Hierarchical Nonlinear Switching Control Design with Applications to Propulsion SystemsThis book presents a general nonlinear control design methodology for nonlinear uncertain dynamical systems. Specifically, a hierarchical nonlinear switching control framework is developed that provides a rigorous alternative to gain scheduling control for general nonlinear uncertain systems. The proposed switching control design framework accounts for actuator saturation constraints as well as system modeling uncertainty. The efficacy of the control design approach is extensively demonstrated on aeroengine propulsion systems. In particular, dynamic models for rotating stall and surge in axial and centrifugal flow compression systems that lend themselves to the application of nonlinear control design are developed and the hierarchical switching control framework is then applied to control the aerodynamic instabilities of rotating stall and surge. For the researcher who is entering the field of hierarchical switching robust control this book provides a plethora of new research directions. Alternatively, for researchers already active in the field of hierarchical control and hybrid systems, this book can be used as a reference to a significant body of recent work. Furthermore, control practitioners involved with nonlinear control design can immensely benefit from the novel nonlinear stabilization techniques presented in the book. |
Contents
1 Introduction | 1 |
12 Brief Outline of the Monograph | 4 |
2 Generalized Lyapunov and Invariant Set Theorems for Nonlinear Dynamical Systems | 7 |
22 Mathematical Preliminaries | 8 |
23 Generalized Stability Theorems | 11 |
24 Conclusion | 19 |
3 Nonlinear System Stabilization via Hierarchical Switching Controllers | 21 |
32 Mathematical Preliminaries | 23 |
524 Governing System Flow Equations | 70 |
525 Plenum and Throttle Discharge | 71 |
53 MultiMode State Space Model | 72 |
54 Finite Element MultiMode State Space Model | 75 |
55 Control for SingleMode versus MultiMode Model | 77 |
56 Stabilization of MultiMode Axial Flow Compression System Models | 80 |
57 Robust Stabilization of Axial Flow Compressors with Uncertain PressureFlow Maps | 84 |
571 Uncertain Finite Element MultiMode State Space Model | 85 |
33 Parameterized System Equilibria and Domains of Attraction | 24 |
34 Nonlinear System Stabilization via a Hierarchical Switching Controller Architecture | 26 |
35 Extensions to Nonlinear Dynamic Compensation | 35 |
36 Inverse Optimal Nonlinear Switching Control | 39 |
37 Conclusion | 46 |
4 Nonlinear Robust Switching Controllers for Nonlinear Uncertain Systems | 47 |
42 Mathematical Preliminaries | 48 |
43 Parameterized Nominal System Equilibria System Attractors and Domains of Attraction | 49 |
44 Robust Nonlinear System Stabilization via a Hierarchical Switching Controller Architecture | 51 |
45 Conclusion | 57 |
5 Hierarchical Switching Control for MultiMode Axial Flow Compressor Models | 59 |
52 Governing Fluid Dynamic Equations for Axial Flow Compression Systems | 62 |
522 Compressor | 68 |
523 Exit Duct | 69 |
572 Hierarchical Robust Control for Propulsion Systems | 87 |
58 Conclusion | 95 |
6 Hierarchical Switching Control for Centrifugal Flow Compressor Models | 97 |
62 Governing Fluid Dynamic Equations for Centrifugal Compression Systems | 98 |
622 Conservation of Momentum | 100 |
623 Turbocharger Spool Dynamics | 104 |
63 Parameterized System Equilibria and Local Set Point Designs | 105 |
64 Hierarchical Nonlinear Switching Control for Centrifugal Compression Systems | 107 |
65 Conclusion | 115 |
7 Conclusions | 117 |
123 | |
131 | |
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Common terms and phrases
As(x assume Assumption 3.1 asymptotically stable axial compressor axial flow compressors C¹ function centrifugal compressor closed-loop system compact positively invariant continuous function Contr controlled system defined developed disturbance velocity potential domain of attraction duct equilibrium manifold equilibrium point exists feedback control law feedback linearization finite flow compression systems follows from Theorem Furthermore gain scheduling gain scheduling control global asymptotic globally stabilizing guarantees Hence hierarchical switching controller hierarchical switching nonlinear homeomorphic inverse optimal isolated points linear lower semicontinuous Lyapunov function Lyapunov stability mass flow nondimensional nonlinear dynamical nonlinear dynamical system nonlinear switching control nonlinear system parameter plenum positively invariant set potential function pressure rise rate saturation constraints robust control robust switching rotating stall space model stall and surge Subcontroller switching control framework switching controller architecture switching nonlinear controller switching set system equilibria system trajectories t₁ throttle opening velocity potential