Nonlinear Control and Modeling of Rotating Stall in an Axial Flow Compressor

This thesis focuses on understanding the use of air injection as a means of controlling rotating stall in an axial flow compressor, involving modeling, dynamical systems analysis, and experimental investigations. The first step towards this understanding was the development of a low order model for air injection control, the starting point of which was the Moore and Greitzer model for axial flow compressors. The Moore and Greitzer model was extended to include the effects of air injection and bifurcation analysis was performed to determine how the closed loop system dynamics are different from those of the open loop system. This low order model was then used to determine the optimal placement of the air injection actuators. Experimental work focused on verifying that the low order model, developed for air injection actuation, qualitatively captured the behavior of the Caltech compressor rig. Open loop tests were performed to determine how the placement of the air injectors on the rig affected the performance of the compressor. The positioning of the air injectors that provided the greatest control authority were used in the development of air injection controllers for rotating stall. The controllers resulted in complete elimination of the hysteresis associated with rotating stall. The use of a throttle actuator for the control of the surge dynamics was investigated, and then combined with an air injection controller for rotating stall; the resulting controller performed quite well in throttle disturbance rejection tests. A higher order model was developed to qualitatively match the experimental results with a simulation. The results of this modeling effort compared quite well with the experimental results for the open loop behavior of the Caltech rig. The details of how the air injection actuators affect the compressor flow were included in this model, and the simulation predicted the same optimal controller that was developed through experimentation. The development of the higher order model also included the investigation of systematic methods for determining the simulation parameters. Based on experimental measurements of compression system transients, the open loop simulation parameters were identified, including values for the compressor performance characteristic in regions where direct measurements were not possible. These methods also provided information on parameters used in the modeling of the pressure rise delivered by the compressor under unsteady flow conditions

Improved gas turbine diagnostics towards an integrated prognostic approach wiht vibration and gas path analysis

The degradation of a gas turbine engine in operation is inevitable, leading to losses in performance and eventually reduction in engine availability. Several methods like gas path analysis and vibration analysis have been developed to provide a means of identifying the onset of component degradation. Although both approaches have been applied individually with successes in identifying component faults; localizing complex faults and improving fault prediction confidence are some of the further benefits that can accrue from the integrated application of both techniques. Although, the link between gas path component faults and rotating mechanical component faults have been reported by several investigators, yet, gas path fault diagnostics and mechanical fault diagnostics are still treated as separated toolsets for gas turbine engine health monitoring. This research addresses this gap by laying a foundation for the integration of gas path analysis and vibration to monitor the effect of fouling in a gas turbine compressor. Previous work on the effect of compressor fouling on the gas turbine operation has been on estimating its impact on the gas turbine’s performance in terms of reduction in thermal efficiency and output power. Another methodology often used involves the determination of correlations to characterize the susceptibility and sensitivity of the gas turbine compressor to fouling. Although the above mentioned approaches are useful in determining the impact of compressor fouling on the gas turbine performance, they are limited in the sense that they are not capable of being used to access the interaction between the aerodynamic and rotordynamic domain in a fouled gas turbine compressor. In this work, a Greitzer-type compression system model is applied to predict the flow field dynamics of the fouled compressor. The Moore-Greitzer model is a lumped parameter model of a compressor operating between an inlet and exit ii duct which discharges to a plenum with a throttle to control the flow through the compression system. In a nutshell, the overall methodology applied in this work involves the interaction of four different models, which are: Moore-Greitzer compression system model, Al-Nahwi aerodynamic force model, 2D transfer matrix rotordynamic model and a gas turbine performance engine model. The study carried out in this work shows that as the rate of fouling increases, typified by a decrease in compressor massflow, isentropic efficiency and pressure ratio, there is a corresponding increase in the vibration amplitude at the compressor rotor first fundamental frequency. Also demonstrated in this work, is the application of a Moore-Greitzer type compressor model for the prediction of the inception of unstable operation in a compressor due to fouling. In modelling the interaction between the aerodynamic and rotordynamic domain in a fouled gas turbine compressor, linear simplifications have been adopted in the compression system model. A single term Fourier series has been used to approximate the resulting disturbed flow coefficient. This approximation is reasonable for weakly nonlinear systems such as compressor operating with either an incompressible inlet flow or low Mach number compressible inlet flow. To truly account for nonlinearity in the model, further recommendation for improvement includes using a second order or two-term Fourier series to approximate the disturbed flow coefficient. Further recommendation from this work include an extension of the rotordynamic analysis to include non-synchronous response of the rotor to an aerodynamic excitation and the application of the Greitzer type model for the prediction of the flow and pressure rise coefficient at the inlet of the compressor when fouled

Analytic Parameterization of Stabilizing Controllers for the Moore-Greitzer Compressor Model

This work presents an extension, simplification and application of a design procedure for dynamic output feedback design for systems with nonlinearities satisfying quadratic constraints (QC). Our method was motivated by the challenges of output feedback control design for the three-state Moore-Greitzer (MG) compressor model. The classical three-state MG model is a nonlinear dynamical system that is widely used in stall/surge analysis and control design. First, we find the parameter set of the stabilizing dynamic output feedback controllers for the surge subsystem by using conditions for stability of a transformed system and the associated matching conditions. Second, we choose the optimal control parameters from the stabilizing set with respect to different desired criteria. We show the set of parameters of the stabilizing controllers for the surge subsystem and the set of parameters of the stabilizing controllers with extended integral part for MG compressor. We present simplified sufficient conditions for stabilization, new constraints for the corresponding parameters and examples of optimal problem for the surge subsystem of the Moore-Greitzer compressor model. We discuss the degree of robustness and clarify an alternative proof of stability of the closed-loop system with the surge subsystem and the stabilizing dynamic output feedback controller without an integral state. In addition, we show the derivation of a quadratic function by using CVX

Stability parameter identification for a centrifugal compression system

This paper presents the application of a lumped parameter model to describe the dynamic behavior of a centrifugal compression system including surge. The response of the model is compared with experimental surge measurements from an industrial single stage compressor test rig. A parametric analysis of the model reveals the large influence of the stability parameter on the transient response. However, a good value for this parameter is not easily obtained fromsurge data. Therefore, an identification method is proposed to uniquely determine the stability parameter that is based on an approximate realization algorithm, making use of the fact that the step response of the system has the characteristics of a first order system. Simulation results show that this method canprovide an estimate for the stability parameter of a centrifugal compression system

Dynamical system analysis of unstable flow phenomena in centrifugal blower

Methods of dynamical system analysis were employed to analyze unsteady phenomena in a centrifugal blower. Pressure signals gathered at different control points were decomposed into their Principal Components (PCs) by means of Singular Spectrum Analysis (SSA). Certain number of PCs was considered in the analysis based on their statistical correlation. Projection of the original signal onto its PCs allowed to draw the phase trajectory that clearly separated non-stable blower working conditions from its regular operation

Tip-Clearance Actuation With Magnetic Bearings for High-Speed Compressor Stall Control

Magnetic bearings are widely used as active suspension devices in rotating machinery, mainly for active vibration control purposes. The concept of active tip clearance control suggests a new application of magnetic bearings as servo-actuators to stabilize rotating stall in axial compressors. This paper presents a first-of-a-kind feasibility study of an active stall control experiment with a magnetic bearing servo-actuator in the NASA Glenn high-speed single-stage compressor test facility. Together with CFD and experimental data a two-dimensional, incompressible compressor stability model was used in a stochastic estimation and control analysis to determine the required magnetic bearing performance for compressor stall control. The resulting requirements introduced new challenges to the magnetic bearing actuator design. A magnetic bearing servo-actuator was designed which fulfilled the performance specifications. Control laws were then developed to stabilize the compressor shaft. In a second control loop, a constant gain controller was implemented to stabilize rotating stall. A detailed closed loop simulation at 100% corrected design speed resulted in a 2.3% reduction of stalling mass flow which is comparable to results obtained in the same compressor by Weigl et al. (1998) using unsteady air injection. The design and simulation results presented here establish the viability of magnetic bearings for stall control in aero-engine high-speed compressors. Furthermore the paper outlines a general design procedure to develop magnetic bearing servo-actuators for high-speed turbomachinery.United States. National Aeronautics and Space Administration (Grant NAG3-1457