Aneke N.P.I. Control of underactuated mechanical systems

Dissertation submitted for the degree of Doctor of Philosophy. — Technische Universiteit Eindhoven, 2003. — 177 p.The last decades have shown an increasing interest in the control of underactuated mechanical systems. These systems are characterized by the fact that there are more degrees of freedom than actuators, i.e., one or more degrees of freedom are unactuated. This class of mechanical systems are abundant in real life; examples of such systems include, but are not limited to, surface vessels, spacecraft, underwater vehicles, helicopters, road vehicles, mobile robots, space robots and underactuated manipulators. Underactuated mechanical systems generate interesting control problems which require fundamental nonlinear approaches.First-order nonholonomic constraints.
Second-order nonholonomic constraints.
Contributions of this thesis.
Outline of the thesis.
Problem formulation.
Second-order chained form transformations.
The feedback stabilization problem.
The tracking control problem.
Robustness considerations.Preliminaries.
Mathematical preliminaries.
Lyapunov stability.
Converse theorems.
Linear time-varying systems.
Perturbation theory.
Cascaded systems.
Homogeneous systems.Trajectory generation.
Problem formulation.
Controllability and stabilizability.
Constructive proof of controllability.
The flatness property.
The point to point steering problem.
A variational method.
A sub-optimal method.Tracking control.
Cascaded backstepping control.
Stability of the tracking-error dynamics.
Robustness considerations.Point stabilization.
Homogeneous feedback stabilization.
Robust stabilizers for the second-order chained form.Computer simulations.
The dynamic model.
The second-order chained form transformation.
Friction Compensation.
Tracking Control.
Feedback Stabilization.
Conclusions.
Experimental results.
Parameter identification.
Experiment with the Tracking Controller.
Experiment with the Homogeneous Stabilizing Controller.
A heuristic modification of the stabilizing controller.
Extension to practical point-to-point control.
Conclusions.
Conclusions and Recommendations.
Conclusions.
Recommendations.
Appendixes.
Stability result for cascaded systems.
Tracking control of the higher-dimensional chained form.
The underactuated H-Drive manipulator.Samenvatting.
Acknowledgements.
Curriculum Vitae.В работе рассматриваются различные задачи управления системами с пассивными степенями свободы. Математические выкладки иллюстрируются практическими примерами.