Dzu K. Le, John C. DeLaat, Clarence T. Chang, and Daniel R. Vrnak

Glenn Research Center, Cleveland, Ohio

Model-Based Self-Tuning Multiscale Method

for Combustion Control

NASA/TM—2006-213855

February 2006

AIAA–2005–3593
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Dzu K. Le, John C. DeLaat, Clarence T. Chang, and Daniel R. Vrnak

Glenn Research Center, Cleveland, Ohio

Model-Based Self-Tuning Multiscale Method

for Combustion Control

NASA/TM—2006-213855

February 2006

National Aeronautics and

Space Administration

Glenn Research Center

Prepared for the

41st Joint Propulsion Conference and Exhibit

cosponsored by the AIAA, ASME, SAE, and ASEE

Tucson, Arizona, July 10–13, 2005

AIAA–2005–3593
Acknowledgments

This research has been funded under the NASA Ultra Efficient Engine Technologies (UEET) project.

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Available electronically at http://gltrs.grc.nasa.gov
NASA/TM—2006-213855 1 

Model-Based Self-Tuning Multiscale 

Method for Combustion Control 

Dzu K. Le, John C. DeLaat, Clarence T. Chang, and Daniel R. Vrnak 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract

A Multi-Scale representation of the combustor dynamics was used to create a self-tuning, scalable controller to 

suppress multiple instability modes in a liquid-fueled aero engine-derived combustor operating at engine-like 

conditions. Its self-tuning features designed to handle the uncertainties in the combustor dynamics and time-delays 

are essential for control performance and robustness. The controller was implemented to modulate a high-frequency 

fuel valve with feedback from dynamic pressure sensors. This scaleable algorithm suppressed pressure oscillations 

of different instability modes by as much as 90 percent without the “peak-splitting” effect. The self-tuning logic 

guided the adjustment of controller parameters and converged quickly toward phase-lock for optimal suppression of 

the instabilities. The forced-response characteristics of the control model compare well with those of the test rig on 

both the frequency-domain and the time-domain. 

Nomenclature 

A 2 m×2 m “state-space” matrix in the finite-difference equation of m acoustics modes (Eq. (1a)) 

T control loop-time, also taken as time step in the “state-space” equation of the “plant” model 

n discrete time index associated with T

un valve-commands for fuel modulation (in Volts) 

b expected valve effectiveness on fuel-flow modulation (in 1/Volt, so that “b un” is dimensionless) 

i (or j) index of the modeled modes, starting with “i = 1” for the fundamental mode 

ωi approximate natural frequency (in radians/second) of combustor acoustics mode i

ζi approximate damping coefficient for acoustics mode i (“critically damped” is when “ζ = 1”)

Xn 2 m-vector of m pairs of “quadratures” (dimensionless, modal state-variables) for m acoustics modes 

Q 2 m-vector function of many variables to model heat-fluctuation lumped effects on acoustics 

(Eq. (1a)) 

κ dimensionless gain parameter for the effect of fuel-flow perturbations on heat-release

τ time-shift operator, also interchangeably denotes the associated (possibly random) delay-time 

v (or w) wide-band, random disturbances 

po reference pressure differential, in psi, comparable to the pressure drop across the injector 

pn

′ combustion zone pressure oscillations (about a mean), in “psi” (pounds per square inch) 

i Sn 2 m-vector of m pairs of “quadratures” extracted from feedback signals {sn} using quadratures filters 

qn

~ 2 m-vector of state-variables in the dynamic equation to project Xn ahead N time-steps, given { }i Sn

qnˆ a prediction for Xn by a Kalman estimate of qn

~ using i Sn as measurement feedback 

I. Introduction 

Lean-burning front-ends (e.g., lean-burn direct injection) for combustors offer the possibility to drastically 

reduce particulate and NOx emissions by aero-engines. The dynamics of this type of combustor, however, are 

susceptible to instability as has been observed in ground-based lean-burning power generators. This is due to the 

reduced internal damping and the increased perturbations from more energetic mixing of liquid-fuel and air. The 

more homogeneous acoustic medium in a typical lean-burn combustor is favorable for well-formed acoustics modes. 
NASA/TM—2006-213855 2 

In addition, reduction or elimination of film-cooling liners in the combustor will result in acoustically hard boundary 

conditions which reflect the perturbations in a coherent manner and further reduce damping. Also, the vigorous 

mixing of liquid fuel and air could generate energetic perturbations that might overcome the injector relative 

pressure-drop. Consequently, acoustic pressure oscillations can occur inside the combustor and couple with the fuelair feed-system dynamics to result in non-steady heat-release that, in turn, will amplify the combustion acoustics. 

Thus, large pressure oscillations could occur inside the combustion chamber, disrupting flame stability and 

interfering with other subsystems (Ref. 1). Active Combustion Control (ACC) via fuel-modulation provides a 

method to suppress combustion instabilities to enable the effective operation of such lean-burning combustors for 

aero-engines (Ref. 2). 

The development of the model-based, self-tuning control for fuel-modulation to be presented in this paper is a 

part of the research on ACC at NASA Glenn to enable direct-injection lean combustion. The interested readers are 

also referred to other related reports from NASA Glenn (Refs. 3 to 5) for further information on this research, 

including a more detailed description of the research combustor (named the “NASA SNR”; Figs. 1 and 2), its 

control system, and other useful findings on combustion control dynamics with this test rig. 

Figure 1.—The single nozzle combustor.

PRE-DIFFUSER

AIRFLOW

Ö

" "

COMBUSTOR

PRE-DIFFUSER

AIRFLOW

Ö

" "

COMBUSTOR

Figure 2.—Schematic of the NASA SNR (in the HF configuration).
NASA/TM—2006-213855 3 

In this direction, a model-based controller was developed to operate a high-frequency fuel-modulation valve 

based on dynamic pressure sensors as feedback to directly affect the instantaneous fuel-air ratio in order to suppress 

the combustion instabilities. This model-based control method for ACC (named the “Multi-Scale Extended Kalman” 

approach, abbreviated MSEK (Ref. 6)) uses multi-scale analyses (Refs. 7 and 8) and an extended Kalman filter 

(Refs. 9 and 10) to predict and control fuel-modulation effects and the combustion thermo-acoustics. A prototype of 

the MSEK core logic (named “the Basic MSEK” throughout this paper) was demonstrated in 2002 on a test rig for 

an instability with high-frequency pressure oscillations (greater than 500 Hz) (Ref. 6). This NASA Glenn single 

nozzle combustion rig operates at engine pressures, temperatures, and flows using liquid jet fuel and incorporates 

many engine-like features, including and actual engine fuel nozzle and swirls, dilution cooling, and an effusioncooled liner (Ref. 11). The rig (Figs. 1 and 2) was developed in partnership with Pratt & Whitney and United 

Technologies Research Center. Although the rig exhibited a higher level of background noise/disturbances than 

observed in the engine (Fig. 3), it adequately replicated an observed engine instability experience. In addition to the 

baseline configuration at “high-frequency” (HF) the combustor rig can also be changed to a “low-frequency” (LF) 

and “mid-frequency” (MF) configuration. For the LF configuration, which exhibits ~280 Hz instability, both spool 

pieces, as shown in Figure 2 are moved to a position between the pre-diffuser and fuel injector. For the MF 

configuration, which exhibits a ~340 Hz instability, only one spool piece is moved to between the pre-diffuser and 

fuel injector. The initial investigation of the Basic MSEK with the NASA SNR in the HF configuration was 

conducted in May and September 2002. This initial investigation, performed with both the Basic MSEK and an 

adaptive controller by Kopasakis (Ref. 5), constituted the first successful demonstration of ACC on a realistic aeroengine combustion rig (Refs. 5, 6, and 12). Prior to that demonstration, partial success in suppressing the LF 

instability had been reported (Ref. 13). The main issue with control-performance in this and other earlier works was 

the so-called “peak-splitting” phenomenon (as illustrated by the pressure amplitude-spectra of Fig. 4). While the 

dominant instability was suppressed, other instability peaks arose around the central frequency; and consequently, 

the reduction in oscillation rms amplitude was poor. 

Such problems (perhaps due to both the valve dynamics and particular control strategies) can be overcome with a 

high-performance valve and by using variable control gains and other real-time adjustment of control parameters, as 

recently demonstrated with the “Self-Tuning MSEK”. In this follow-on development of the MSEK, various 

parameter optimizations and “self-tuning triggers” were used to effectively minimize the time-scale averaged 

variances of the combustion sensed pressure without aggravating the existing instability at any time. Such selftuning features (based on multi-scale variances or higher moments of pressure oscillations for the triggers to adjust 

the parameters and setting their increments and search ranges) are essential for handling the severe uncertainties 

inherent in combustion time-delays and other characteristics, while keeping the embedded predictor model in the 

controller simple. The resulting Self-Tuning MSEK controller showed good results on the MF and LF configurations 

of the NASA SNR, including a very fast convergence towards optimal “phase-lock.” For the LF SNR configuration, 

where the signal-to-noise ratio is high, the Self-Tuning MSEK controller was able to reduce the amplitude-spectrum 

peak by 90 percent as well as the overall pressure oscillations rms value by 80 percent without causing peaksplitting. 

This paper describes the improvements recently made on the Basic MSEK to create the Self-Tuning MSEK. In 

sections II and III, the reduced-order model and validation results based on some open-loop forced-response data of 

the SNR are presented. The MSEK controller formulation, self-tuning features, and ACC demonstration results on 

0 100 200 300 400 500 0

1

2

3

4

5

6

7

Combustor Pressure Amplitude, (psi)

Frequency, (Hz)

Combustor LF Instability - Run 114, Pt 55 and 42, 8/19/2000

uncontrolled

controlled

Figure 4.—A case of severe “peak-splitting” under active 

combustion control for the LF instability (Ref. 13).

0 100 200 300 400 500 600 700 800 900 1000 0

0.1

0.2

0.3

0.4

Frequency (Hz)

Amplitude (psi)

Rig Engine

Figure 3.—Engine and NASA HF SNR comparison. 
NASA/TM—2006-213855 4 

the SNR are presented in sections IV and V. Some conclusions and highlights of these ACC experiments, and control 

and model developments are given in section VI. 

II. Reduced-Order Thermo-Acoustics Model 

The reduced-order thermo-acoustics model for this control development, the same as presented in the previous 

report for the 2002 work (Ref. 6), is reviewed here for further clarification. Except for parameter values, this same 

model is applicable for all three configurations (HF, MF, and LF) of the SNR. It is formulated for the two dominant 

thermo-acoustics modes of the SNR as follows (see nomenclature list for the variables description): 

Xn 1 AXn Q( a Xn, bun, cPn, Wn ) ~ + = + τ τ τ ; (1a) 

1 2 00 n n

p′ =⎡ ⎤ ccX ⎣ ⎦ (1b) 

n nn S pV = ′ + (1c) 

In equation (1a), the 4×4 state matrix A is approximated by the following expression, with λi ≡ exp (–2ζ iωiT): 

[ ]

[ ] ⎥

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎢

⎣

⎡

⎥

⎦

⎤ ⎢

⎣

⎡ − λ

⎥

⎦

⎤ ⎢

⎣

⎡ − λ

=

sin( ) cos( )

cos( ) sin( ) 0

0 sin( ) cos( )

cos( ) sin( )

2 2

2 2

2

1 1

1 1

1

ω T ω T

ω T ω T

ω T ω T

ω T ω T

Α (1d) 

Typically, ω1 (“Mode 1”) could be 2π×290 radians/sec to 2π×340 radians/sec, depending on the rig; and ω2 

(“Mode 2”) could be 2π×520 radians/sec or higher. The two damping coefficients ζ i (for i = 1, 2) are typically about 

0.01 to 0.05. The heat-release fluctuation, Q, affecting the acoustics is a 4×1 vector-valued function of delayed 

acoustics states, internal pressure feedback on fuel-flow, and fuel-modulating valve position u n ~ (about a mean 

position); with delay effects modeled by random time-shift operators τa , τb , τc (of non-zero mean values) applied on 

the various variables. The calculation of Q with these variables is described in the following intermediate steps, in 

which the parameters {hi j} and “g” are constant, internal feedback gains; “b” represents the effectiveness of fuelmodulating on pressure oscillations; “po” a reference pressure comparable to the mean pressure drop across the 

injector: 

( )

( )

( )

min 1 2 max

21 22

11 12

2

1

subject to bounds: ,

~

1

1

0 0

0 0

p p p p

w

p

u

b g

b g τ X h h

h h

p

p

n

c n

b n

a n

′ ≤ ≤ ′

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎣

⎡

τ

τ

⎥

⎦

⎤ ⎢

⎣

⎡ ⎥ +

⎦

⎤ ⎢

⎣

⎡ ≡⎥

⎦

⎤ ⎢

⎣

⎡

 (1e) 

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎟ + − ⎠

⎞ ⎜

⎝

⎛ = 1 1 o

i

i p

p κ Q i (for i = 1, 2) (1f) 

[ ]t Q ≡ 0 Q1 0 Q 2 (1g) 

The superscripted operator [...]t

 as in Equation (1g) and elsewhere denotes matrix/vector transpose. The imposed 

bounds on p1 and p2 following Equation (1e), for the calculation of Q, was implemented differently by substituting 

the following expressions instead of Qi(for i = 1, 2) into (1g): 

( ) 2 / arctan 0.5 / U Q eU i ii π π+ ( ( ) ) (1h) 
NASA/TM—2006-213855 5 

The inputs Qi for expression (1h) are defined as in (1f), except that the bounds previously imposed on pi are no 

longer needed (Instead, the quantity 0 ≤ Ui ≤ 1, for i = 1, 2, are constant fractions now provide the necessary upperbounds for the quantity (1h)); and, “e” is a bias. These parameters as well as {hi j}, b, and κ will be chosen to match 

the open-loop forced response characteristics of the combustion chamber pressure (see section III). Note that, the 

dynamics of the heat-fluctuation term Q is very complex, as it is the result of heat convection, diffusion, air flow and 

fuel flow, and combustion. The simplistic approximation of Q in (1e) to (f), with some imposed bounds (empirical, 

implemented as in (1h)), and the Euler expression for the fuel-air ratio fluctuations as in (1f) is only for modeling its 

average (non-linear) effects on the acoustics. For example, the model data for the Low-Frequency Configuration as 

set-up at Glenn in 2004 are chosen as follows: 

First, choose po = 20.0 psi; T = 0.0002 sec; κ1 = 1.2 po

= 24.0; κ2 = 0.4 po = 8; g = 0.001; and, b = 0.3. Next, 

ω1 = 1822 radians/sec; ζ1 = 0.042; c1 = 1.0; h11 = 1.0; 

U1 = 0.9; and, e1 = 2.64 (Mainly for matching mode-1 

characteristics). Then, ω2 = 3456 radians/sec; ζ2 = 0.01; 

c2 = 1.0; h2 2 = 1.0; U2 = 0.3; e2 = 3.2 (For mode-2 

characteristics). And lastly, h1 2 = 0.1; h2 1 = 2.0 

(The influence of mode 1 on mode 2 appeared strong 

in the LF SNR); aτ = 0.0038; bτ = 0.0033; 

cτ = 0.0002 sec (Empirical, mean values). 

Model validation with this parameter set will be 

presented in the next section. 

III. Model Validation With the “SNR” Test Data 

The reduced-order model and associated 

parameters for the HF configuration of the SNR had 

been validated in an earlier work (Ref. 6). 

Therefore, this section will be devoted only to 

validation of model for the LF configuration (LF) of 

the SNR. This configuration is particularly 

important for validating the model, because its 

internal instability is much more prominent

compared to the external disturbances. The latest 

MSEK and self-tuning features were built and 

enhanced mainly with modeling data from this test 

rig configuration. The characteristics of the LF SNR 

self-sustained instabilities and open-loop responses 

to fuel-modulation by a high-frequency valve 

(Fig. 5) are shown next to validate the described 

reduced-order plant model and its parameter values. 

To highlight the agreement of model results with 

test data, this validation will be shown here with 

more refined parameters than typically done for 

preliminary control tuning prior to testing— 

preliminary tuning of control parameters prior to 

testing on the rig required only rough estimates of 

model parameters on the instability magnitude and 

the valve “control-authority” (i.e., the response 

characteristics of the combustor pressure under 

open-loop commands). 

Some typical non-linear response characteristics 

of the LF SNR under sinusoidal fuel-modulation 

with the high-frequency fuel-valve are shown in 

Figures 6 and 7. In these figures, the signal named 

Figure 5.—A photo of the high-frequency 

“Georgia Tech valve” used for fuel-pulsing. 

0 200 400 600 800 0

2

4

6

8

1 0

1 2

Fre que ncy, Hz

P L A 1C 1p si

Max=11.82 @ 314.94H z, PSD R MS=9.56

R u n 425, 040602 , P o in t p t016

0 5 1 0 -1 5

-1 0

- 5

0

5

1 0

1 5

2 0

psi

T im e , se c

Tim e R M S =9.56, M ean =-0.2

0 200 400 600 800 0

0.5

1

1.5

2

2.5

3

3.5

Fre que ncy, Hz

P L A 1C 1p si

Max=3.16 @ 100.1H z, PSD R MS=3.04

R u n 4 25, 040602 , P o in t p t023

0 5 1 0 -1 5

-1 0

- 5

0

5

1 0

1 5

psi

T im e , se c

Tim e R M S =3.07, M ean =-0.3

Figure 6.—(Upper subplots) The LF SNR self-sustained 

instabilities (oscillations in psi); (Lower) Effects 

of 100 Hz sinusoidal valve commands with 3-V 

amplitude on the instabilities, resulting in about 

10 psi change in pressure oscillations. 
NASA/TM—2006-213855 6 

0

1

2

3

REFAread

Max=2.93 @ 200.2Hz, PSD RMS=2.11

Run 424, 040601 , Point pt019

-4

-2

0

2

4

Volts

Time RMS=2.11, Mean=0

0 500 1000

0

5

10

15

Frequency, Hz

PLA1C1psi

Max=4.89 @ 308.84Hz, PSD RMS=5.26

0 0.05 0.1 0.15 0.2

-20

-10

0

10

20

psi

Time, sec

Time RMS=5.31, Mean=0.1

Figure 7.—Effects of 200 Hz sinusoidal valve commands of 3-V 

amplitude on the LF SNR instabilities, resulting in about 

7 psi change in pressure oscillations. 

 Figure 8.—(Upper subplots) Model results of LF self-sustained instabilities; (Lower) Effects of 100 Hz sinusoidal 

valve commands of 3-V amplitude on the LF SNR Model instabilities. 

“PLA1C1” is the combustion pressure oscillation signals sensed at about 2 inches downstream of the fuel injector; 

and “REFAread” (in Volts) represents the valve command. For example, the two upper subplots of Figure 6 show 

the amplitude spectra and time-domain trace of the combustor pressure self-sustained oscillations (in psi) without 

fuel-modulation. The main instability frequency is about 315 Hz. The higher frequency mode, at about 620 Hz, is 

also visible on the amplitude spectra plot. The two lower subplots of Figure 6 show the responses of the internal 

pressures to 100 Hz, 3-V sinusoidal open-loop commands on the valve. The lower subplots in Figure 6 as well as 

Figure 7 (for 200 Hz open-loop inputs) clearly show the nonlinear response characteristics of the combustion 

instabilities and the significant effects of the fuel-valve pulsation. 
NASA/TM—2006-213855 7 

Figure 8 shows the simulation data of the LF SNR 

reduced-order model to be compared to the test data of 

Figure 6. It shows that, the modeled self-sustained 

instabilities as well as their responses to the 100 Hz, 3-V 

sinusoidal fuel-modulation open-loop commands, 

including non-linear characteristics, compare well on both 

the frequency-domain and the time-domain with the test 

data of the rig. Likewise, the model results of Figure 9 

compare well with the test results shown in Figure 7. 

IV. The Self-Tuning MSEK Controller 

The top-level structure of the Self-Tuning MSEK 

controller for ACC is still the same as that of the “basic 

MSEK”(Ref. 6) tested in 2002 on the HF SNR (see 

Fig. 10). The control scheme formulation, and additional 

self-tuning features as in the latest version will be 

described in more detail in the following sub-sections. The 

subsection titles refer to the individual sub-block names in Figure 10. Except for the last subsection (Automatic 

Tuning of Critical Control Parameters), these subsections are reviews of the basic control scheme that had been 

briefly described in the previous work (Ref. 6).

A. Multi-Scale Tone Analysis Using “QA” 

This pre-filtering part of controller MSEK (Fig. 10) is performed by a “Quadratures Filter Bank” of wavelet-like 

filters to extract the dominant “tones” of the sensed pressures. By definition, a “Quadrature Analysis” (QA) on a 

frequency range of a signal stream {s n } (a time-series with n being the time index) is any decomposition of the 

signal contents within that range into two mutually orthogonal components {S1 n } and { S2 n } by using an 

Orthogonal Wavelets Decomposition and Partial Reconstruction scheme (e.g., using “quadrature mirror filters”) 

(Ref. 7). For simplicity, instead of such a wavelet scheme, a pair of Finite Impulse Response (FIR) band-pass filters 

is designed for each frequency range to extract (approximate) “quadratures” from the signal: One filter with unity 

gain and 45-degrees lead at the center of the frequency range of interest, to extract the time-series { S1 n }; and 

another, also with unity gain, but with 45-degrees lag at the same frequency, to extract { S2 n }. Using the described 

QA process, for each of the two main frequency ranges (LF and HF) of the SNR, a “filter-bank” consist of three 

Quadrature Filter pairs (hence a minimum of six filters for each range) was used to analyze the sensed pressure 

oscillations and, for each time point n, extract the dominant pair among the three pairs of quadrature components. In 

particular, for the LF range, one pair of Quadrature Filter as described is designed for the central LF, and the other 

two are for 0.98 LF and 1.02 LF, respectively. These are then used to extract the dominant LF QA sequence, 

denoted { S

1

n ≡ [S

1

1 n S

1

2 n ]

t } as in the formulation of the predictor dynamics in the next section. Likewise is done 

to extract the HF QA sequence which will be denoted { S

2

n ≡ [S

2

1 n S

2

2 n ]

t }. The advantage of this (approximate) 

QA process is its simplicity; also, the polar angle of the vector [ S

i

1 n S

i

2 n ]

t (being the phase angle of { Si

1 n } ) 

represents the instantaneous “phase” angle of the tone i plus π/4 radians. 

B. EK States Prediction 

Although the evolution equation for S

i

n can be derived from the state-equations (1a) to (1h) to develop the 

prediction scheme, such route is avoided because it is excessively complicated for real-time calculation. Thus, the 

state-equations (1a) to (1h) will be used directly in the following development of the Predictor (Eqs. (3a) to (3e)). 

Note also that, if the “QA” process is applied to the output {sn} simulated by the model in equation (1c), then the 

resulting S

i

n is approximately i ci Xn (for i = 1, 2) with about 45-degree phase-lead. Hence, the following fictitious

random process would be a good projection of the actual state variables Xn ahead N sampling steps (such that, N × T

~total delay-time) if certain augmented input “L” can be designed based on S

i

n (for i = 1, 2) to make the output 

yn track the measurable output “ 1 2 c1 Xn + c2 Xn ” despite the random disturbances w and v: 

Figure 9.—Response characteristics of the 

LF SNR Model to 200 Hz valve 

commands of 3-V amplitude. 
NASA/TM—2006-213855 8 

⎟

⎠

⎞ ⎜

⎝

⎛ + = + + + ~ ~ ~ 1 2

1 n , S n qn Αqn Q w L S (2a) 

ν n n N n N y ≡ c q + c q + − − ~ 1 ~ 2

1 2 (2b) 

The random effects w and v need to be included here in the design of the Kalman filter for qn

~ estimation, so that 

the predictions would be robust against disturbances. Also, to simplify the Kalman filter, the projected “Q”-term 

shown in Equation (2a) will be approximated using Si

n (for i = 1, 2) (but, without time-delays in the formulation; 

(see Eqs. (3c) and (3d)) rather than by integration as part of the above process. Furthermore, the first two terms of 

the right-hand-side of Equation (2b) add up to n N Mq − ~ , where M ≡ [c I c I] 1 , 2 , and “I” denotes the 2×2 identity 

matrix. So, if the 5th-order Pade approximation is used for the N-step delay to apply on the 2-vector M qn

~ to 

compute the delayed sequence, the combined state matrices of that transformation individually applied on the two 

vector components would result in the state-space matrices U, F, E, D (of dimensions 10×10, 10×2, 2×10, and 2×2, 

respectively) that yield the following reformulation of Eq. (2b): 

z n Uzn FMqn

~ + 1 = + (2c) 

yn ≈ Ezn + DMqn + v ~ (2d) 

Equations (2a), (2c), and (2d) result in the following Quadratures Kalman Predictor obtained by estimating qn

~ ; 

the estimation is denoted qnˆ for simplicity, and meant as a projection for Xn , N time-steps ahead: 

( ) 1 2

1 1 ˆ ˆ ˆ ˆ n n n n n n q = Α q + Q + K E Z + DMq − S − S +

 (3a) 

( ) 1 2

1 2 ˆ ˆ n n n n n n n Z = UZ + FMq + K E Z + DMq − S − S +

   (3b) 

min 1 2 max

2

1

21 2 2

11 12

2

1

' ˆ ˆ '

ˆ

ˆ

0 0

0 0

p p p p

u

b

b

k k

k k

p

p

,

n

n

n

S

S

≤

⎥

⎦

⎤

⎢

⎣

⎡ ⎥

⎦

⎤ ⎢

⎣

⎡

⎥

⎦

⎤ ⎢

⎣

⎡ ⎥ ≡

⎦

⎤ ⎢

⎣

⎡

≤

+

subjected to :

 (3c) 

 

Pressure Variance

Parameters 

Tuning

EK States 

Damper

Tone Suppression 

Phase - Adjusted 

Reconstruction 

Phase - Drift 

Multi- Scale 

Tone Analysis 

Time- Scale Averaged 

Pressure Variance

Parameters 

Tuning

EK States 

Prediction Damper

Tone Suppression 

Phase - Adjusted 

Reconstruction 

 

Multi- Scale 

Tone Analysis 

Phase - Drift 

Estimation Fuel 

Modulation 

Command 

 

 

Sensed 

Combustion

Pressure 

 

Figure 10.—The MSEK controller functional block diagram. 
NASA/TM—2006-213855 9 

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ ⎟ + − ⎠

⎞ ⎜

⎝

⎛ ≡ 1 1 ˆ ˆ

o

i Q i p

p

i κ

 (for i = 1, 2) (3d) 

[ ]t Q Q Q 2 ˆ 1 0 ˆ 0 ˆ ≡ (3e) 

In Equation (3c) the parameters “ ki j ” are related to “ hi j ” such that: hi j ≈ ci ki j (for i, j = 1, 2), where “ci” and 

“ hi j” are the model parameters shown in Equations (1b) and (1e). The matrices K1 and K2 (of dimension 4×2 and 

10×2, respectively) are the two vertical sub-blocks of the Kalman matrix computed for states estimation, assuming 

certain covariance matrices for the random vectors v and w. Note that, the time-delay of the “Q”-term in the actual 

process Xn was dropped to affect the desired lead time for this prediction scheme (i.e., comparing Eq. (3c) to (1e)). 

It is also sufficient to use the simple bounds after Equation (3c) instead of the more refined expressions (1h). 

C. The Damper 

If S ≡ { [S1 n , S2 n]

t } denotes the time-series of “quadrature pairs” extracted from a signals { s n } by a “QA” 

process as described previously, then the linear combination (associated with an angle α, in radian) denoted 

Sα ≡ {S1 n cosα – S2 n sinα} represents the extracted tone of {sn} phase-shifted by “α+π/4” radians. Such 

combination is used on the predicted quadratures, namely i

i n i Sn ≡ c qˆ  (for i = 1, 2), to prescribe a Linear Quadratic 

Regulator-type damper (This part of the fuel-modulation command, as in Fig. 10, is distinguished here by the 

superscript “d,” with the time-index “n” suppressed and the superscript being the mode index): 

( ) ⎥⎦

⎤ ⎢⎣

⎡ = + − 1 2

1 2

ˆ 1 ˆ

β β

'd ' u μ l S l S (4) 

where “l” is a chosen “mode-1 fraction” (with 0 ≤ l ≤ 1) (basically a Loop-Shaping means for performance 

optimization), and “μ” is the overall gain for the “Damper”. The terms i

i β S

ˆ (for i = 1, 2) are the phase shifted signals 

constructed from the predicted “quadratures,” using the respective phase angles βi ≡ β

⎯

 + δi n (for i = 1, 2), with β

⎯

 

being a certain bias and δi n , a predicted phase-drift. The drifts δi n (over the time interval of expected control 

transport-delay, for tones i = 1, 2) are predicted by a dynamic, linear regression scheme applied on the quadrature 

phases { αi n } as defined in equation (5) of the next sub-section. 

D. The “Phase-Adjusted Reconstruction” and Tone Suppression 

This part of the control scheme is for countering the non-steady heat-release effects. For this purpose, the 

instantaneous amplitudes and phases of the combustion pressure near the LF and HF are first estimated by projecting 

the quadratures pair i Sn (for i = 1, 2, as 2×1 vectors) onto an orthogonal frame rotating at the respective speed ωi

(referring to the frequencies in Equation (1d)). To minimize the effect of random noises, these projections are next 

passed through low-pass filters with cut-off frequencies at 100 and 200 Hz, respectively, before computing the 

amplitudes and phases. Note that, these cut-off frequencies are about 1/3 of the respective central frequencies (So 

that variations in amplitude for every three oscillation at such frequency should be detected). Those estimations form 

the following expression for feedback to the tone-suppression logic (for modes i = 1, 2): 

σi = rin cos( n ωi T + αin ) , (5) 

where { ri n } is the computed amplitude, and { αi n } the phase angle at time tn of the filtered, projected quadratures 

vector. Then, { αi n } is used to predict the phase drifts δi n (for the expected control transport-delay, for i = 1, 2) 

using a dynamic linear regression scheme. Since the quantities σi should be highly coherent with the non-steady 
NASA/TM—2006-213855 10 

heat-release, the fuel-modulation command un will include a compensation term (distinguished by the superscript 

‘c’) of the following form for Tone Suppression (see Fig. 10) to minimize these effects:

[ ( ) ( ) ( ) ] n α δ n n ω T α n r n l χ n α δ n n ω T α n r n u γ l 'c '

n 2 2 2 cos 2 2 1 1 1 1 cos 1 1 = χ + + + + − + + + , (6) 

where “γ” is the overall gain for Tones-Suppression and “0 ≤ l ≤ 1”, the same “mode-1 fraction” used in 

Equation (4). A varying factor, { χi n } (for i = 1, 2), is also introduced to allow for gradual reduction of the ToneSuppression actions when “ ri ” is sufficiently small (This is essential for rendering absolute stability to the 

controlled model as shown in the 2002 study) (Ref. 6). It is basically a unit-gain with an integral adjustment, 

calculated by digitizing the following expression (also, “χi n” is subjected to certain bounds χ min and χ max to 

maintain numerical stability): 

( ) ∫ χ ≡ + η r − ρ dt i 1 i i , (7) 

where “η ” is a constant, and “ρi ” is a reduction level expected to be maintainable for “ ri ” with this scheme. In 

summary, the Tones-Suppression command is generated with these gains on “ σi ” after having phase-shifted it by a 

bias α⎯ plus δi n . 

E. Automatic Tuning of Critical Control Parameters 

The fuel-modulation command { un } issued to the valve is the sum of the expressions (4) and (6). For all SNR 

configurations, the parameters in the predictor as well as in the described command scheme appear to be fairly 

deterministic, except for the phase biases ( α⎯ and β

⎯ )and the control authority represented by “b” (see Eq. (3c)). The 

critical control parameters of the MSEK that require automatic tuning are: α⎯ , β

⎯ , b , μ , and γ. The remaining 

parameters, including “l” (also of importance) can be preset based on the model, or calibrated empirically (In 

particular, the parameter “l” can also be searched in real-time automatically, at a very safe and slow pace as 

demonstrated on the model as in the last subsection of section V (Control Evaluation). 

The three parameters α⎯ , β

⎯ , and b are determined by the Parameters Tuning logic (Fig. 10) via sequential, globaltype searches. These searches are to minimize the Time-Scale Averaged Pressure Variance (in Fig. 10, obtained by 

applying a 0.2-Hz low-pass filter on the total square-norm of the two vectors S i

n , for i = 1, 2). The searches are 

activated only if performance degrades below a certain threshold (a scalable threshold based on the model). The 

search neighborhood is also narrowed down if performance is improving. In parallel, fast management of μ, and γ

(with a common variable factor) are done to avoid aggravating the instabilities at wrong values of α⎯ , β

⎯ , and b . 

That is, these gains are dropped quickly to zero when an overshoot trend is detected in the pressure variances near 

the instability frequencies. 

The “Basic MSEK” (the core of the “Self-Tuning MSEK,” namely the control actions formulated in 

Equations (4) and (6) was implemented for testing in 2002 on the HF SNR, but with only manual activation of the 

real-time search for optimal α⎯ , β

⎯ , and b . Also, the gains μ and γ were probed and adjusted manually during the 

tests in 2002. But, for the Self-Tuning version of MSEK, multi-scale based variances and third-moments of pressure 

oscillations are used as activation functions in the Parameter Tuning block to automatically trigger the searches and 

fine-tunings as described. Upon search activation, the search diameter is adjusted according to a Time-Scale 

Averaged Pressure Variance computed with a sufficiently large time-constant for averaging. Also, the gains “μ” and 

“γ” in the Self-Tuning version are adjusted automatically, and continuously based on a Time-Scale Averaged 

Pressure Variance computed with a much smaller time-constant for averaging. 

V. Controller Evaluation 

First, the “Basic MSEK” (the core logic of the “Self-Tuning MSEK”) was validated and successfully 

demonstrated at UTRC in 2002 with the HF SNR, also using the high-frequency valve designed by the Georgia 

Institute of Technology for fuel pulsing (Fig. 5) (Ref. 6). The validation for this part of the controller will be briefly 

summarized in the next subsection. 
NASA/TM—2006-213855 11 

A. Model-Based Validation and Experimental Results of the “Basic MSEK” 

The SNR was operated at a pressure, temperature, and fuel-air ratio corresponding to a mid-power engine 

condition (T3 = 770 °F, P3 = 200 psia, fuel-air ratio = 0.03). This HF configuration of the SNR (Fig. 2) exhibited 

roughly the same engine combustor instability behavior as shown in Figure 3. The SNR combustor pressure was 

sensed about 2 inches downstream of the fuel injector. The control algorithms were implemented on a real-time 

processor for an I/O rate of 5000 Hz. As in the LF case, the parameters of the (reduced-order) model for that HF 

configuration (to be shown in the next paragraph) are with “psi” as unit for the pressure feedback, and Volt for the 

fuel-modulation command un issued to the fuel-valve. This valve command is limited to 2 Volts in amplitude for the 

HF rig, which corresponds to the maximum valve displacement allowed about the mean positions. The mean valve 

position was set for the optimal flow number regarding control-authority. 

Without loss of generality, the measurement gain and the internal feedback gain for the dominant mode (Eq. (1b)

and (1e), respectively) were normalized and balanced such that: c2 = h2 2 = 1.0. With this balance normalization and 

the mentioned unit choice, the rest of model parameters were then chosen to match empirical open-loop 

characteristics of the combustor (e.g., Fig. 3). And, this was done in the order of matching mode 2 characteristics 

and responses to fuel modulations first, as it is more dominant, and then mode 1: 

First, po = 20.0 psi; T = 0.0002 sec; κ1 = κ2 = 0.6 po = 12.0; g = 0.01; and, b = 0.2322. Next, ω2 = 

3456 radians/sec; ζ2 = 0.04; and, p ’max = 0.09 po (for matching mode 2 characteristics). Then, ω1 = 1822 radians/sec; 

ζ1 = 0.3; c1 = 0.8; h11 = 1.0 (for mode 1 characteristics); and h1 2 = h2 1 = 0.1 (Modal-couplings in the HF 

configuration of the SNR apparently were low); ⎯τ a = 0.0038; ⎯τ b = 0.0033; ⎯τ c = 0.0002 seconds (Empirical, mean 

values). 

Figure 11 shows the predicted Amplitude Spectra and Probability Density of combustor pressure oscillations; the 

control-ON compared to the control-OFF case for a rather high level of disturbances comparable to the actual HF 

SNR environment. Figure 12 shows similar results from test data in 2002 with the Basic MSEK controller on the HF 

SNR. Both the model prediction and test data show a reduction of about 30 percent in pressure oscillation amplitude 

at the HF peak. Reference 6 also includes some analytical results showing the controlled “absolute stability” 

achieved by this core logic. Note that, controlled “absolute stability” is possible if the time-delay of fuel-modulation 

effect (“τb”, Eq. (1a)) are comparable to, if not less than, that of the internal heat-release feedback (“τa”). 

Figure 12.—(9-11-02 HF SNR test) Amplitude spectra 

showing the effects of the Basic MSEK controller on 

the combustion instability peak pressure oscillation. 

Figure 11.—MSEK, HF SNR Simulation: pressure 

oscillations amplitude-spectrum (Upper) and 

probability density of pressure oscillations 

(Lower), with/without control. 
NASA/TM—2006-213855 12 

B. Model-Based Validation and Experimental Results of the “Self-Tuning MSEK” 

The “Mid-Frequency” (MF) and “Low-Frequency” (LF) SNR configuration were also used in the 2004 ACC 

demonstrations at NASA Glenn. The MSEK and it self-tuning features and parameters were designed and validated 

on the Reduced-Order model shown in sections II and III, and also on a Sectored 1–D model (1–D CFD, by Paxson, 

Ref. 14) before testing on the SNR (see Figs. 13 and 14 for some validation results of this controller on the Sectored 

1–D model). 

The main findings for the optimal operation of the Self-Tuning MSEK on the LF rig include: The setting of the 

valve “flow-number” for optimal fuel-modulation effects; the nominal search steps (for α⎯ , β

⎯ , and b ); the threshold 

for initiating global search; and lastly the optimal loop-shaping fraction “l”. Initially, “l” had been set at 0.5. With 

that value of “l” and the optimal search steps and threshold, the automatic tuning actions of the MSEK controller 

was able to suppress the instabilities by 80 percent after having been engaged for about 5 sec. However, such 

suppression could not be held steady with setting l = 0.5 because of some low-frequency oscillations (see Fig. 15). 

Such low-frequency oscillations are most likely due to the mutual “beating” between mode-1 instability (315 Hz) 

with the fuel-modulation effects by the controller near 320 Hz that appeared to have suppressed mode-1 almost 

completely. The left subplot of Figure 15 shows the amplitude-spectrum of the pressure oscillations of the middle 

subplot for this case; and the right subplot shows the spectrum of the valve command signal. This command 

spectrum is broadband, but concentrated mostly around 300 Hz. This setting reduced the peak of the pressure 

amplitude spectrum down to about 1.2 psi/Hz. This is a significant reduction of the instability, as compared to when 

the controller is turned off, which is about 11 psi/Hz (e.g., the case of Fig. 6). 

When “l” is set near 1.0 such as in the case of Figure 16, the resulting command spectrum was sharper and more 

concentrated at 300 Hz. But, the instabilities appeared to be suppressed by only 70 percent and yet not steady, again 

because of some low-frequency oscillations. Although the original instability that had been at 315 Hz was 

Figure 13.—MSEK on a HF Sectored 1-D model. Figure 14.—MSEK on an LF Sectored 1-D model.

Figure 16.—Preliminary test results of the self-tuning 

MSEK on the LF (315 Hz) SNR–June 2, 2004. 
NASA/TM—2006-213855 13 

eliminated entirely this time, the fuel-modulation produced an undesirable disturbance at 273 Hz with unsteady 

amplitude. 

The instability suppression by the Self-Tuning MSEK was best and steady when the command was more 

broadband towards the high-frequency range as shown in Figure 17. This was when “l” was set near 0.1. Under this 

setting, the controller was able to suppress the oscillation (rms) amplitude from about 10 psi (e.g., shown in the 

upper subplots of Fig. 6) to about 1.7 psi. This was so because the instabilities were concentrated mostly at 315 Hz 

while fuel-modulation with the GT valve was able to affect this frequency most deeply over a fairly wide range of 

commanded frequencies. Apparently, fuel-modulation at high-frequencies for the LF configuration would not excite 

the higher modes, but instead affects significant energy transfer towards suppressing the low-frequency instability. 

So, the role of “ 0 ≤ l ≤ 1 ” is clearly that of typical loop-shaping with a sensitive control parameter. This seems to 

be essentially the same phenomenon discovered previously by Kopasakis on the same rig when focusing control on 

the “2nd harmonic ” with an adaptive phase-shifting controller (Ref. 3). 

Lastly, the MF SNR exhibited an instability at 340 Hz (Fig. 18(a)), a frequency fairly close to the LF; but, its 

nature is more like that of the HF instability. The plots shown in Figure 18(b) are from a preliminary study of the 

MSEK on the MF configuration that show some moderate reduction in instabilities; about 50 percent reduction of 

the amplitude spectra peak relative to the noise floor compared to open-loop. Also, the rms amplitude of overall 

pressure oscillation was reduced to about 1.4 psi. This is probably the limit for active fuel-modulation effect with 

this valve (Fig. 5) for this case. This is consistent 

with the 2002 results on the HF rig, and the test 

results on the LF rig shown in Figure 17 (Noting 

that, the time-plot in Fig. 17 also showed peaks near 

4 psi, comparable to the time-plot of Fig. 18(b)). 

C. MSEK Model-Based Control Dynamics 

Discussion 

The LF Configuration experimental result of 

Figure 17 is an important case that had not 

previously been simulated. It was found from 

simulating this case that the non-linear heat-release 

over the frequency range between mode-1 and 

mode-2 seems to be crucial for the steady 

suppression of the instability. Therefore, some 

numerical results of the MSEK on the validated 

Figure 17.—The LF (315 Hz) suppressed by the self-

 Tuning MSEK controller–June 2, 2004 Test. 

 Figure 18(a).—MF self-sustained instability. Figure 18(b).—MF instability suppressed by MSEK. 
NASA/TM—2006-213855 14 

reduced-order model are presented here for further 

understanding of the control dynamics and for validating 

the model against test data for the close-loop case. First, 

Figure 19(a) shows the self-tuning control in action on the 

LF model, and the combustion pressure being quickly 

reduced to a level comparable to an actual test case on the 

LF SNR (Compare Fig. 17 of an actual test case with a 

“zoomed-in” portion of the simulation run case in 

Fig. 19(a), as shown in Fig. 19(b)). The “mode-1 fraction,

l” of Equations (4) and (6) of the Damper and Tone 

Suppressor actions, used as a “loop-shaping” parameter, 

is shown in the third subplot of Figure “19(a)”. Note that, 

comparing to those results within the first second time 

interval when the control had not been activated, the 

pressure oscillations afterwards have never been 

worsened by the tuning actions. Figure 19(c) shows the 

difference in the unsteadiness of heat-addition of two 

zoomed-in time portions in Figure 19(a): one portion at 

0.5 sec from start when the controller had not been 

activated; and another at time 20 sec when the controller 

parameters has already converged to a good region. It 

shows that, fuel-modulation under good control likely has 

the effects of preventing the heat addition from dropping 

too low in resonance with the acoustics. Thus, fuelmodulation might also be effective for stabilizing the 

flame when the combustor is operated near its “leanblowout” margin. Such potential application of active 

fuel-modulation (e.g., to “lean-direct injection 

combustors), however, needs further investigations. 

VI. Conclusion 

This combustion stability control scheme, the selftuning Multi-Scale Extended Kalman (MSEK) controller, 

has been used to experimentally suppress thermo-acoustic 

instabilities up to 90 percent. The controller employed a 

Quadratures Filter Bank to perform multi-scale analyses

in real-time on the sensed pressure signals for control 

feedback. An approximate evolution equation of the 

extracted “Quadratures” (representing the acoustics 

states) was used to formulate a Kalman predictor for these 

acoustics states for the damper logic. The variable gains, 

phase bias, and other automatic control tuning logics were 

based on such multi-scale analysis. This model-based, 

self-tuning control scheme was thoroughly tested on a 

liquid-fuel combustor rig operated at engine-like 

conditions, for three configurations emulating different 

cases of combustion instability. The combustion control 

study on this rig confirmed earlier NASA observations 

and provided a plausible explanation about an important 

internal mechanism of cross-frequency couplings in 

combustion thermo-acoustics. The dynamic couplings are 

very prominent in its Low-Frequency configuration, and 

in general could be strongly affected by local fuel/air 

modulations. The reduced-order thermo-acoustics model 

for control development, using a simplistic parametric 

Figure 19(b).—Simulation analysis of the selftuning MSEK controller (see Fig 19(a)). 

Figure 19(c).—Instability and heat unsteadiness—

simulation (see Fig 19(a)).

Figure 19(a).—Simulation results with the selftuning MSEK controller on the reduced-order plant 
NASA/TM—2006-213855 15 

formulation for the non-linear heat-fluctuations that drive the acoustics, exhibits the same response characteristics of 

the rig on both the frequency-domain and time-domain. The self-tuning MSEK based on this model was able to 

adjust it own parameters and control gains to suppress nearly completely the combustion instabilities by modulating 

the fuel injector flow with a high-frequency valve. The main contributors to the effective suppression of combustion 

instabilities as demonstrated by this controller were the control-authority of the high-bandwidth fuel valve and the 

cross-frequency couplings in heat-release under fuel modulation. 

References 

 1. Lefebvre, A.H.: Gas Turbine Combustion, 2nd edition, Taylor & Francis, 1999. 

 2. Annaswamy, A.M. and Ghoniem, A.F.: “Active Combustion Instability: Theory and Practice,” IEEE Control 

Systems Magazine, December 2002, Vol. 22, Number 6. 

 3. Kopasakis, G., DeLaat J.C., and Chang C.T.: “Validation of an Adaptive Combustion Instability Control Method 

for Gas-Turbine Engines,” presented at the AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Fort 

Lauderdale, Florida, July 2004, NASA/TM—2004–213198, AIAA–2004–4028. 

 4. Kopasakis, G.: “Systems Characterization of Combustor instabilities with Controls Design Emphasis,” presented 

at the 42nd AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, January 2004, NASA/TM—2004–

212912, AIAA–2004–0638. 

 5. Kopasakis, G.: “High Frequency Adaptive Instability Suppression Controls in a Liquid-Fueled Combustor,” 

AIAA 39th Joint Propulsion Conference and Exhibit, Huntsville, AL, July 2003, NASA/TM—2003–212535, 

AIAA–2003–9581. 

 6. Le, D.K., Delaat J.C., and Chang C.T.: “Control of Thermo-Acoustics Instabilities: The Multi-Scale Extended 

Kalman Approach,” NASA/TM—2003–212536, AIAA–3003–4934 presented at the 39th Joint Propulsion 

Conference, Huntsville, Alabama, July 20–23, 2003. 

 7. Meyer Y., 1991, Wavelets: Algorithms and Applications, English translation and revision by Robert D. Ryan, 

SIAM edition 1994. 

 8. Houdre, C., 1993: “Wavelets, probability, and statistics: Some bridges,” Wavelets Mathematics and Applications 

(Studies in Advanced Mathematics), edited by J.J. Benedetto and Michael W. Frazier, GRC Press, 1994 edition. 

 9. Misawa, E.A. and Hedrick, J.K.: “Nonlinear Observers—A State-of-the-Art Survey,” Transaction of the ASME, 

Journal of Dynamic Systems, Measurement, and Control, Vol. 111, pp. 344–352, September 1989. 

10. Jazwinski A.H., “Stochastic Processes and Filtering Theory,” Mathematics in Science and Engineering Vol. 64, 

Academic Press, 1970. 

11. Cohen, J.M. et al.: “Experimental Replication of an Aeroengine Combustion Instability,” International Gas 

Turbine and Aero-Engine Congress and Exhibition, Munich, Germany, 2000. 

12. DeLaat, J.C. and Chang, C.T.: “Active Control of High Frequency Combustion Instability in Aircraft GasTurbine Engines,” presented at the 16th International Symposium on Air breathing Engines, Cleveland, Ohio, 

August 31–September 5, 2003. 

13. Barooah, P., Anderson, T.J., and Cohen, J.M.: “Active Combustion Instability Control with Spinning Valve 

Actuator,” Proceedings of ASME Turbo Expo, Amsterdam, Netherlands, 2002. GT–2002–30042. 

14. Paxson, D.E.: “A Sectored-One-Dimensional Model for Simulating Combustion Instabilities in Premix 

Combustors,” presented at the 38th AIAA Aerospace Sciences Meeting & Exhibit, Reno, Nevada, January 2000, 

NASA/TM—1999–209771, AIAA–2000–0313.
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WBS–22–714–70–33

21

Model-Based Self-Tuning Multiscale Method for Combustion Control

Dzu K. Le, John C. DeLaat, Clarence T. Chang, and Daniel R. Vrnak

Active combustion control

Unclassified -Unlimited

Subject Category: 07

Prepared for the 41st Joint Propulsion Conference and Exhibit cosponsored by the AIAA, ASME, SAE, and ASEE,

Tucson, Arizona, July 10–13, 2005. Responsible person, Dzu K. Le, organization code DEI, 216–433–5640.

A multi-scale representation of the combustor dynamics was used to create a self-tuning, scalable controller to suppress

multiple instability modes in a liquid-fueled aero engine-derived combustor operating at engine-like conditions. Its selftuning features designed to handle the uncertainties in the combustor dynamics and time-delays are essential for control

performance and robustness. The controller was implemented to modulate a high-frequency fuel valve with feedback

from dynamic pressure sensors. This scalable algorithm suppressed pressure oscillations of different instability modes by

as much as 90 percent without the “peak-splitting” effect. The self-tuning logic guided the adjustment of controller

parameters and converged quickly toward phase-lock for optimal suppression of the instabilities. The forced-response

characteristics of the control model compare well with those of the test rig on both the frequency-domain and the timedomain.