Pseudo Euler-Lagrange and Piecewise Affine Control Applied to Surge and Stall in Axial Compressors

摘要

This thesis addresses the control of the axial compressor surge and stall phenomena using Pseudo Euler-Lagrange and Piecewise Affine (PWA) controller synthesis techniques. These phenomena are considered as major gas turbine compressor instabilities that may result in failures such as the engine flame-out or severe mechanical damages caused by high blade vibration. The common approach towards the detection of the rotating stall and surge is to install various types of pressure sensors, hot wires and velocity probes. The inception of the rotating stall and surge is recognized by the presence of pressure fluctuation and velocity disturbances in the gas stream that are obtained through sensors. The necessary measure is then taken by applying proper stall and surge stabilizing control actions. The Lyapunov stability of pseudo Euler-Lagrange systems in the literature is extended to include additional nonlinear terms. Although Lyapunov stability theory is considered as the cornerstone of analysis of nonlinear systems, the generalization of this energy-based method poses a drawback that makes obtaining a Lyapunov function a difficult task. Therefore, proposing a method for generating a Lyapunov function for the control synthesis problem of a class of nonlinear systems is of potential importance. A systematic Lyapunov-based controller synthesis technique for a class of second order systems is addressed in this thesis. It is shown, in terms of stability characteristics, that the proposed technique provides a more robust solution to the compressor surge suppression problem as compared to the feedback linearization and the backstepping methods. The second contribution is a proposed new PWA approximation algorithm. Such an approximation is very important in reducing the complexity of nonlinear systems models while keeping the global validity of the models. The proposed method builds upon previous work on piecewise affine (PWA) approximation methods, which can be used to approximate continuous functions of n-variables by a PWA function. Having computed the PWA model of the stall and surge equations, the suppression problem is then solved by using PWA synthesis techniques. The proposed solution is shown to have higher damping characteristics as compared to the backstepping nonlinear method.