Control of Total Radiation in an Industrial Furnace by Optical Sensing of Flame Emissions

A new approach of H∞ filtering for combustion systems using optical instrumentation

“…On the other hand, the Hammerstein model where the nonlinear input function G is followed by a linear model and the output function F(ν(k)) = ν(k), describes a linear process controlled via a nonlinear saturating actuator [26] or nonlinear processes represented by a variable gain [27][28][29]. A block-oriented Hammerstein-Wiener model is suitably reduced to a Hammerstein model [22,30], because energy transfer in a combustion process measured by optical instrumentation presents a nonlinear response with respect to inlet air or fuel flow [2,5,6,31]. Besides, knowing that the optical output sensor (spectrometer) E c presents a linear relation with respect to the intensity of the photons emitted by the flame E c = T *…”

“…Radt could be related to an additive colored noise. From the combustion process point of view, total radiation variance is directly related to flame turbulence [5,30], since realistic flames in a combustion process are characterized by a turbulent environment with Reynolds number (Re) of the order 10 5 [43]. The core of the proposed approach is featured by modeling the noise as a not colored and non-ergodic random variable.…”

“…( 7), ( 9) and (10) were derived according to system (5), where all matrices are precisely known. Although system (5) is described as an LTI system (following the approach from [30]), the combustion process is affected by time-varying disturbances, due to changes in the operating points and other factors, as turbulence or fuel composition [43], which can modify the value of the variable gain around the operating condition u 0 . To improve the model's accuracy given these issues, the filtering technique proposed in the sequence considers a general LPV system, where all system matrices can be affected by time-varying parameters.…”