Stabilisation and Motion Control of Unstable Objects

Systems with mechanical degrees of freedom containing unstable objects are analysed in this monograph and algorithms for their control are developed, discussed, and numerically tested. This is achieved by identifying unstable modes of motion and using all available resources to suppress them. By using this approach the region of states from which a stable regime can be reached is maximised.

The systems discussed in this book are models for pendula and vehicles and find applications in mechatronics, robotics as well as in mechanical and automotive engineering.

Autorentext

Alexander Formalskii, Lomonosov State University, Moscow, Russia.

Inhalt

Preface
Chapter 1. Devices Containing One-Link Pendulum
§ 1. Physical pendulum with fixed suspension point

1. Motion equations
2. Controllability domain
3. Maximization of attraction domain
4. Delay in feedback loop
5. Nonlinear control
6. Controllability domain for nonlinear model
   § 2. Pendulum with suspension point located at the center of a wheel
7. Motion equations
8. Controllability domain
9. Maximization of attraction domain
10. Nonlinear control
    § 3. Pendulum with flywheel
11. Design of the pendulum with flywheel
12. Motion equations
13. Local stabilization of the pendulum in the upper unstable equilibrium
14. Damping of the flywheel angular speed
15. Rocking and damping of the pendulum
16. Transferring the pendulum from the lower equilibrium to the upper one
17. Numerical study
18. Experiments
    § 4. Wheel rolling control using a pendulum
19. Mathematical model of the device
20. Steady motions
21. Stability of steady motions
    § 5. Optimal rocking and damping of the swing
22. On design of optimal feedback control for second-order systems
23. Mathematical model of the swing
24. Maximization of the swing amplitude
25. Minimization of the swing amplitude
26. Control of the swing with consideration of aerodynamic resistance and dry friction
    § 6. Pendulum control with minimal energy cost
27. Energy cost estimation
28. Transferring the pendulum to the unstable equilibrium
29. Transferring the pendulum to the stable equilibrium
    Chapter 2. Two-link Physical Pendulum
    § 7. Local stabilization of inverted pendulum with one control torque
30. Mathematical model of the pendulum
31. Linearized model
32. Controllability domains
33. Feedback control design, maximization of the attraction domain
34. Numerical study
    § 8. Optimal control design of two-link pendulum rocking and damping
35. Mathematical model
36. Reduced angle
37. Optimal control for rocking the pendulum
38. Optimal control for damping the pendulum
39. On transferring the pendulum from the lower equilibrium to the upper one
    § 9. Global stabilization of inverted pendulum with control applied at the hinge between links
40. Mathematical model
41. Cascade form of dynamics equations
42. Control for rocking the pendulum
43. Tracking of desired inter-link angle variation
44. Local stabilization of the inverted pendulum
45. Numerical study
    § 10. Global stabilization of the inverted pendulum with control applied at the suspension point
46. Mathematical model
47. Pendulum rocking
48. Straightening of the pendulum
49. Linear model, local stabilization
50. Numerical study
    § 11. Multilink pendulum on a movable base
51. Multilink pendulum on a wheel
52. One-link pendulum on a wheel
53. Global stabilization of inverted pendulum
54. Controllability domain
55. Design of time-optimal trajectories
56. Pendulum on a cart
57. Decrease of frequencies under imposed constraint
    Chapter 3. Ball on a Beam
    § 12. Stabilization of a ball on a rectilinear beam
58. Mathematical model of the system
59. Linearized model
60. Feedback control synthesis
61. Numerical study
    § 13. Stabilization of a ball on a circular beam
62. Mathematical model
63. Linearized model
64. Feedback control
65. Numerical study
    Chapter 4. Gyroscopic Stabilization of Robot-Bicycle
    § 14. Designs of two bicycle types
66. Bicycle with one steering wheel
67. Bicycle with two steering wheels
68. Gyroscopic stabilizer
69. Equations of bicycle roll oscillations
    § 15. Control law for stabilizing bicycle in the upright position
70. Measurement of bicycle roll angle with accelerometers
71. Bicycle motion along a straight line
72. Bicycle motion along a circular line
73. Numerical and experimental study
    References