Backstepping Control of Nonlinear Dynamical Systems addresses both the fundamentals of backstepping control as well as the advances in the field. The latest techniques that are explored include 'active backstepping control', 'adaptive backstepping control', 'fuzzy backstepping control' and 'adaptive fuzzy backstepping control' - this exploits a gap in the market as it plainly discusses the process, history, and definition of backstepping control. The reference book provides numerous simulations using MATLAB and circuit design. These illustrate the main results of theory and applications of backstepping control of nonlinear control systems. Backstepping control encompasses varied aspects of mechanical engineering and has many different applications within the field. For example, the book covers aspects related to robot manipulators, aircraft flight control systems, power systems, mechanical systems, biological systems and chaotic systems. This multi-faceted aspect of the subject area means that the subject matter will be a useful reference resource for a large cross section of the mechanical engineering community. Details the real-world applications of backstepping control Gives an up-to-date insight into the theory, uses, and application of backstepping control Bridges the gaps for different fields of engineering including mechanical engineering, aeronautical engineering, electrical engineering, communications engineering, robotics and biomedical instrumentation
Author(s): Sundarapandian Vaidyanathan; Ahmad Taher Azar
Series: Advances in Nonlinear Dynamics and Chaos
Publisher: Academic Press
Year: 2020
Language: English
Pages: 500
City: London
Contents
Contributors
Preface
About the book
Objectives of the book
Organization of the book
Book features
Audience
Acknowledgments
1 An introduction to backstepping control
1.1 Introduction
1.2 Backstepping design for a 2-D linear system
1.3 Backstepping design for a 2-D nonlinear system
1.4 Backstepping design for a 3-D linear system
1.5 Backstepping design for the 3-D Vaidyanathan jerk chaotic system
1.6 Backstepping control method
1.7 Examples of backstepping control design
1.8 Conclusions
References
2 A new chaotic system without linear term, its backstepping control, and circuit design
2.1 Introduction
2.2 Properties of the system
2.3 Dynamics of the system
2.4 Backstepping control for the global stabilization of the new chaos system
2.5 Backstepping control for the synchronization of the new chaos systems
2.6 Circuit design
2.7 Conclusions
Acknowledgment
References
3 A new chaotic jerk system with egg-shaped strange attractor, its dynamical analysis, backstepping control, and circuit simulation
3.1 Introduction
3.2 System details
3.3 Backstepping control of the jerk system
3.4 Backstepping synchronization of the jerk system
3.5 Circuit design
3.6 Conclusions
References
4 A new 4-D chaotic hyperjerk system with coexisting attractors, its active backstepping control, and circuit realization
4.1 Introduction
4.2 System model
4.3 Dynamic analysis of the new hyperjerk system
4.4 Active backstepping stabilization of the new hyperjerk system
4.5 Active backstepping synchronization of the new hyperjerk system
4.6 Circuit simulation of the new hyperjerk system
4.7 Conclusions
Acknowledgment
References
5 A new 3-D chaotic jerk system with a saddle-focus rest point at the origin, its active backstepping control, and circuit realization
5.1 Introduction
5.2 System model
5.3 Dynamic analysis of the new jerk system
5.4 Backstepping control of the jerk system
5.5 Backstepping synchronization of the jerk system
5.6 Electronic circuit simulation of the chaotic jerk system
5.7 Conclusions
Acknowledgments
References
6 A new 5-D hyperchaotic four-wing system with multistability and hidden attractor, its backstepping control, and circuit simulation
6.1 Introduction
6.2 System model
6.3 Dynamic analysis of the 5-D hyperchaotic four-wing model
6.3.1 Rest points
6.3.2 Multistability
6.4 Active backstepping control for the global stabilization design of the new 5-D hyperchaotic four-wing system
6.5 Active backstepping control for the global synchronization design of the new 5-D hyperchaotic four-wing systems
6.6 Circuit simulation of the new 5D hyperchaotic four-wing system
6.7 Conclusions
References
7 A new 4-D hyperchaotic temperature variations system with multistability and strange attractor, bifurcation analysis, its active backstepping control, and circuit realization
7.1 Introduction
7.2 System model
7.3 Dynamic analysis of the hyperchaotic temperature variations model
7.3.1 Bifurcation analysis
7.3.2 Rest points
7.3.3 Multistability
7.4 Active backstepping control for the global stabilization design of the new hyperchaotic temperature variations system
7.5 Active backstepping control for the global synchronization design of the new hyperchaos temperature variation systems
7.6 Circuit simulation of the new 4D hyperchaotic temperature variation system
7.7 Conclusions
References
8 A new thermally excited chaotic jerk system, its dynamical analysis, adaptive backstepping control, and circuit simulation
8.1 Introduction
8.2 A new jerk system with two nonlinearities
8.3 Dynamic analysis of the new thermo-mechanical jerk model
8.3.1 Rest points of the new jerk model
8.3.2 Bifurcation analysis
8.3.3 Multistability and coexisting attractors
8.4 Adaptive backstepping control of the new thermo-mechanical jerk system
8.5 Adaptive backstepping synchronization of the new thermo-mechanical jerk systems
8.6 Electronic circuit simulation of the new thermo-mechanical chaotic jerk system
8.7 Conclusions
References
9 A new multistable plasma torch chaotic jerk system, its dynamical analysis, active backstepping control, and circuit design
9.1 Introduction
9.2 A new plasma torch chaotic jerk system with two nonlinearities
9.3 Dynamic analysis of the new plasma torch chaotic jerk model
9.3.1 Rest points of the new chaotic jerk model
9.3.2 Bifurcation analysis
9.3.3 Multistability and coexisting attractors
9.4 Active backstepping control for the global stabilization of the new plasma torch chaotic jerk system
9.5 Active backstepping control for the global synchronization of the new plasma torch chaotic jerk systems
9.6 Electronic circuit simulation of the new plasma torch chaotic jerk system
9.7 Conclusions
References
10 Direct power control of three-phase PWM-rectifier with backstepping control
10.1 Introduction
10.2 Mathematical model of PWM-rectifier
10.2.1 Vector representation
10.2.2 A brief review of direct power control
10.3 Principle and definitions of backstepping control
10.4 Control of DC-voltage by backstepping
10.5 Simulation results
10.6 Conclusion
References
11 Adaptive backstepping controller for DFIG-based wind energy conversion system
11.1 Introduction
11.2 Wind sensor-less rotor speed reference optimization
11.3 Modeling `AC/DC/AC converter-DFIG' association
11.3.1 DFIG-AC/DC modeling
11.3.2 AC/DC rectifier modeling
11.4 Controller design
11.4.1 Control objectives
11.4.2 Speed and stator flux norm regulator design
11.4.3 PFC and DC voltage controller
11.4.3.1 Controlling rectifier output current to meet PFC
11.4.3.2 DC voltage loop
11.5 Simulation results and discussions
11.6 Conclusion
References
12 Dynamic modeling, identification, and a comparative experimental study on position control of a pneumatic actuator based on Soft Switching and Backstepping-Sliding Mode controllers
12.1 Introduction
12.2 Related works
12.3 Experimental setup of the PneuSys
12.4 Dynamic modeling of the pneumatic system
12.4.1 Cylinder dynamics
12.4.2 Pressure dynamics
12.4.3 State space representation of the PneuSys
12.5 GA-based identification of the PneuSys and validation
12.5.1 Identification of the unknown parameters
12.5.2 Validation of the identified dynamic model
12.6 Proposed controllers; Model-free and Model-based controllers
12.6.1 Model-free; Soft Switching controller
12.6.2 Model-based; Backstepping-Sliding Mode controller
12.7 Experimental results
12.8 Discussion
12.9 Conclusion
References
13 Optimal adaptive backstepping control for chaos synchronization of nonlinear dynamical systems
13.1 Introduction
13.2 Chaos detection and chaos synchronization
13.2.1 Chaos detection
13.2.1.1 Lyapunov exponent
13.2.1.2 0-1 test for chaos in dynamical system
13.2.2 Chaos synchronization and recurrence
13.3 Problem statement and preliminaries
13.4 Stability analysis of adaptive backstepping control systems
13.4.1 Lyapunov stability theory and the invariance principle
13.4.2 Adaptive backstepping controller design
13.4.2.1 Principle of backstepping control method
13.4.2.2 Adaptive backstepping control process
13.4.2.3 Optimal backstepping controller based on genetic algorithms
13.5 The PID controller based on genetic algorithms
13.6 Simulation examples and discussion
13.6.1 Lorenz system description
13.6.2 Optimal adaptive backstepping control and genetically optimized PID control for chaos synchronization of Lorenz systems
13.6.2.1 Adaptive backstepping stabilization control for Lorenz system
13.6.2.2 Optimal adaptive backstepping control for Lorenz system synchronization
13.6.2.3 Genetically optimized PID control for chaos synchronization of Lorenz systems
13.6.2.4 Discussion
13.7 Conclusion
References
14 Backstepping controller for nonlinear active suspension system
14.1 Introduction
14.2 Plant model and problem statement
14.2.1 Nonlinear active suspension system
14.2.2 Problem statement
14.3 Backstepping controller synthesis
14.3.1 Backstepping controller
14.3.2 Fuzzy PD controller
14.3.3 Conventional PD controller
14.3.4 Tuning of gains of controllers
14.3.4.1 Grey Wolf optimizing algorithm
14.3.4.2 Cost function
14.4 Results and discussions
14.4.1 Bump road surface
14.4.1.1 Sprung mass uncertainty
14.4.1.2 Uncertainty in height of bump
14.4.2 Multiple bumps road profile
14.5 Conclusions
References
15 Single-link flexible joint manipulator control using backstepping technique
15.1 Introduction
15.2 Single-link flexible joint manipulator model
15.3 Controller design using backstepping technique
15.4 Optimization algorithms
15.4.1 Jaya algorithm
15.4.2 Teaching learning based optimization algorithm
15.4.3 Genetic algorithm
15.5 Results and discussions
15.6 Conclusion
References
16 Backstepping control and synchronization of chaotic time delayed systems
16.1 Introduction
16.2 Related work
16.3 Backstepping stabilization of time delayed systems
16.4 Backstepping synchronization of time delayed chaotic systems
16.5 Numerical examples
16.5.1 Example 1: Stabilization of the time delayed Lorenz chaotic system
16.5.2 Example 2: Synchronization of the time delayed Rössler chaotic system
16.6 Discussion
16.7 Conclusion
References
17 Multi-switching synchronization of nonlinear hyperchaotic systems via backstepping control
17.1 Introduction
17.2 Problem formulation
17.3 System description
17.3.1 Chaotic attractor of the system
17.3.2 Dissipation and existence of chaotic attractor
17.3.3 Symmetry and invariance
17.3.4 Poincaré map
17.4 Simulation results and discussions
17.4.1 Switch 1
17.4.1.1 Design of η1 and η2
17.4.1.2 Design of η3 and η4
17.4.1.3 Numerical simulations
17.4.2 Switch 2
17.4.2.1 Design of η2 and η3
17.4.2.2 Design of η1 and η4
17.4.2.3 Numerical simulations
17.4.3 Switch 3
17.4.3.1 Design of η1 and η2
17.4.3.2 Design of η3 and η4
17.4.3.3 Numerical simulations
17.5 Conclusion
References
18 A 5-D hyperchaotic dynamo system with multistability, its dynamical analysis, active backstepping control, and circuit simulation
18.1 Introduction
18.2 System model
18.3 Dynamic analysis of the 5-D hyperchaotic dynamo model
18.3.1 Rest points
18.3.2 Multistability
18.4 Active backstepping control for the global stabilization design of the new 5-D hyperchaotic dynamo system
18.5 Active backstepping control for the global synchronization design of the new 5-D hyperchaotic dynamo systems
18.6 Circuit simulation of the new 5D hyperchaotic system
18.7 Conclusions
References
19 Design and implementation of a backstepping controller for nonholonomic two-wheeled inverted pendulum mobile robots
19.1 Introduction
19.2 Distributed controller design based on backstepping approach
19.3 Discrete event modeling and control net representation
19.4 Implementation issues on a multi-task processing architecture
19.5 Conclusion
References
20 A novel chaotic system with a closed curve of four quarter-circles of equilibrium points: dynamics, active backstepping control, and electronic circuit implementation
20.1 Introduction
20.2 A new chaotic system with closed-curve equilibrium
20.3 Dynamic analysis of the new chaotic system with a closed-curve equilibrium
20.3.1 Lyapunov exponents analysis
20.3.2 Multistability and coexisting attractors
20.4 Active backstepping control for the global stabilization of the new chaos system with a closed-curve equilibrium
20.5 Active backstepping control for the synchronization of the new chaos systems
20.6 Circuit design for the new chaotic system with a closed-curve equilibrium
20.7 Conclusions
Acknowledgment
References
Index
