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Research Papers

Pulsed Control of Thermoacoustic Instabilities: Analysis and Experiment

[+] Author and Article Information
J. Matthew Carson

1112 Donelea Lane Northwest, Concord, NC 28027mcars@vt.edu

William T. Baumann

Department of Electrical Engineering, Virginia Tech, 302 Whittemore Hall, Blacksburg, VA 24061baumann@vt.edu

William R. Saunders

J. Dyn. Sys., Meas., Control 131(4), 041007 (May 18, 2009) (7 pages) doi:10.1115/1.3117192 History: Received September 16, 2007; Revised January 28, 2009; Published May 18, 2009

Abstract

Thermoacoustic instabilities in combustors have been suppressed using phase-shift algorithms pulsing an on-off actuator at the limit cycle frequency $(flc)$ or at the subharmonics of $flc$. It has been suggested that control at a subharmonic rate may extend the actuator lifetime and possibly require less actuator bandwidth. This paper examines the mechanism of subharmonic control in order to clarify the principles of operation and subsequently identify potential advantages for combustion control. Theoretical and experimental arguments show that there must be a Fourier component of the subharmonic control signal at $flc$ in order to stabilize the limit cycling behavior. It is also demonstrated that the magnitude of that Fourier component must be equivalent to the signal magnitude for a linear phase-shift controller that operates directly at $flc$. The concept of variable-subharmonic control is introduced whereby the actuator is pulsed at the instability frequency to initially stabilize the system and then is pulsed at a subharmonic frequency to maintain stability. These results imply that an actuator used for subharmonic control cannot be effective unless its bandwidth spans the instability frequency. The advantage of reduced cycling may still be realized but will require higher control authority to produce the same effect as an actuator pulsed at the instability frequency.

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Figures

Figure 1

Combustion block diagram

Figure 2

Pulse generator block diagram

Figure 3

Typical pulse train

Figure 4

Describing function with fixed-amplitude pulse heights

Figure 5

Describing function with two intersections

Figure 6

Depiction of pole movement in the complex plane as the control gain is increased

Figure 7

Describing function with proportional height pulses

Figure 8

Control algorithm illustration

Figure 9

Test system layout

Figure 10

Linear phase shifter hysteresis curve

Figure 11

Actual versus expected ratios for half-harmonic signals

Figure 12

Actual versus expected ratios for third-harmonic signals

Figure 13

Describing function plots superimposed on hysteresis curve

Figure 14

Instability level for fixed-pulse height controller

Figure 15

Gain of fixed-pulse height controller

Figure 16

Results with variable-subharmonic forcing

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