Adaptive Control of Self-Excited Systems with Application to a Gas Turbine Combustor

Abstract

A self-excited system (SES) has the property that constant inputs produce oscillatory outputs. SES arise in biochemical systems, aeroelasticity, and combustion. In particular, gas-turbine combustors are SES since a constant fuel rate yields thermoacoustic oscillations. This behavior arises due to the interaction between combustion and acoustics, and it can result in performance degradation and failure.

In practice, the dynamics of a thermoacoustic system may change due to varying operating conditions as well as hardware and environmental changes. With this motivation, the present work applies adaptive control to thermoacoustic systems. This dissertation applies retrospective cost adaptive control (RCAC) to thermoacoustic systems under extremely limited modeling information and actuator limitations.

The first part of the dissertation analyzes discrete-time Lur'e systems that are self-excited in the sense that 1) for all initial conditions the response is bounded, and 2) for almost all initial conditions, the response is nonconvergent. The main contribution of this section is a proof that, under specific assumptions on the linear dynamics and feedback nonlinearity, discrete-time Lur'e systems are self-excited.

The second part of the dissertation develops a system identification method based on discrete-time, self-excited Lur'e models. The main contribution of this section is the application of mixed-integer optimization to automating the selection of parameters needed for the identification procedure. This method is applied to illustrative examples as well as to experimental data from the Dual Independent Swirl Combustor (DISCo), which is a gas-turbine model combustor.

The third part of the dissertation applies RCAC to a Rijke-tube experiment, which is an SES due to the interaction between the heat source and the acoustics dynamics. The main contribution of this section is the demonstration of a design methodology wherein an initial set of hyperparameters required by RCAC is determined by a rudimentary model fit using open-loop data from a single experimental scenario. Using the single, fixed choice of hyperparameters, adaptive control experiments show that RCAC achieves an oscillation suppression greater than 45 dB over a range of operating conditions. Further tests are performed to examine the robustness of the adaptive controller under off-nominal perturbations that reflect real-world conditions.

The final part of the dissertation applies RCAC to DISCo; this application differs fundamentally from the Rijke-tube experiment due to significantly more complex physics as well as constraints on the bandwidth of the control actuation. In particular, the control inputs to DISCo are air-injection inputs with 5-Hz bandwidth, which is significantly below the oscillation frequencies of DISCo, the lowest of which is approximately 274 Hz. The main contribution of this section is the development and demonstration of an extension of RCAC that accounts for the actuator bandwidth limitation; this extension is called quasi-static RCAC (QSRCAC). QSRCAC uses an extended Kalman filter to estimate the gradient of the effect of the actuation on the performance variables. QSRCAC is then applied to DISCo in a multi-input, multi-output setting, with two input signals corresponding to inner and outer swirler air-injection valves, and two output signals given by pressure and temperature sensors. Experimental results show that QSRCAC achieves an oscillation suppression of 28 dB while reaching a specified exit temperature corresponding to a desired flame length.