Advanced nonlinear multi-layer process control for autotrophic cultivations ⁎

12th IFAC Symposium on Dynamics and Control of 12th IFAC Symposium on Dynamics and Control of Process including Biosystems 12th IFACSystems, Symposium on Dynamics and Controlonline of Available at www.sciencedirect.com Process including Biosystems 12th IFACSystems, Symposium on Dynamics Control of Florianópolis - SC,including Brazil, April 23-26,and 2019 Process Systems, Biosystems Florianópolis - SC, Brazil, April 23-26, 2019 Process Systems, including Biosystems Florianópolis - SC, Brazil, April 23-26, 2019 Florianópolis - SC, Brazil, April 23-26, 2019

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IFAC PapersOnLine 52-1 (2019) 733–738

Advanced nonlinear multi-layer process Advanced nonlinear multi-layer process Advanced nonlinear multi-layer process  control for autotrophic cultivations Advanced nonlinear multi-layer process control for autotrophic cultivations control for autotrophic cultivations  control for autotrophic cultivations Flavia Neddermeyer ∗∗ Rudibert King ∗∗

Flavia Neddermeyer ∗∗∗ Rudibert King ∗∗∗ Flavia Neddermeyer ∗ Rudibert King ∗ Flavia Neddermeyer Rudibert King ∗ of Measurement a ∗ Chair of Measurement and and Control, Control, Technische Technische Universit¨ Universit¨ att Berlin, Berlin, ∗ ∗ Chair Chair of Measurement and Control, Technische Universit¨ at Berlin, Secr. ER 2-1, Hardenbergstraße 36a, 10623 Berlin, Germany ∗ Secr. ER 2-1, Hardenbergstraße 36a, 10623 Berlin, Germany Chair Measurement and Control,36a, Technische Universit¨ at Berlin, Secr.of ER 2-1, Hardenbergstraße 10623 Berlin, Germany (e-mail: [email protected], [email protected]). (e-mail: [email protected]). [email protected], ER 2-1, Hardenbergstraße 36a, 10623 Berlin, Germany (e-mail: [email protected], [email protected]). (e-mail: [email protected], [email protected]). Abstract: Abstract: This This paper paper presents presents a a control control architecture architecture suitable suitable for for autotrophic autotrophic cultivations cultivations in in aa stirred tank reactor feeding a gas mixture of H2/CO2/O2. Based on the employed multi-layer Abstract: This paper presents a control architecture suitable for autotrophic cultivations in a stirred tankThis reactor feeding a gas mixturearchitecture of H2/CO2/O2. Based on the employed multi-layer Abstract: paper presents acontrol control suitable for autotrophic cultivations in Aa structure, for simple gas phase no metabolic information of strain is required. stirred tank reactor feeding a gas mixture of H2/CO2/O2. Based on the employed multi-layer structure, forreactor simplefeeding gas phase control no ofmetabolic information of the the employed strain is required. A stirred tank a gas mixture H2/CO2/O2. Based on multi-layer structure, for simple gas phase control no metabolic information of the strain is required. A MIMO-PI controller connected to feedforward disturbance rejection based MIMO-PI controller connected to an an adaptive adaptive feedforward disturbance rejection based on on Aaa structure, for simple gas phase control no metabolic information of the strain is required. physical model allows for a gas phase feedback control. Thus, without further knowledge of MIMO-PI controller connected to an adaptive feedforward disturbance rejection based on a physical model allowsconnected for a gas to phase feedbackfeedforward control. Thus, without further knowledge MIMO-PI controller an adaptive disturbance rejection basedmodel on of a the autotrophic strain, experiments can be run to generate data and develop a process physical model allows for a gas phase feedback control. Thus, without further knowledge of the autotrophic strain, for experiments canfeedback be run tocontrol. generate datawithout and develop a process model physical model allows a gas phase Thus, further knowledge of including strain biological Combining both control and the autotrophic strain, experiments can be run to generate data gas andphase develop a process model including strain specific specific biological details. details. Combining both layers, layers, phase control and feeding feeding the autotrophic strain, experiments can model, be run results to generate data gas and develop a that process model including strain specific biological details. Combining both layers, gas phase control and feeding trajectory optimization with the process in a control architecture is suitable trajectory optimization with the process results in alayers, controlgas architecture thatand is suitable including strain specific biological details.model, Combining both phase control feeding for optimizing the process in a closed-loop. trajectory optimization with the process model, results in a control architecture that is suitable for optimizing the process in the a closed-loop. trajectory optimization with process model, results in a control architecture that is suitable for optimizing the process in a closed-loop. © 2019, IFAC (International of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. for optimizing the process Federation in a closed-loop. Keywords: Keywords: autotrophic autotrophic cultivation, cultivation, closed-loop, closed-loop, Ralstonia Ralstonia eutropha, eutropha, model-based model-based control, control, Keywords: autotrophic cultivation, closed-loop, Ralstonia eutropha, model-based control, modelling, gas phase control, optimization, multi-layer control modelling, gas phase control, optimization, multi-layer control Keywords: autotrophic cultivation, closed-loop, Ralstonia eutropha, model-based control, modelling, gas phase control, optimization, multi-layer control modelling, gas phase control, optimization, multi-layer control 1. INTRODUCTION should should be be controlled, controlled, but but only only three three manipulating manipulating varivari1. 1. INTRODUCTION INTRODUCTION ables are as gaseous feed flows. The has should beavailable controlled, but only three manipulating ables are available as gaseous feed flows. The controller controllervarihas 1. INTRODUCTION should be controlled, but only three manipulating varito compensate for harsh and quick external disturbances ables are available as gaseous feed flows. The controller has Using waste gases from industry for cultivating microto compensate for harsh and quick external disturbances Using waste gases from industry for cultivating microarepressure available as gaseous feed flows. The controller has to compensate for harsh and quick external disturbances Using waste gases frominvestigated industry forin cultivating micro- ables such as drops due to sampling, slow internal disorganisms is not only research projects such as pressurefor drops due to quick sampling, slow disturbances internal disorganisms is not only investigated in research projects to compensate harsh and external Using waste gases from industry for cultivating microsuch as pressure drops due to sampling, slow internal disorganisms is not only investigated in research projects turbances like nonlinear drifts in microbial gas consump(Takors et et al. (2018), (2018), Liew Liew et et al. (2016)), (2016)), but but also applied applied turbances like nonlinear drifts in microbial gas consump(Takors as pressure drops due to sampling, slow changes internal disorganisms is processes not onlyLiew investigated in research projects (Takors et al. al. (2018), et al. al. (2016)), but also also applied such tion rates and moderately quick metabolic due turbances drifts in microbial consumpin industrial (Humphreys and Minton (2018)). tion rates like and nonlinear moderately quick metabolicgas changes due in industrial processes (Humphreys and Minton (2018)). turbances like nonlinear drifts in microbial gas consump(Takors et al. (2018), Liew et al. (2016)), but also applied in industrial processes (Humphreys andCupriavidus Minton (2018)). to nutrient limitations. Due to the system’s nonlinearity tion rates and moderately quick metabolic changes due Ralstonia eutropha (R. e.), also named necato nutrient limitations. Due to the system’s nonlinearity Ralstonia eutropha (R. e.), also named Cupriavidus necation rates and moderately changes due in industrial processes (Humphreys andthe Minton (2018)). to nutrient limitations. Duequick to themetabolic system’s concepts nonlinearity Ralstonia eutropha (R. e.), also named Cupriavidus necaand its different time constants, controller for tor, is a bacterium which assimilates industrial offand its different time constants, controller concepts for tor, is a bacterium which assimilates the industrial offto nutrient limitations. Due to the system’s nonlinearity Ralstonia eutropha (R. e.), also named Cupriavidus necaand its different time constants, controller concepts for tor, is a bacterium which assimilates the industrial offlinear systems fail and robust approaches are too slow into gas component carbon-dioxide. R. e. converts CO 2 linear systems fail and robust approaches are too slow for into gas component carbon-dioxide. R. e. converts CO 2 and its different time constants, controller concepts for tor, component is a bacterium whichpolyhydroxybutyrate, assimilates the industrial offinto gas carbon-dioxide. R. e. converts CO setpoint tracking when fast disturbances occur. Instead, a linear systems fail and robust approaches are too slow for the bioplastic molecule which is, 2 2 setpoint tracking when fast disturbances occur. Instead, a the bioplastic molecule polyhydroxybutyrate, which is, linear systems failwhen and robust approaches are too slow for gas component carbon-dioxide. R. e. converts CO 2 into smart disturbance rejection, which is independent of the setpoint tracking fast disturbances occur. Instead, a amongst others, applied in tissue engineering (Ribeirothe bioplastic molecule polyhydroxybutyrate, which is, smart disturbance rejection, which is independent of the amongst others, applied in tissue engineering (Ribeirosetpoint tracking when fast disturbances occur. Instead, the bioplastic molecule polyhydroxybutyrate, which is, smart disturbance rejection, which is thus independent of thea metabolic behaviour of the cells and can be applied Samy et al. (2013), Reinecke and Steinb¨ u chel (2009)). This amongst others, applied in tissue engineering (Ribeirobehaviour of the cells andis thus can be applied Samy et al. (2013),applied Reinecke and Steinb¨ uchel (2009)). This metabolic disturbance rejection, which independent of the amongst others, inproteins tissue engineering (RibeiroSamy et al. (2013), Reinecke and Steinb¨ uchel hydrogenases (2009)). This smart for all kind of autotrophic gas cultivations, combined metabolic behaviour of the cells and thus canis applied bacterium also translates named for all kind of autotrophic gas cultivations, isbe combined bacterium also translates proteins named hydrogenases metabolic behaviour of the cells and thus can be applied Samycan et al. (2013), Reinecke and Steinb¨ uchel hydrogenases (2009)). This for here with a double loop PI controller. Such a control, which all kind of autotrophic gas cultivations, is combined that be employed in biotransformations due to their bacterium also translates proteins named with a double loop PI controller. Such a control, which that can bealso employed in biotransformations due to their here for all kind of different autotrophic gas cultivations, is combined bacterium translates proteins named hydrogenases can be used for organisms, has not been proposed here with a double loop PI controller. Such a control, which reduction potential towards co-factors (Lauterbach et al. that can be employed in biotransformations due to their can be used for different organisms, has not been proposed reduction potential towards co-factors (Lauterbach et al. here with a double loop PI controller. Such control, which that canCurrently, be employed inisbiotransformations due to et their can be used for different organisms, has nota been proposed so far. The implementation and performance results are (2011)). R. e. investigated for the production reduction potential towards co-factors (Lauterbach al. so far. The for implementation and performance results are (2011)). Currently, R. e. is investigated for the production can be used different organisms, has not been proposed reduction potential towards co-factors (Lauterbach et al. (2011)). Currently, R. e. is investigated for the production presented in this work. so far. The implementation and performance results of terpenes (Krieg et al. (2018)) and other basic chemicals presented in this work. of terpenes (Krieg etR.al. (2018)) and other basic chemicals so far. The implementation and performance results are are (2011)). Currently, e. is investigated for the production This paper focusses on this work. (Cr´ eepin (2016)). of terpenes (Krieg et al. (2018)) and other basic chemicals presented This paperin focusses on the the adaptive adaptive gas gas phase phase control control layer layer (Cr´ pin et et al. al. (2016)). presented in this work. of terpenes (Krieg et al. (2018)) and other basic chemicals and is organized as follows: After the paper focusses the adaptive gas phase control layer In order to optimize (Cr´ epin et (2016)).the and is organized ason follows: After describing describing the process process In order toal. optimize the target target compound compound yields, yields, closedclosed- This This paper focusses on the adaptive gasthe phase control layer (Cr´ epin et al. (2016)). and is organized as follows: After describing the process setup in sec. 2, information about overall control loop process control is desirable. In an autotrophic process, In order to optimize the target compound yields, closedsetupis in sec. 2, as information about the overall control loop process control isthe desirable. In an autotrophic process, and organized follows: After describing the process In order to optimize target compound yields, closedloop process control is desirable. In an autotrophic process, scheme is provided in sec. 3, briefly. Details about the setup in sec. 2, information about the overall control where the are supplied form, the provided in sec. 3, about briefly.the Details about the whereprocess the substrates substrates suppliedInin inangaseous gaseous form, process, the disdis- scheme setup inis sec. 2, phase information overall control loop control isare desirable. autotrophic model-based gas control layer are given in sec. 4. In scheme is provided in sec. 3, briefly. Details about the solved gas concentrations represent the biologically availwhere the substrates are supplied in gaseous form, the dismodel-based gas phase control layer are given in sec. 4. In solved gas concentrations represent the biologically availisevaluate provided incontroller, sec. 3, layer briefly. Details about the where the substrates are supplied in gaseous form, carbontheavaildis- scheme order to the results of cultivations are model-based gas phase control are given in sec. 4. In able nutrients that need to be controlled. Besides solved gas concentrations represent the biologically order to evaluate the controller, results of cultivations are able nutrients that need to be controlled. Besides carbongas phase control layer are given in sec. 4.are In solved gas concentrations represent the biologically avail- model-based order toinevaluate the controller, results of cultivations shown sec. 5. Finally, potentials of the designed control dioxide, R. e. needs hydrogen and oxygen for growth. able nutrients that need to be controlled. Besides carbonshowntoinevaluate sec. 5. Finally, potentials of theofdesigned control dioxide, R. e. needs hydrogen and oxygen for growth. order the controller, results cultivations are able nutrients that need to be controlled. Besides carbondioxide, R. e. needs hydrogen and oxygen for growth. architecture are pointed out in sec. 6. shown in sec. 5. Finally, potentials of the designed control Measuring all dissolved gases H O2 directly is architecture are pointed out in sec. 6. 2 and Measuring all dissolved gases and H22 ,, CO CO 2 and 2 directly is shown in sec.are 5. Finally, dioxide, R. as e. needs hydrogen oxygen forO architecture pointed potentials out in sec.of6.the designed control impossible in-line sensors are unavailable. Measuring all dissolved gasesfor H22hydrogen , CO Ogrowth. 2 2 2 and 2 directly is impossible as in-line sensors for hydrogen are unavailable. architecture are pointed out in sec. 6. Measuring all dissolved gases H , CO and O directly is 2 2 Even if hydrogen measurable, traimpossible as in-line sensorswere for 2hydrogen are planned unavailable. 2. MATERIALS AND Even if dissolved dissolved hydrogen were measurable, planned tra2. MATERIALS AND METHODS METHODS impossible as in-line sensors for hydrogen are unavailable. Even if dissolved hydrogen were measurable, planned trajectories for the three gas compounds often would not be 2. MATERIALS AND METHODS jectories for the three gas compounds often would not be Even if dissolved hydrogen were measurable, planned 2. MATERIALS AND METHODS All feeding jectories for the three gas compounds often would nottrabe The strain used realizable due to an initially unknown gas consumption by realizablefor duethe to three an initially unknown gas consumption jectories gas compounds often would not by be The strain used was was Ralstonia Ralstonia eutropha eutropha (H16). (H16). All feeding the bacterium. realizable due to an initially unknown gas consumption by compositions are found in 1. volume of strain used Ralstonia (H16). All feeding the bacterium. realizable due to an initially unknown gas consumption by The compositions arewas found in Tab. Tab.eutropha 1. The The initial initial volume of the the Instead of controlling the dissolved gases, a gas phase the bacterium. The strain used was Ralstonia eutropha (H16). All feeding cultivation was 10 L of defined medium including inocuInstead of controlling the dissolved gases, a gas phase compositions are found in Tab. 1. The initial volume of the the bacterium. cultivation was 10 L of defined medium including inocuInstead of controlling the dissolved gases, a gas phase control is in work that realizes desired cultivation compositions are10 found Tab. 1.medium The initial volumeinocuof the was L of indefined including lum. The medium concentrations of iron trace control isofsuggested suggested in this this work that gases, realizesa the the Instead controlling the dissolved gasdesired phase lum. The initial initial medium concentrations of iron and andinocutrace control is suggested in this work that realizes the desired gas composition as well as a constant excess pressure in cultivation was 10 L of defined medium including lum. The initial medium concentrations of iron and trace elements were 1/100 of those in the feeding. Ammonium gas composition as well as work a constant excess pressure in elements were 1/100 of those in the feeding. Ammonium control is suggested in four this thatofrealizes the desired the headspace. Ideally, the phase gas composition as well as variables a constant pressure in lum. The were initial medium concentrations of iron and trace concentration was 1/50 the and 1/10 1/100 of of those in the feeding. Ammonium the headspace. Ideally, four variables of excess the gaseous gaseous phase gas composition as well as a constant excess pressure in elements concentration was 1/50 of the feeding feeding and phosphate phosphate 1/10 the headspace. Ideally, four variables of the gaseous phase elements were 1/100 of those in the feeding. Ammonium  of the feeding concentration. The digital control unit of concentration was 1/50 of the feeding and phosphate 1/10 This work was supported by the DFG in the framework of the  the headspace. theframework gaseous phase of the feeding concentration. The digital control unit of This work was Ideally, supportedfour by variables the DFG inofthe of the concentration 1/50 of15the feeding and phosphate 1/10  of the feeding was concentration. The digital control unit of3 the explosion-protected L stirred tank reactor with cluster of excellence UniCat. by the DFG in the framework of the This work was supported the explosion-protected 15 L stirred tank reactor with 3 cluster of excellence UniCat.  of the feeding concentration. The digital control unit This of work was supported the explosion-protected 15 L stirred tank reactor with of3 cluster excellence UniCat. by the DFG in the framework of the the explosion-protected 15 L stirred tank reactor with 3 cluster of excellence UniCat. 2405-8963 © 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

Copyright © 2019 IFAC 733 Copyright © under 2019 IFAC 733 Control. Peer review responsibility of International Federation of Automatic Copyright © 2019 IFAC 733 10.1016/j.ifacol.2019.06.150 Copyright © 2019 IFAC 733

2019 IFAC DYCOPS 734 Flavia Neddermeyer et al. / IFAC PapersOnLine 52-1 (2019) 733–738 Florianópolis - SC, Brazil, April 23-26, 2019

Table 1. Feedings composition for R. e. cultivations Feeding

Chemical

Phosphate (P)

Na2 HPO4 (2H2 O) KH2 PO4 NH4 Cl MgSO4 (7H2 O) CaCl2 (2H2 O) FeCl3 (6H2 O) NiCl2 (6H2 O) ZnSO4 (7H2 O) MnCl2 (2H2 O) H3 BO3 CuCl2 (2H2 O) Na2 MoO4 (2H2 O) CoCl2 (6H2 O)

Ammonium (N) Iron and trace elements

Conc. [g L

1]

39 13 296 20 1 1 0.024 0.01 0.003 0.03 0.001 0.003 0.02

rushton turbines regulated the temperature at 30 ◦ C, the pH at 6.8, and the stirrer speed at 500 rpm. The dissolved gas probes were Mettler Toledo InPro6800 and InPro5000i, the gas phase sensors were BlueInOne Cell and BCP-H2 from BlueSens, the mass flow controllers and the pressure sensor were produced by Bronkhorst. Since the mass flow controllers pumped the gas mix into the reactor headspace, a transport into the liquid phase was enhanced by a compressor type N726FT.29E manufactured by KNF Neuberger. It sucked the cooled and filtered gas from the headspace and blowed it through a microfilter and a sparger into the liquid phase at a rate of about 7 L min−1 . 3. CLOSED-LOOP CONTROL SCHEME Since R. e. is grown autotrophically, the system’s input vector u see eq. (1), encompasses flow rates ui for liquid feedings (uN , uFe , uP ), correction fluids (ubase , uacid , uantifoam ) and gaseous feed flows (qH2 , qCO2 , qO2 ). uTsystem =(uN uFe uP qH2 qCO2 qO2 (1) ubase uacid uantifoam ) where the indices relate to the substance. All flows of the correction fluids were calculated during the cultivation by standard PI controller located in the DCU of the bioreactor. Volumina of the correction fluids were measured and considered in the employed models. All volumetric gaseous feed flows (qH2 , qCO2 , qO2 ) were calculated by a PIMIMO controller in order to maintain the desired excess statesest

DEKF, SPKFprocess model ugas,est

FFDR

EKFgas model

qff rΔP rgas

PI-MIMO gas phase controller

qgas

uN, uP, uFe

ΔP, xgas OD, cgas, Vacid, Vbase

on-line optimization

Fig. 1. Control scheme for the autotrophic cultivation of R. e. Basic closed-loop controller for pH, foam level and temperature are independent and not depicted. 734

pressure r∆P and the desired gas fractions (rH2 , rCO2 , rO2 ). Trajectories of the latter and liquid feed flows resulted from model-based optimizations done beforehand, and from closed-loop control active during the cultivation, e.g. for optimal experimental design described in Neddermeyer et al. (2016) or product maximization as in Neddermeyer et al. (2015), using a process model initially described in the latter. Employing the same model, the state vector was estimated (est) by a Sigma Point Kalman Filter (SPKF) or an Extended Kalman Filter with a dynamic system noise matrix (DEKF). The overall process control scheme is depicted in Fig. 1. Optical density (OD), dissolved gas concentrations (cgas ), fed amounts of base and acid (Vbase , Vacid ), gas fractions in the headspace xgas and excess pressure ∆P serve as on-line or at-line measurements for state estimation. Details about the gas phase control layer (grey) are given in the next section. 4. MODEL-BASED FFDR PI-MIMO GAS PHASE CONTROLLER In the present system, gas fractions of the headspace together with pressure are adjusted in two serial PI control loops, CLP and CLgas , as originally suggested by Rossner (2014). Note, that the index ’gas’ represents hydrogen, carbon-dioxide and oxygen. Each individual feed flow can be expressed as qgas = xgas,feed · qt , (2) where xgas,feed represents the gas content of a specific component in the total feed flow qt . The latter is used for maintaining a constant excess pressure and manipulated by CLP . The former is obtained via CLgas for the specific component ’gas’. As the time constant of the headspace changes by a factor of almost 50 during the course of a cultivation, this is taken into account by a feedforward disturbance rejection (FFDR). To calculate the FFDR, the consumption rates of the gases have to be known, which are estimated with a headspace model described in sec. 4.1, before sec. 4.2 outlines the controllers. Tuning parameters of the EKF to estimate the consumption rates are provided in sec. 4.3. 4.1 Nonlinear headspace model A nonlinear model of the reactor headspace was formulated with the aim to estimate the gas consumption rates and forward them in terms of a disturbance rejection. Fig. 2 illustrates major state and manipulating variables of the headspace model. The headspace model consists of 9 state variables which are system pressure (P ), amount (ngas ) of material (gas) in the headspace of the three gas compounds. A fourth gas amount, nrest , compensates for remains of nitrogen and evaporated water in the gas phase. The amount of nitrogen might increase by incoming air in periods of underpressure. Three gas consumption rates, νgas , mainly describe gas volume flows across the liquid-gas interface, which is indicated by an arrow in Fig. 2, but also compensate for sudden pressure drops due to sampling. Since the headspace volume (Vhead ) changes due to liquid feedings ui , the liquid volume (Vl ) has to be considered as well. This results in the state vector xT = (P nH2 nCO2 nO2 nrest νH2 νCO2 νO2 Vl ). (3)

2019 IFAC DYCOPS Flavia Neddermeyer et al. / IFAC PapersOnLine 52-1 (2019) 733–738 Florianópolis - SC, Brazil, April 23-26, 2019

qgas

O2 H2 CO2 P ugas

qleak

ui Vl

Fig. 2. Scheme of the headspace model derived from two connected systems. Both system boundaries are indicated with broken lines. States are shown in black and manipulating variables in grey. According to Fig. 2, inlet gaseous volume flows qgas as well as a variable leakage flow qleak both given in L h−1 , represent additional manipulating variables of the model. When reformulating qgas as molar flows with temperature T and general gas constant R qH2 · 10−3 n˙ H2,feed = P · (4) R·T qCO2 · 10−3 n˙ CO2,feed = P · (5) R·T qO2 · 10−3 n˙ O2,feed = P · , (6) R·T and considering the leakage gasflow (qleak ) P · qleak · 10−3 (7) n˙ leak = R·T the undisturbed dynamic model given in SI units, with the exception of V expressed in L, is defined as  n˙ gas · R · T ˙ (8) P = Vhead · 10−3 n˙ H2 =n˙ H2 ,feed − νH2 n H2 − n˙ leak · ·R·T (9) P · Vhead · 10−3 n˙ CO2 =n˙ CO2 ,feed − νCO2   (nrest + nH2 + nO2 ) · R · T − n˙ leak · 1 − (10) P · Vhead · 10−3 n˙ O2 =n˙ O2 ,feed − νO2 nO2 − n˙ leak · ·R·T (11) P · Vhead · 10−3 n˙ rest =0 (12) (13) ν˙ H2 =0 ν˙ CO2 =0 (14) (15) ν˙ O2 =0 V˙ l =uN + uFe + uP + uantifoam + uacid + ubase − usampling . (16) The variable Vhead is Vhead = Vreactor − Vl , (17) with a total reactor volume of Vreactor = 16 L including vessel and tubing. 735

735

The input vector of the headspace model is similar to eq. (1), but for a more generalized applicability qleak is assumed to be variable and thus represents an additional input. Since all gas phase compounds are measured as gas fractions (xgas ) and ∆P = P − P0 is monitored as excess pressure (mbar), the measurement vector as a function of states yields P − P0 (18) y1 = y∆P = 100 R·T (19) y2 = xH2 = nH2 · P · Vhead · 10−3 R·T (20) y3 = xCO2 = nCO2 · P · Vhead · 10−3 R·T (21) y4 = xO2 = nO2 · P · Vhead · 10−3 (22) y5 = Vl . It is assumed that in the process major changes of the liquid volume are caused by correction fluids and feedings. Thus, an on-line calculated volume serves as synthetic measurement whereas y1 to y4 are detected every 5 seconds by the sensors introduced in sec. 2. For applying a Kalman filter, all equations are assumed to be extended by appropriate noise terms. By this, the gas consumption rates νgas can be estimated (est), which change drastically over the course of a cultivation. This information will be used to determine the FFDR. Reusing the ideal gas law again leads to the desired feedforward part for each individual gas component. qgas,ff = qgas,est + qgas,leak (23) R·T + xgas,est · qleak . (24) = νgas,est · −3 10 · P The overall feedforward gas flow is  R·T · νgas,est + qleak (25) qff = −3 10 · P 4.2 Gas phase control laws

Ideally, in the present cultivation system, three manipulating variables qgas , see eq. (1), serve to adjust four control variables, which are the gas fractions xgas and the excess pressure ∆P . This is impossible in practice because the problem is underactuated. Hence, one gas compound has to remain uncontrolled, which can be selected by choosing an appropriate mode. For this work, due to the large solubility of CO2 , hydrogen xH2 and oxygen xO2 were controlled in parallel PI loops (CLH2 and CLO2 ) that together represent the first part of the two stage gas phase controller. In Fig. 3, both control loops (gas content in white and pressure in grey) and their interface are shown schematically. Manipulating variables qgas are calculated in two stages. In stage two, the required total gas flow (qt ) needed to maintain the desired excess pressure is calculated by a PI controller (CLP ) with FFDRmodulated gain scheduling and feedforward disturbance rejection (qff ). The total gasflow qt thus consists of the feedforward and a closed-loop part qc . qt = qff +qc . (26)  FFDR

Combining the equations of the headspace model with eq. (26) leads to the dynamic evolution of the excess pressure

2019 IFAC DYCOPS 736 Flavia Neddermeyer et al. / IFAC PapersOnLine 52-1 (2019) 733–738 Florianópolis - SC, Brazil, April 23-26, 2019

xH , xO 2

rH , rO 2

CLH2 ,CLO2

2

FF

FFDR

qff

rΔP

qt

2

uH2 , uO2 , uCO

2

Normalization  ugas = qt

qgas

CLP ΔP

Fig. 3. Block diagram of a serial PI-MIMO gas phase controller for the adjustment of pressure, hydrogen and oxygen in the gas phase. Broken and solid lines represent data and mass transport, respectively. qc qc · ∆P + · P0 ∆P˙ = Vhead Vhead     R·T νgas,est − + −3 νgas , (27) 10 · Vhead    z

where P0 , νgas,est and z represent the ambient pressure, the estimated rates of gas transfer, which will be obtained below, and a disturbance, respectively. In a more standard control oriented notation x(t) ˙ = (a · x(t) + b) · u(t) + z(t) (28) results. As ax << b, a simple linear control law is suggested. To guarantee exact set-point tracking for constant reference values of the excess pressure, r∆P , given in mbar, integral action will be necessary. Combining an integral controller with the nonlinear model eq. (28) leads to a locally only marginally stable system. Asymptotic stability of the linearized system can be recovered by adding a proportional term. The dynamic behaviour of the plant can be characterized by a time constant Vhead , (29) TP = qff that approximates the residence time in the headspace. From a root locus argument and for a fixed integral gain KP,I = 0.1 the proportional gain KP,P is adjusted such that the zero of the PI controller is slightly to the right of the system pole −1/TP . However, as this time constant significantly decreases in the course of a cultivation, it turned out to be beneficial when the closedloop bandwidth was increased accordingly. This can be achieved in an adhoc fashion by multiplying qc with qff , finally resulting in (30) qc = KP,P · eP + KP,I · qff · eP,int , with the pressure related control error (31) eP = r∆P − ∆P. Using the trapezoidal rule for integration, yields the integrated error according to (eP + eP,prior ) dt, (32) eP,int = eP,int + 2 with dt being the sampling time, and eP,prior the control error of the previous time step. The total feed flow qt has to be realized by the individual feeds (33) qt = qH2 + qCO2 + qO2 . With the CLgas controller only two of them are determined. An obvious solution as 736

qCO2 = qt − qH2 + qO2 (34) will be ruled out below to allow for softer changes of the gas fractions and thus preventing overshootings. Starting point are reference values rgas for the individual component fractions that cannot be chosen independently, but have to obey rH2 + rCO2 + rO2 + xH2 O = 100 %, (35) with xH2 O being the constant gas fraction of evaporated water. Simple PI controllers designed again by a root locus argument and based on control errors egas = rgas − xgas , gas = {O2 , H2 } (36) are used with tuned gains Kgas,P and Kgas,I . The output ∆ugas = Kgas,P · egas + Kgas,I · egas,int of a controller multiplied by qt represents a designed feed flow that can be realized by a mass flow controller. A feed forward term (FF) based on the desired reference value is added to unburden the controller, i. e., the controller output reads uH2 = uH2 ,ref + ∆uH2 · qt = rH2 · qt + ∆uH2 · qt (37) uO2 = (rO2 + ∆uO2 ) · qt . (38) The desired feed flow of CO2 is written down in a similar fashion uCO2 = (rCO2 + ∆uCO2 ) · qt , (39) however, as pointed out above, the unknown part calculated according to ∆uCO2 = −(∆uH2 + ∆uO2 ) (40) leads to unsatisfactory results. For that reason, the correction of the CO2 feed stream is filtered according to the feed gas composition of the prior sampling instant ∆uCO2 = −xCO2 ,feed,prior · (∆uH2 + ∆uO2 ). (41) All feed rates ugas are constrained from below zero as negative flow rates cannot be realized. As with eq. (37)-(39) the desired overall flow qt is not met, the normalized and actually applied feed streams read qt · u H2 (42) qH2 = uH2 + uCO2 + uO2 qt · uCO2 (43) qCO2 = uH2 + uCO2 + uO2 qt qO2 = · uO2 , (44) uH2 + uCO2 + uO2 with xgas,feed = ugas /(uH2 + uCO2 + uO2 ). 4.3 Extended Kalman filter parameter In chapter 4.1, a headpace gas model was introduced which enables aFFDR by estimating the needed summarized gasflow ( νgas ) in each timestep during the cultivation. To do so, the estimated gas amount rates of (13) to (15) are transformed to volume flows R · T 1000 L · , (45) qgas,est = νgas,est P m3 and later inserted in (23) to calculate the FFDR. When using an EKF to estimate νgas of (45), three matrices have to be designed. Matrix Q describes the system’s noise, matrix P0 gives the variance of the initial values and matrix R is the covariance matrix of the measurements. In the following, the matrix designs are explained. Offdiagonal entries of Q were set to zero and the diagonal

2019 IFAC DYCOPS Flavia Neddermeyer et al. / IFAC PapersOnLine 52-1 (2019) 733–738 Florianópolis - SC, Brazil, April 23-26, 2019

elements/variances (Qii ) of the EKF Q-matrix were calculated empirically. Starting point is a simple example system x(t) ˙ = ξ(t) (46) that produces a Brownian motion upon integration with variance q 2 t, when ξ(t) is white, i.e., the slope of an envelop bounding about 68 % of all realization x(t) is q. In x(t) ˙ = a · x(t) + ξ(t) (47) ξ(t) is responsible for the ’uncertainty’ of the right hand side, i.e., the slope of x(t). This is now used in the nonlinear case. To obtain the maximal slopes of the differential equations, x˙ i,max , prior experiments were evaluated. It is assumed that a dynamical inaccuracy of max 10 % in the right hand side is described by the system noise, which is resembled by an entry in the Q-matrix. This leads to the Q-matrix with squared values on the diagonal   4.42 · 104 Pa2  8.52 · 10−6 mol2     1.1 · 10−5 mol2   2  1.1 · 10−5 mol2    x˙ i,max   Qii = (48) =  2.13 · 10−5 mol2  . 5.63 · 10−2 m6 h−2  10    7.7 · 10−9 m6 h−2    7.41 · 10−3 m6 h−2  1.69 · 10−3 L2 Also, for the initial states covariance matrix P0 , all offdiagonal entries were set to zero. To calculate P0,ii , a relative error (ei ) of each initial state (index: 0) was assumed, multiplied by the initial value and squared   (0.1 · P0 )2  (0.08 · n0,H2 )2    (0.08 · n0,CO2 )2     (0.08 · n0,O2 )2   2 2  (49) P0,ii = (ei · xi,0 ) =  (0.05 · nrest )  .  (0.3 · ν )2    H  (0.3 · ν 2 )2  CO2    (0.3 · νO )2  2 (0.02 · V0,l )2 Known initial values were inserted, and for all unknown initial states, namely nrest and νgas , a set of estimates derived from a prior experiment was taken (50) nrest = 0.02 mol −1 (51) νH2 = 2.13 mol h −1 (52) νCO2 = 0.28 mol h (53) νO2 = 0.71 mol h−1 . To build the covariance matrix of the measurement noise R, relative (index: rel) sample errors were postulated since the linear gas sensors are calibrated by a onepoint calibration. Slightly wrong calibrated slopes lead to smaller errors at lower concentrations than at higher ones. Due to the detection limit at very low concentrations, a minimum (min) error is suggested (see Tab. 2) leading to (54) Rii = max(emin , erel ). The relative error of Vl in the measurement noise matrix R (see Tab. 2) is set to a higher value than for the initial system’s noise P0 in eq. (49) to account for the unmodelled microbial water production during the cultivation. As for Q and P0 , all off-diagonal elements in R were set to zero. For the gas phase model, global observability was proven 737

737

Table 2. Postulated measurements errors Measurement P xH2 xCO2 xO2 Vl

emin 0.5 0.5 0.3 0.3 0.05

erel 0.01·y1 0.01·y2 0.02·y3 0.02·y4 0.05·y5

Unit mbar % % % L

analytically by Lie-derivatives using the toolbox STRIKEGOLDD2 v2.0.1 developed by Villaverde A.F. et al. (2019). 5. RESULTS The employed controller kept the reference trajectories for pressure and gas composition to a satisfactorily extent as presented in Fig. 4, left column. Even when large volumes of cultivation broth were sampled, causing a sudden pressure drop as it was the case between batch age 22-26 h, the excess pressure was adjusted immediately. Due to an employed gas model estimation sampling rate of 0.1 h, which was chosen to obtain smoother trajectories, these pressure drops were not compensated for by a correction of the estimates of νgas . Instead, the CLP unit of the double layer PI-controller in Fig. 3 adjusted fast pressure changes with its lower sampling time 0.0042 h. Internal disturbances resulting in quickly changing gas uptake rates were also compensated for by the controller. Here, between batch age 7-17 h indicated by vertical lines, the gas uptake rates decreased abruptly due to the punctual feeding of antifoam agent, which inhibits gas transfer and thus all dissolved gas concentrations (not shown) decreased. When gases are missing in the liquid phase, the organisms starve and thus their gas uptake diminishes as well. It can be observed that a gas uptake drop leads to a short overshoot in pressure until the gas flow rates are adjusted by the CLP control unit. The developed gas controller also worked when atmospheric air entered the system and thus nitrogen polluted the gas phase. In Fig. 4 right column, the gas phase variables of a cultivation period are presented, where data exchange was interrupted for one hour (vertical lines) due to a server breakdown. Accordingly, no gas was fed, the excess pressure dropped drastically below zero and thus passed the tightness limit causing an inflow of air. In such an event, summarizing the three measured gas fractions plus evaporated water yields a value below 100 % and indirectly confirms the presence of nitrogen in the system. Restarting the gas phase controller after fixing the server communication problems, first leads to oscillations and after an hour the setpoints are well tracked again. Oscillations after the communication gap result from the large discrepancies between pressure and gas composition towards their corresponding set values. These initially large control errors are integrated in both layers CLP and CLgas and slowly reduced in an oscillating manner. Large control errors result from software or hardware interruptions, but also from stepwise setpoint changes. To avoid oscillations in standard operation, setpoint trajectories should be ramped. Microorganisms change their metabolism and thus gas uptake composition during a cultivation. At batch age 10 h in the left part of Fig. 4, 5.7 L h−1 of the entire gasflow (34.1 L h−1 ) was oxygen representing 16.7 % of qt .

2019 IFAC DYCOPS 738 Flavia Neddermeyer et al. / IFAC PapersOnLine 52-1 (2019) 733–738 Florianópolis - SC, Brazil, April 23-26, 2019

100

∆P

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0 100

0 80 60 40 20

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60 40

30 20 10

20 0 10

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5

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Fig. 4. Left: Gas phase variables ∆P in mbar and xgas in % of a cultivation with abrupt changes in the fed gas flows (qgas in L h−1 ) due to antifoam adding. Control setpoints are given in red and measured values in black. Right: A cultivation phase with a strong disturbance. Due to a one-hour database disconnection (vertical lines), the gas phase was uncontrolled and environmental nitrogen entered the system caused by a negative pressure. Nonetheless, only the commanded 7 % oxygen are measured in the gas phase. Apparently, the controller needs to feed relatively more oxygen to maintain this low reference at this time of the cultivation. In the course of the experiment, this relation shifts towards the opposite. These rather slow changes are tracked and compensated for by the integral part of CLgas . 6. CONCLUSION In this contribution, an autotrophic control architecture for R. e. consuming H2 /CO2 /O2 was shown containing an adaptive gas phase controller to track the set trajectories of pressure and two out of three gas fractions. It allows also to select the controlled gas components and can be adapted to a different gas composition. Without knowledge of the metabolism and without parameter adjustment, any strain suitable for autotrophic cultivations can be grown to generate data for a process model which is required for a subsequent optimized closed-loop control. REFERENCES Cr´epin, L., Lombard, E., and Guillouet, S.E. (2016). Metabolic engineering of Cupriavidus necator for 738

heterotrophic and autotrophic alka(e)ne production. Metab. Eng., 37, 92–101. Humphreys, C.M. and Minton, N.P. (2018). Advances in metabolic engineering in the microbial production of fuels and chemicals from C1 gas. Curr. Opin. Biotech., 50, 174–181. Krieg, T., Sydow, A., Faust, S., Huth, I., and Holtmann, D. (2018). CO2 to terpenes: Autotrophic and electroautotrophic α-humulene production with Cupriavidus necator. Angew. Chem. Int. Edit., 57(7), 1879– 1882. Lauterbach, L., Liu, J., Horch, M., Hummel, P., Schwarze, A., Haumann, M., Vincent, K.A., Lenz, O., and Zebger, I. (2011). The hydrogenase subcomplex of the NAD+reducing [NiFe] hydrogenase from Ralstonia eutropha – insights into catalysis and redox interconversions. Eur. J. Inorg. Chem., 2011(7), 1067–1079. Liew, F., Martin, M.E., Tappel, R.C., Heijstra, B.D., Mihalcea, C., and K¨opke, M. (2016). Gas fermentation-a flexible platform for commercial scale production of lowcarbon-fuels and chemicals from waste and renewable feedstocks. Front. Microbiol., 7, 694. Neddermeyer, F., Rossner, N., and King, R. (2015). Model-based control to maximise biomass and PHB in the autotrophic cultivation of Ralstonia eutropha. IFAC-PapersOnLine, 48(8), 1100–1107. Neddermeyer, F., Marhold, V., Menzel, C., Kr¨ amer, D., and King, R. (2016). Modelling the production of soluble hydrogenase in Ralstonia eutropha by on-line optimal experimental design. IFAC-PapersOnLine, 49(7), 627– 632. Reinecke, F. and Steinb¨ uchel, A. (2009). Ralstonia eutropha strain h16 as model organism for pha metabolism and for biotechnological production of technically interesting biopolymers. J. Mol. Microbiol. Biotechnol., 16(1-2), 91–108. Ribeiro-Samy, S., Silva, N.A., Correlo, V.M., Fraga, J.S., Pinto, L., Teixeira-Castro, A., Leite-Almeida, H., Almeida, A., Gimble, J.M., Sousa, N., Salgado, A.J., and Reis, R.L. (2013). Development and characterization of a PHB-HV-based 3D scaffold for a tissue engineering and cell-therapy combinatorial approach for spinal cord injury regeneration. Macromol. Biosci., 13(11), 1576– 1592. Rossner, N. (2014). Robuste modellbasierte Prozessf¨ uhrung auf Basis von Gaußschen Mischdichten am Beispiel der Bray-Liebhafsky-Reaktion und der autotrophen Kultivierung von Ralstonia eutropha H16. Dissertation (in german), Technische Universit¨at Berlin, Berlin. Takors, R., Kopf, M., Mampel, J., Bluemke, W., Blombach, B., Eikmanns, B., Bengelsdorf, F.R., WeusterBotz, D., and D¨ urre, P. (2018). Using gas mixtures of CO, CO2 and H2 as microbial substrates: The do’s and don’ts of successful technology transfer from laboratory to production scale. Microb. Biotechnol., 11(4), 606– 625. Villaverde A.F., Evans N.D., Chappell M.J., and Banga J.R. (2019). Input-dependent structural identifiability of nonlinear systems. IEEE Contr. Syst. Lett., 3(2), 1– 6.