Multivariable Backstepping and Adaptive LQ Control of Thermoacoustic Coupling in Jet Engine Systems

Jet engines are highly complex systems that have many internal processes which may become unstable under certain non-ideal conditions. These potentially unstable processes can induce instability in the overall engine process if left uncontrolled. One such process is known as thermoacoustic coupling. This is a process through which acoustic waves in the combustion chamber may become coupled with unsteady heat release at the flameholders, forming a positive feedback loop. Additionally, acoustic modes of close resonant frequency may become coupled and force the system to an unstable operating point. This process results in high amplitude pressure oscillations which in serious cases may result in permanent damage to the engine.

In this research, an indirect adaptive linear quadratic control scheme is first developed for a multi-input multi-output dynamic model of thermoacoustic coupling with unknown parameters and time delays. For this model, the controlling variable is the fuel mass flow into the combustion chamber. The time delays are modeled by a first-order Pade approximation. An adaptive controller design is developed to estimate the system and delay parameters, and an in-depth simulation study is conducted that verifies our results. The developed adaptive scheme has the ability to guarantee the desired stabilization properties in the presence of noisy inputs. When delays are large, it may not be appropriate to approximate time delays since it can introduce large errors into the system model. It is desirable to develop techniques that can directly handle large actuator delays. For this purpose, a nominal (non-adaptive) backstepping based actuator delay compensation scheme is derived and analyzed for systems in which time delays may be arbitrarily large. An extensive simulation study is also conducted to verify the developed backstepping delay control algorithm.