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

Hopf Bifurcations of Moore-Greitzer PDE Model with Additive Noise

The Moore-Greitzer partial differential equation (PDE) is a commonly used mathematical model for capturing flow and pressure changes in axial-flow jet engine compressors. Determined by compressor geometry, the deterministic model is characterized by three types of Hopf bifurcations as the throttle coefficient decreases, namely surge (mean flow oscillations), stall (inlet flow disturbances) or a combination of both. Instabilities place fundamental limits on jet-engine operating range and thus limit the design space. In contrast to the deterministic PDEs, the Hopf bifurcation in stochastic PDEs is not well understood. The goal of this particular work is to rigorously develop low-dimensional approximations using a multiscale analysis approach near the deterministic stall bifurcation points in the presence of additive noise acting on the fast modes. We also show that the reduced-dimensional approximations (SDEs) contain multiplicative noise. Instability margins in the presence of uncertainties can be thus approximated, which will eventually lead to lighter and more efficient jet engine design

Model Analysis and Nonlinear Control of Air Compressors

RÉSUMÉ Pendant des décennies, les turbines à gaz ont été des dispositifs importants et fiables dans les domaines de la production d'énergie, de l'industrie pétrochimique, et de l'aéronautique. Ces machines utilisent les compresseurs centrifuges et axiaux qui se dégradent en présence d’instabilités aérodynamiques telles que le pompage et le décrochage tournant. Ces dernières limitent la performance et peuvent causer des sollicitations mécaniques importantes, une réduction de la durée de vie, du bruit et des vibrations. De plus, dans les compresseurs axiaux à vitesse variable (CAVV), les variations de vitesse affectent la stabilité des systèmes et peuvent entraîner le pompage et le décrochage tournant. Cela limite le taux de variation de vitesse et pénalise la performance. Le travail présenté dans cette thèse dresse premièrement l'analyse de bifurcation du modèle des CAVVs afin d’étudier l'impact de la dynamique de la vitesse sur la stabilité de points de fonctionnement efficaces. Ici, le taux de variation de vitesse (accélération) est défini comme un nouveau paramètre du modèle et une analyse détaillée de bifurcation numérique est fournie. Les résultats des simulations dans le domaine temporel valident non seulement l'analyse de bifurcation, mais élargissent aussi nos connaissances sur la réponse transitoire du modèle, qui est d’une importance majeure. L'analyse réalisée révèle que les variations de vitesse peuvent mener à un décrochage tournant entièrement développé ainsi qu’au décrochage temporaire mentionné précédemment. Les résultats montrent que les instabilités développées dépendent fortement du taux d'accélération. L'impact des autres paramètres du modèle, les vitesses initiale et finale, et la contribution des modes du décrochage sont également étudiés. Au niveau du contrôle, malgré toutes les réalisations présentées, la conception d’une commande robuste même pour des systèmes de compression axiaux à vitesse constante demeure encore un problème difficile. Ici, deux méthodes de commande non linéaires: le contrôle par modes glissants et le contrôle par passivité sont proposées pour résoudre ce problème de stabilité. Ces deux approches traitent de tous les aspects difficiles du sujet qui apparaissent dans la littérature : l'impact des perturbations externes, le manque de connaissance précise des paramètres du modèle, et l'absence d’un retour d’état complet.---------- ABSTRACT For decades, gas turbines have been important, widespread, and reliable devices in the field of power generation, petrochemical industry, and aeronautics. They employ centrifugal and axial compressors which suffer from aerodynamic instabilities, namely, surge and rotating stall. These performance limiting instabilities can cause component stress, lifespan reduction, noise, and vibration. Furthermore, in variable speed axial compressors (VSACs), speed variations affect the system stability and can lead to surge and rotating stall. This limits the rate of speed variations and results in important performance penalties. The present work firstly addresses the bifurcation analysis of VSACs’ model to investigate the impact of speed dynamics on the stability of efficient operating points. Here, the rate of speed variations (acceleration rate) is defined as a new parameter of the model and a detailed numerical bifurcation analysis is provided. The results of time-domain simulations not only validate the results of bifurcation analysis, but also broaden our knowledge about the transient response of the model, which is a matter of importance as well. The analysis reveals that speed variations can lead to a fully developed rotating stall as well as the previously reported temporary stall developments. The results show that the developed instabilities depend to a great extent on the acceleration rate. The impact of other key issues such as throttle gain, viscosity factor, initial speed, final speed, and the contribution of stall modes are also explored. From the control point of view, despite reported achievements, robust control design for compression systems remains a challenging problem. In this work, at first, two nonlinear approaches are proposed to tackle the stability problem of constant-speed axial compressors (CSACs). The first approach is a robust passivity-based control and the second one is a second order sliding mode control. The approaches tackle the challenging problems being addressed in the literature such as: the impact of external perturbations, the lack of detailed parameters knowledge, and the absence of full-state feedback. They drive the control from pressure and mass flow measurements and use throttle and close-coupled valve actuations. Finally, this study reports that these methods can be used in the case of VSACs by applying the required modifications to simultaneously control speed and instabilities. This simultaneous control design has been an open problem and the proposed method can improve the performance of VSACs

Dynamic control of rotating stall in axial flow compressors using aeromechanical feedback

August 1993Includes bibliographical references (pages 250-252)Dynamic control of rotating stall in an axial flow compressor has been implemented using aeromechanical feedback. The control strategy developed used an array of wall jets upstream of a single stage compressor which were regulated by locally reacting reed valves. These reed valves responded to pressure perturbations in the flow that were associated with small amplitude perturbations that precede rotating stall. The control strategy was designed such that the combined system of compressor plus the reed valve controller was stable in previously unstable operating conditions. A 10% decrease in the stalling flow coefficient was achieved using this dynamic feedback control strategy, and the stable flow range was extended with no noticeable change in the steady state performance of the compression system.The experimental demonstration is the first use of aeromechanical feedback to extend the stable operating range of an axial flow compressor, as well as the first use of locally reacting feedback and dynamic compensation techniques to stabilize rotating stall in an axial flow compressor. The design of the experiment was based on a two-dimensional model of the rotating stall dynamics which incorporated the effect of aeromechanical feedback. The physical mechanism responsible for rotating stall in axial flow compressors was examined with focus on the role of dynamic feedback in stabilizing compression system instability. The effectiveness of the aeromechanical control strategy was predicted, and experimentally demonstrated, to be a function of a set of non-dimensional control parameters that determine the interaction of the control strategy and the rotating stall dynamics.Predictions based on linear stability analyses and non-linear numerical simulations agreed qualitatively with the steady state and time resolved experimental data. During the experimental investigations, large amplitude, one-dimensional acoustic oscillations were observed in the compression system with aeromechanical feedback stabilization. Based on these observations, the role of the compression system parameters in the acoustic oscillations was examined analytically and a method was developed to reduce these oscillations. The mechanism responsible for the generation of self-excited acoustic oscillations, and the implications for dynamic control of compression system instabilities was also examined

Acta Universitatis Sapientiae - Electrical and Mechanical Engineering

Series Electrical and Mechanical Engineering publishes original papers and surveys in various fields of Electrical and Mechanical Engineering

Aeronautical Engineering: A continuing bibliography with indexes

This bibliography lists 725 reports, articles and other documents introduced into the NASA scientific and technical information system in April 1985

Bibliography of Lewis Research Center technical publications announced in 1987

This compilation of abstracts describes and indexes the technical reporting that resulted from the scientific and engineering work performed and managed by the Lewis Research Center in 1987. All the publications were announced in the 1987 issues of STAR (Scientific and Technical Aerospace Reports) and/or IAA (International Aerospace Abstracts). Included are research reports, journal articles, conference presentations, patents and patent applications, and theses

Aeronautical engineering: A continuing bibliography with indexes (supplement 216)

This bibliography lists 505 reports, articles and other documents introduced into the NASA scientific and technical information system in July, 1987

Bibliography of Lewis Research Center technical publications announced in 1986

This compilation of abstracts describes and indexes the technical reporting that resulted from the scientific and engineering work performed and managed by the Lewis Research Center in 1986. All the publications were announced in the 1986 issues of Scientific and Technical Aerospace Reports (STAR) and/or International Aerospace Abstracts (IAA). Included are research reports, journal articles, conference presentations, patents and patent applications, and theses