Stabilization and set-point regulation of underactuated mechanical systems

13th International Conference on Motion and Vibration Control; 12th International Conference on Recent Advances in Structural Dynamics

Loccufier, Mia^1

Ghent University, Dept. Electrical Energy, Systems and Automation, Research Group DySC, Technologiepark Zwijnaarde 914, Zwijnaarde

9052, Belgium^1

关键词: Dissipation functions;    Dynamic output feedback;    Energy based approach;    Engineering applications;    Euler-Lagrange systems;    Number of degrees of freedom;    Static output feedback;    Under-actuated mechanical systems;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/744/1/012065/pdf
DOI  :  10.1088/1742-6596/744/1/012065

来源: IOP

【 摘 要 】

Mechanical systems are referred to as underactuated if the number of independent actuators are fewer than the number of degrees of freedom, a general encountered problem in engineering applications. The considered mechanical systems belong to the class of Euler- Lagrange systems where both kinetic energy and potential energy are modeled in their most general form and energy dissipation is modeled according to the dissipation function of Rayleigh, i.e. viscous damping forces are assumed. The control objectives are stabilization and set-point regulation. The structure of the controller is a parallel combination of static output feedback with dynamic output feedback where nonlinear amplifiers are included. An energy based approach with Liapunov functions and the Kalman-Yacubovich-Popov main lemma yields alternative stability theorems. A number of conditions are introduced with respect to the controller's structure in order to guarantee stability. However, sufficient design freedom is left to choose a proper tuning principle and obtain the specified control objectives such as fast convergence to a set-point combined with disturbance rejection. A restriction on the control input energy can be incorporated as well. The applicability of the method will be illustrated with planar manipulators. The main contribution is that a methodology is developed which incorporates many controllers and tuning facilities.