Least-Mean-Square-Based Algorithms

In this study, the work in adaptive algorithms for realistic controllers is divided between LMS-based approaches and direct optimization approaches. The difference is in the amount of a priori information required for the controller. In the LMS case, a model of the control to error path over the relevant bandwidth is required [3]. In current implementation, this model is identified in real time when the controller is first turned on. 

Although LMS controllers assume a linear control structure, and therefore assume proportional actuation will be used, the algorithm with fixed-pulse-height and on-off actuation has been run and significant suppression of the instability 

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The outputs of the sensors were used in two closed-loop control strategies developed for combustor performance optimization [7]. The objective of the first strategy, based on an adaptive least-mean squares (LMS) algorithm, was to maximize the magnitude and coherence of temperature oscillations at the forcing frequency /o in the measured region. The LMS algorithm was used to determine... 

Parameter determination is accomplished by laboratory measurements or by a least-mean-squares method if reference data are available. With such methods, it is possible to use a current measurement with a low accuracy. This can reduce costs for a SoC measurement capability. Singh et al. [18] and Heinemann [19] describe SoC determination methods based on fuzzy logic. This approach relies on the use of expert knowledge in lieu of complex mathematical models. It is also possible to combine a fuzzy SoC algorithm with other methods to increase the accuracy. 

This chapter reports experimental and analytical results for pulsed control of combustion instabilities at both fundamental and subharmonic frequencies. Two suites of control algorithms have been developed one based on least-mean-square (LMS) techniques that is suitable for inner-loop stabilization of combustion instabilities, and one bcised on direct optimization that can be used either for stabilization or outer-loop optimization of combustion process objectives, such as flame compactness or emissions. 

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