Robust energy shaping control of mechanical systems without solving PDEs and extension to constant speed tracking

Jose Guadalupe Romero (1) , Roméo Ortega (2) , Alejandro Donaire (3)

1 ITAM - Instituto Tecnológico Autónomo de México
2 L2S - Laboratoire des signaux et systèmes
3 UoN - University of Newcastle [Australia]

In a recent contribution, it was shown that a class of mechanical systems, which contains many practical examples, can be stabilized via energy shaping without solving partial differential equations. The proposed controller consists of two terms, a partial linearizing state-feedback and a linear PID loop around two new passive outputs. In this brief note we prove that the first, admittedly non-robust, step can be obviated leaving only the linear PID. A second contribution of the note is to propose a slight modification to the controller to go beyond regulation tasks-being able to follow ramp references in the actuated coordinates.

Domains: Automatic Control Engineering

Jose Guadalupe Romero, Roméo Ortega, Alejandro Donaire. Robust energy shaping control of mechanical systems without solving PDEs and extension to constant speed tracking. IEEE Transactions on Automatic Control, 2016, 61 (11), pp.3551-3556. ⟨10.1109/tac.2016.2521725⟩. ⟨hal-01633842⟩