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E-raamat: Block Backstepping Design of Nonlinear State Feedback Control Law for Underactuated Mechanical Systems

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  • Formaat: PDF+DRM
  • Ilmumisaeg: 08-Sep-2016
  • Kirjastus: Springer Verlag, Singapore
  • Keel: eng
  • ISBN-13: 9789811019562
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Block Backstepping Design of Nonlinear State Feedback Control Law for Underactuated Mechanical SystemsSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 08-Sep-2016
  • Kirjastus: Springer Verlag, Singapore
  • Keel: eng
  • ISBN-13: 9789811019562
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This book presents a novel, generalized approach to the design of nonlinear state feedback control laws for a large class of underactuated mechanical systems based on application of the block backstepping method. The control law proposed here is robust against the effects of model uncertainty in dynamic and steady-state performance and addresses the issue of asymptotic stabilization for the class of underactuated mechanical systems. 

An underactuated system is defined as one for which the dimension of space spanned by the configuration vector is greater than that of the space spanned by the control variables. Control problems concerning underactuated systems currently represent an active field of research due to their broad range of applications in robotics, aerospace, and marine contexts.
 
The book derives a generalized theory of block backstepping control design for underactuated mechanical systems, and examines several case studies that cover interesting examples of underactuated mechanical systems. The mathematical derivations are described using well-known notations and simple algebra, without the need for any special previous background in higher mathematics. The chapters are lucidly described in a systematic manner, starting with control system preliminaries and moving on to a generalized description of the block backstepping method, before turning to several case studies. Simulation and experimental results are also provided to aid in reader comprehension.
1 Introduction
1(10)
1.1 Underactuated Mechanical System
1(2)
1.2 Brief State-of-the-Art on the UMSs Control
3(4)
1.2.1 Linear Control Approaches
3(1)
1.2.2 Nonlinear Control: Present Day Approaches
4(2)
1.2.3 Block Backstepping Approach
6(1)
1.3 Motivations of Designing an Advanced Control Law
7(3)
1.4 Outline of the Book
10(1)
2 Theoretical Preliminaries
11(20)
2.1 Feedback Linearization
11(10)
2.1.1 Input-State Feedback Linearization
11(3)
2.1.2 Output Feedback Linearization
14(3)
2.1.3 Partial Feedback Linearization
17(4)
2.2 Control Lyapunov Function
21(2)
2.3 Integrator Backstepping
23(5)
2.4 Block Backstepping Design
28(2)
2.5 Notes
30(1)
References
30(1)
3 Block Backstepping Control of the Underactuated Mechanical Systems
31(22)
3.1 Formulation of Generalized Block Backstepping Control Law for Underactuated Systems with Two Degrees of Freedom (2-DOF)
32(7)
3.1.1 Problem Formulation
32(1)
3.1.2 Derivation of the Control Algorithm for 2-DOF Underactuated Mechanical Systems
33(4)
3.1.3 Zero Dynamics Analysis of 2-DOF Underactuated Mechanical System
37(2)
3.2 Formulation of Generalized Block Backstepping Control Law for Underactuated Systems with N Degrees of Freedom
39(9)
3.2.1 Problem Formulation
39(1)
3.2.2 Derivation of the Control Law for n-DOF Underactuated Mechanical Systems
40(6)
3.2.3 Zero Dynamics Analysis of n-DOF Underactuated Mechanical System
46(2)
3.3 Analysis of Global Diffeomorphism of the Control Law
48(1)
3.4 Stability Analysis of the Proposed Controller
49(2)
3.5 Notes
51(2)
References
52(1)
4 Applications of the Block Backstepping Algorithm on 2-DOF Underactuated Mechanical Systems: Some Case Studies
53(56)
4.1 Application on the Inertia Wheel Pendulum
54(8)
4.1.1 Derivation of the Control Law for Inertia Wheel Pendulum
55(3)
4.1.2 Simulation Results and Performance Analysis
58(4)
4.2 Application on the TORA System
62(7)
4.2.1 Derivation of the Control Law for TORA System
63(3)
4.2.2 Simulation Results and Performance Analysis
66(3)
4.3 Application on the Furuta Pendulum
69(8)
4.3.1 Derivation of the Control Law for Furuta Pendulum System
71(3)
4.3.2 Simulation Results and Performance Analysis
74(3)
4.4 Application on the Acrobot System
77(7)
4.4.1 Derivation of the Control Law for Acrobot System
78(3)
4.4.2 Simulation Results and Performance Analysis
81(3)
4.5 Application on the Pendubot System
84(7)
4.5.1 Derivation of the Control Law for Pendubot System
86(3)
4.5.2 Simulation Results and Performance Analysis
89(2)
4.6 Application on the Inverted Pendulum
91(8)
4.6.1 Derivation of the Control Law for Inverted Pendulum
93(3)
4.6.2 Results Obtained from Real-Time Experiments
96(3)
4.7 Application on the Single Dimension Granty Crane
99(6)
4.7.1 Derivation of the Control Law for Granty Crane System
100(3)
4.7.2 Results Obtained from Real-Time Experiments
103(2)
4.8 Notes
105(4)
References
106(3)
5 Applications of the Block Backstepping Algorithm on Underactuated Mechanical Systems with Higher Degrees of Freedom: Some Case Studies
109(36)
5.1 Application on the VTOL
110(10)
5.1.1 Derivation of the Control Law for VTOL
112(5)
5.1.2 Simulation Results and Performance Analysis
117(3)
5.2 Application on the USV
120(12)
5.2.1 Derivation of the Control Law for USV
122(5)
5.2.2 Simulation Results and Performance Analysis
127(5)
5.3 Application on Three Degree of Freedom Redundant Manipulator
132(10)
5.3.1 Derivation of the Control Law for 3-DOF Robotic Manipulator
133(6)
5.3.2 Simulation Results and Performance Analysis
139(3)
5.4 Notes
142(3)
References
143(2)
6 Challenges and New Frontiers in the Field of Underactuated Mechanical Systems Control
145(10)
6.1 Different Aspects of the Proposed Control Law
145(2)
6.2 Major Inferences
147(1)
6.3 Scope of the Future Work
147(3)
6.3.1 Robust Adaptive Block Backstepping Design for Underactuated Mechanical Systems
148(1)
6.3.2 Industrial Needs
149(1)
6.3.3 High-DOF Complex UMS
149(1)
6.3.4 Fault Tolerant Deduction and Control
150(1)
6.3.5 Networked UMS
150(1)
6.4 Notes
150(5)
References
151(4)
Appendix: Modeling of Different Underactuated Mechanical Systems 155
Dr. Shubhobrata Rudra received his Bachelors degree in Electrical Engineering in 2007 from West Bengal University of Technology, India, and Master of Electrical Engineering in 2010 and Ph.D. in Electrical Engineering 2015 from Jadavpur University, India. He has secured the University gold medal for standing first in the order of merit at the Master of Engineering examination. He pursued his doctoral research with Inspire Fellowship, awarded by the Department of Science and Technology (Govt. of India). He has published a few research articles in reputed international journals and presented several papers in different international conferences. His fields of interest include nonlinear control engineering, underactuated mechanical systems and motion control systems. Dr. Ranjit Kumar Barai graduated in Bachelor of Electrical Engineering in 1993 and Master of Electrical Engineering in 1995 from Jadavpur University, India, and Ph.D. in Artificial Systems Science in 2007 from Chiba University, Japan. He has more than 20 years of working experience in industry, research and teaching at graduate and postgraduate levels. He has supervised several masters and Ph.D. theses in the areas of mechatronics, robotics and control systems. His research interests include mechatronics, robotics, control systems, machine learning and soft-computing, modelling and system identification, and real-time systems. Prof. Madhubanti Maitra graduated in Bachelor of Electrical Engineering in 1989, Master of Electrical Engineering in 1991 and Ph.D. in Electrical Engineering in 2005 from Jadavpur University, India. She has more than 25 years of working experience in research and teaching at graduate and postgraduate levels. She has supervised several masters and Ph.D. theses in the areas of mobile communication, robotics and control systems. Her research interests include mobile communication, robotics, control systems, machine learning and softcomputing, modelling and system identification, and real-time systems.
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