Nonlinear Control

Inbunden, Engelska, 2014

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Beskrivning

For a first course on nonlinear control that can be taught in one semester

This book emerges from the award-winning book, Nonlinear Systems, but has a distinctly different mission and¿organization. While Nonlinear Systems was intended as a reference and a text on nonlinear system analysis and its application to control, this streamlined book is intended as a text for a first course on nonlinear control. In Nonlinear Control, author Hassan K. Khalil employs a writing style that is intended to make the book accessible to a wider audience without compromising the rigor of the presentation.

Teaching and Learning Experience

This program will provide a better teaching and learning experience–for you and your students. It will help:

Provide an Accessible Approach to Nonlinear Control: This streamlined book is intended as a text for a first course on nonlinear control that can be taught in one semester.
Support Learning: Over 250 end-of-chapter exercises give students plenty of opportunities to put theory into action.

Produktinformation

Utgivningsdatum:2014-02-27
Mått:0 x 10 x 0 mm
Vikt:0 g
Format:Inbunden
Språk:Engelska
Antal sidor:400
Upplaga:1
Förlag:Pearson Education
ISBN:9780133499261

Utforska kategorier

Energiteknik inom Naturvetenskap och teknik

Innehållsförteckning

1 Introduction 11.1 Nonlinear Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Nonlinear Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.3 Overview of the Book . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 Two-Dimensional Systems 152.1 Qualitative Behavior of Linear Systems . . . . . . . . . . . . . . . . . . 172.2 Qualitative Behavior Near Equilibrium Points . . . . . . . . . . . . . . 212.3 Multiple Equilibria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.4 Limit Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.5 Numerical Construction of Phase Portraits . . . . . . . . . . . . . . . . 312.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333 Stability of Equilibrium Points 373.1 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.2 Linearization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.3 Lyapunov’s Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.4 The Invariance Principle . . . . . . . . . . . . . . . . . . . . . . . . . . 543.5 Exponential Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . 583.6 Region of Attraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613.7 Converse Lyapunov Theorems . . . . . . . . . . . . . . . . . . . . . . . 683.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 704 Time-Varying and Perturbed Systems 754.1 Time-varying Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 754.2 Perturbed Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 804.3 Boundedness and Ultimate Boundedness . . . . . . . . . . . . . . . . . 854.4 Input-to-State Stability . . . . . . . . . . . . . . . . . . . . . . . . . . 944.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 995 Passivity 1035.1 Memoryless Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 1035.2 State Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1075.3 Positive Real Transfer Functions . . . . . . . . . . . . . . . . . . . . . 1125.4 Connection with Lyapunov Stability . . . . . . . . . . . . . . . . . . . 1155.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1186 Input-Output Stability 1216.1 L Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1216.2 L Stability of State Models . . . . . . . . . . . . . . . . . . . . . . . . 1276.3 L2 Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1326.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1377 Stability of Feedback Systems 1417.1 Passivity Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1427.2 The Small-Gain Theorem . . . . . . . . . . . . . . . . . . . . . . . . . 1527.3 Absolute Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1557.3.1 Circle Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . 1577.3.2 Popov Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . 1647.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1688 Special Nonlinear Forms 1718.1 Normal Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1718.2 Controller Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1798.3 Observer Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1878.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1949 State Feedback Stabilization 1979.1 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1979.2 Linearization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1999.3 Feedback Linearization . . . . . . . . . . . . . . . . . . . . . . . . . . 2019.4 Partial Feedback Linearization . . . . . . . . . . . . . . . . . . . . . . 2079.5 Backstepping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2119.6 Passivity-Based Control . . . . . . . . . . . . . . . . . . . . . . . . . . 2179.7 Control Lyapunov Functions . . . . . . . . . . . . . . . . . . . . . . . . 2229.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22710 Robust State Feedback Stabilization 23110.1 Sliding Mode Control . . . . . . . . . . . . . . . . . . . . . . . . . . . 23210.2 Lyapunov Redesign . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25110.3 High-Gain Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . 25710.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25911 Nonlinear Observers 26311.1 Local Observers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26411.2 The Extended Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . 26611.3 Global Observers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27011.4 High-Gain Observers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27111.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27712 Output Feedback Stabilization 28112.1 Linearization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28212.2 Passivity-Based Control . . . . . . . . . . . . . . . . . . . . . . . . . . 28312.3 Observer-Based Control . . . . . . . . . . . . . . . . . . . . . . . . . . 28612.4 High-Gain Observers and the Separation Principle . . . . . . . . . . . . 28812.5 Robust Stabilization of Minimum Phase Systems . . . . . . . . . . . . 29612.5.1 Relative Degree One . . . . . . . . . . . . . . . . . . . . . . . 29612.5.2 Relative Degree Higher Than One . . . . . . . . . . . . . . . 29812.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30413 Tracking and Regulation 30713.1 Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31013.2 Robust Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31213.3 Transition Between Set Points . . . . . . . . . . . . . . . . . . . . . . 31413.4 Robust Regulation via Integral Action . . . . . . . . . . . . . . . . . . 31813.5 Output Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32213.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325A Examples 329A.1 Pendulum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329A.2 Mass—Spring System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331A.3 Tunnel-Diode Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . 333A.4 Negative-Resistance Oscillator . . . . . . . . . . . . . . . . . . . . . . 335A.5 DC-to-DC Power Converter . . . . . . . . . . . . . . . . . . . . . . . . 337A.6 Biochemical Reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338A.7 DC Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339A.8 Magnetic Levitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340A.9 Electrostatic Microactuator . . . . . . . . . . . . . . . . . . . . . . . . 342A.10 Robot Manipulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344A.11 Inverted Pendulum on a Cart . . . . . . . . . . . . . . . . . . . . . . . 344A.12 Translational Oscillator with Rotating Actuator . . . . . . . . . . . . . 347B Mathematical Review 349C Composite Lyapunov Functions 355C.1 Cascade Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355C.2 Interconnected systems . . . . . . . . . . . . . . . . . . . . . . . . . . 357C.3 Singularly Perturbed Systems . . . . . . . . . . . . . . . . . . . . . . . 359D Proofs 363