13. Stabilization of a ball on a curvilinear beam

Chapters in this book

1. Frontmatter I
2. Contents V
3. Preface to English Edition IX
4. Preface XI
5. Part I: Devices containing a single-link pendulum
6. 1. A pendulum with stationary pivot 5
7. 2. A pendulum with wheel-based pivot 21
8. 3. A pendulum with a flywheel 31
9. 4. Wheel rolling control by means of a pendulum 50
10. 5. Optimal swinging and damping of a swing 58
11. 6. Pendulum control that minimizes energy consumption 71
12. Part II: Double physical pendulum
13. 7. Local stabilization of an inverted pendulum by means of a single control torque 91
14. 8. Optimal control design for swinging and damping a double pendulum 110
15. 9. Global stabilization of an inverted pendulum controlled by torque in the inter-link joint 126
16. 10. Global stabilization of an inverted pendulum controlled by torque in the pivot 134
17. 11. Multi-link pendulum on a moving base 145
18. Part III: Ball on a beam
19. 12. Stabilization of a ball on a straight beam 165
20. 13. Stabilization of a ball on a curvilinear beam 176
21. Part IV: Gyroscopic stabilization of a two-wheel bicycle
22. 14. Bicycle design 189
23. 15. Designing a control law to stabilize the bicycle tilt 198
24. Part V: Avoiding undesired vibrations
25. 16. Bang-bang control and fluent control 209
26. 17. Trapezoidal control for a system with compliant elements 217
27. Bibliography 229
28. Index 237