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E-raamat: Backstepping Control of Nonlinear Dynamical Systems

Edited by (Research Associate Professor, Prince Sultan University, Riyadh, Kingdom Saudi ArabiaAssociate Professor, Faculty of Computers), Edited by (Professor, Research and Development Centre, Vel Tech University, Avadi, Chennai-600 062, Tamil Nadu, India)
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Backstepping Control of Nonlinear Dynamical SystemsSuurem pilt
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Backstepping Control of Nonlinear Dynamical Systems addresses both the fundamentals of backstepping control and advances in the field. The latest techniques explored include ‘active backstepping control’, ‘adaptive backstepping control’, ‘fuzzy backstepping control’ and ‘adaptive fuzzy 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 multifaceted view of subject areas means that this useful reference resource will be ideal 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
Contributors xv
Preface xix
1 An introduction to backstepping control
Sundarapandian Vaidyanathan
Ahmad TaherAzar
1.1 Introduction
1(1)
1.2 Backstepping design for a 2-D linear system
2(2)
1.3 Backstepping design for a 2-D nonlinear system
4(3)
1.4 Backstepping design for a 3-D linear system
7(4)
1.5 Backstepping design for the 3-D Vaidyanathan jerk chaotic system
11(4)
1.6 Backstepping control method
15(6)
1.7 Examples of backstepping control design
21(6)
1.8 Conclusions
27(1)
References
28(5)
2 A new chaotic system without linear term, its backstepping control, and circuit design
Viet-Thanh Pham
Sundarapandian Vaidyanathan
Ahmad Taher Azar
Vo Hoang Duy
2.1 Introduction
33(1)
2.2 Properties of the system
34(1)
2.3 Dynamics of the system
35(1)
2.4 Backstepping control for the global stabilization of the new chaos system
35(5)
2.5 Backstepping control for the synchronization of the new chaos systems
40(5)
2.6 Circuit design
45(3)
2.7 Conclusions
48(1)
Acknowledgment
48(1)
References
48(5)
3 A new chaotic jerk system with egg-shaped strange attractor, its dynamical analysis, backstepping control, and circuit simulation
Sundarapandian Vaidyanathan
Viet-Thanh Pham
Ahmad Taher Azar
3.1 Introduction
53(2)
3.2 System details
55(2)
3.3 Backstepping control of the jerk system
57(4)
3.4 Backstepping synchronization of the jerk system
61(4)
3.5 Circuit design
65(2)
3.6 Conclusions
67(2)
References
69(4)
4 A new 4-D chaotic hyperjerk system with coexisting attractors, its active backstepping control, and circuit realization
Aceng Sambas
Sundarapandian Vaidyanathan
Sen Zhang
Mohamad Afendee Mohamed
Yicheng Zeng
Ahmad Taher Azar
4.1 Introduction
73(2)
4.2 System model
75(3)
4.3 Dynamic analysis of the new hyperjerk system
78(1)
4.4 Active backstepping stabilization of the new hyperjerk system
79(3)
4.5 Active backstepping synchronization of the new hyperjerk system
82(6)
4.6 Circuit simulation of the new hyperjerk system
88(2)
4.7 Conclusions
90(1)
Acknowledgment
91(1)
References
91(4)
5 A new 3-D chaotic jerk system with a saddle-focus rest point at the origin, its active backstepping control, and circuit realization
Aceng Sambas
Sundarapandian Vaidyanathan
Sen Zhang
Mohamad Afendee Mohamed
Yicheng Zeng
Ahmad Taher Azar
5.1 Introduction
95(1)
5.2 System model
96(3)
5.3 Dynamic analysis of the new jerk system
99(1)
5.4 Backstepping control of the jerk system
100(3)
5.5 Backstepping synchronization of the jerk system
103(5)
5.6 Electronic circuit simulation of the chaotic jerk system
108(2)
5.7 Conclusions
110(1)
Acknowledgments
111(1)
References
111(4)
6 A new 5-D hyperchaotic four-wing system with multistability and hidden attractor, its backstepping control, and circuit simulation
Sundarapandian Vaidyanathan
Aceng Sambas
Ahmad Taher Azar
K.P.S. Rana
Vineet Kumar
6.1 Introduction
115(1)
6.2 System model
116(3)
6.3 Dynamic analysis of the 5-D hyperchaotic four-wing model
119(1)
6.3.1 Rest points
119(1)
6.3.2 Multistability
119(1)
6.4 Active backstepping control for the global stabilization design of the new 5-D hyperchaotic four-wing system
119(5)
6.5 Active backstepping control for the global synchronization design of the new 5-D hyperchaotic four-wing systems
124(6)
6.6 Circuit simulation of the new 5D hyperchaotic four-wing system
130(2)
6.7 Conclusions
132(2)
References
134(5)
7 A new 4-D hyperchaotic temperature variations system with multistability and strange attractor, bifurcation analysis, its active backstepping control, and circuit realization
Sundarapandian Vaidyanathan
Aceng Sambas
Ahmad Taher Azar
K.P.S. Rana
Vineet Kumar
7.1 Introduction
139(1)
7.2 System model
140(4)
7.3 Dynamic analysis of the hyperchaotic temperature variations model
144(4)
7.3.1 Bifurcation analysis
144(1)
7.3.2 Rest points
145(1)
7.3.3 Multistability
146(2)
7.4 Active backstepping control for the global stabilization design of the new hyperchaotic temperature variations system
148(2)
7.5 Active backstepping control for the global synchronization design of the new hyperchaos temperature variation systems
150(5)
7.6 Circuit simulation of the new 4D hyperchaotic temperature variation system
155(4)
7.7 Conclusions
159(1)
References
160(5)
8 A new thermally excited chaotic jerk system, its dynamical analysis, adaptive backstepping control, and circuit simulation
Sundarapandian Vaidyanathan
Aceng Sambas
Ahmad Taher Azar
Fernando E. Serrano
Arezki Fekik
8.1 Introduction
165(2)
8.2 A new jerk system with two nonlinearities
167(4)
8.3 Dynamic analysis of the new thermo-mechanical jerk model
171(2)
8.3.1 Rest points of the new jerk model 1
71(100)
8.3.2 Bifurcation analysis
171(1)
8.3.3 Multistability and coexisting attractors
172(1)
8.4 Adaptive backstepping control of the new thermo-mechanical jerk system
173(4)
8.5 Adaptive backstepping synchronization of the new thermo-mechanical jerk systems
177(4)
8.6 Electronic circuit simulation of the new thermo-mechanical chaotic jerk system
181(3)
8.7 Conclusions
184(1)
References
185(6)
9 A new multistable plasma torch chaotic jerk system, its dynamical analysis, active backstepping control, and circuit design
Sundarapandian Vaidyanathan
Aceng Sambas
Ahmad Taher Azar
Shikha Singh
9.1 Introduction
191(2)
9.2 A new plasma torch chaotic jerk system with two nonlinearities
193(3)
9.3 Dynamic analysis of the new plasma torch chaotic jerk model
196(4)
9.3.1 Rest points of the new chaotic jerk model
196(2)
9.3.2 Bifurcation analysis
198(1)
9.3.3 Multistability and coexisting attractors
198(2)
9.4 Active backstepping control for the global stabilization of the new plasma torch chaotic jerk system
200(2)
9.5 Active backstepping control for the global synchronization of the new plasma torch chaotic jerk systems
202(3)
9.6 Electronic circuit simulation of the new plasma torch chaotic jerk system
205(3)
9.7 Conclusions
208(2)
References
210(5)
10 Direct power control of three-phase PWM-rectifier with backstepping control
Arezki Fekik
Hakim Denoun
Ahmad Taher Azar
Nashwa Ahmad Kamal
Mustapha Zaouia
Nabil Benyahia
Mohamed Lamine Hamida
Nacereddine Benamrouche
Sundarapandian Vaidyanathan
10.1 Introduction
215(1)
10.2 Mathematical model of PWM-rectifier
216(4)
10.2.1 Vector representation
218(1)
10.2.2 A brief review of direct power control
219(1)
10.3 Principle and definitions of backstepping control
220(5)
10.4 Control of DC-voltage by backstepping
225(1)
10.5 Simulation results
225(5)
10.6 Conclusion
230(2)
References
232(3)
11 Adaptive backstepping controller for DFIG-based wind energy conversion system
Ismail Drhorhi
Abderrahim El Fadili
Chaker Berrahal
Rachid Lajouad
Abdelmounime El Magri
Fouad Ciri
Ahmad Taher Azar
Sundarapandian Vaidyanathan
11.1 Introduction
235(2)
11.2 Wind sensor-less rotor speed reference optimization
237(1)
11.3 Modeling `AC/DC/AC converter-DFIG' association
238(6)
11.3.1 DFIC-AC/DC modeling
239(3)
11.3.2 AC/DC rectifier modeling
242(2)
11.4 Controller design
244(8)
11.4.1 Control objectives
244(1)
11.4.2 Speed and stator flux norm regulator design
244(6)
11.4.3 PFC and DC voltage controller
250(2)
11.5 Simulation results and discussions
252(4)
11.6 Conclusion
256(2)
References
258(3)
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
Amir Salimi Lafmejani
Mehdi Tale Masouleh
Ahmad Kalhor
12.1 Introduction
261(3)
12.2 Related works
264(2)
12.3 Experimental setup of the PneuSys
266(1)
12.4 Dynamic modeling of the pneumatic system
267(3)
12.4.1 Cylinder dynamics
267(1)
12.4.2 Pressure dynamics
268(2)
12.4.3 State space representation of the PneuSys
270(1)
12.5 CA-based identification of the PneuSys and validation
270(5)
12.5.1 Identification of the unknown parameters
271(1)
12.5.2 Validation of the identified dynamic model
272(3)
12.6 Proposed controllers; Model-free and Model-based controllers
275(4)
12.6.1 Model-free; Soft Switching controller
275(1)
12.6.2 Model-based; Backstepping-Sliding Mode controller
275(4)
12.7 Experimental results
279(1)
12.8 Discussion
280(6)
12.9 Conclusion
286(1)
References
287(4)
13 Optimal adaptive backstepping control for chaos synchronization of nonlinear dynamical systems
Mohsen Alimi
Ahmed Rhif
Abdelwaheb Rebai
Sundarapandian Vaidyanathan
Ahmad Taher Azar
13.1 Introduction
291(6)
13.2 Chaos detection and chaos synchronization
297(5)
13.2.1 Chaos detection
297(3)
13.2.2 Chaos synchronization and recurrence
300(2)
13.3 Problem statement and preliminaries
302(1)
13.4 Stability analysis of adaptive backstepping control systems
303(11)
13.4.1 Lyapunov stability theory and the invariance principle
303(3)
13.4.2 Adaptive backstepping controller design
306(8)
13.5 The PID controller based on genetic algorithms
314(2)
13.6 Simulation examples and discussion
316(23)
13.6.1 Lorenz system description
316(9)
13.6.2 Optimal adaptive backstepping control and genetically optimized PID control for chaos synchronization of Lorenz systems
325(14)
13.7 Conclusion
339(1)
References
340(7)
14 Backstepping controller for nonlinear active suspension system
Vineet Kumar
K.R.S. Rana
Ahmad Taher Azar
Sundarapandian Vaidyanathan
14.1 Introduction
347(3)
14.2 Plant model and problem statement
350(3)
14.2.1 Nonlinear active suspension system
350(2)
14.2.2 Problem statement
352(1)
14.3 Backstepping controller synthesis
353(8)
14.3.1 Backstepping controller
353(4)
14.3.2 Fuzzy PD controller
357(2)
14.3.3 Conventional PD controller
359(1)
14.3.4 Tuning of gains of controllers
359(2)
14.4 Results and discussions
361(8)
14.4.1 Bump road surface
361(6)
14.4.2 Multiple bumps road profile
367(2)
14.5 Conclusions
369(1)
References
370(5)
15 Single-link flexible joint manipulator control using backstepping technique
Nishtha Bansal
Aman Bisht
Sruti Paluri
Vineet Kumar
K.P.S. Rana
Ahmad Taher Azar
Sundarapandian Vaidyanathan
15.1 Introduction
375(4)
15.2 Single-link flexible joint manipulator model
379(2)
15.3 Controller design using backstepping technique
381(8)
15.4 Optimization algorithms
389(6)
15.4.1 Jaya algorithm
389(2)
15.4.2 Teaching learning based optimization algorithm
391(1)
15.4.3 Genetic algorithm
392(3)
15.5 Results and discussions
395(5)
15.6 Conclusion
400(2)
References
402(5)
16 Backstepping control and synchronization of chaotic time delayed systems
Ahmad Taher Azar
Fernando E. Serrano
Sundarapandian Vaidyanathan
Nashwa Ahmad Kamal
16.1 Introduction
407(2)
16.2 Related work
409(1)
16.3 Backstepping stabilization of time delayed systems
409(2)
16.4 Backstepping synchronization of time delayed chaotic systems
411(2)
16.5 Numerical examples
413(5)
16.5.1 Example 1: Stabilization of the time delayed Lorenz chaotic system
413(4)
16.5.2 Example 2: Synchronization of the time delayed Rossler chaotic system
417(1)
16.6 Discussion
418(1)
16.7 Conclusion
419(2)
References
421(4)
17 Multi-switching synchronization of nonlinear hyperchaotic systems via backstepping control
Shikha Singh
Sandhya Mathpal
Ahmad Taher Azar
Sundarapandian Vaidyanathan
Nashwa Ahmad Kamal
17.1 Introduction
425(3)
17.2 Problem formulation
428(1)
17.3 System description
429(3)
17.3.1 Chaotic attractor of the system
429(3)
17.3.2 Dissipation and existence of chaotic attractor
432(1)
17.3.3 Symmetry and invariance
432(1)
17.3.4 Poincare map
432(1)
17.4 Simulation results and discussions
432(10)
17.4.1 Switch 1
434(2)
17.4.2 Switch 2
436(3)
17.4.3 Switch 3
439(3)
17.5 Conclusion
442(1)
References
443(6)
18 A 5-D hyperchaotic dynamo system with multistability, its dynamical analysis, active backstepping control, and circuit simulation
Sundarapandian Vaidyanathan
Aceng Sambas
Ahmad Taher Azar
18.1 Introduction
449(1)
18.2 System model
450(3)
18.3 Dynamic analysis of the 5-D hyperchaotic dynamo model
453(2)
18.3.1 Rest points
453(1)
18.3.2 Multistability
454(1)
18.4 Active backstepping control for the global stabilization design of the new 5-D hyperchaotic dynamo system
455(3)
18.5 Active backstepping control for the global synchronization design of the new 5-D hyperchaotic dynamo systems
458(7)
18.6 Circuit simulation of the new 5D hyperchaotic system
465(2)
18.7 Conclusions
467(1)
References
468(5)
19 Design and implementation of a backstepping controller for nonholonomic two-wheeled inverted pendulum mobile robots
Gen'ichi Yasuda
19.1 Introduction
473(1)
19.2 Distributed controller design based on backstepping approach
474(3)
19.3 Discrete event modeling and control net representation
477(3)
19.4 Implementation issues on a multi-task processing architecture
480(3)
19.5 Conclusion
483(1)
References
483(2)
20 A novel chaotic system with a closed curve of four quarter-circles of equilibrium points: dynamics, active backstepping control, and electronic circuit implementation
Aceng Sambas
Sundarapandian Vaidyanathan
Sukono
Ahmad Taher Azar
Yuyun Hidayat
Cugun Cundara
Mohamad Afendee Mohamed
20.1 Introduction
485(2)
20.2 A new chaotic system with closed-curve equilibrium
487(2)
20.3 Dynamic analysis of the new chaotic system with a closed-curve equilibrium
489(3)
20.3.1 Lyapunov exponents analysis
489(1)
20.3.2 Multistability and coexisting attractors
489(3)
20.4 Active backstepping control for the global stabilization of the new chaos system with a closed-curve equilibrium
492(3)
20.5 Active backstepping control for the synchronization of the new chaos systems
495(4)
20.6 Circuit design for the new chaotic system with a closed-curve equilibrium
499(2)
20.7 Conclusions
501(2)
Acknowledgment
503(1)
References
503(6)
Index 509
0 Ahmad Azar is a Research Associate Professor at the Prince Sultan University, Riyadh, Kingdom Saudi Arabia. He is also an associate professor at the Faculty of Computers and Artificial intelligence, in Benha University, Egypt. He is the Editor in Chief of the International Journal of System Dynamics Applications (IJSDA), International Journal of Service Science, Management, Engineering, and Technology (IJSSMET), and International Journal of Intelligent Engineering Informatics (IJIEI), among others. He is currently Associate Editor of ISA Transactions, Elsevier, and the IEEE systems journal. Dr. Azar works in the areas of control theory & applications, process control, chaos control and synchronization, nonlinear control, renewable energy, computational intelligence.
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