Identification of Nonlinear Feedback Parameters of a Noise-Driven Limit-Cycling Combustion System

We present a procedure for estimating nonlinear feedback parameters obtained from time series data (power spectral density (PSD), and probability density function (pdf)) with application to the identification of the unsteady heat-release coupling of a limit-cycling thermoacoustic system. The limit cycling and Gaussian components are identified from the pdf of the output signal. The respective describing function gains, along with a phase-shifting element are fit to a nominal acoustic oscillator model by using the PSD. The nonlinear feedback parameters are determined from the describing function gains and their Gaussian and harmonic inputs. The estimation procedure is demonstrated on a benchmark oscillator problem and is applied to time-series data obtained from a limit-cycling combustor rig. Relations between the feedback parameters and the equivalence ratio are discussed

[1]  Prashant G. Mehta,et al.  Linear and nonlinear analysis of controlled combustion processes. I. Linear analysis , 1999, Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No.99CH36328).

[2]  Arthur Gelb,et al.  Multiple-Input Describing Functions and Nonlinear System Design , 1968 .

[3]  Jeffrey M. Cohen,et al.  Active Control of Combustion Instabilities in Gas Turbine Engines for Low Emissions. Part I: Physics-Based and Experimentally Identified Models of Combustion Instability , 2000 .

[4]  A. Dowling.  Nonlinear self-excited oscillations of a ducted flame , 1997, Journal of Fluid Mechanics.

[5]  A. Dowling,et al.  Experimental investigation of the nonlinear response of turbulent premixed flames to imposed inlet velocity oscillations , 2005 .

[6]  Richard M. Murray,et al.  System identification for limit cycling systems: a case study for combustion instabilities , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[7]  Prashant G. Mehta,et al.  FRAMEWORK FOR STUDYING LIMITATIONS OF ACHIEVABLE PERFORMANCE IN CONTROL OF NONLINEAR COMBUSTION PROCESSES , 2002 .

[8]  A. Peracchio,et al.  Nonlinear heat-release/acoustic model for thermoacoustic instability in lean premixed combustors , 1998 .

[9]  Andrzej Banaszuk,et al.  Active Control of Combustion Instabilities in Gas Turbine Engines for Low Emissions. Part II: Adaptive Control Algorithm Development, Demonstration and Performance Limitations , 2000 .

[10]  Tim Lieuwen,et al.  Experimental Investigation of Limit Cycle Oscillations in an Unstable Gas Turbine Combustor , 2000 .

[12]  Tim Lieuwen,et al.  Nonlinear kinematic response of premixed flames to harmonic velocity disturbances , 2005 .

[13]  Jeffrey M. Cohen,et al.  Active Combustion Instability Control With Spinning Valve Actuator , 2002 .

[14]  Sergio M. Savaresi,et al.  Fitting nonlinear low-order models for combustion instability control , 2001 .

[15]  Tim Lieuwen,et al.  Statistical characteristics of pressure oscillations in a premixed combustor , 2003 .

[16]  Y. Neumeier,et al.  Nonlinear pressure-heat release transfer function measurements in a premixed combustor , 2002 .

[17]  Henry Stark,et al.  Probability, Random Processes, and Estimation Theory for Engineers , 1995 .

[18]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .