Detrimental combustion instability is unwanted in gas turbines, aeroengines, rocket motors, and many other combustion systems. In this work, we design and implement a sliding mode controller (SMC) to mitigate self-sustained combustion oscillations in an open-ended thermoacoustic system. An acoustically compact heat source is confined and modeled by using a modified form of King's Law. Coupling the heat source model with a Galerkin series expansion of flow disturbances provides a platform to conduct pseudospectra analysis to gain insight on the system stability behaviors, and to evaluate the performance of the SMC. Two thermoacoustic systems with monopole-like actuators implemented are considered. One is associated with 1 mode and the other is with four modes. Both systems are shown to be controllable. Furthermore, it is found that self-sustained limit cycle oscillations can be successfully generated in both systems, when the actuators are not actuated. In order to gain insight on the thermoacoustic mode selection and triggering, the acoustical energy exchange between neighboring eigenmodes are studied and discussed. As the controller-driven actuators are actuated, the nonlinear limit cycle oscillations are quickly dampened. And both thermoacoustic systems are stabilized by reducing the sound pressure level by approximately 40 dB. Comparison is then made between the performance of the SMC and that of the classical LQR (linear-quadratic-regulator) one. The successful demonstration indicates that the SMC can be applied to stabilize unstable thermoacoustic systems, even with multiple unstable modes.

References

References
1.
Richards
,
G. A.
, and
Janus
,
M. C.
,
1998
, “
Characterization of Oscillations During Premix Gas Turbine Combustion
,”
ASME J. Eng. Gas Turbines Power
,
120
(
2
), pp.
294
302
.
2.
Eisinger
,
F. L.
, and
Sullivan
,
R. E.
,
2003
, “
Thermoacoustically-Based Combustion Oscillation in a Gas Turbine—A Brief Note
,”
Trans. ASME
,
125
(
4
), pp.
454
459
.
3.
Heckl
,
M. A.
,
1988
, “
Active Control of the Noise From a Rijke Tube
,”
J. Sound Vib.
,
124
(
1
), pp.
117
133
.
4.
Raun
,
R. L.
,
Beckstead
,
M. W.
,
Finlinson
,
J. C.
, and
Brooks
,
K. P.
,
1993
, “
A Review of Rijke Tubes, Rijke Burners and Related Devices
,”
Prog. Energy Combust. Sci.
,
19
(
4
), pp.
313
364
.
5.
Matveev
,
K. I.
,
2003
, “
Thermoacoustic Instabilities in the Rijke Tube: Experiments and Modeling
,” Ph.D. thesis, California Institute of Technology, Pasadena, CA.
6.
Juniper
,
M. P.
,
2011
, “
Triggering in the Horizontal Rijke Tube: Non-Normality, Transient Growth and Bypass Transition
,”
J. Fluid Mech.
,
667
, pp.
272
308
.
7.
Kulkarni
,
R.
,
Balasubramanian
,
K.
, and
Sujith
,
R. I.
,
2011
, “
Non-Normality and Its Consequences in Active Control of Thermoacoustic Instabilities
,”
J. Fluid Mech.
,
670
, pp.
130
149
.
8.
Balasubramanian
,
K.
, and
Sujith
,
R. I.
,
2008
, “
Thermoacoustic Instability in a Rijke Tube: Non-Normality and Nonlinearity
,”
Phys. Fluids
,
20
(
4
), p.
044103
.
9.
Waugh
,
I.
,
Geuß
,
M.
, and
Juniper
,
M.
,
2011
, “
Triggering, Bypass Transition and the Effect of Noise on a Linearly Stable Thermoacoustic System
,”
Proc. Combust. Inst.
,
33
(
2
), pp.
2945
2952
.
10.
Richards
,
G. A.
,
Straub
,
D. L.
, and
Robey
,
E. H.
,
2003
, “
Passive Control of Combustion Dynamics in Stationary Gas Turbines
,”
J. Propul. Power
,
19
(
5
), pp.
795
810
.
11.
Zhao
,
D.
, and
Li
,
X. Y.
,
2015
, “
A Review of Acoustic Dampers Applied to Combustion Chambers in Aerospace Industry
,”
Prog. Aerosp. Sci.
,
74
(
1
), pp.
114
130
.
12.
McManus
,
K. R.
,
Poinsot
,
T.
, and
Candel
,
S. M.
,
1993
, “
A Review of Active Control of Combustion Instabilities
,”
Prog. Energy Combust. Sci.
,
19
(
1
), pp.
1
29
.
13.
Annaswamy
,
A. M.
, and
Ghoniem
,
A. F.
,
2002
, “
Active Control of Combustion Instability: Theory and Practice
,”
Control Syst. Mag.
,
22
(
6
), pp.
37
54
.
14.
Sattinger
,
S. S.
,
Neumeier
,
Y.
,
Nabi
,
A.
,
Zinn
,
B. T.
,
Amos
,
D. J.
, and
Darling
,
D. D.
,
2000
, “
Sub-Scale Demonstration of the Active Feedback Control of Gas-Turbine Combustion Instabilities
,”
ASME J. Eng. Gas Turbines Power
,
122
(
2
), pp.
262
268
.
15.
Zhong
,
Z.
, and
Zhao
,
D.
,
2012
, “
Time-Domain Characterization of the Acoustic Damping of a Perforated Liner With Bias Flow
,”
J. Acoust. Soc. Am.
,
132
(
1
), pp.
271
281
.
16.
Bothien
,
M. R.
,
Noiray
,
N.
, and
Schuermans
,
B.
,
2013
, “
A Novel Damping Device for Broadband Attenuation of Low-Frequency Combustion Pulsations in Gas Turbines
,”
ASME J. Eng. Gas Turbines Power
,
136
(
4
), p.
041504
.
17.
Bothien
,
M. R.
, and
Wassmer
,
D.
,
2015
, “
Impact of Density Discontinuities on the Resonance Frequency of Helmholtz Resonators
,”
AIAA J.
,
53
(
4
), pp.
877
887
.
18.
Schuermans
,
B.
,
Bellucci
,
V.
, and
Paschereit
,
C. O.
,
2003
, “
Thermoacoustic Modeling and Control of Multi Burner Combustion Systems
,”
ASME
Paper No. GT2003-38688.
19.
Narendra
,
K. S.
, and
Parthasarathy
,
K.
,
1990
, “
Identification and Control of Dynamical Systems Using Neural Networks
,”
IEEE Trans. Neural Networks
,
1
(
1
), pp.
4
27
.
20.
Cammarata
,
L.
,
Fichera
,
A.
, and
Pagano
,
A.
,
2002
, “
Neural Prediction of Combustion Instability
,”
Appl. Energy
,
72
(
2
), pp.
513
528
.
21.
Bittanti
,
S.
,
Marco
,
A. D.
,
Poncia
,
G.
, and
Prandoni
,
W.
,
2002
, “
Identification of a Model for Thermoacoustic Instabilities in a Rijke Tube
,”
IEEE Trans. Control Syst. Technol.
,
10
(
4
), pp.
490
502
.
22.
Murugappan
,
S.
, and
Acharva
,
S.
,
2003
, “
Optimal Control of a Swirl-Stabilized Spray Combustor Using System Identification Approach
,”
Combust. Sci. Technol.
,
175
(
1
), pp.
55
81
.
23.
Dowling
,
A. P.
, and
Morgans
,
A. S.
,
2005
, “
Feedback Control of Combustion Oscillations
,”
Annu. Rev. Fluid Mech.
,
37
(
1
), pp.
151
182
.
24.
Yang
,
V.
,
Sinha
,
A.
, and
Fung
,
Y. T.
,
1992
, “
State-Feedback Control of Longitudinal Combustion Instabilities
,”
J. Propul. Power
,
8
(
1
), pp.
66
73
.
25.
Hathout
,
J.
,
Annaswamy
,
A.
,
Fleifil
,
M.
, and
Ghoniem
,
A.
,
1998
, “
A Model-Based Active Control Design for Thermoacoustic Instability
,”
Combust. Sci. Technol.
,
132
(
1–6
), pp.
99
138
.
26.
Fleifil
,
M.
,
Hathout
,
J. P.
,
Annaswamy
,
A.
, and
Ghoniem
,
A.
,
1998
, “
The Origin of Secondary Peaks With Active Control of Thermoacoustic Instability
,”
Combust. Sci. Technol.
,
133
(
4–6
), pp.
227
265
.
27.
Annaswamy
,
A. M.
,
El Rifai
,
O. M.
,
Fleifil
,
M.
,
Hathout
,
J. P.
, and
Ghoniem
,
A. F.
,
1998
, “
A Model-Based Self-Tuning Controller for Thermoacoustic Instability
,”
Combust. Sci. Technol.
,
135
(
1–6
), pp.
213
240
.
28.
Hervas
,
J. R.
,
Reyhanoglu
,
M.
, and
MacKunis
,
W.
,
2015
, “
Sliding Mode Control of Rijke-Type Thermoacoustic Systems
,” International Workshop on Recent Advances in Sliding Modes (
RASM
), Istanbul, Turkey, Apr. 9–11, pp.
1
6
.
29.
Billoud
,
G.
,
Galland
,
M.
,
Huynh Huu
,
C.
, and
Cancele
,
S.
,
1992
, “
Adaptive Active Control of Combustion Instabilities
,”
Combust. Sci. Technol.
,
81
(
4–6
), pp.
257
283
.
30.
Agharkar
,
P.
,
Subramanian
,
P.
,
Kaisare
,
N. S.
, and
Sujith
,
R. I.
,
2013
, “
Thermoacoustic Instabilities in a Ducted Premixed Flame: Reduced-Order Models and Control
,”
Combust. Sci. Technol.
,
185
(
6
), pp.
920
942
.
31.
Zhao
,
D.
, and
Reyhanoglu
,
M.
,
2014
, “
Feedback Control of Acoustic Disturbance Transient Growth in Triggering Thermoacoustic Instability
,”
J. Sound Vib.
,
333
(
16
), pp.
3639
3656
.
32.
Hervas
,
J. R.
,
Zhao
,
D.
, and
Reyhanoglu
,
M.
,
2014
, “
Nonlinear Feedback Control of Thermoacoustic Oscillations in a Rijke Tube
,”
23rd International Symposium on Industrial Electronics
(
ISIE
), Istanbul, Turkey, June 1–4, pp.
173
177
.
33.
Zhao
,
D.
, and
Li
,
X.
,
2015
, “
Minimizing Transient Energy Growth of Nonlinear Thermoacoustic Oscillations
,”
Int. J. Heat Mass Transfer
,
81
, pp.
188
197
.
34.
Hu
,
K.
,
Basker
,
V.
, and
Crisalle
,
O.
,
1998
, “
Sliding Mode Control of Uncertain Input-Delay Systems
,”
American Control Conference
, Philadelphia, PA, June 21–26, Vol.
1
, pp.
564
568
.
35.
Li
,
X.
, and
Yurkovich
,
S.
,
1999
, “
Sliding Mode Control of Systems With Delayed States and Controls
,”
Variable Structure Systems, Sliding Mode and Nonlinear Control
,
Springer
, London, pp.
93
107
.
36.
Healey
,
A.
, and
Lienard
,
D.
,
1993
, “
Multivariable Sliding Mode Control for Autonomous Diving and Steering of Unmanned Underwater Vehicles
,”
IEEE J. Oceanic Eng.
,
18
(
3
), pp.
327
339
.
37.
DeCarlo
,
R.
,
Zak
,
S. H.
, and
Matthews
,
G. P.
,
1988
, “
Variable Structure Control of Nonlinear Multivariable Systems: A Tutorial
,”
Proc. IEEE
,
76
(
3
), pp.
212
232
.
38.
Edwards
,
C.
,
Spurgeon
,
S. K.
, and
Patton
,
R. J.
,
2000
, “
Sliding Mode Observers for Fault Detection and Isolation
,”
Automatica
,
36
(
4
), pp.
541
553
.
39.
Heckl
,
M. A.
,
1990
, “
Non-Linear Acoustic Effects in the Rijke Tube
,”
Acta Acust. Acust.
,
72
(
1
), pp.
63
71
.
40.
Zhao
,
D.
,
2012
, “
Transient Growth of Flow Disturbances in Triggering a Rijke Tube Combustion Instability
,”
Combust. Flame
,
159
(
6
), pp.
2126
2137
.
41.
Lieuwen
,
T. C.
, and
Yang
,
V.
,
2005
,
Combustion Instabilities in Gas Turbine Engines: Operational Experience, Fundamental Mechanisms and Modeling
, (Progress in Astronautics and Aeronautics), American Institute of Aeronautics and Astronautics, Reston, VA, pp.
8
25
.
42.
Dowling
,
A. P.
,
1995
, “
The Calculation of Thermoacoustic Oscillations
,”
J. Sound Vib.
,
180
(
4
), pp.
557
581
.
43.
Li
,
X.
,
Zhao
,
D.
,
Li
,
S.
, and
Ji
,
C.
,
2015
, “
Effect of Heat Source on Transient Energy Growth Analysis of a Thermoacoustic System
,”
Energy Conv. Manag.
,
89
, pp.
309
317
.
44.
Matveev
,
K. I.
, and
Culick
,
F.
,
2003
, “
A Model for Combustion Instability Involving Vortex Shedding
,”
Combust. Sci. Technol.
,
175
(
6
), pp.
1059
1083
.
45.
Utkin
,
V.
,
1993
, “
Sliding Mode Control Design Principles and Applications to Electric Drives
,”
IEEE Trans. Ind. Electron.
,
40
(
1
), pp.
23
36
.
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