Ames Laboratory Accepted Manuscripts Ames Laboratory

8-2019

Multiple-Model Adaptive Control of a Hybrid Solid Oxide Fuel Cell Multiple-Model Adaptive Control of a Hybrid Solid Oxide Fuel Cell

Gas Turbine Power Plant Simulator Gas Turbine Power Plant Simulator

Alex Tsai United States Coast Guard Academy

Paolo Pezzini Ames Laboratory, ppezzini@ameslab.gov

David Tucker United States Department of Energy

Kenneth M. Bryden Iowa State University and Ames Laboratory, kmbryden@iastate.edu

Follow this and additional works at: https://lib.dr.iastate.edu/ameslab_manuscripts

Part of the Energy Systems Commons

Recommended Citation Recommended Citation Tsai, Alex; Pezzini, Paolo; Tucker, David; and Bryden, Kenneth M., "Multiple-Model Adaptive Control of a Hybrid Solid Oxide Fuel Cell Gas Turbine Power Plant Simulator" (2019). Ames Laboratory Accepted Manuscripts. 375. https://lib.dr.iastate.edu/ameslab_manuscripts/375

This Article is brought to you for free and open access by the Ames Laboratory at Iowa State University Digital Repository. It has been accepted for inclusion in Ames Laboratory Accepted Manuscripts by an authorized administrator of Iowa State University Digital Repository. For more information, please contact digirep@iastate.edu.

Multiple-Model Adaptive Control of a Hybrid Solid Oxide Fuel Cell Gas Turbine Multiple-Model Adaptive Control of a Hybrid Solid Oxide Fuel Cell Gas Turbine Power Plant Simulator Power Plant Simulator

Abstract Abstract A multiple model adaptive control (MMAC) methodology is used to control the critical parameters of a solid oxide fuel cell gas turbine (SOFC-GT) cyberphysical simulator, capable of characterizing 300 kW hybrid plants. The SOFC system is composed of a hardware balance of plant (BoP) component, and a high fidelity FC model implemented in software. This study utilizes empirically derived transfer functions (TFs) of the BoP facility to derive the MMAC gains for the BoP system, based on an estimation algorithm which identifies current operating points. The MMAC technique is useful for systems having a wide operating envelope with nonlinear dynamics. The practical implementation of the adaptive methodology is presented through simulation in the matlab/simulink environment.

Disciplines Disciplines Energy Systems

This article is available at Iowa State University Digital Repository: https://lib.dr.iastate.edu/ameslab_manuscripts/375

Alex TsaiUnited States Coast Guard Academy,

New London, CT 06320

Paolo PezziniAmes Laboratory,

Iowa State University,

Ames, IA 50011

David TuckerU.S. Department of Energy,

National Energy Technology Laboratory,

Morgantown, WV 26505

Kenneth M. BrydenAmes Laboratory,

Iowa State University,

Ames, IA 50011

Multiple-Model Adaptive Controlof a Hybrid Solid Oxide Fuel CellGas Turbine Power PlantSimulatorA multiple model adaptive control (MMAC) methodology is used to control the criticalparameters of a solid oxide fuel cell gas turbine (SOFC-GT) cyberphysical simulator,capable of characterizing 300 kW hybrid plants. The SOFC system is composed of a hard-ware balance of plant (BoP) component, and a high fidelity FC model implemented insoftware. This study utilizes empirically derived transfer functions (TFs) of the BoP facil-ity to derive the MMAC gains for the BoP system, based on an estimation algorithmwhich identifies current operating points. The MMAC technique is useful for systems hav-ing a wide operating envelope with nonlinear dynamics. The practical implementation ofthe adaptive methodology is presented through simulation in the MATLAB/SIMULINK

environment. [DOI: 10.1115/1.4042381]

Introduction

The National Energy Technology Laboratory (NETL) of theU.S. Department of Energy (DoE) has researched fuel cell (FC)gas turbine hybrid systems for over a decade [1–3]. Studies haveshown that pressurizing a solid oxide fuel cell (SOFC) increasesits efficiency and in turn would increase the efficiency of existingconventional power plants by 65% based on coal, or 70% basedon natural gas, when the FC is coupled to a gas turbine [4,5].Given the fragility of the ceramic material which the SOFC elec-trolyte is composed of, an obvious concern arises when this deviceis coupled to a robust pressure source, as is the compressor of anauxiliary pressure unit. Within a conventional power plant, the FCwould replace the combustor, providing the thermal heat requiredby the turbine. By utilizing the compressor’s pressurized air, theSOFC in turn benefits, and it is this reciprocity between the twopower generating devices which produces the overall predictedefficiency. The synergy that results in this concept holds the prom-ise of a reduced emissions system with the potential for the inclu-sion of renewable sources of energy [4,5].

However, much research is still needed to fully understand allthe aspects concerning the stability and performance of the hybridplant. One major concern is the difference in pressure that woulddevelop between the anode and cathode sides of the FC, when thefuel and air streams are independently controlled. This raises thequestion of whether it is best to control the system with a central-ized or de-centralized controller, a linear or a nonlinear algorithm,or an adaptive control methodology [6–9]. An additional problemis the issue of compressor stall and surge due to the added volumeto the compressor plenum, as well as thermal heat gradients withinthe FC when insufficient cathode airflow is present, or when it isin excess. It has been determined that most of these issues aredirectly related to the regulation of FC cathode airflow [10,11].Hence, a thermal managing approach stemming from the routingof cathode FC airflow has been developed. The hybrid perform-ance project (HyPer) shown in Figs. 1 and 2 is a cyber-physicalfacility used for the study of hybrid systems [12–14]. It comprisesa FC in simulation, with physical balance of plant (BoP) compo-nents that interact with the FC model in real-time. The model’s

inputs are the temperature, pressure, and mass flow rates through-out the BoP, while the model’s output is a calculated FC thermalexhaust that drives a fuel valve, burning natural gas. This cyber-physical approach thus allows the safe study of the dynamic cou-pling between a FC and a gas turbine GT, and the characterizationof the entire operating envelope of the hybrid system, which rep-resents the main motivation behind the current study.

A unique feature of having a cyber-physical plant is the abilityto derive empirical models of all the operating points of the entiresystem. The previous work has identified multiple operatingpoints with the use of transfer functions [15]. These transfer func-tion (TF) matrices can be derived with ease for the entire operat-ing envelope using classical identification techniques, bymodulating the BoP actuators, one at a time at different frequen-cies, or with the use of open-loop tests [14].

If enough models are gathered, a methodology which exploitsthis availability can be used to effectively control each operatingpoint with its own independent controller. The method to identifyan operating point from an N number of models using a statisticalprobability calculation is known as multiple model adaptive esti-mation (MMAE) [16–18]. Initial simulation of the MMAE algo-rithm on the HyPer BoP facility demonstrated an accurate matchbetween an estimated model and the true system. Multiple modeladaptive control (MMAC) is the extension of the MMAE algo-rithm, which includes the independent controllers for regulatingthe individual operating points.

The paper is divided into different sections, in the first place adescription of the three operating points that were chosen to testthe algorithm was presented, subsequently the MMAE approachthat was used to identify the current operating point, then theMMAC methodology that describes the integration of the control-lers in one single control law.

Empirical Transfer Function Matrices

The TF matrices used in this study are those related to the coldair (CA) bypass valve and the electrical load (EL) actuation.These BoP inputs have the most weight in the thermal manage-ment of the system, and are essential to the performance and effi-ciency of the FC hybrid [7,15]. The inputs u1 and u2 in Eqs.(1)–(3) are the EL and CA actuators, respectively, while the out-puts y1 and y2 are the turbine speed and FC mass flow rate. Theseequations provide three distinct operating points, each producinga different effect on the system response in terms of the dynamicperformance, as explained in Ref. [6]. Equation (1) is the TF

Manuscript received May 30, 2018; final manuscript received December 19,2018; published online February 19, 2019. Assoc. Editor: Vittorio Verda.

The United States Government retains, and by accepting the article for publication,the publisher acknowledges that the United States Government retains, a non-exclusive,paid-up, irrevocable, worldwide license to publish or reproduce the published form ofthis work, or allow others to do so, for United States Government purposes.

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matrix for operating point 1 (OP1), Eq. (2) for the second operat-ing point (OP2), and Eq. (3) for the third (OP3). The EL input u1

for all three operating points is normalized with respect to itsnominal operating point of 30 kW. A unit step in this actuator isequivalent to a 6D20 kW change. The CA input changes betweenthe three operating points. In OP1, the CA opens/closes from 40%to 80%, whereas in OP2 its range is from 20% to 40%. Tests haveshown that the two regions exhibit a nonlinear relationshipbetween the CA and the turbine speed, when all other parametersare held constant.

In contrast, the TF elements of OP3 (Eq. (3)) were modified toexemplify the effect no EL load would have on the turbine speedand FC mass flow rate, i.e., all the poles of the TF elements. Thepoles or inverse time constants were increased five times those ofOP2. Figure 3 shows an open-loop step response for all threeoperating points. This is evidenced by the sign change in the TFelement relating y1, the turbine speed to u2, the CA valve in thefollowing equations:

y1

y2

" #¼

�0:25 � e�0:1�s

ðsþ 0:225Þ�0:065 � e�0:5�s

ðsþ 0:125Þ�0:22 � e�0:56�s

ðsþ 0:69Þ�1:43 � e�0:7�s

ðsþ 1:43Þ

266664

377775 �

u1

u2

" #(1)

y1

y2

" #¼

�0:25 � e�0:1�s

ðsþ 0:225Þþ0:08 � e�0:32�s

ðsþ 0:14Þ�0:22 � e�0:56�s

ðsþ 0:69Þ�1 � e�0:88�s

ðsþ 0:83Þ

266664

377775 �

u1

u2

" #(2)

y1

y2

" #¼

�1:125 � e�0:1�s

ðsþ 1:125Þþ0:4 � e�0:32�s

ðsþ 0:7Þ�1:1 � e�0:56�s

ðsþ 3:45Þ�5 � e�0:88�s

ðsþ 4:15Þ

266664

377775 �

u1

u2

" #(3)

Note that for OP3, an opening of the CA valve from 20% to 40%increases the turbine speed, but decreases the FC cathode airflowto a larger extent, as seen in Fig. 3.

Multiple-Model Adaptive Estimation

The goal of the MMAE algorithm is to assign a probability to asimulated plant model when the output of the model matches thereal plant outputs in real-time. The inputs to the algorithm are theresiduals, or differences between the real plant output and the out-put of a bank of Kalman filters (KF’s). The bank of KF’s,designed offline, produces an estimate of the states of all modeledoperating points, when the real output signal contains measure-ment and system noise. The effectiveness of this method wasshown to produce good results when the system noise is bounded[18,19]. Equations (4) and (5) show the discretized states spacemodel for one operating point, where w(k) and v(k) are the systemand measurement noise vectors, respectively, and the cathodemass flow rate and turbine speed represent the components of thestate-vector

xðk þ 1Þ ¼ AdxðkÞ þ BduðkÞ þ LwðkÞ (4)

yðkÞ ¼ CdxðkÞ þ vðkÞ (5)

To produce the state estimates, the expected value of the error orthe covariance matrix P is minimized with respect to the states

Fig. 2 HyPer BoP test facility

Fig. 1 NETL HyPer project

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(Eqs. (6)–(8)), resulting in the Kalman gain Ke (Eqs. (9) and (10)),which in turn is used in Eq. (11) to calculate the estimated states x

Pðk þ 1Þ ¼ E½eðk þ 1Þ � eTðk þ 1Þ� (6)

eðk þ 1Þ ¼ xðk þ 1Þ � xðk þ 1Þ (7)

Q ¼ diag ðr2w1;r

2w2ÞR ¼ diag ðr2

v1;r2v2Þ (8)

Ke ¼ AdPCT ðRþ CPCTÞ�1|fflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflffl}H

(9)

Pi ¼ LQLT þ AdPATd � AdPCTHCPAT

d (10)

xp ¼ Adx þ Bduin þ Ke ðy� yÞ|fflfflffl{zfflfflffl}residual

y ¼ C � x (11)

The MMAE algorithm then uses the calculated value of the covar-iance matrix P from the KF algorithm, in the computation of S(Eq. (12)), or the covariance matrix of the residual of the error.The inverse of S is equivalent to the variance of the sampled data,where R is the measurement noise covariance matrix. The scalar bis a weight attached to each probability, based on the value offfiffiffiffiffiffiffi

Sij jp

, which is equivalent to the standard deviation of thesampled data. In Eq. (13), L is the number of outputs, which forour case is 2: the turbine speed and the FC mass flow rate. Giventhat the KF’s are built offline, P, S, and b values are also calcu-lated offline

Si ¼ CiPiCTi þ R (12)

bi ¼1

2pL2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffidet Sið Þ

p (13)

PBi kð Þ ¼ bi � e12�ri kð ÞT �S�1

i �r1 kð Þ½ � � PBi k � 1ð ÞPNj¼1

bi � e12�rj kð ÞT �S�1

j �rj kð Þ� �

� PBi k � 1ð Þ(14)

The final probability is given by Eq. (14), where PB is the proba-bility that system model i matches the real output sampled data.This iterative equation is normalized by dividing the numerator bythe total sum of all the N model probabilities. Note that the resid-uals ri are the only real-time inputs to the probability equation.

Multiple-Model Adaptive Control

Once the probabilities for each system model have been com-puted, it is an easy task to attach a control algorithm to thisscheme, as shown in Fig. 4. The addition of individual controllersto the MMAE approach is called MMAC. By multiplying the sys-tem model probabilities to the independent controllers designedfor each individual model and then merging all the control signalsinto one, the outcome is an actuating control output that can beimplemented for all operating points. Simply put, when the resid-uals are large, the probability is small, and the control effort forthat model is small. The contribution of each controller to the totalcontrol signal is scaled by the probabilities, as shown in the belowequation:

uðkÞT ¼XN

i¼1

uðkÞi � PðkÞi (15)

The control structure chosen for each operating point is shown inEqs. (16)–(19) and in Fig. 5. It is a model-based linear referencefollowing state space controller with full state feedback. Since thestates are not available for measurement, the KF estimates thestates, and these are fed back to the controller. Figure 5 does not

Fig. 3 Open-loop response for three operating points

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show the KF subsystem. In Eqs. (17) and (18), Ad is the discretetransmission matrix, Bd is the input matrix, and Cd is the outputmatrix [20,21]. The state feedback matrix K in Eq. (18) is calcu-lated with the use of the pole placement design, where the desiredclosed-loop poles b are assigned according to a specified dynamicperformance, i.e., percent overshoot to a step input and settlingtime

uðkÞi ¼ Nu þ Ki � Nxð Þ � r � Kixi (16)

Nx

Nu

� �¼ Ad � I Bd

Cd 0

� ��1

� 0

I

� �(17)

z � I � Ad þ Bd � Kj j ¼ 0 (18)

zi ¼ b1; b2;…;bn (19)

In order to simulate a sequential changing of operating points inSIMULINK, a logical subsystem shown in Fig. 6 was developed toswitch between plants at various time intervals. By using else-if

action subsystems activated with logical gates which are fed bytime threshold inequalities, the MMAC algorithm can be testedfor a known set of sequential events. Each subsystem in Fig. 6represents a TF matrix of Eqs. (1)–(3). The fourth subsystem isone of the three OP repeated.

As previously stated, a bank of KF’s is designed offline foreach of the three operating points analyzed. Figure 7 shows thebank used, each receiving the measured output Y and the overallcontrol signal U. The output is an estimated state x and an esti-mated output y. Figure 8 shows the prediction type KF (PTKF)used, highlighted in yellow.

Figure 9 shows the SIMULINK controller subsystem, having eachblock follow the architecture of Fig. 5. The output of each control-ler block is multiplied by the probability corresponding to themodel the controller is designed for. The total control signal isthus the addition of all control efforts scaled by their respectivemodel probabilities.

The final component to the MMAC algorithm is the probabilityfunction described by Eq. (14). Figure 10 shows the SIMULINK rep-resentation of Eq. (14) with residual inputs.

Fig. 4 Multiple model adaptive control SIMULINK model

Fig. 5 Model of the full state feedback reference controller [2]

Fig. 6 Switching mechanism for changing Op Pts

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Fig. 7 SIMULINK KF bank subsystem

Fig. 8 Prediction type KF SIMULINK subsystem

Fig. 9 SIMULINK controller subsystem

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Fig. 10 Probability equation in a SIMULINK subsystem

Fig. 11 Closed-loop response: individual Op Pts and its controller

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Results

Figure 11 shows the closed-loop response of each of the threeindividual TF matrices to a normalized step input, using the con-trol law of Fig. 5. This response does not represent the multiplemodel arrangement, but rather a single input/single output systemused to validate the individual controller performance. Alldesigned controllers follow the pole placement methodology.

Figure 12 illustrates the effectiveness of the KF estimate, for anoisy turbine speed and FC airflow measurement signal inputs.

Since the steady-state KF’s are all designed offline Eqs. (9) and(10), the computational burden of inverting matrices in real-timeis removed, allowing for a faster implementation of the MMACalgorithm, i.e., Eq. (11) is the only equation implemented online.

To understand the importance of having an individual controllerdesigned for a specific operating point, the actuator response ofthe two OP’s of the CA bypass valve is displayed in Fig. 13, forthe correct control assignment, i.e., for a well-matched controllerto plant pairing. It is evident that in order for the turbine speedand FC cathode airflow to follow the reference commands of

Fig. 12 KF estimation effectiveness

Fig. 13 Actuator CL response comparison for OP1 and OP2

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Fig. 11, a different EL is required when the CA is in the 40–80%range (OP1) than when it is in the 20–40% lower range (OP2). Acloser look at Fig. 11 shows that between 50 and 120 s, the timesin which a reference command for FC flow and turbine speed areset, the EL changes direction in Fig. 13. This is also the case whena separate reference command is set between 270 s and 320 s.

To further demonstrate the detrimental effect a linear controllerdesigned for a single operating point would have on other operat-ing points, the multiple model switching logic of Fig. 6 wasapplied to the controller for OP1. The response of Fig. 14 showsthe controller’s inability to follow reference commands when the

plant changes at 100 s, 150 s, and 300 s. To scale the response ofthis figure, the turbine speed is multiplied by 500, and the nominalvalue of 40,500 rpm added. To scale the FC mass flow rate toactual values, the number is multiplied by 0.2 kg/s and its nominalvalue of 1.7 kg/s added.

In contrast to Fig. 14, Fig. 15 shows the response of the systemto the MMAC algorithm, when the plant changes fromOP1–OP2–OP3–OP1 at time intervals 0 s, 100 s, 150 s, and 300 s.It is clearly seen that the controller response in tracking the refer-ence command signal is greatly improved from the response ofFig. 14. Although an over- and under-shoot transients are still

Fig. 14 Single controller response for multiple plant changes

Fig. 15 System response to the MMAC algorithm

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present at the moment of system change, the recovery is nonethe-less achieved at an acceptable pace in accordance with the conver-gence time of the MMAC algorithm.

The closed-loop EL and CA actuator response is shown inFig. 16. Compared to the actuator response of Fig. 13 when OP1and OP2 are separately controlled, the EL load of Fig. 16 fluctu-ates intermittently between the behavior observed in OP1 and thatof OP2. Hence, having two different controllers operating at thesame OP, produce an opposite response in the EL load. Since thefinal control signal is composed of all the individual control sig-nals weighted by their respective model probabilities, the MMACis able to track the command well, even in the face of the nonli-nearity. The actuator signals are bounded within the allowedlimits.

Figure 17 shows the model residuals for each OP. There aretwo residuals per OP—one for the estimated versus real turbinespeed and the other for the estimated and real FC cathode airflow.In the simulation, the lower residuals indicate a match betweenestimated and true values, indicating a greater probabilityassigned to that particular model. As expected, the residuals fol-low the sequence of system plant changes designated asOP1–OP2–OP3–OP1. The closeness of the residuals betweenregions of plant change 2–3 are a result of the similarity the TFmatrices have. Note that the third OP was built according to thesecond OP, but with a faster response, i.e., faster poles or timeconstants.

Figure 18 shows the probabilities of the models, according tothe system plant change sequence OP1-2-3-1. The graph demon-strates that from the initial 1/3 probability each model has, theMMAE algorithm correctly converges to a probability of 1 forOP1 up to 100 s, when the true plant was switched. After 100 s,OP2 is switched and the estimation outputs a probability of 1 formodel 2. The third OP is then switched between 150 s and 300 safter which OP1 is switched again until the end of the simulation.The noticeable spikes between the probabilities of OP2 and OP3indicate a convergence difficulty when the residuals are similar,as noted in Fig. 17. This is expected, since the model for OP3 wasbased on the model of OP2, i.e., OP3 is OP2 with faster poles.Even with the convergence discrepancy, the robustness of the con-troller is validated in Fig. 15.

To further validate the MMAC method, a second sequence ofplant changes was performed, as shown in Figs. 19–22. In thisinstance, the sequence of operating points wasOP3–OP1–OP2–OP1.

As with the previous sequence of plant switches, the probabil-ities correctly match a model to the particular plant output, with

Fig. 16 Actuator CL response of the MMAC

Fig. 17 Multiple model adaptive estimation calculated residuals for the three OP’s

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similar discrepancies between OP2 and OP3. The times of the sec-ond sequence are the same as the time for sequence no. 1. TheMMAC controller is still able to manage a better response fromthat observed in Fig. 14.

Discussion

The previous graphs demonstrate the performance and limita-tions of the MMAC methodology. One very important advantageof the MMAC is the ability for this algorithm to merge variouscontrollers into one signal by scaling each control componentwith a probability weight. This is ideal for highly nonlinear sys-tems, where no two controllers are alike. In this study, the poleplacement approach was used for all three OP’s, but could haveeasily had incorporated an entirely different control scheme. If forexample, the startup of the hybrid system can benefit from opera-tor expertise, a fuzzy logic controller can be designed for this OP.If on the other hand, a robust and safe shutdown is desired, anoptimal H1 can be implemented. The ease of control switching isonly restricted by the convergence of the adaptive estimation.

As is the case with all control algorithms, there are disadvan-tages to the MMAC which can result in undesired responses. Anotable problem arises when the OP’s are similar and have staticgains which are close to each other. This was the case for models2 and 3. A close look at Eqs. (2) and (3) reveals that the only dif-ference between these TF matrices is the speed of the response.All the poles of the TF elements are modified to be five times

faster. The apparent change in static gain is only the result of themathematical manipulation of increasing the value of the poles.As can be seen in Fig. 3, the steady-state gain for both OP2 andOP3 is the same, only that OP3 is faster. The result of having sim-ilar parameters between OP’s is the difficulty for the MMAE toconverge to one specific probability model, given that the resid-uals are almost identical. This can be observed in Figs. 18 and 21,at the times when the probabilities experience “noise.”

Convergence is also dependent upon whether the models arespaced at regular intervals. This is reflected in the b parameterwhich in turn relates to the variance of the sampled data S matrix.When all the model b are similar, no OP “dominates” with respectto how distant it is from the rest of the OP’s. The b values for allthree OP’s were found to be within 1–7% of each other, allowingfor a satisfactory convergence, apart from the residual issue.

From Figs. 17 and 20, the residual effect of OP2 and OP3 canalso be inferred in the EL and CA actuators. Both actuators showa smoother trend when OP1 is encountered. Small ripples arepresent during the OP2 and OP3 plant switches. This can be seenat times prior to 50 s in Fig. 23 where OP3 is present, as well as intime 150 s, when OP2 is assigned. A similar trend is shown inFig. 17.

With regard to the practical implementation of the MMACalgorithm, it is best to utilize actuators with enough bandwidth tobe able to reduce the system noise. The previous work confirmedthe difficulty in convergence when the system noise is increased,as opposed to the measurement noise of the sensors [2]. It is thusessential to diminish plant disturbances stemming from faulty ordegrading actuators. The covariance matrices Q and R used in thisstudy had scaled down values in accordance with the normaliza-tion of the turbine speed and FC airflow signals. An increase inthe Q matrix diagonal elements will result in a noisier probabilityplot.

A minor, but important detail comes with the implementationof the probability function of Eq. (14). Given that the denominatoris used to normalize the calculated value to be a number between0 and 1, none of the probabilities can ever reach zero. A small evalue is added to all probabilities to account for the otherwisedivision by zero.

Finally, the use of the MMAC methodology can be extended tocontrolling the FC-GT hybrid in the presence of disturbances, asis the case with sudden increases in load requirements. By addinga controller to mitigate disturbances when these are detected bythe MMAE estimation algorithm, a more robust system can beachieved. These disturbances might actually cause a more drastic

Fig. 18 Model probabilities for the response in Fig. 16

Fig. 19 Probabilities of second plant switching sequence Fig. 20 Residuals for plant sequence no. 2

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change in the system dynamics than the one shown by the influ-ence of the CA bypass valve. The MMAE not only is useful forOP matching, but also for sensor failure detection, as noted inRef. [2].

Conclusions

The MMAC methodology was proven to be a relevant and fea-sible control algorithm in the hybrid performance system, givenits ability to simultaneously operate plant actuators with a varietyof control strategies. The strong coupling of the FC-GT systemrequires a controller to be flexible and adaptive to changing oper-ating conditions. Having a control strategy that is able to mergevarious control algorithms into one is ideal for the nonlinear oper-ating envelope. With MMAC, the benefit of linear and nonlinearcontrollers can thus be exploited, reducing the control issues asso-ciated with hybrid plants.

Acknowledgment

This work was completed through a collaboration between theU.S. Department of Energy Crosscutting Research Program,administered through the National Energy Technology Labora-tory, Ames Laboratory, and the U.S. Coast Guard Academy.

Nomenclature

A ¼ state matrixB ¼ input matrix

C ¼ output matrixe ¼ error between the estimated state and the state vectorE ¼ expected value of the errork ¼ discrete time variable

Ke ¼ Kalman gainsL ¼ process noise matrixP ¼ covariance matrixQ ¼ process covariance matrixs ¼ Laplace variableu ¼ inputsv ¼ measurement noise vectorw ¼ process noise vectorx ¼ state vectorx ¼ state vector estimationy ¼ outputs

References[1] Tucker, D., Lawson, L., and Gemmen, R., 2003, “Preliminary Results of a Cold

Flow Test in a Fuel Cell Gas Turbine Hybrid Simulation Facility,” ASMEPaper No. GT2003-38460.

[2] Tucker, D., Liese, E., and Gemmen, R., 2009, “Determination of the OperatingEnvelope for a Direct Fired Fuel Cell Turbine Hybrid Using Hardware BasedSimulation,” International Colloquium on Environmentally Preferred AdvancedPower Generation, Newport Beach, CA, Feb. 10–12, Paper No. ICEPAG2009-1021.

[3] Tucker, D., and Gemmen, L. Lawson, R., 2005, “Characterization of Air FlowManagement and Control in a Fuel Cell Turbine Hybrid Power System UsingHardware Simulation,” ASME Paper No. PWR2005-50127.

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Fig. 21 Closed-loop response of sequence no. 2

Fig. 22 Actuator response for sequence no. 2

Journal of Electrochemical Energy Conversion and Storage AUGUST 2019, Vol. 16 / 031003-11

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