Survey Constructive nonlinear control: a historical perspective

Provably safe and robust learning-based model predictive control

Nonlinear observers: a circle criterion design and robustness analysis

A computational study to define the phenomena that lead to the onset of short length-scale (spike) rotating stall disturbances has been carried out. Based on unsteady simulations, we hypothesize there are two conditions necessary for the formation of spike disturbances, both of which are linked to the tip clearance flow. One is that the interface between the tip clearance and oncoming flows becomes parallel to the leading-edge plane. The second is the initiation of backflow, stemming from the fluid in adjacent passages, at the trailing-edge plane. The two criteria also imply a circumferential length scale for spike disturbances. The hypothesis and scenario developed are consistent with numerical simulations and experimental observations of axial compressor stall inception. A comparison of calculations for multiple blades with those for single passages also allows statements to be made about the utility of single passage computations as a descriptor of compressor stall.

Criteria for Spike Initiated Rotating Stall

No parts of this publication may be reproduced by any means, transmitted, or translated into machine language without the written permission of the author. Requests for permisson to reproduce parts of the book should be adressed directly to Professor Olav Egeland, Preface Modeling and simulation of dynamic processes are very important subjects in control systems design. Most processes that are encountered in practical controller design are very well described in the engineering literature, and it is important that the control engineer is able to take advantage of this information. It is a problem that several books must be used to get the relevant modeling information of a particular process, and it may take a long time to go through all the necessary material. The idea of this book is to supply the control engineer with a sufficient modeling background to design controllers for a wide range of processes. In addition, the book provides a good starting point for going into the specialist literature of different engineering disciplines. In this connection the references indicate where to start. The book also contains more material than what will normally be covered in the lectures of a typical course, so that students may return to the book at a later stage and find additional information about a particular subject. This will be more efficient than to extract the required information from a series of other books. In this sense the book will be of great value for practising control engineers. The development of new products and systems is often done in a team of experts with different backgrounds. It is hoped that this book will help control engineers to communicate with other experts in this type of team. To achieve this we have been careful to use standard terminology and notation from the different engineering disciplines in question. Here we deliberately break the tradition evident in many books in the control literature where the emphasis is on having a unified formulation specific to automatic control. The selection of the material is based on the experience of the authors in teaching and research at the Norwegian University of Science and Technology. In addition to this, material has been selected on the basis of extensive industrial activity through research programs between university and industry, and product development in industry. In this activity there has been close cooperation with experts from other disciplines, and this has given …

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Modeling and simulation for automatic control

An approximate theory is presented for post-stall transients in multistage axial compression systems. The theory leads to a set of three simultaneous nonlinear third-order partial differential equations for pressure rise, and average and disturbed values of flow coefficient, as functions of time and angle around the compressor. By a Galerkin procedure, angular dependence is averaged, and the equations become first order in time. These final equations are capable of describing the growth and possible decay of a rotating-stall cell during a compressor mass-flow transient. It is shown how rotating-stall-like and surgelike motions are coupled through these equations, and also how the instantaneous compressor pumping characteristic changes during the transient stall process.

A Theory of Post-Stall Transients in Axial Compression Systems: Part I—Development of Equations

Using the theory developed in Part I, calculations have been carried out to show the evolution of the mass flow, pressure rise, and rotating-stall cell amplitude during compression system post-stall transients. In particular, it is shown that the unsteady growth or decay of the stall cell can have a significant effect on the instantaneous compressor pumping characteristic and hence on the overall system behavior. A limited parametric study is carried out to illustrate the impact of different system features on transient behavior. It is shown, for example, that the ultimate mode of system response, surge or stable rotating stall, depends not only on the B parameter, but also on the compressor length-to-radius ratio. Small values of this latter quantity tend to favor the occurrence of surge, as do large values of B. Based on the analytical and numerical results, several specific topics are suggested for future research on post-stall transients.

A Theory of Post-Stall Transients in Axial Compression Systems: Part II—Application

A Theory of Rotating Stall of Multistage Axial Compressors: Part III—Limit Cycles

An analysis is made of rotating stall in compressors of many stages, finding conditions under which a flow distortion can occur which is steady in a traveling reference frame, even though upstream total and downstream static pressure are constant. In the compressor, a pressure-rise hysteresis is assumed. Flow in entrance and exit ducts yield additional lags. These lags balance to give a formula for stall propagation speed. For small disturbances, it is required that the compressor characteristics be flat in the neighborhood of average flow coefficient. Results are compared with the experiments of Day and Cumpsty. If a compressor lag of about twice that due only to fluid inertia is used, predicted propagation speeds agree almost exactly with experimental values, taking into account changes of number of stages, stagger angle, row spacing, and number of stall zones. The agreement obtained gives encouragement for the extension of the theory to account for large amplitudes.

A Theory of Rotating Stall of Multistage Axial Compressors: Part II—Finite Disturbances

A theory is presented for post stall transients in multistage axial compressors. The theory leads to a set of coupled first-order ordinary differential equations capable of describing the growth and possible decay of a rotating-stall cell during a compressor mass-flow transient. These changing flow features are shown to have a significant effect on the instantaneous compressor pumping characteristic during unsteady operation, and henace on the overall system behavior. It is also found from the theory that the ultimate mode of system response, stable rotating stall or surge, depends not only on the B parameter but also on other parameters, such as the compressor length-to-diameter ratio. Small values of this latter quantity tend to favor the occurrence of surge, as do large values of B. A limited parametric study is carried out to show the impact of the different system features on transient behavior. Based on analytical and numerical results, several specific topics are suggested for future research on post-stall transients.

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F. K. Moore

Papers

A Theory of Post-Stall Transients in Axial Compression Systems: Part I—Development of Equations

A Theory of Post-Stall Transients in Axial Compression Systems: Part II—Application

A Theory of Rotating Stall of Multistage Axial Compressors: Part III—Limit Cycles

A Theory of Rotating Stall of Multistage Axial Compressors: Part II—Finite Disturbances

A theory of post-stall transients in multistage axial compression systems