Shaping the energy of mechanical systems without solving partial differential equations

Alejandro Donaire (1) , Rachit Mehra (2) , Roméo Ortega (3) , Sumeet Satpute (2) , Jose Guadalupe Romero (3) , Faruk Kazi (2) , Navdeep Singh (2)

1 UoN - University of Newcastle [Callaghan, Australia]
2 VJTI - Veermata Jijabai Technological Institute
3 L2S - Laboratoire des signaux et systèmes

Control of underactuated mechanical systems via energy shaping is a well-established, robust design technique. Unfortunately, its application is often stymied by the need to solve partial differential equations (PDEs). In this paper a new, fully constructive, procedure to shape the energy for a class of mechanical systems that obviates the solution of PDEs is proposed. The control law consists of a first stage of partial feedback linearization followed by a simple proportional plus integral controller acting on two new passive outputs. The class of systems for which the procedure is applicable is identified imposing some (directly verifiable) conditions on the systems inertia matrix and its potential energy function. It is shown that these conditions are satisfied by three benchmark examples.

Domaines: Automatique

Alejandro Donaire, Rachit Mehra, Roméo Ortega, Sumeet Satpute, Jose Guadalupe Romero, et al.. Shaping the energy of mechanical systems without solving partial differential equations. IEEE Transactions on Automatic Control, 2016, 61 (04), pp.1051-1056. ⟨10.1109/ACC.2015.7170921⟩. ⟨hal-01632603⟩