ASME2003 Draft 38418 b - MITweb.mit.edu/aaclab/pdfs/ASME2003_38418.pdfLPP combustion in industrial...

February 18, 2003 22:41

Proceedings of ASME Turbo Expo 2003Power for Land, Sea, and Air

June 16-19, 2003, Atlanta, Georgia, USA

GT-2003-38418

ADAPTIVE CLOSED-LOOP CONTROL ON AN ATMOSPHERIC GASEOUSLEAN-PREMIXED COMBUSTOR

A. J. RileyDepartment of EngineeringUniversity of Cambridge

Cambridge, CB2 1PZ, UK

S. ParkDepartment of Mechanical EngineeringMassachusetts Institute of Technology

Cambridge, MA, 02139, USA

A. P. Dowling�

Department of EngineeringUniversity of Cambridge

Cambridge, CB2 1PZ, UK

S. EvesqueLehrstuhl fuer Thermodynamik

Technische Universitaet MuenchenBoltzmannstrasse 15, 85748

Garching, Germany

A. M. AnnaswamyDepartment of Mechanical EngineeringMassachusetts Institute of Technology

Cambridge, MA, 02139, USA

ABSTRACTActive control of pressure oscillations has been successfully

applied to a lean premixed prevapourised (LPP) combustion rigoperating at atmospheric conditions. The design of the rig isbased on the primary stage of the Rolls-Royce RB211-DLE in-dustrial gas turbine. Control was achieved by modulating thefuel flow rate in response to a measured pressure signal. Thefeedback control is an adaptive, model-based self-tuning regu-lator (STR), which only requires the total time delay betweenactuation and response to achieve control. The STR algorithmachieves a reduction of up to 30 dB on the primary instabilityfrequency. This performance was an improvement of 5-15 dBover an empirical control strategy (simple time-delay controller)specifically tuned to the same operating point. Initial robustnessstudies have shown that the STR retains control for a 20% changein frequency and a 23% change in air mass flow rate.

NOMENCLATUREγ STR adaptation gainsτ∆ change in total time delay

�Address all correspondence to this author.

τtot total time delayφ equivalence ratioω angular frequencyλ smith controller component in the STRa characteristic constant of 1st order filterDDV direct drive valvedt sampling time stepfDDV valve oscillation frequencyk0 gain of the combustion transfer functionk1 STR gain parameterk2 STR gain parameterma air mass flowm f fuel mass flown number of the Smith controller componentLp plenum lengthLc combustor lengthPre f combustor pressures Laplace variableSPL sound pressure levelSTR self-tuning regulatorRo

�s � poles of the combustion transfer function

t time

1 Copyright 2003 by ASME

umean mean fuel jet velocityurms rms fuel jet velocityVc DDV input voltageW

�s � combustion transfer function

Wo�s � combustion transfer function without delay

Zo�s � zeros of the combustion transfer function

zc location of the zero of the phase-lead component in the STR

INTRODUCTIONThe use of lean premixed prevapourised (LPP) combustion

in industrial gas turbines is a well-known method of producinglow levels of NOx and CO emissions. Such systems eliminatelocal regions of high temperature within the flame that increasethe level of NOx output. However, the practical application ofsuch systems is challenged by the presence of strong pressureoscillations in the combustor at lean equivalence ratios.

The mechanism producing such flow instabilities is an in-teraction between unsteady combustion and acoustic waves. Un-steady combustion produces acoustic waves, which reflect at theboundaries of the system to further perturb the flame. This gener-ates even more unsteady combustion. According to Rayleigh [1],if the rate of heat addition and the acoustic waves are in phase,the heat addition amplifies the acoustic waves and self-excitedoscillations can occur. In gas turbines this basic mechanism hasbeen seen to occur in various forms, leading to ’buzz’ in after-burners and low frequency ’rumble’ in aeroengine combustors atidle/sub-idle conditions (Bloxsidge et al [2], Zhu et al [3]).

LPP combustion in industrial gas turbines is very suscepti-ble to the self-excited oscillations. Small pressure fluctuationscan produce resultant fluctuations in the air flow entering thepremix ducts. This in turn produces small changes in the flameequivalence ratio, which, near the lean limit, lead to appreciablevariations in the combustor reaction rate (Richard and Janus [4]).Amplification occurs when these variations in the combustor re-action rate reinforce the pressure oscillations. This may result insignificant damage to the combustor and hence limit the opera-tional envelope of the gas turbine.

As emissions regulations become stricter for both industrialgas turbines and aeroengines, control methods to reduce thesedetrimental effects are currently required by engine manufactur-ers. It is still difficult to predict the occurrence of combustioninstabilities at the development stage of an industrial combus-tor. When instabilities are found during testing, the solutionscurrently available will be either passive or active techniques.

Passive control techniques tend to be tuned to particular fre-quencies and require substantial development time. They canaddress the high frequency combustor modes that occur in LPPsystems. However, passive absorption is ineffective at low fre-quencies unless very large volume resonators are used, whichincrease the mass, volume and cost of the combustion chamber.

Aspects such as low maintenance and high durability make pas-sive techniques an attractive proposal above about 300 Hz (seePutnam [5] for a general discussion).

Active control techniques have a greater potential for moreeffective control across a range of running conditions, but thereare a number of practical issues that still need to be resolved.Active feedback control uses a quantity that characterizes the in-stability as the input signal for a feedback loop: pressure pertur-bations and the fluctuating light emission from the combustionzone are commonly used input signals, however these both havethe disadvantage of introducing a long time delay to the controlloop. Currently pressure transducers are more robust and easierto locate in a combustor, not requiring line-of-sight to the flame.In the future, a measurement of either velocity or equivalenceratio in the premix ducts would make the control task simpler.The feedback signal is processed by a controller and then sent toan actuator. The role of the actuator is to influence the acousticsand/or the combustion process in order to alter the energetics ofthe interaction between acoustic waves and combustion, hencedamping out oscillations.

The application of feedback control was initially conductedusing loudspeakers and fluctuating valves to modulate the airflow (see McManus et al [6] for a review of this early work).However, this is not an easy task in full-scale applications andhence fuel modulation was found to be a more practical option.This was first applied to the problem of buzz in afterburners.Langhorne et al [7] showed that only 3% modulation of the fuel,using a simple on-off valve, could lead to a significant decreasein pressure levels for longitudinal disturbances in a simple pre-mixed ducted flame. This was quickly followed by a full-scaledemonstration of active control on the afterburner of a RB199aeroengine (Moran et al [8]). The recent problems in industrialturbines lend themselves to a similar approach in terms of activecontrol and also do not have the obvious restrictions of weightand safety that come with aeroengine technology.

Solenoid valves have been used in more recent studies tomodulate the fuel since they have the potential to take advantageof linear control theory. Seume et al [9] have reported the ap-plication of control to a Siemens heavy-duty gas turbine, usingmodulation of the pilot fuel supply as the actuator. Hibshmanet al [10] have also demonstrated control at full-scale, on a sec-tion of a liquid-fuelled lean premixed combustor. However, thelimited bandwidth of solenoid valves means that they have onlybeen applied to low frequency instabilities ( � 400 Hz). In addi-tion, solenoid valves also have issues over durability and integritythat could lead to maintenance problems over the life cycle of anindustrial gas turbine. Magneto-restrictive valves have the poten-tial to overcome bandwidth limitations, so long as the authorityof the valve can be maintained at higher frequencies (Neumeierand Zinn [11]).

The design of the control algorithm perhaps presents thebiggest challenge to active control. The controller needs to be


effective across all regimes of plant operation and must not gounstable, causing damage to the plant. Simple time delay con-trollers, forcing heat release out of phase to unstable pressureoscillations, have been successfully applied to full-scale rigs (Se-ume et al [9], Hibshman et al [10]). However, without knowledgeof the open-loop transfer function, such a controller needs to betuned in order to obtain the correct phase for each operating con-dition. In addition, new modes of instability have been amplifiedas the controller gain is increased (Langhorne et al [7], Hibshmanet al [10]).

Other control techniques that have been applied to combus-tion problems include Least Mean Square (LMS) filter (Billoudet al. [12]) and an adaptive application of Rayleigh’s criterion(Neumeier and Zinn [11]). LMS applications have had mixed re-sults and have a number of unresolved issues, perhaps their great-est disadvantage is that there are no theorems to guarantee globalstability. The adaptive Rayleigh technique addresses the fact thatthe dominant frequency can shift during out of phase forcing bydetermining the unstable frequency in real time. However, thiscontroller still requires information from an open loop transferfunction to obtain effective control.

The STR is an adaptive controller that can track changes inunstable frequencies and modify the control parameters appro-priately. It does not require any prior knowledge of the transferfunction for the system, except for the overall time delay betweenactuation and response (see Evesque et al. [13] for a detaileddescription). The end-goal of the STR controller is to have analgorithm that can achieve robust control over a variety of com-bustors and operating conditions with very little prior knowledgeof the system.

This paper presents results for the STR algorithm appliedto a simplified atmospheric combustor rig, which is based onthe Rolls-Royce RB211-DLE industrial gas turbine. Initially ashort resume of the controller theory is given. The character-istics of the rig are then described, including the experimentalset-up, instrumentation and the self-excited oscillations. The ac-tuation system includes details of the high speed valve, the ef-fects of open-loop forcing and how the controller inputs weredetermined. This is followed by results for the STR algorithmincluding comparisons with a fixed time delay controller, and fi-nally discussion and conclusions.

BACKGROUND THEORYThe STR design is based on a one-dimensional open-loop

actuated combustion model, which is characterized by the trans-fer function below.

W�s �� Pre f

�s �

Vc�s � � W0

�s � e

� sτtot (1)

where Vc�s � is the voltage sent to the actuator, Pre f

�s � is the fluc-

tuating pressure in the combustor and τtot is the total time delayin the actuated system. Evesque et al. [13] show that an expres-sion for W0

�s � , based on physical models of the flame dynamics,

the actuator dynamics and the acoustics of the combustor, cantake a rational form (once a Pade approximation to the exponen-tial terms has been applied) and hence

W�s � �� k0

Z0�s �

R0�s � e

� sτtot (2)

where Z0 and R0 are two coprime (no common factors) andmonic polynomials (the leading coefficient is unity). W0

�s � is

dominated by the properties of the actuator transfer function,which is assumed to have a low relative order (

�2), positive gain

and no unstable zeros. The STR controller updates the controlsignal Vc as

Vc�t �� kT �

t � d�t �� k̇T �

t � da�t � (3)

k̇�t �� sign

�k0 � Pre f Γda

�t � τtot � (4)

where k and d are the controller parameters and data vectors,respectively and defined as

k�t � T �� k1

�t �� k2

�t �� λn

�t �� λ1

�t �� (5)

d�t � T ��Pre f

�t �� V �

t �� Vc�t � ndt �� Vc

�t � dt �� (6)

where V�t �� 1

s � zcVc

�t �� 1, Γ is the diagonal matrix whose diag-

onal values, γ1, γ2, ... ,γn � 2, are the adaptation gains and da�t ��

1s � a d

�t �� . In k and d, k1, k2 and zc represent the phase-lead com-

ponents of a delay free system as Vc�t �� k1

s � zcs � zc � k2

Pre f�t �� , the

λ’s are the Smith controller components to compensate the timedelay of the system (Smith [14]), dt is the sampling time step andndt � τtot .

It is shown in Evesque et al. [13] that the stability of the sys-tem is guaranteed with the adaptation law in Eq. 4 if the relativedegree of W0

�s � is less than or equal to 2 and Z0

�s � (effectively

the actuator transfer function) has all stable zeros.The only knowledge that the STR requires of the transfer

function, based on the assumptions above, is the total time delaybetween actuation and response. This is input into the controlalgorithm in terms of the sampling frequency and the numberof Smith components. Other required inputs are the adaptationgains γ1, γ2 and γ3 (γ3=γ4..γ21) and the characteristic constants, aand zc.

1R � s �� ! , where R � s � is a rational function and the variable s denotes an oper-

ator of ddt ; thus V � t �#" 1

s $ zc�Vc � t ��! means that dV % t &

dt ' zcV � t �#" Vc � t �3 Copyright 2003 by ASME

RIG CHARACTERISTICSRig set-up

The facility is a generic combustor designed to model thefuel injection/premix ducts of a Rolls-Royce RB211-DLE indus-trial gas turbine. The swirler unit is a scale model, however thegeometry of the plenum and combustor has been reduced to sim-ple cylindrical pipes. This is because their influence on the insta-bility can be easily quantified provided the experimental set-uphas well-defined acoustic boundary conditions. A schematic ofthe working section is shown in Fig. 1.

Air128

1000

70

Fuel

plenumcombustor

swirlerchoke

Lp

��

��

��

��

��

��

��

��

��

��

� � � � ��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

!�!�!�!�!�!!�!�!�!�!�!!�!�!�!�!�!

"�"�"�"�"�""�"�"�"�"�""�"�"�"�"�"

#�#�##�#�##�#�##�#�#

$�$$�$$�$$�$

Figure 1. Schematic of the rig downstream of the choke plate, showing

the plenum/combustion chambers and the swirler unit. All dimensions in

mm, diagram not to scale.

A metered and steady air flow is supplied to the plenum(128mm ID) through a choked plate. This effectively decouplesthe air supply from pressure fluctuations in the working section,enabling air to be supplied at a constant mass flow rate (ma) andproviding a well-defined acoustic boundary condition. The maxi-mum mass flow rate available is approximately 0.2 kg/s, howeverthe typical operating range is 0.03-0.08 kg/s. The downstreamend of the plenum chamber incorporates an annular section priorto the swirler unit. The swirler exit is connected to a quartz tube(70 mm ID) along which combustion takes place. This providesideal optical access to the flame region. The exit of the tube isopen to atmospheric pressure and is not choked.

The fuel (ethylene, C2H4) and air are mixed using a Rolls-Royce DLE counter-rotating, radial swirler unit, scaled to fit theexisting facilities (approx. 54%). Once the airflow has passedinto the annular section, it is split into two streams that flowthrough concentric channels. In the channels, blades are fixedto induce two counter-rotating flows. The fuel is injected up-stream into the annular channels through eight cylindrical barseach fitted with two exit holes of 1.0 mm diameter (see Fig. 2). Apressurised commercial cylinder is used to supply the fuel for theswirler unit. The fuel line comprises a pressure regulator, controlvalve and turbine flow meter (see Fig. 4). Together with suitablylocated pressure transducers and thermocouples, the turbine flowmeter is used to provide a mass flow reading. Fuel mass flowrates (m f ) are in the range 1.6-3.0 g/s in order to obtain equiva-lence ratios (φ) from 0.5-1.0 for the air mass flow rates used inthese tests.

The airflow rate, the equivalence ratio and the geometricconfiguration (including the fuel bars) are all used to define theoperating points of the combustor rig.

inner channel

outer channel

fuel

air

fuel

fuel/air

Figure 2. Detailed schematic showing a cross-section of the swirler unit

and the orientation of the fuel injection bars.

InstrumentationThe feedback signal for the control algorithms is provided

by a Kistler piezo-electric pressure transducer (type 601A) mea-suring combustor pressure 700 mm downstream of the swirlerunit. The transducer is located in a side arm, 30 mm from thecombustor wall. The semi-infinite line technique (Englund andRichards [15]) is used to provide adequate thermal isolation fromthe hot products of combustion, while also ensuring that the pres-sure signal at the transducer is not distorted by reflecting waves.

A photomultiplier, together with a UV filter, was used tolook at the heat release rate of the flame. The UV narrow bandfilter is centred at 310 nm in order to look at the radiation emittedfrom OH radicals. This has been shown to linearly track the heatrelease rate for premixed flames, Drederichsen and Gould [16].

The two closed-loop control algorithms proceed in threesteps: acquisition of the unsteady pressure signal, processing ofthe control signal by the control algorithm in real-time and thensending of the resulting signal to drive the DDV valve. The al-gorithms have been implemented on a 32-bit M62 digital signal


processing (DSP) board, developed by Innovative Integration,based on the Texas Instruments TMS320C6201 processor.

Unsteady measurements of pressures, light and valve dis-placements are recorded on a PC-based data acquisition systemincorporating a sixteen-channel PCI-MIO-16XE-10 acquisitionboard from National Instruments. The signals are conditionedusing an isolation amplifier and an eighth-order elliptic low-passfilter. The cut-off frequency is automatically set to one-third ofthe sampling rate (5 kHz). The SPL data presented are acquiredover periods of up to 20 seconds and averaged over the maximumnumber of 1 second frames available.

Self-excited oscillationsThe instability characteristics of the rig have been investi-

gated for a range of flow conditions and plenum and combustorlengths. Within the typical envelope of the operating parameters(ma=0.03-0.08 kg/s, φ=0.5-1.0) several intense combustion in-stabilities with multiple frequencies have been observed. Typicalpressure spectra contain dominant peaks at one or two low fre-quencies (100 - 300 Hz) and an additional high frequency peak(550 - 700 Hz). Previous work has shown that these frequenciesrelate approximately to half-wavelength modes of the plenumand to quarter wavelength modes of the combustor. The reasonfor this is that the premix ducts have a much higher velocity thaneither the plenum or the combustor chambers, leading to a highimpedance boundary condition. Hence the plenum modes areapproximately those for a duct with two high impedance ends.Similarly, the combustor modes are approximately those for aduct with a high impedance end and an open end.

In the current set of feedback control tests the experimen-tal data has been obtained in the ranges ma=0.03-0.05 kg/s andm f =1.6-2.5 g/s, resulting in φ=0.5-0.75. For the geometric con-figuration shown in Fig. 1 (Lp=1.73 m., Lc=1.0 m.) the rigexhibits a 207 Hz plenum mode instability. In order to ob-tain different unstable frequencies the plenum length was varied(Lp=1.46/1.73/1.97 m.). The pressure spectra for these cases allcontain dominant low frequency peaks ( � 300Hz) with magni-tudes of up to 165 dB that set an ideal challenge for active control(Fig. 3).

These dominant modes correspond to the second harmonicof the plenum (wavelength=Lp). The fundamental and the higherharmonics are also present. In addition, for the Lp=1.97 m casethere is a peak at 244 Hz which corresponds to the quarter wave-length mode of the combustor tube. The appearance of the com-bustor modes is not as predictable as the plenum modes.

ACTUATION SYSTEMValve set-up

Actuation for control was achieved using a high frequencyvalve to modulate the fuel flow rate into the swirler and hence

0 100 200 300 400 500110

120

130

140

150

160

170

SP

L, d

B

frequency, Hz

Lp = 1.73 m

Lp = 1.46 m

Lp = 1.97 m

Figure 3. SPL spectrum of the self-excited combustion oscillations;

ma=0.04 kg/s, φ=0.7

produce variations in equivalence ratio in the premix ducts. Thisleads to unsteady combustion with a significant time delay thatneeds to be accounted for in the control strategy. A pressuretransducer located in the combustor section provides feedbackfor the control algorithms.

cylinderethylene

Filter

flowturbine

metervalve

Metering

Solenoid valve

swirler unit

regulatorpressure

constant highpressure supply

mass flow rateapprox. constant

DDV

plenum

��

��

��

��

��

��

�� !�!!�!"�""�"#$

Figure 4. Detailed schematic of the fuel system, together with the DDV

and the plenum chamber.

A Direct Drive Valve (DDV) manufactured by Moog was


used to modulate the fuel flow, as shown in the fuel systemschematic (Fig. 4). The DDV uses a linear force motor wherethe stroke is proportional to the applied voltage. The spool inthe DDV can be moved from the fully closed position (no flowthrough the valve, 0% open) to the fully opened position (maxi-mum flow through the valve, 100% open) by increasing the ap-plied voltage from 0 to 10 Volts. The large pressure drop acrossthe regulator and the inertia of the flow meter means that the massflow rate is effectively constant upstream of the plenum, in spiteof the high frequency modulations downstream. The plenum pro-vides mass storage, so that the fuel flow rate through the DDVcan change as its open area is modulated. The pipe length be-tween the DDV and the swirler unit was kept as short as possiblein order to decrease the attenuation and time delay. The transferfunction between the spool position and the input voltage showsuniform gain for frequencies below 350 Hz. The phase changethroughout this frequency range is linear and indicates a time de-lay equal to 1.5 ms. However the transfer function between thefuel flow rate and input voltage is of more direct relevance. Thiswas investigated in a series of bench tests with different fuel barexit areas. These tests showed that reducing the valve oscillationfrequency and the pressure drop across the valve, and increasingthe fuel bar exit area were positive factors in achieving modu-lation of the fuel flow. Based on these results the total fuel barexit area was chosen to be 12.6 mm2 (eight cylindrical bars eachfitted with two exit holes of 1.0 mm diameter).

Figure 5 shows the percentage increase obtained in the fueljet velocity rms, with a decrease in valve frequency. The meanmass flow was kept constant at 1.62 g/s, corresponding to a φ=0.6for a ma=0.04 kg/s (standard test case). The valve inlet voltagewas oscillated harmonically at maximum amplitude around the50% open position, i.e. from 0-10 V.

A similar increase in fuel jet velocity rms was found for adecrease in the mean mass flow through the valve, which corre-sponds to a reduction in pressure drop for a fixed exit area. How-ever the effect of a variation in the mean fuel mass flow was notas significant as the effect of the valve frequency, for the equiv-alence ratios and air mass flow rates used in these experiments.For the current set of tests (ma=0.03-0.05 kg/s and φ=0.5-0.75),the valve produces 5.0-10.0% rms fuel modulation in the valvefrequency range 150-250 Hz.

Open-loop forcingThe response of the flame to the valve at a forcing frequency

of 200Hz is presented in Fig. 6, in terms of the combustor pres-sure and the unsteady heat release monitored through the OHradical light emission. In this test a much shorter plenum hasbeen used increasing the fundamental resonance frequency of thechamber to above 400 Hz (Lp=0.41 m.). This results in no self-excited oscillations in the frequency range of interest and henceimproves the signal-to-noise ratio in the open-loop tests. The ef-

0 50 100 150 200 250 300 3500

10

20

30

40

50

60

valve frequency, Hz

u rms/u

mea

n, %

mf=1.62 g/s (φ=0.6)

Figure 5. Variation in the fuel jet velocity rms with valve frequency for

maximum amplitude harmonic oscillations around 50% open position;

m f =1.62 g/s (φ=0.6 for an air mass flow of ma=0.04 kg/s).

fect of this change can be seen by comparing Fig. 3 and Fig. 6.Without forcing there are no narrow-band peaks in the pressurespectrum and the unsteady heat release decreases with frequency(the peak at 50 Hz is due to electrical noise). Forcing the DDVharmonically at maximum amplitude shows an increase of up to17 dB above background noise throughout the valve frequencyrange 50-300 Hz.

Determination of τtot

The total time delay, τtot , is needed to determine the adap-tation law in Eq. 4 and n in Eq. 5, respectively. This can be de-termined through open-loop forcing and investigating the trans-fer function W

�s �� Pre f � Vc at a range of frequencies through

system-identification tests (Murugappan et al [17]). At the de-sired operating condition a simple time delay controller was ap-plied, in order to minimise the self-excited oscillation. In addi-tion to this a sine sweep of Vc

�t � , with changing frequency from

40Hz to 430Hz, was also supplied to the DDV valve. The re-sulting pressure data was post processed with a bandpass filter[80Hz - 230Hz] to better capture dynamics around the unsta-ble frequency. W

�s � was obtained using a linear AutoRegressive

with eXternal input (ARX) model-structure (Ljung [18]) and τtot

was found to be 9.6 msec.Initial tests with the STR were conducted using a system-

identification reduced order model to obtain optimal starting val-ues for the control parameters. To obtain this another system-identification was carried out using Vc

�t � τtot � and Pre f

�t � to

yield an ARX model, which resulted in a W�s � given by


W�s �� (7)

� 0 � 8787 s3 � 1071s2 � 2 � 105e6s � 7 � 894e6s4 � 24 � 75s3 � 2 � 366e6s2 � 3 � 312e7s � 1 � 169e12

e� 0 � 0096s

where sign�k0 � = -1 (see Eq. 2). This negative gain was an unex-

pected result. A system-identification of the fuel supply systemfound that the transfer function contained three low frequencypoles. These produced a change in phase at the unstable fre-quency that could account for the negative gain. The additionaldynamics in the fuel supply system were not addressed in themodel (see Background theory section). For the current tests thesign of k0 was changed in the adaptation scheme (Eq. 4).

We note that identifying sign�k0 � and τtot simultaneously,

rather than sequentially, will warrant the identification of a high-order system which is prone to large numerical errors. It shouldalso be noted that in the present set-up, no other parameters ofthe transfer function W

�s � are required to design the adaptive

controller except the values of sign�k0 � and τtot .

In the current tests, the user inputs into the STR were asampling rate of 2kHz, n � 19, a=zc=1000, γ1=γ2=100,000 andγ3=10, unless otherwise stated. The reason of reduced samplingrate from 5 to 2KHz is to minimize computation time for the λ’s.This is due to the number of λ’s, n, being inversely proportionalto the sampling rate, dt, by n � τtot � dt. The γ’s are determinedto have reasonable settling time and overshoot of control param-eters. Depending on the speed of change of the combustion char-

0 100 200 300 400 50030

40

50

60

70

80

90

100

110

120

130

140

dB

frequency, Hz

pressure − open−loop forcingpressure − no forcingheat release − open−loop forcingheat release − no forcing

Figure 6. The effect on the combustor pressure and the OH emission of

forcing the fuel flow at 200 Hz. The valve driven harmonically at maximum

amplitude, about 50% open position; ma=0.04 kg/s, φ=0.60, Lp=0.41 m,

fDDV =200 Hz.

acteristics, desired settling time of the controller and valve satu-ration, these values must be fine tuned to get the optimal ‘tran-sient’ response. They do not, however, affect the steady-stateperformance.

RESULTSNominal Case - Lp=1.73 m

Initial tests of the STR controller produced reductions innoise that were 5-15dB larger than those gained with the appro-priately tuned fixed time delay controller. However inspection ofa typical time series indicates that control is lost intermittently,as shown in Fig. 7, which degraded the performance of the STR.

0 2 4 6 8 10 12 14 16 18 20−20

−10

0

10

20

time, secsP

ress

ure

fluct

uatio

n, k

Pa

0 2 4 6 8 10 12 14 16 18 200

20

40

60

80

100

time, secs

valv

e op

enin

g, %

On Off

Figure 7. Time series showing the low frequency present fluctuations

present in the combustor when the STR controller is activated; ma=0.04

kg/s, φ=0.65, τtot =9.6 ms, Lp=1.73 m, zero initial conditions for control

parameters.

Analysis of the valve time series, just prior to the controllerdivergence, suggested that there was significant control actionaround 100Hz growing rapidly in amplitude. A bandpassfilter (120-500 Hz) was introduced between detection and thecontroller input to remove the low frequency dynamics. Thefilter generated approximately a 20 degree phase lead at 200Hz. In the range 170-300Hz, the impact of the filter dynamicson the overall system was negligible. Fig. 8 shows the resultingimprovement in performance. The controller is turned on at4.4 seconds and stabilization is achieved in about 3.6 seconds.The control parameters such as k1,k2 start at zero and convergeto a specific value, as shown for k1 in Fig. 8. The zero initial


conditions simply imply that the controller does not know thecombustion dynamics initially and these values are automaticallytuned by the STR to give optimal performance. However, itshould be mentioned that the settling time for other test cases,under nominally the same operating conditions, can be large (upto 7 seconds). This was due to two reasons; 1) higher pressureoscillations (more than 10kPa) made the valve saturate (alreadypresent to some degree in Fig. 8) and 2) zero initial conditions ofthe control parameters requires time for the controller to searchfor the optimal control parameters. When the pressure amplitudewas smaller than 10kPa and the initial conditions were chosenbased on W

�s � , the settling time could be reduced to less than

1 second as shown in Fig. 9. Fig. 10 shows typical pressurespectrum for the control on/off cases where there is a reductionof approximately 15 dB by the fixed time delay controllerand 30 dB for the STR controller at the 207Hz instability(Note: all pressure spectra presented are for pre-filtered data).One of the reasons for the limited performance of the time delaycontroller was due to a low frequency mode, which can be seenin Fig. 10 and is similar to that seen in Fig. 7. In some cases,when this low frequency mode was not present, the time delaycontroller was able to reduce pressure oscillations up to 26dB.

0 2 4 6 8 10 12 14 16 18 20−20

−10

0

10

20

pres

sure

(kP

a)

0 2 4 6 8 10 12 14 16 18 200

25

50

75

100

valv

e op

enin

g, %

0 2 4 6 8 10 12 14 16 18 20−40

−20

0

time, secs

k 1

On Off

Figure 8. Time series showing the improvement on the pressure fluc-

tuations in the combustor gained by filtering the STR controller in-

put; ma=0.04 kg/s, φ=0.65, τtot =9.6 ms, Lp=1.73 m., controller input

filter=120-500 Hz

−3 −2 −1 0 1 2 3 4 5 6−20

−10

0

10

20

time(s)

pres

sure

(kP

a)

−3 −2 −1 0 1 2 3 4 5 6−10.006

−10.005

−10.004

−10.003

−10.002

−10.001

−10

−9.999

time(s)

k 1

Controller On

Figure 9. Time series showing the improvement in the settling time of the

STR controller when appropriate initial conditions are chosen; ma=0.04

kg/s, φ=0.65, τtot =9.6 ms, Lp=1.73 m, initial conditions of k1=-10, k2=10.

0 50 100 150 200 250 300 350 400 450 500100

110

120

130

140

150

160

170

SP

L, dB

frequency, Hz

no controltime delay controlSTR control

Figure 10. SPL spectra showing the reduction in noise when the STR

and the delay controllers are turned on; ma=0.04 kg/s, φ=0.70, τtot =9.6

ms, Lp=1.73 m, controller input filter=120-500 Hz.

Robustness StudiesAs mentioned previously, the STR controller can automati-

cally tune its control parameters when the combustion dynamicschange. In this section, we carry out extensive robustness stud-ies with respect to changes in the resonant frequency, total timedelays, changes in operating conditions and initial conditions ofcontrol parameters.


Changes in the Resonant Frequency The resonantfrequency varies as the temperature of a combustor changes. Ba-naszuk et al. [19] reported a 20% change in resonant frequencyover a 9 second period during warming up of an experimentalcombustor. As a result, at a start up or during thrust change,the STR needs to be able to cope with possible changes in fre-quency. As explained in the Self-excited oscillations section, theresonant frequency was varied by changing the plenum length,Lp. Initially, Lp was changed from 1.73 to 1.46m and both thetime delay and the STR controllers were tested with input param-eters predetermined in the nominal case (Lp=1.73 m). Note: theSTR still had zero initial conditions for the control parameters.Fig. 11 shows the pressure spectrum and as expected, the reso-nant frequency moved to 240Hz. The STR controller produceda 28 dB reduction at the unstable frequency. It is worth notingthat k1 converges to positive values of approximately 25-30 forthis case, whereas it converges to a negative value in the nominalcase in Fig. 8. The simple time delay controller, using time de-lay/gain inputs determined in the nominal case, did not have anyeffect and has not been included in Fig. 11.

0 50 100 150 200 250 300 350 400 450 500100

110

120

130

140

150

160

170

SP

L, d

B

frequency, Hz

no controlSTR controller

Figure 11. SPL spectra showing the reduction in noise when the STR

is turned on in the shorter plenum case; ma=0.04 kg/s, φ=0.70, τtot =9.6

ms, Lp=1.46 m, controller input filter=120-500 Hz.

Next, Lp was increased to 1.97 m, and the delay and theSTR controllers were tested with parameters predetermined inthe nominal case. Once again the time delay controller had nosignificant effect. Fig. 12 shows the pressure spectrum for theno control and STR cases and interestingly, two modes at 180and 244Hz were observed in the no control case. The latter isthe quarter wavelength mode for the combustor tube. The op-

timal k1 values are different for these two modes and hence k1

is found to oscillate as it tries to control first one and then theother mode (Fig. 13). Finally, k1 converges to a value that is inbetween these two optimal values (Note: average k1 negative inthis case). Large adaptation gains may generate overshoot dur-ing convergence, but this can be reduced using a smaller adapta-tion gain, γ1. When the adaptation gain was halved to γ1=50000,k1 showed less oscillatory behaviour (Fig. 13) and the resultingpressure reduction was 15 dB (4dB lower than that achieved withγ1=100000).

For both cases described above, the performance of the sim-ple time delay controller could be improved by optimizing thetime delay input. However, for Lp=1.46 m. only a 7 dB reductionwas achieved, compared with 28 dB for the STR. For Lp=1.97m., a 22 dB reduction was achieved, compared with only 15 dBfor the STR. In this case, though, there was also a 10 dB increaseat the fundamental.

0 50 100 150 200 250 300 350 400 450 500100

110

120

130

140

150

160

170

SP

L, d

B

frequency, Hz

no controlSTR control

Figure 12. SPL spectra showing the reduction in noise when the STR is

turned on in the longer plenum case; ma=0.04 kg/s, φ=0.65, τtot =9.6 ms,

Lp=1.97 m, controller input filter=120-500 Hz.

Variation in total time delay The impact of a changein the total time delay on the performance of the STR controllerwas also evaluated. Such a change can occur with a change inthe flow rate or a change of the burning zone location. Insteadof changing the operating conditions, the total time delay in theSTR was changed by τ∆. Experimental results show that the STRstill maintains control up to a maximum of τ∆=1.1msec less thanthe τtot derived from the system identification. However, controlwas lost if τtot was increased beyond 9.6 ms. Please note that the


0 5 10 15 20 25 30−7

−6

−5

−4

−3

−2

−1

0

time(s)

k 1γ1=100,000

γ1=50,000

Figure 13. Change of the controller parameter, k1 in a longer plenum

case with different adaptation gain, γ1.; ma=0.04 kg/s, φ=0.65, τtot =9.6

ms, Lp=1.97 m.

algorithm is not currently capable of adapting to a variable τtot .

Changes in flow rate and equivalence ratio The ro-bustness of the STR controller was investigated with respect tochanges in the mass flow rate of the air. The controller was turnedon at the nominal case with an air flow rate of 0.04 kg/s, whichwas then decreased slowly by 23% (0.009 kg/s) over 100 sec-onds while keeping the equivalence ratio constant. Fig. 14 showsthat the controller was able to maintain control as the flow ratechanges. After 100 seconds, once the controller was turned off,the pressure amplitude returned to previous levels indicating thatthe final operating condition was also unstable. The air massflow rate was also increased from 0.04 kg/s to 0.055 kg/s. How-ever, at higher air flow rate, the combustion was stable. Also, thecontroller parameters remained constant due to low amplitude ofpressure oscillations.

The rig exhibits an unstable mode at 207Hz when ma=0.04kg/s and φ=0.6-0.7, and φ=0.6 is very close to the flammabilitylimit. The STR controller maintains control as φ is varied withinthis range. At φ larger than 0.75, a combustor tube mode above600 Hz was excited. As a result, the STR can only be testedin the range φ=0.6-0.7 due to bandwidth limitation of the DDVvalve and the flammability limit.

Initial Conditions of the Control Parameters Asmentioned earlier, carefully chosen initial conditions can reducethe settling time of the STR significantly. We can also test thesensitivity of the STR controller to the initial conditions of con-

0 10 20 30 40 50 60 70 80 90−15

−10

−5

0

5

10

15

time(s)

pres

sure

(kP

a)

0 10 20 30 40 50 60 70 80 9030

32

34

36

38

40

42

time(s)

mas

s flo

w o

f air(

g/s)

Figure 14. Time series showing the effect of the STR controller with

changes in the mass flow rate of air, while the equivalence ration is kept

constant; φ=0.7, Lp=1.73 m, controller input filter=120-500 Hz.

trol parameters, by deliberately setting the control parameters farfrom the optimum values. The control gain, k1, was set to +10initially, which is opposite in sign to the optimal value. Fig. 15shows that the STR still converges to the optimal parameters andthat it is robust with respect to the initial conditions of the controlparameters. However, the settling time increased by an order ofmagnitude over that shown in Fig. 9 where the initial conditionof k1 is set close to the optimal value.

DISCUSSIONForced unsteady combustion has been successfully achieved

by using a high frequency valve to modulate the rate of fuel in-jection into a Rolls Royce RB211-DLE swirler unit. The DDVvalve can exert significant authority over the combustion systemfor frequencies in the range 50 to 300 Hz. This has allowed theapplication of feedback control algorithms to the system in anattempt to reduce the amplitude of certain unstable frequencies.

The STR adaptive controller has been designed to accountfor variations in the unstable frequency. It has a fixed struc-ture, consisting of a phase-lead compensator and a Smith con-troller, and theoretically only requires the total time delay be-tween actuation and response, since the control parameters arefound adaptively. Tests on the current combustion rig, which hasa significant time delay (9.6 ms), have shown that it can success-fully reduce noise levels by an additional 5-15dB compared to atuned fixed time delay controller pulsing the same amount of fuel(6.5%). Better performance of the STR controller in a nominalcondition can be attributed as follows: 1) Since the closed loop


0 2 4 6 8 10 12−20

−10

0

10

20

time(s)

pres

sure

(kP

a)

0 2 4 6 8 10 12−40

−30

−20

−10

0

10

time(s)

k1

Figure 15. Time series showing the effect of the STR controller with in-

correct initial condition in the control parameter; ma=0.04 kg/s, φ=0.65,

τtot =9.6 ms, Lp=1.73 m, controller input filter=120-500 Hz.

is essentially a delay free system due to the design of the STR,the transport delay does not interact with the inherent dynamicsof the combustor. Hence, it is not likely to introduce secondarypeaks. 2) Due to 1), larger gain is permitted which results inlarger pressure reduction at the unstable frequency without gen-erating secondary peaks.

System-identification of the rig, in order to test the assump-tions of the modeling, has found that sign

�k0 � = -1 (see Eq. 2).

Although this does not affect the stability of the system, it doessuggest that there are unmodeled dynamics in the system. Thesource of this unmodeled dynamics is found to be the fuel supplysystem. In terms of future applications of the STR, this would notbe a detrimental result, since actuation systems are easily char-acterized without the need for combustion.

Robustness studies have been started to test the STR con-troller over a wide range of frequencies and operating condi-tions. The initial results have been encouraging. With changesin the resonant frequency of 20%, the STR controller was able toadjust its control parameters and produce a significant pressurereduction. Even with two unstable modes, the STR controlleradjusted its parameters to compromise and produce a pressurereduction in both modes. The algorithm is not currently capableof adapting to a variable τtot , however 1.1msec delay change wasachievable. For air flow rate and equivalence ratio, 23% and 14%changes, respectively, were allowable.

Due to limited authority of the actuator and no prior knowl-edge of combustion dynamics (zero initial conditions of controlparameters), the settling time could be large (up to 7 seconds).Also, when two unstable modes are present, large adaptation gain

produced overshoot in control parameters. These suggest thatadaptation gain and initial conditions of control parameters needto be selected carefully to make the STR controller better per-form in the ’transient region’. After the control parameters wereconverged, the performance of the controller was not changedwith changes in the adaptation gain and the initial conditions.

The simple fixed time delay controller, which was used asa benchmark for the STR, was designed to generate cancelingpressures waves and hence stabilize the combustor, as predictedby the Rayleigh criterion. This led to a noise reduction of 15-26dB at the primary instability frequency for Lp=1.73 m. How-ever, this kind of controller is limited by the constant time de-lay employed, as demonstrated by the lack of success once theinstability frequency was changed. Detailed knowledge of thephase of the system transfer function and the frequency of insta-bility is needed to choose this time delay appropriately, since thevalue of the time delay must be continually adjusted as the op-erating conditions vary and the frequencies of instability change.The advantage of the STR is that theoretically it does not requiresuch detailed information regarding the open loop transfer func-tion and the frequency of instability, needing only the total timedelay of the system which is independent of frequency. In addi-tion, the combustion dynamics do not interact with a delay in thesystem.

The hope for future applications of the STR on different rigsis that once the actuation system is characterized, the total timedelay of the system can be estimated based on a knowledge ofthe convection and combustion properties of the rig. It has beendemonstrated that the STR has a stability band of approximately1 ms in the present set-up, in terms of total time delay. If theconvection time delay was shown to be the dominant factor overthe combustion time delay (time delay once the fuel has arrivedin the combustion zone), then a simple look-up table could beused whenever the operating conditions are changed.

CONCLUSIONS� Closed loop control of a generic LPP combustor has beenachieved using a high-speed solenoid valve to modulate therate of fuel injection into a scaled Rolls-Royce RB211-DLEswirler unit and hence force unsteady combustion.

� An STR control algorithm has outperformed a simple timedelay controller at a single operating point by 5-15dB.

� The STR has been shown to maintain control at differentunstable frequencies, and also while adapting to changingoperating conditions, without any additional information in-put to the controller.

� Initial robustness studies have shown that the STR algo-rithm has the potential to act as a controller in an industrialenvironment, where limited system information and a rangeof frequencies/operating conditions are encountered.


ACKNOWLEDGMENTThe authors would like to gratefully acknowledge the sup-

port of Trinity College, Cambridge, the Cambridge EuropeanTrust, the European Union Brite Euram Programme ResearchProject ACIACOC (Project No: BE 97 4324), the Engineeringand Physical Sciences Research Council ESR21 Programme, theNational Science Foundation (grant no. ECS 9713415), and theOffice of Naval Research (grant no. N00014-99-1-0448). P. Fordhas helped extensively in running the rig.

REFERENCES[1] Rayleigh, Lord, 1896, ”The theory of sound”, London,Macmillan.[2] Bloxsidge, G.J., Dowling, A.P. and Langhorne, P.J., 1988,”Reheat buzz: an acoustically coupled combustion instability.Part 2. Theory”, J. Fluid Mech., 193, pp. 445-473.[3] Zhu, M., Dowling, A.P. and Bray, K.N.C., 2000, ”Forcedoscillations in combustors with spray atomisers”, ASME 2000-GT-108.[4] Richard, G.A. and Janus, M.C., 1998, ”Characterizationof oscillations during premix gas turbine combustion”, Trans.ASME, J. Engineering for Gas Turbine and Power, 120, pp.294-302.[5] Putnam, A.A., 1971, ”Combustion-driven oscillations in in-dustry”, Elsevier, New York.[6] McManus, K.R., Poinsot, T. and Candel, S.M., 1993, ”Areview of active control of combustion instabilities”, Prog. En-ergy Combust. Sci., 19, pp. 1-29.[7] Langhorne, P.J., Dowling, A.P. and Hooper, N., 1990, ”Prac-tical active control systems for combustion oscillations”, J.Propulsion and Power, 6, pp. 324-333.[8] Moran, A.J., Steele, D. and Dowling, A.P., 2000, ”Ac-tive control and its applications”, RTO Meeting Proceedings:MP-051, NATO symposium: Active control technology for en-hanced performance operational capabilities of military aircraft,land vehicles and sea vehicles.[9] Seume, J.R., Vortmeyer, N., Krause, W., Hermann, J.,Hantschk, C-C., Zangl, P., Gleis, S., Vortmeyer, D. and Orth-mann, A., 1998, ”Application of active combustion instabilitycontrol to a heavy duty gas turbine”, ASME J. Engineering forGas turbines and Power, 120, pp. 721-726.[10] Hibshman, J.R., Cohen, J.M., Banaszuk, A., Anderson,T.J. and Alholm, H.A., 1999, ”Active Control of CombustionInstability in Liquid-Fueled Sector Combustor”, ASME 99-GT-215.[11] Neumeier, Y. and Zinn, B.T., 1996, ”Experimental demon-stration of active control of combustion instabilities using real-time modes observation and secondary fuel injection” 26thSymposium on Combustion, The Combustion Institute, pp.2811-2818.[12] Billoud, G., Galland, M.A., Huynh Huu, C. and Candel,

S., 1992, ”Adaptive active control of combustion instabilities”,Combust. Sci. and Tech., 81, pp. 257-283.[13] Evesque, S., Dowling, A.P. and Annaswamy, A.M., 2000,’Adaptive algorithms for control of combustion’, RTO AVTSymposium, Braunschweig, Germany, 8-11 May 2000.[14] Smith O., 1959, ”A controller to overcome dead time” ISA6(2), 28-33.[15] Englund, D.R. and Richards, W.B., 1984, Proceedings ofthe 30th International Instrumentation Symposium, May 7-10Denver CO, pp. 115-124.[16] Drederichsen J. and Gould R.D., 1965, Combustion andFlame, 2, pp. 25.[17] Murugappan, S., Acharya, S., Allgood, D. C., Park, S.,Annaswamy, A. M. and Ghoniem, A. F., 2003, ”Optimal controlof a swirl stabilized spray combustor using system identificationapproach”, Combust. Sci. and Tech., 175, pp. 55-81.[18] Ljung, L., 1999, ”System Identification: Theory for theUser”, 2nd edition, Upper Saddle River, N. J., Prentice-HallInc.[19] Banaszuk, A., Zhang, Y. and Jacobson, C. A., 2000,”Adaptive Control of Combustion Instability Using Extremum-Seeking”, American Control Conference, Chicago, USA.


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