tested on the photosynthetic reactor S~~~~~~~.The reactor is fed with a given input flow, and the biomass is harvested with the same output flow. The controlled variable is the biomass production, which is the product of the output flow and the internal concentration of biomass. The manipulated variable is the light radiant flux. The presented non linear scenario strategy is used to determine the radiant flux in order to satisfy the production setpoint and the output flow is considered as a disturbance variable. The output flow being given, the production is fixed by the concentration. This control law has been tested on the reactor for different steps of production setpoint, and for a step of output flow. The experimental results are represented in figure 5. They correspond to three increasing steps of production setpoint, and a decreasing step of production. There is a constraint on the biomass concentration C xA, equal to 1500 mg/l. So the third increase of production is realized with an increase of flow, and not an increase of concentration. For the decreasing phase, the time response is greater than for the increasing phase. The phenomena are not equivalent. During the decreasing phase, the light flux is equal to its minimal value, and the decrease is limited to the dilution rate. CONCLUSION The control and optimisation of a complete loop of a regenerative Life Support system is a complex task, A high degree of mathematical modeling and control is necessary. The progressive study pursuits in the MELISSA project presents the advantages to be useful for the understanding i.e quanti~cation of the percentage of recycling, the optimisation and the control of the loop. There is no “black box” whatsoever. With this concept a model based predictive control law has been built and tested with satisfying results (below 5%). The same strategy will be applied for the control of the other compa~ments, in the closest future to the biomass production of Rhodobacter. REFERENCES Binot R.B.“Life support and habitability manuai”. Vol. I, Chap. 1. ESA PSS 03-406. 1991. Comet J.F., Dussap C.G., Dubertret G.“A structured model for simulation of cultures of the cyanobacterium: I coupling between light transfer and growth kinetics Biotechnologies & Bioengineering, Vol. 40, 1992, p.817-825. Comet J.F., Dussap C.G., Cluzel P., Dubertret G.“A structured model simulation of cultures of the cyanobacterium: II Identification of kinetic parameter under light and mineral limitations. Biotechnoiogies & Bioengineering, Vol. 40, 1992, p. 826-834. Comet J.F., Dussap CC., Gros J.B. “Conversion of radiant light energy in photobioreactors” American Institute of Chemical Engineers Journal, Vol40, N6, 1994, p 1055 1066. Comet J.F., Dussap C.G., Gras J.B., Binois C.“ A monodimensionnal approach for modelling coupling between radiant light energy transfer and growth kinetics in photobioreactors” Chemical Engineering Sciences, 1995. Dussap C.G., Comet J.F.,Gros J.B. “Simulation of mass fluxes in the MELISSA microorganism based ecosystem” Proceedings of the 23rd ~ntemational Conference on Environmental Systems, July 12-15, 1993, Colorado springs, USA. Lasseur Ch., Binot R.B. “Control system for artificial ecosystems. Application to MELISSA” 21st International Conference on Environmental Systems, July 15-18 1991, San Fransisco, USA, Mergeay M., Verstraete W., Dubertret G., Lefort-tran M., Chipaux C., Binot R.B. “MELISSA a microorganisms based model for CELSS development” Proceedings of the 3rd symposium on space thermal control & life support system. Noordwijk, The Netherlands, October 1988, ~~65-68. Richalet J., “Pratique de la commande predictive”, Hermes, Edition, 1993,349~. Sezer M.E., Siljak D.D. “On structural decomposition and stabilization of large scale control systems” Transactions on automatic control, Vo126, N2, 1981, p.439-444.