Control-relevant Modelling and Linear Analysis of Instabilities in Oxy-fuel Combustion

Transcription

1 Control-relevant Modelling and Linear Analysis of Instabilities in Oxy-fel Combstion Dagfinn Snarheim, Lars Imsland and Bjarne A Foss Abstract Semi-closed gas trbine cycles based on oxyfel combstion have been proposed as an alternative to conventional gas trbine cycles for achieving CO -captre for CO seqestration prposes While combstion instabilities is a problem in modern conventional gas trbines in general, recent experimental reslts indicate that sch instabilites also occr in oxy-fel combstion For conventional combstion processes, model based controllers have been sccessfl at sppressing thermoacostic instabilities As a first step towards achieving the same for oxy-fel combstion, we develop a control relevant model of oxy-fel combstion In oxy-fel combstion CO is sed as working medim instead of air From a control point of view, this gives an extra degree of freedom compared to conventional combstion control Analysis on the developed model show that secondary injection of CO close to the flame is probably a better maniplated variable than fel-injection, which has been a poplar choice for control in conventional combstion processes I INTODUCTION Gas trbines are widely sed for power prodction from gaseos fossil fels Althogh gas trbine engines are relatively clean brning, there is inevitably a prodction of CO from combstion of fossil fels Ths, with today s increasing concern abot global warming and climate change, there is an incentive to investigate gas trbine processes with CO captre One attractive concept for this is the semi-closed gas trbine cycles sing CO as working medim This process has been stdied in eg [1], [], [3] Central in the concept is that combstion of natral gas together with a mixtre of CO as gas trbine working medim and O leaves the exhast consisting mainly of water and CO The water can be removed sing a condenser, and we are left with almost pre CO, of which most is recycled for se as working medim, while to avoid accmlation, some mst be removed from the cycle The removed CO mst be compressed for long term safe storage, to have the desired positive effect on the global warming carbon seqestraion While overall process dynamics has been stdied in [4], [5], in this paper, we concentrate on the dynamics of the combstion chamber It is known that conventional gas trbine combstion chambers might exihibit detrimental instabilities nder some operating conditions [6, eg] ecent experimental work [7] indicates that similar instabilities also occr in oxy-fel combstion, possibly even more severe than in the conventional case Dagfinn Snarheim and Bjarne A Foss are with the Department of Engineering Cybernetics, Norwegian University of Science and Technology, N 7491 Trondheim, Norway {DagfinnSnarheim,BjarneAFoss}@itkntnno L Imsland is with SINTEF ICT, Applied Cybernetics, N 7465 Trondheim, Norway LarsImsland@sintefno This gives a clear motivation for stdying if it is possible to se active feedback control for alleviating these instabilities for oxyfel combstion, as has been sccessflly done for conventional combstion [6] This paper provides a first step in that direction: We will first develop a new linear low-order model, inspired from similar models for conventional combstion, for stdying the dynamics that are at the root of the observed instabilities De to the fact that the nmber of control degrees of freedom is higher for oxyfel combstion than for conventional combstion, we thereafter se the developed model to stdy which of the control degrees of freedom is more sitable for doing active feedback stabilization, and to give indications towards reqirements for actation devices The paper is briefly otlined as follows: In Section II we give som brief backgrond on combstion instabilities in general, then we proceed to discss the special case oxyfel combstion The modelling of the process is presented in Section III, while Section IV looks at reqirements for the inpt part of a control system to stabilize the plant We end the paper with some conclding remarks II THEMODYNAMIC INSTABILITIES IN OXY-FUEL COMBUSTION Thermodynamic instabilites have been recognized as a problem in combstion processes for a long time These instabilities take the form of large pressre oscillations in the combstion chamber That the copling between nsteady heat release oscillations and acostic pressre can be a driving mechanism for thermodynamic instabilities was identified as early as 1878 [8] The heat release and acostics are copled in a feedback loop, and depending on the phase difference between the signals, the heat release either remove from or add energy to the pressre oscillations, the latter case making the system nstable Obvios implications of these instabilities are vibration and mechanical stress that may lead to strctral damage and system failre Alleviating the oscillations might allow for better energy tilization and less polltant emissions Modern conventional premixed gas trbines have to operate at very lean conditions de stringent reqirements on NO x emissions These operating conditions make the gas trbines extra prone to instabilities, and is an important reason for all the attention active control of thermoacostic instabilities has received recently This is also reflected in the nmeros pblications within the field in recent years eviews on thermoacostic instabilities and active control can be fond in [6], [9], [10]

2 However, when it comes to oxy-fel, the literatre on instabilities is scarce Experimental reslts on a laboratory scale combstor are pblished in [7] They show that p to a certain threshold in oxidizer composition the ratio between oxygen and carbone dioxide in the oxy-fel mixtre, the instability patterns are similar to what yo find when brning fel with air Above this threshold the instabilities tends to grow even stronger Figre 1 shows sond pressre level plots from these experiments The nstable freqencies are easy to identify in the peaks De to the geometry in the experiment, there exists several acostic modes that can be triggered Which one is triggered depends on the operating conditions This gives a clear incentive to investigate active control strategies for this type of combstion Moreover, it also indicates that a good controller mst be able to redce pressre oscillations over a broad freqency range, possibly broader than for conventional combstion instabilities In oxy-fel combstion it is possible to change the composition of the oxidizer the ratio between O and CO Compared to conventional combstion in air, this is the eqivalent of changing the ratio between nitrogen and oxygen, which generally is hard/expensive The difference between plot b and c in Figre 1 indicates that the oxidizer composition is very important From a control point of view, this means that for oxy-fel there exists a new degree of freedom that can be sed to stabilize the system One focs of this paper is to model the effect of pertrbations in oxidizer composition, and investigate the se of this variable for control The extra degree of freedom is illstrated in Figre III MODELLING In combstion processes there are several components that contribte to the overall dynamics These inclde acostics, flid dynamics, transport processes, chemical kinetics, flame kinematics, heat transfer, feedline dynamics of the reactants, and atomization and vaporization dynamics These components can cople with each other in varios ways, and developing a detailed model of sch a complex system is an extremely challenging task [6] Moreover, sch models are not well sited for controller design For active control of conventional combstion, model-based controllers have proven to spress thermoacostic instabilites better than empirical controllers We expect the same to be tre for oxyfel combstion Ths there is a need for low order models of oxy-fel combstion A common approach that captres the most important dynamics is to model the acostics and the heat release A linear form of the wave eqation is then sed for the acostics For the heat release dynamics we will se a thin wrinkled flame model developed by [11] This model where extended for pertrpations in eqivalence ratio by [1], and we will in the following extend it to pertrbations in oxidizer ratio An early version of the modelling herein can be fond in [13] The combstion chamber that we model is of length L and has a width D As in [14] the brner consists of a perforated plate with n f holes, each with a radis In each of these holes there is a flame at location x f Figre 3 shows a skecth of one sch flame Fig 1: Experimental reslts from oxy-fel combstor The triggered freqency and instability peak is dependant on operating conditions: a λ O = 04, φ = 09, e = 3000; b λ O = 041, φ = 09, e = 000; c λ O = 04, e = 000, φ = 09 from [7] CH 4 Air Combstor a Conventional combstion chamber CH 4 O CO Combstor b Oxy-fel combstion chamber Fig : Conceptal difference between a conventional combstion chamber and an oxy-fel combstion chamber from a control point of view

3 in φ and λ O and will be assmed constant We denote mean vales as and deviation vale as, and linearize arond ū, φ, λ O and ξ, and get ξ t = + S ξ + ξ S φ φ + S λ O λ 4 O Fig 3: The flame front in the combstion chamber One important difference between oxy-fel combstion and conventional combstion is the possibility of changing the oxidizer composition To describe the composition we define the oxidizer ratio as n O λ O =, 1 n O + n CO where n x refers to the nmber of moles of component x Together with eqivalence ratio φ = n fel /n O actal n fel /n O stoichiometric and the total mass flow ṁ tot we have fll information of the mass flows of the different components A Heat release The starting point for the modelling is the the flame srface eqation from [11] with modifications to take λ O into accont ξ t = v ξ S φ, λ O 1 + ξ, where ξr, t is a single-valed fnction describing the axial displacement of the flamesrface, is axial velocity, v is radial velocity and S is the laminar brning velocity The different variables are illstrated in Figre 3 The area of the flame can be fond by performing a srface integral of the variable ξ, and the heat release from the flame is assmed to be proportional to the flame area A f, Q = ρ φ, λ O S φ, λ O h r φ, λ O A f, 3 ξ A f = π r 1 + dr 0 Here, ρ is the density of the nbrnt mixtre, h r is the heat of reaction per nit mass of the mixtre and is the radis of the brner So far the main difference from conventional combstion is that λ O enters the eqations throgh ρ, h r and λ O We now proceed to extend the model in a similar way as in [1], with necessary modifications for λ O We assme very small radial velocity and v is ths neglected Also, ρ will not change mch with pertrbations Note here that for brevity we se the notation S φ for Similar notation is sed throghot the φ= φ,λo = λ O S φ docment The bondary and initial conditions for ξ is ξ, t = 0, ξ r, 0 = 0 Similarily, linearization of the heat release eqation 3 gives where Q = κ 0 ξ r, t dr + d 1 φ + d 5 κ = πρ S h r, and h r d 1 = πρ S φ + h S r ξ r dr, φ 0 h r d = πρ S + h S r ξ r dr λ O λ O Differentiatiating eqation 5 and inserting eqation 4 gives Q = κ ξ + S ξ 0 + S φ φ + S λ O λ O which is integrated over r as 0 dr + d 1 φ + d λ O 6 Q = κ S ξ 0, t + d 5 φ + d 6 + d1 φ + d λo 7 where d 5 = ξ0 S φ, d 6 = ξ0 S λ O To proceed we need an expression for ξ 0, t This is fond by taking the Laplace transform of eqation 4 and solving the reslting differential eqation in r ξ r, s = s + ξ S φ φ s + S λ O λ O s 1 e r S s 8 Taking the inverse Laplace transform gives ξ r, t = where τ r = r S τ dτ + ξ + ξ S φ S λ O φ τ dτ λ O τ dτ 9

4 As in [14] we approximate τ dτ r S 10 and in a similar way φ τ dτ r φ S, 11 τ dτ r λ S O Using these approximations in eqation 9, then inserting in eqation 5 and solving the reslting integral gives Q = κ S + d 1 + κ S d 5 φ + d + κ S d 6 1 If we now evalate ξ 0, t sing the approximations in eqation 10 and 11 we get ξ 0, t = S + d 3 S φ + d 4 S 13 We then get an expression for from eqation 1 and insert it in eqation 13 reslting in ξ 0, t = Q d 1 + κ κ κ S d 5 κ S d 3 φ κ d + κ S d 6 κ S d 4 14 Now this eqation can be inserted into eqation 7 and we arrive at Q + S Q = κ S d 1 κ d 3 φ S S d κ d 4 λ S O + d φ 1 + d λo 15 B Acostics We consider a tbe with length L and se a onedimensional wave eqation to describe the pressre flctations p = p p p t c p x = γ 1 q x, t, t where p is pressre, q is the heat release per area Q q = n πd/ f, c is the speed of sond and γ is the specific heat ratio The pressre oscillations are copled to velocity pertrbations by p t + γ p x = γ 1 q 16 The combstion chamber is closed at the inlet and open at the otlet, reslting in the following bondary conditions p L, t = 0, 0, t = 0 The wave eqation is discretized sing the Galerkin expansion n p x, t = p ψ i xη i t, i=1 where ψ i x and η i t are modal shape and amplitde, ψ i x = cosk i x Using this expansion within the waveeqation and integrating over the combstor length L gives as in [14] η i + ω i η ι = b i q f where b i = γa 0 ψ x f /E, E = L 0 ψ i x dx, a 0 = γ1 γ p and ω i = k i c As in [1] we also add a damping term ζ to accont for heat and friction losses within the combstor η i + ζω i η i + ω i η i = b i q f In a similar way the Galerkin expansion is sed on eqation 16 Integration over the combstor length L then gives n = c i η i + θa 0 q + c, i=1 where c i = 1 dψ i γki dx x f, a 0 = γ 1 /γ p and θ represents the effect of the velocity ahead and behind the flame on q and c is the velocity added by potential secondary injectors We assme perfect mixing of the components in the nbrnt mixtre, and ths the pressre oscillations have no effect on the eqivalance ratio φ and the oxidizer ratio λ O Inserting the velocity relation into eqation 15 gives Q S n f + Q = κθa 0 A c n κ c i η i + κ c i=1 S d 1 κ S d 3 φ S d κ S d 4 + d 1 φ + d λo 17 As the flame is nearly conical, the slope at the tip will be close to zero As d 3 and d 4 are proportional to the derivative of the mean flameshape at r = 0, they are close to zero and can be neglected The reslting heatrelase model then becomes Q S + κθa n f n 0 Q = κ c i η i + κ c A c i=1 S d 1φ S d + d φ 1 + d λo 18 C Actators In this paper we stdy the se of secondary injectors to control the system We choose to not model the dynamics in the actators This in spite of that the dynamics in the actators are important becase their bandwith will typically be close to the nstable freqencies they are sed to stabilize However, the actator dynamics will have similar inflence on all the inpts, and will not be important in the choice of maniplated variable for the system The actator dynamics will also be dependent on the specific valve chosen to actate the system Instead we se the model to analyse which reqirements there will be on the actators to be able to stabilize the system see Section IV

5 However, we do need linear relations between φ, and the different mass flows w Starting with the definition of λ O and φ eqation 1 and, linearization arond the operation point gives φ 1 = w CH w O α 4 φ w O 0 w 19 O = 1 λ O α 1 MW O w O λ O α 1 MW CO w CO where α 0 = wch4 w O stoichiometric and α 1 = w O MW O + w CO MW CO and MW x is the moleclar weight of compononent x Then remembering that we have n f holes with radis, we get the following eqation for c c = w CH4 + w O + w CO ρ n f π There will also be a transport delay τ c assosciated with convection from the injector to the brning zone, τ c = L c /ū, where L c is the distance from the injector to the brning zone D Heat of reaction and flame speed The heat of reaction is the maximm heat release per kg fel that can occr within the combstor We calclate it sing the lower heating vale LHV for methane, h r = LHV CH4 m CH4 /m tot We can express h r as a fnction of φ and λ O, h r = LHV CH4 φλ O MW CH4 λ O MW O + MW CO 1 λ O + φλ O MW CH4 We can now calclate the partial derivates of h r that enters the model eqations h r φ = LHV CH 4 λ O MW CH4 MW CO 1 λ O + λ O MW O λ O MW O + MW CO 1 λ O + φλ O MW CH4 h r = LHV CH4 λ O φmw CH4 MW CO λ O MW O + MW CO 1 λ O + φλ O MW CH4 As these eqations only enter the model as constants, it is not necessary to linearize them It seems difficlt to derive analytical expressions for S that ses thermodynamic property tables We chose instead to perform eqilibrim calclations sing a methane mechanism GI 30 to generate a lookp table for S Crvefitting of this data was then sed as a model Figre 4 shows this relation, were the φ = 1 line has been pblished in [7] Note that S varies significantly more with λ O than with φ In a conventional combstion process, where λ O is 1%, and yo can only change φ, S is close to constant On the other hand, for oxy-fel combstion S can vary a lot, Fig 4: The laminar flames speed S as a fnction of eqivalence ratio and oxidizer ratio and we expect this to have an impact on the controllability of the process Based on the crvefits we get the following eqations for the partial derivatives of S S φ = 1793λ O 03780φλ O + 043λ O S = 35846φλ O 01890φ + 043φ + 837λ O λ O E Implementation and model validity The complete model was implemented in Simlink sing two modes for the acostics We kept the inpts on velocity form d/dt, reslting in the following inpt vector = [ c φ λ ] O ẇ CH4 ẇ O ẇ CO We sed a similar geometry as in [14] The length of the combstion chamber L = 049 m, the width is D = 004 m and the flame is located at x f = 04 m The chamber consists of n f = 80 brners, each with a radis = 075 mm The cost of oxygen implies operation at close to stoichiometric conditions [7] Ths we choose to operate the system near φ = 1 and λ O = 035 Based on this we can calclate c = 3106, ρ = 147 kg / m 3 and h r = 3315MJ/ kg We se p = 10 5 Pa, γ = 14,, θ = 05 and ζ = 001 As the literatre on dynamics in oxy-fel combstion is scarce, it is difficlt to find data for validation of the model De to the need to keep the model simple low order and becase we se a linear model, there are certain effects that the model cannot captre Figre 5 shows the response of the ncontrolled system to a distrbance in the oxidizer ratio λ O The system is clearly nstable In real combstion processes, the pressre oscillations will enter a limit cycle, an effect that this model cannot captre If we look back at Figre 1, we cannot do similar sond pressre level calclations based on the model otpt To calclate the sond pressre level only makes sense when the pressre oscillations are limited by a limit cycle We can, however, se forier transforms to calclate the freqency of the oscillations In Figre 5 the system oscillates with a freqency eqal to ω 3000 rad / s, indicating that it is the second mode of the combstor that is nstable Also note that there is a low freqency oscillation that brings the system

6 be the same However this means that the scaling did not have the effect that all inpts are limited to be between 1 and 1 Fig 5: esponse of ncontrolled system to a distrbance in λ O back to zero, before the high freqency oscillations grows large This is becase the first acostic mode is stable If we look back at the experimental reslts Figre 1, the nstable freqency differs for the different operating points This is de to the geometry in the brner, where there exist modes based on the whole combstor length, and on the length of the premixing chamber and brning chamber only A more advanced model for acostics will be able to represent this The growth rate of the instability is dependent on the damping ζ For ζ > 0039 the model becomes stable F Scaling To be able to compare the different maniplated variables available in the system, scaling is necessary With scaling the process gains from the different maniplators will be comparable We choose to scale the system from the maniplators inflence on φ and λ O This ensres that the system is operated close to the operating point it was designed for The following bonds are sed on φ and λ O φ max = 005 λ max O = 005 We then se the relations between each of the mass flows and φ, λ O eqation 19 to scale each of the mass flows so that they independently cannot violate the bonds on φ and λ O This gives w CH max 4 = w O α 0 φ max, w max λo 1 CO = α 1M CO λ max O, and w O max = 1 max{ φ w O φ 1 λo 1 max, α 1M O λ max O } The bond on c is then dependent on the largest mass flow Looking at the nmerical vales for the scaling reveals that this is w CO, reslting in c max = w CO max ρ n f π We then collect all the scaling factors in a scaling vector D If we denote the original system by Ĝ, the scaled system is G = ĜD Note here that the actal maniplated variables are the derivatives on the variables we sed for the scaling process Differentiating the variables shold have the same effect on all inpts, ths the relation between the variables shold still IV MODEL ANALYSIS In this section we will stdy the inpt part of the system The variable we wish to control is the pressre p Other alternatives, for instance Q, are also possible However, stabilization of p will lead to stabilization of Q Based on the derived model, we will look at bandwith reqirements for the injectors, and how close to the flame we have to place the injectors to achieve good control There are three different mass streams that can be sed to maniplate the system As mentioned earlier it is special for oxy-fel that the composition of the oxidizer can be changed We will se the developed model to investigate how the CO stream compares to the other mass flows It is also possible to se combination of inpts to control the process Becase φ, λ, and c enters the modelling eqations directly and are examples of combinations, we will inclde these in the analysis We choose to se the derivatives of the streams as inpts The reslting model we se for analysis have 6 different inpts, = [ c φ λ ] O ẇ CH4 ẇ O ẇ CO A Poles and zeros The location of the poles and zeros of a plant G gives information abot how easy it is to control G The developed model have a pair of conjgate HP-poles right half plane located at p = 0119 ± 3005i To stabilize a plant with HP-poles, we need to react sfficently fast, and we mst reqire that the closed loop bandwith is larger than ω c > 067 x + 4x + 3y for a pair of complex HPpoles p = x ± jy, [15] Ths we get a lower bond on ω c = 3564 rad / s However, all the inpts except c have zeros located close to z = 750 HP-zeros will always imply an inverse response in the time domain, and ths limit the achievable bandwidth Using a low-freqency performance weight, [15] gives ω c < z/ = 350 rad / s as an pper bond on the achievable bandwith It is of corse impossible to satisfy both of these bonds, which means that this plant is difficlt to control All the inpts also have a set of zeros located at the imaginary axis, which again implies control problems at steady state A HP-zero z will give a very small gain at freqencies close to z Ths, one might consider tight control at freqencies sfficently higher than z In this case the zero will give a lower bond on the bandwith By sing a performance weight for tight control at high freqencies, [15] gives ω c > z = 1500 rad / s as a lower bond on the bandwith As the focs in this application is to redce high freqency oscillations, it makes sense to se this performance limitation Ths it is the HP-poles that determine the limit on lower bandwidth Conversion to Hz gives 567 Hz as the bandwith limitation This is a very high bandwith and might be problematic In general solenoid valves have been poplar for active control of combstion For instance, the MOOG D633 DDV valve have been sed in several experiments, and [16] showed that this valve had a flat freqency response p

7 Fig 6: The bandwith limitation imposed by a time delay de to the distance between injector and flame to 380 Hz An alternative is to se magnetostrictive valves, for instance [17] sed a valve from Etrama Prodcts Inc with a bandwith of 1000 Hz Ths there shold exist valves that are fast enogh Another problem is of corse that this limits the complexity of the controller to be sed B Time delay Depending on the location of the injectors, there will be a time delay associated with the transport of inpt changes to the flame zone, τ c = L c /ū, where L c is the distance from the injector to the brning zone The time delay will impose a serios limitation on the achievable bandwith, becase every control action will be delayed by τ c An pper bond for the achievable bandwith in a plant with a time delay θ is derived in [15] as ω c < 1/θ Figre 6 shows the minimm bandwith reqirement as a fnction of distance between injector and flameholder As the poles already give a necessary bandwith of 3564 rad / s, there is not mch freedom in injector location To satisfy the bond imposed by the HP-pole, we need L c < 05 mm This is a very difficlt reqirement to handle, and in practice one will probably have to violate it A time delay is a nonlinear phenomena, which might lead to oscillations if the design bandwidth of the controller is too high too large gain However, since setpoint control is not an objective and there is considerable measrement noise, these oscillations might not be too serios in closed loop operations anyway An example of control of a conventional combstion process with large time delay can be fond in [1] A problem that might occre when L c is small, is poor mixing When sing fel injectors, this have reslted in generation of hot spots on the flame srface, de to pockets of pre fel entering the flamezone In additon to hot spots, secondary diffsion flames de to poor mixing where reported in [18] If sing CO injectors for control, the opposite might occr Pockets of CO might case the flame temperatre to be redced However, this is probably not as problematic as the hot spots Anyway, the injector placement will always be a trade-off between good mixing Fig 7: Bode plots for transfer fnction between ẇ CH4, ẇ O, ẇ CO and p and problems related to time delay C Maniplated variables When the system is scaled as in Section III-F, we can compare the different maniplated variables control athority by investigating their process gain According to [15] we shold choose maniplators with a high gain at freqencies where control is needed For a system with a single otpt, comparing the gains give the same reslts as relative gain array GA analysis Figre 7 shows a Bode plot for the for the transfer fnction between mass flows, ẇ CH4, ẇ O and ẇ CO, and the pressre p We recognize the HP-poles and zeros from the sharp peaks in the Bode plots The Bode plot shows that the gain is largest for ẇ CO This indicates that ẇ CO shold be prefered as a maniplated variable over ẇ CH4, which is the common maniplated variable in active control of conventional combstion processes It might seem srprising that ẇ O has the lowest gain This is the only variable that can inflence both φ and λ O However, if we look at eqation 19 we see that it enters φ and λ O with opposite signs As these variables enter 18 with the same sign, increasing φ and λ O tend to cancel each other Why the gain is larger for ẇ CO can also be nderstood from the model eqations If we look back at Figre 4 we see that S has a mch stronger dependance on λ O than φ A conseqence is that, d is larger than d 1 and when we look at eqation 18 we see that these are the constants that decide the gains of the system It is also possible to se several injectors simoltanosly to control the system This will reslt in a mch more complex control strctre and plant However, if the gain

8 to design a model based controller Also, the model shold be validated with experimental data ACKNOWLEDGMENTS The athors grateflly acknowledge Mario Ditaranto at SINTEF Energy esearch for helpfl discssions, and in particlar for assistance in generating the data shown in Figre 4 The Gas Technology Center NTNU-SINTEF and the NF BIGCO project are acknowledged for financial spport Fig 8: Bode plots for transfer fnction between c, φ, λo and p from sch an inpt is mch higher than for the mass flows, one might consider to se sch an inpt Examples of sch combinations are φ, λ O, and c Figre 8 shows the Bode plots for these variables The only variable that have a gain comparable to ẇ CO is λ O However, as they are really close, we still prefer ẇ CO as the controlled variable for the system It is somewhat srprising that sing several injectors do not reslt in better control However, other combinations of injectors might perform better than the ones analyzed There exist other advantages with sing ẇ CO as the inpt, which is not revealed by the model First, oxy-fel will be sed in processes where CO is captred, ths the sage of CO is free Becase we operate at near stoichiometric conditions, the sage of either ẇ O or ẇ CH4 will reslt in either incomplete combstion, or combstion with excess of oxygen As both fel and oxygen costs money, they are less desireable as inpts Also, sage of CO does not inflence the total amont heat prodced in the combstion, and will therefore not case significant flctations in power prodction in for instance a gas trbine V CONCLUSIONS We have presented a linear low order model sitable for active control of oxy-fel combstion Analysis on this model shows that a secondary injector modlating a CO stream can perform better than fel injection, which has been a poplar choice for active control of conventional combstion processes The analysis also show that oxyfel combstion is difficlt to control Especially de to high bandwith reqirements and transport delays A natral contination of this work will be to se the derived model EFEENCES [1] O Bolland and S Saether, Comparison of two removal options in combined cycle power plants, Energy Conversion and Management, vol 33, pp 5 8, 199 [] I Ulizar and P Pilidis, A semiclosed-cycle gas trbine with carbon dioxide-argon as working flid, Jornal of Engineering for Gas Trbines and Power, vol 119, pp , 1997 [3] E Ulfsnes, O Bolland, and K Jordal, Modelling and simlation of transient performance of the semiclosed O /CO gas trbine cycle for CO -captre, in Proceedings of ASME TUBO EXPO, 003 [4] D Snarheim, L Imsland, Ulfsnes, O Bolland, and B A Foss, Control design for a gas trbine plant with CO captre capabilities, in Proc 16th IFAC World Congress, Prage, Czech epblic, 005 [5] L Imsland, D Snarheim, B A Foss, Ulfsnes, and O Bolland, Control isses in the design of a gas trbine cycle for CO captre, International Jornal of Green Energy, vol, no, 005 [6] A M Annaswamy and A F Ghoniem, Active control of combstion instability: Theory and practice, IEEE Control Systems Magazine, vol, pp 37 54, 00 [7] M Ditaranto and J Hals, Combstion instabilities in sdden expansion oxy-fel flames, Combstion and Flame, vol 146, pp , 006 [8] L J ayleigh, The explanation of certain acostical phenomena, Natre, vol 18, 1878 [9] S Candel, Combstion dynamics and control: Progress and challanges, Proceedings of the Combstion Institte, vol 9, pp 1 8, 00 [10] A P Dowling and A S Morgans, Feedback control of combstion oscillations, Annal review of Flid Mechanics, vol 37, pp , 005 [11] M Fleifil, A Annaswamy, Z Ghoniem, and A Ghoniem, esponse of a laminar premixed flame to flow oscillations: A kinematic model and thermoacostic instability reslts, Combstion and Flame, vol 106, pp , 1996 [1] J Hathot, A Annaswamy, and A Ghoniem, Modeling and control of combstion instability sing fel injection, in Meeting on Active Control Technology, 000 [13] H A Nilsen, Modelling and control of oxy-fel combstion, Master s thesis, Norwegian niversity of science and technology, 006 [14] A Annaswamy, M Fleifil, J Hathot, and A Ghoniem, Impact of linear copling on the design of active controllers for the thermoacostic instability, Combstion, Science and Technology, vol 18, pp , 1997 [15] S Skogestad and I Postlethwaite, Mltivariable Feedback Control Analysis and Design, nd ed Wiley, 005 [16] D Bernier, S Dcrix, F Lacas, and S Candel, Transfer fnction measrements in a model combstor: Application to adaptive instability control, Combstion, Science and Technology, vol 175, pp , 003 [17] S S Sattinger, Y Nemeier, A Nabi, B T Zinn, D J Amos, and D D Darling, Sb-scale demonstration of the active feedback control of gas-trbine combstion instabilities, Jornal for Engineering for Gas Trbines and power, vol 1, pp 6 68, 000 [18] J P Hathot, M Fleifil, A M Annaswamy, and A F Ghoniem, Active control sing fel-injection of time-delay indced combstion instability, AIAA Jornal of Proplsion and Power, vol 18, pp , 00