Model-based tracking control of nonlinear systems

Model-Based Control of Nonlinear Systems presents model-based control techniques for nonlinear, constrained systems. It covers constructive control design methods with an emphasis on modeling constrained systems, generating dynamic control models, and designing tracking control algorithms for the models.

The book's interdisciplinary approach illustrates how system modeling and control theory are essential to control design projects. Organized according to the steps in a control design project, the text first discusses kinematic and dynamic modeling methods, including programmed constraints, Lagrange's equations, Boltzmann−Hamel equations, and generalized programmed motion equations. The next chapter describes basic control concepts and the use of nonlinear control theory. After exploring stabilization strategies for nonlinear systems, the author presents existing model-based tracking control algorithms and path-following strategies for nonlinear systems. The final chapter develops a new model reference tracking strategy for programmed motion.

Throughout the text, two examples of mechanical systems are used to illustrate the theory and simulation results. The first example is a unicycle model (nonholonomic system) and the second is a two-link planar manipulator model (holonomic system). With a focus on constructive modeling and control methods, this book provides the tools and techniques to support the control design process.

Author Notes

Elżbieta Jarzębowska is an associate professor in the Institute of Aeronautics and Applied Mechanics at the Warsaw University of Technology. She is a member of ASME, IEEE, GAMM, IFToMM Technical Committee of Mechatronics, and International SAR. Her research and teaching interests encompass dynamics modeling and analysis of multibody systems, nonlinear control of multibody systems, and geometric control theory.

Preface	p. xi
The Author	p. xiii
1 Introduction	p. 1
1.1 Scope and Outline	p. 3
1.2 Mechanics and Nonlinear Control	p. 6
1.3 Role of Modeling in a Control Design Process	p. 20
References	p. 21
2 Dynamics Modeling of Constrained Systems	p. 25
2.1 Introduction-Art of Modeling	p. 25
2.1.1 Selection of Coordinates	p. 26
2.1.2 Generalized Velocities and Quasi-Velocities	p. 29
2.2 Constrained Systems	p. 31
2.2.1 Holonomic Constraints	p. 32
2.2.2 Nonholonomic Constraints	p. 33
2.2.3 Programmed Constraints	p. 35
2.3 Equations of Motion for Systems with First Order Constraints	p. 37
2.3.1 D'Alembert Principle	p. 38
2.3.2 Lagrange's Equations for Holonomic Systems	p. 45
2.3.3 Lagrange's Equations for First Order Nonholonomic Systems	p. 50
2.3.4 Maggi's Equations	p. 52
2.3.5 Nielsen's Equations	p. 55
2.3.6 Equations of Motion in Quasi-Coordinates	p. 58
2.4 Equations of Motion for Systems with High Order Constraints	p. 67
2.4.1 An Extended Concept of Constraints-Programmed Constraints	p. 67
2.4.2 Generalized Programmed Motion Equations Specified in Generalized Coordinates	p. 76
2.4.3 Generalized Programmed Motion Equations Specified in Quasi-Coordinates	p. 88
Problems	p. 94
References	p. 94
3 Introduction to Nonlinear Control Theory	p. 99
3.1 Stability Properties of Nonlinear Systems	p. 99
3.1.1 State-Space Representation of Nonlinear Systems	p. 99
3.1.2 Stability Theorems of the Lyapunov Direct Method	p. 101
3.1.3 Special Formulations of Stability Theorems	p. 103
3.2 Classification of Control Problems	p. 111
3.2.1 Stabilization	p. 112
3.2.2 Trajectory and Morion Tracking	p. 115
3.2.3 Path Following	p. 117
3.3 Control Properties of Nordinear Systems	p. 118
3.3.1 Classification of Constrained Control Systems	p. 118
3.3.2 Accessibility and Controllability	p. 122
3.3.3 Stabilizability	p. 131
3.3.4 Differential Flatness	p. 135
3.4 Kinematic Control Models	p. 136
3.5 Dynamic Control Models	p. 144
3.6 Feedback Linearization of Nonlinear Systems	p. 147
3.7 Model-Based Control Design Methods	p. 152
3.8 Flatness-Based Control Design Methods	p. 155
3.8.1 Basic Notions of Equivalence and Flatness	p. 155
3.8.2 Flatness in Control Applications	p. 159
3.8.3 Flatness-Based Control Design-Examples	p. 161
3.8.4 Concluding Remarks-Verifying Flatness	p. 167
3.9 Other Control Design Techniques for Nonlinear Systems	p. 167
3.9.1 Backstepping	p. 169
3.9.2 Sliding Mode Control	p. 173
Problems	p. 175
References	p. 176
4 Stabilization Strategies for Nonlinear Systems	p. 183
Problems	p. 189
References	p. 189
5 Model-Based Tracking Control of Nonlinear Systems	p. 191
5.1 A Unified Control-Oriented Model for Constrained Systems	p. 191
5.2 Tracking Control of Holonomic Systems	p. 196
5.3 Tracking Control of First Order Nonholonomic Systems	p. 200
5.4 Tracking Control of Underactuated Systems	p. 206
5.5 Tracking Control Algorithms Specified in Quasi-Coordinates	p. 212
Problems	p. 222
References	p. 222
6 Path Following Strategies for Nonlinear Systems	p. 225
6.1 Path Following Strategies Based on Kinematic Control Models	p. 226
6.2 Path Following Strategies Based on Dynamic Control Models	p. 229
Problems	p. 231
References	p. 231
7 Model Reference Tracking Control of High Order Nonholonomic Systems	p. 233
7.1 Model Reference Tracking Control Strategy for Programmed Motion	p. 234
7.1.1 A Reference Dynamic Model for Programmed Motion	p. 234
7.1.2 Architecture of the Model Reference Tracking Control Strategy for Programmed Motion	p. 235
7.1.3 A Controller Design for Programmed Motion Tracking	p. 237
7.2 Non-Adaptive Tracking Control Algorithms for Programmed Motions	p. 240
7.2.1 Programmed Motion Tracking for a Unicycle	p. 240
7.2.2 Programmed Motion Tracking for a Planar Manipulator	p. 242
7.2.3 Programmed Motion Tracking for a Two-Wheeled Mobile Robot	p. 246
7.3 Adaptive Tracking Control Algorithms for Programmed Motions	p. 249
7.3.1 Adaptive Programmed Motion Tracking for a Planar Manipulator	p. 250
7.3.2 Adaptive Programmed Motion Tracking for a Unicycle	p. 254
7.4 Learning Tracking Control Algorithms for Programmed Motions	p. 258
7.5 Tracking Control Algorithms for Programmed Motions Specified in Quasi-Coordinates	p. 261
7.5.1 Tracking Control of the Unicycle Model Specified in Quasi-Coordinates	p. 262
7.5.2 Tracking Control of the Planar Manipulator Model Specified in Quasi-Coordinates	p. 262
7.6 Tracking Control Algorithms for Programmed Motions with the Velocity Observer	p. 264
7.7 Other Applications of the Model Reference Tracking Control Strategy for Programmed Motion	p. 270
7.7.1 Hybrid Programmed Motion-Force Tracking	p. 270
7.7.2 Application of a Kinematic Model as a Reference Model for Programmed Motions	p. 277
7.7.3 Robot Formation Control	p. 281
Problems	p. 290
References	p. 290
8 Concluding Remarks	p. 293
Index	p. 297

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