Nonlinear Systems and Controls

• Autore: Adamy Jürgen
• Pubblicazione: Berlin, Heidelberg : , : Springer Berlin / Heidelberg, , 2024; ©2024
• Edizione: 2nd ed.
• Descrizione fisica: 1 online resource (760 pages)
• Disciplina: 629.836
• Nota di contenuto: Intro -- Preface -- Contents -- 1 Fundamentals of Nonlinear Systems -- 1.1 System Description and System Behavior -- 1.1.1 Linear and Nonlinear Systems -- 1.1.2 System Description and Nonlinear Control Loops -- 1.1.3 Equilibrium Points of Nonlinear Systems -- 1.1.4 Example: Satellite -- 1.1.5 Equilibrium Points of Linear Systems -- 1.1.6 Stability and Asymptotic Stability -- 1.1.7 Exponential Stability of Equilibrium Points -- 1.1.8 Instability of Equilibrium Points -- 1.1.9 Stability in the Case of Variable Input Signals -- 1.1.10 Limit Cycles -- 1.1.11 Sliding Modes -- 1.1.12 Chaos -- 1.1.13 Discrete-Time Systems -- 1.2 Solution of Nonlinear Differential Equations -- 1.2.1 Existence of Solutions -- 1.2.2 Numerical Solution and Euler Method -- 1.2.3 Accuracy of the Numerical Solution -- 1.2.4 The Modified Euler Method -- 1.2.5 The Heun and Simpson Methods -- 1.2.6 The Runge-Kutta Methods -- 1.2.7 Adaptation of the Step Size -- 1.2.8 The Adams-Bashforth Methods -- 1.2.9 The Adams-Moulton Predictor-Corrector Methods -- 1.2.10 Stability of Numerical Integration Methods -- 1.2.11 Stiff Systems and Their Solutions -- 1.3 Exercises -- 2 Limit Cycles and Stability Criteria -- 2.1 The Describing Function Method -- 2.1.1 Idea behind the Method -- 2.1.2 Illustrative Example -- 2.1.3 Characteristic Curves and Their Describing Functions -- 2.1.4 Stability Analysis of Limit Cycles -- 2.1.5 Example: Power-Assisted Steering System -- 2.2 Absolute Stability -- 2.2.1 The Concept of Absolute Stability -- 2.2.2 The Popov Criterion and Its Application -- 2.2.3 The Aizerman and Kalman Conjectures -- 2.2.4 Example: Controlling a Ship -- 2.2.5 The Circle Criterion -- 2.2.6 The Tsypkin Criterion for Discrete-Time Systems -- 2.3 Lyapunov's Stability Theory -- 2.3.1 The Concept and the Direct Method -- 2.3.2 Illustrative Example -- 2.3.3 Quadratic Lyapunov Functions. ; 2.3.4 Example: Mutualism -- 2.3.5 The Direct Method for Discrete-Time Systems -- 2.3.6 The Indirect Method -- 2.3.7 Determining Exponential Stability -- 2.3.8 Example: Underwater Glider -- 2.3.9 Catchment Regions -- 2.3.10 LaSalle's Invariance Principle -- 2.3.11 Instability Criterion -- 2.4 Passivity and Stability -- 2.4.1 Passive Systems -- 2.4.2 Stability of Passive Systems -- 2.4.3 Passivity of Connected Systems -- 2.4.4 Passivity of Linear Systems -- 2.4.5 Example: Transporting System for Material Webs -- 2.4.6 Positive Real Transfer Functions -- 2.4.7 Equivalence of Positive Realness and Passivity -- 2.4.8 Lossless Hamiltonian Systems -- 2.4.9 Example: Self-Balancing Vehicle -- 2.4.10 Dissipative Hamiltonian Systems -- 2.4.11 Example: Separately Excited Direct-Current Machine -- 2.4.12 Linear Hamiltonian Systems -- 2.5 Exercises -- 3 Controllability and Flatness -- 3.1 Controllability -- 3.1.1 Definition of Controllability -- 3.1.2 Global and Local Controllability -- 3.1.3 Proving Controllability -- 3.1.4 Example: Industrial Robot -- 3.1.5 Small-Time Local Controllability of Driftless Systems -- 3.1.6 Example: Motor Vehicle with Trailer -- 3.1.7 Omnidirectional Controllability -- 3.1.8 Example: Steam Generator -- 3.2 Flatness -- 3.2.1 Basic Concept and Definition of Flatness -- 3.2.2 The Lie-Bäcklund Transformation -- 3.2.3 Example: VTOL Aircraft -- 3.2.4 Flatness and Controllability -- 3.2.5 Flat Outputs of Linear Systems -- 3.2.6 Verification of Flatness -- 3.3 Nonlinear State Transformations -- 3.3.1 Transformations and Transformed System Equations -- 3.3.2 Illustrative Example -- 3.3.3 Example: Park Transformation -- 3.3.4 Determining the Transformation Rule -- 3.3.5 Illustration Using Linear Systems -- 3.4 Exercises -- 4 Nonlinear Control of Linear Systems -- 4.1 Control with Anti-Windup -- 4.1.1 The Windup Effect. ; 4.1.2 PID Controller with Anti-Windup Element -- 4.1.3 Example: Direct-Current Motor -- 4.1.4 A General Anti-Windup Method -- 4.1.5 Dimensioning the General Anti-Windup Controller -- 4.1.6 Stability -- 4.2 Time-Optimal Control -- 4.2.1 Fundamentals and Fel'dbaum's Theorem -- 4.2.2 Computation of Time-Optimal Controls -- 4.2.3 Example 1/s2 -- 4.2.4 Time-Optimal Control of Low-Order Systems -- 4.2.5 Example: Submarine -- 4.2.6 Time-Optimal Pilot Control -- 4.3 Variable Structure Control Without Sliding Mode -- 4.3.1 Fundamentals of Variable Structure Control -- 4.3.2 Piecewise Linear Control -- 4.3.3 Example: Ship-to-Shore Gantry Crane -- 4.4 Saturation Controllers -- 4.4.1 Basics and Stability -- 4.4.2 Design in Multiple Steps -- 4.4.3 Example: Helicopter -- 4.5 Exercises -- 5 Nonlinear Control of Nonlinear Systems -- 5.1 Gain-Scheduling Control -- 5.1.1 Mode of Operation and Design -- 5.1.2 Illustrative Example -- 5.1.3 Example: Solar Power Plant -- 5.2 Input-Output Linearization -- 5.2.1 Basic Concept and Nonlinear Controller Canonical Form -- 5.2.2 Nonlinear Controller and Linear Control Loop -- 5.2.3 Example: Magnetic Bearing -- 5.2.4 Plants with Internal Dynamics -- 5.2.5 Design Procedure -- 5.2.6 Example: Lunar Module -- 5.2.7 Input-Output Linearization of General SISO Systems -- 5.2.8 Relative Degree and Internal Dynamics of Linear Systems -- 5.2.9 Control Law for the Linear Case -- 5.2.10 Stability of Internal and Zero Dynamics -- 5.2.11 Input-Output Linearization of MIMO Systems -- 5.2.12 MIMO Control Loops in State-Space Representation -- 5.2.13 Example: Combustion Engine -- 5.3 Full-State Linearization -- 5.3.1 Full-State Linearization of SISO Systems -- 5.3.2 Example: Drilling Rig -- 5.3.3 Full-State Linearization of MIMO Systems -- 5.3.4 Flatness of Full-State Linearizable Systems -- 5.3.5 Example: Rocket. ; 5.4 Feedforward and Feedback Control of Flat Systems -- 5.4.1 Fundamentals -- 5.4.2 Feedforward Controls Using Fictitious Flat Outputs -- 5.4.3 Flatness-Based Feedforward Control of Linear Systems -- 5.4.4 Example: Propulsion-Based Aircraft Control -- 5.4.5 Flatness-Based Feedback Control of Nonlinear Systems -- 5.4.6 Example: Pneumatic Motor -- 5.4.7 Flat Inputs and Their Design -- 5.4.8 Flat Inputs of Linear Systems -- 5.4.9 Example: Economic Market Model -- 5.5 Control Lyapunov Functions -- 5.5.1 Fundamentals -- 5.5.2 Control Lyapunov Functions for Linear Systems -- 5.5.3 Control Lyapunov Functions for Control-Affine Systems -- 5.5.4 Illustrative Example -- 5.5.5 Example: Power Plant with Grid Feed-In -- 5.6 The Backstepping Method -- 5.6.1 Fundamentals -- 5.6.2 Recursive Scheme for the Controller Design -- 5.6.3 Illustrative Examples -- 5.6.4 Example: Fluid System with Chaotic Behavior -- 5.7 Exercises -- 6 Nonlinear Control of Linear and Nonlinear Systems -- 6.1 Model-Based Predictive Control -- 6.1.1 Basics and Functionality -- 6.1.2 Linear Model Predictive Control without Constraints -- 6.1.3 LMPC with Constraints -- 6.1.4 Example: Drainage System -- 6.1.5 Nonlinear Model Predictive Control -- 6.1.6 Example: Evaporation Plant -- 6.2 Variable Structure Control with Sliding Mode -- 6.2.1 Basics and Characteristics -- 6.2.2 Design for Linear Plants -- 6.2.3 Dynamics in the Sliding Mode -- 6.2.4 Verification of Robustness -- 6.2.5 Example: DC-to-DC Converter -- 6.2.6 Design for Nonlinear Plants -- 6.2.7 Example: Optical Switch -- 6.3 Passivity-Based Control -- 6.3.1 Control of Passive Systems Using Static Controllers -- 6.3.2 Example: Damping of Seismic Building Vibrations -- 6.3.3 Passivation of Non-Passive Linear Systems -- 6.3.4 Passivation of Non-Passive Control-Affine Systems -- 6.3.5 Passivity-Based Control with IDA. ; 6.3.6 Example: Paper Machine -- 6.4 Fuzzy Control -- 6.4.1 Introduction -- 6.4.2 Fuzzification -- 6.4.3 Inference -- 6.4.4 Defuzzification -- 6.4.5 Fuzzy Systems and Fuzzy Controllers -- 6.4.6 Example: Distance Control for Automobiles -- 6.5 Exercises -- 7 Observers for Nonlinear Systems -- 7.1 Observability of Nonlinear Systems -- 7.1.1 Definition of Observability -- 7.1.2 Observability of Autonomous Systems -- 7.1.3 Example: Synchronous Generator -- 7.1.4 Observability of General Nonlinear Systems -- 7.1.5 Nonlinear Observability Canonical Form -- 7.1.6 Observability of Control-Affine Systems -- 7.2 Canonical Forms and the Canonical Form Observer -- 7.3 Luenberger Observers for Nonlinear Control Loops -- 7.4 Observer Design Using Linearization -- 7.4.1 Basics and Design -- 7.4.2 Control Loop with Observer -- 7.4.3 Example: Bioreactor -- 7.5 The Extended Kalman Filter -- 7.5.1 Kalman Filter for Linear Systems -- 7.5.2 The EKF for Nonlinear Systems -- 7.5.3 Example: Jet Engine -- 7.6 High-Gain Observer -- 7.6.1 Concept and Design -- 7.6.2 High-Gain Observers in General Form -- 7.6.3 Example: Chemical Reactor -- 7.6.4 The Case of Control-Affine Systems -- 7.7 Exercises -- 8 Solutions to the Exercises -- A Appendix -- A.1 Proof of the General Circle Criterion -- A.2 Parameters of the Container Crane Control -- B List of Symbols -- References -- Index.
• Titolo autorizzato: Nonlinear Systems and Controls
• ISBN: 3-662-68690-2
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910847075303321
• Lo trovi qui: Univ. Federico II