Michael A. Vaudrey

Stability and operating constraints of adaptive LMS-based feedback control

The filtered-X LMS algorithm has enjoyed widespread usage in both adaptive feedforward and feedback controller architectures. For feedforward controller designs the filtered-X LMS algorithm has been shown to exhibit unstable divergence for plant estimation errors in excess of +/-90^o. Typical implementations of this algorithm in adaptive feedback controllers such as filtered-U and filtered-E have previously been assumed to conform to these same identification constraints. Here we present two instability mechanisms that can arise in filtered-E control that violate the 90^o error assumption: feedback loop instabilities and LMS algorithm divergence. Analysis of the adaptive feedback system indicates that the conventionally interpreted plant estimation error can be arbitrarily small yet induce algorithm divergence; while other cases may have very large estimation errors and feedback loops cause controller instability. These analytical observations are supported by simulations. The implications of the actual plant estimation error, calculated here for the filtered-E controller, are extended to practical constraints placed on applications including filtered-U, on-line system identification, and self-excited system control.

Perspectives on linear compensator designs for active combustion control

Some of the earliest research in active combustion control (ACC) showed that the use of simple phase-shifter circuits feeding back acoustic pressure to voice-coil actuators was sufficient to achieve some reduction of the acoustic pressure caused by thermoacoustic instabilities in atmospheric combustors. Since that time, many researchers have continued to use phase-shifter controllers to suppress pressure fluctuations for a variety of combustion testbeds. In addition, other researchers have proposed the use of somewhat more’ sophisticated linear controllers and demonstrated their capabilities in reducing peak pressures. All of the ACC results motivate a series of interesting questions from a linear systems theory perspective: Why does a simple phase inverter controller generally ‘work’ for this problem? What is the effective Gequency response function for the phase-shifter compensator and how does it impact the controlled response? Can critical performance characteristics of the controlled system (magnitude of suppression and occurrence of controller-induced instabilities) be predicted a priori? Are there common features between the simple phase shift controller and other linear controllers that have been successful? Are there ‘untried’ linear controller designs that are motivated by these analyses and existing results for suppression of instabilities in combustors? This paper focuses on a subset of these perspectives, relying on the use of relevant linear control theory concepts to provide some answers and illuminate the need for more extensive nonlinear analyses (the subject of future publications) for predicting certain information. Specifically, this paper Copyright 63 1999 by t+ American Institute of Aeronautics and Astronautics provides a detailed discussion of the phase-shifter control method that has been so popular for active combustion control. Analytical and experimeutal considerations demonstrate how to predict frequencies and approximate amplitudes of controller-induced instabilities (also referred to as ‘spillover’ or ‘secondary peaks’) when using acoustic control and a phase-shifter compensator. This investigation also illustrates the intluence of the phase-shifter controller on the degree of controllability achieved for acoustic control of thermoacoustic insrabilities in a simple tube combustor.

Time-Averaged Gradient Control of Thermoacoustic Instabilities

Active control of thermoacoustic instabilities has been an important topic of research for many years. In particular, adaptive-control approaches are continually investigated because of their potential ability to adjust to changing and unknown operating conditions. Most adaptive controllers are model based and require accurate knowledge of the plant to which they are applied; this is currently an extremely challenging solution for the limit-cycling combustion plant. A more versatile controller approach, based on a gradient descent algorithm, is presented here. The time-averaged gradient controller can automatically adapt to changing plants and can assume a variety of different controller architectures and actuator styles, without the need for any explicit knowledge of the plant dynamics. We present the controller in a variety of forms and provide simulation and experimental results illustrating its effectiveness in stabilizing an unstable Rijke tube combustor and a 50-kW kerosene-fueled lean direct-injection combustor.

A comparison of ANR headset performance for loopshaping and H∞ control system design

Active noise reduction (ANR) has been widely accepted as a critical component in circumaural hearing protectors and communication headsets for many commercial and military applications. That is because ANR headsets provide the end‐user with at‐ear noise suppression that is more effective than passive configurations alone can offer. In the past few years, there have been significant advances in this technology area. These are largely related to attempts to transition from traditional analog control hardware to digital implementations. One benefit of digital controller design is the ease of constructing optimal and robust compensators. The traditional approach in designing feedback ANR headsets is usually ‘‘loopshaping,’’ which is a somewhat heuristic design method. The desire for further improvements in feedback ANR headset performance is leading engineers toward more analytical approaches for controller design, including the robust techniques of H∞. This presentation compares and contrasts loopshaping and...