Control of Thermoacoustic Instabilities: Actuator-Sensor Placement

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Control of Thermoacoustic InstabilitiesActuator
-Sensor Placement

• Pushkarini Agharkar, Priya Subramanian, Prof. R.
  I. Sujith
• Department of Aerospace Engineering
• Prof. Niket Kaisare
• Department of Chemical Engineering
• Indian Institute of Technology, Madras
• Acknowledgements
• Boeing Travel Grant, IIT Madras
• Alumni Affairs Association, IIT Madras

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Thermoacoustic Instabilities

• Occur due to positive feedback mechanism between
  combustion and acoustic subsystems

• Representative system
• ducted premixed flame

Schuller (2003)
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Model of the ducted premixed flame

• Control Framework
• LQ Regulator
• Kalman filter

• Actuator Placement
• LMI based techniques
• based on Hankel singular values

Conclusions
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Model of the ducted premixed flame

• acoustic subsystem

• combustion subsystem

• single actuator and sensor pair
• actuator adds energy to the system
• sensor measures acoustic pressure

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Combustion Subsystem

• Governing equation (linear)

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Acoustic Subsystem

• Governing equations

fluctuating heat release
contribution from controller
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Properties of the Model

• Non-normality due to coupling between combustion
  and acoustic subsystems
• Nonlinearity due to the equations of evolution
  of the flame front
• Motivation Reducing the transient growth and
  avoiding triggering

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State-Space Representation
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Linear Quadratic (LQ) Regulator
such that the cost functional
is minimized.
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Linear Quadratic (LQ) Regulator
Open loop plant (without control)
Closed loop plant (with control)
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LMI optimization problem
- Linear Matrix Inequalities (LMI) inequalities
defined for matrix variables
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Actuator Placement using LMI based Optimization
Techniques
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ControllabilityObservability Measures

• Other ways to determine optimal placement of
  actuators and sensors
• Controllability-Observability measure based on
  Hankel singular values (HSVs).
• measure
• Hankel singular value

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ControllabilityObservability Measures

• Measure of controllability-observability based on
  HSVs calculated for various actuator and sensor
  locations
• Locations of the antinodes of the third acoustic
  pressure mode give highest measure
• From numerical simulations, the third acoustic
  mode is also the highest energy state

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Locations closer to the flame
Antinodes of the least stable modes
LMI based techniques
Measures based on HSVs.

• The techniques give contradictory results

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Actuator Placement Numerical Validation
In the presence of transient growth, actuators
placed according to LMI techniques give better
performance than when placed based on HSV measures
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Actuator Placement Numerical Validation
0.5
0.833
0.3
In the absence of transient growth, actuators
placed according to HSV measures give better
performance than in the presence of transient
growth, but still not better than LMI techniques.
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Conclusions

• Actuator-Sensor placement of non-normal systems
  requires different approaches than the ones used
  conventionally.
• For the ducted premixed flame model, actuators
  placed nearer to the flame give better overall
  performance.
• Controllers based on these actuators results in
  low transient growth as well as less settling
  time.