Closed-loop and constrained mechanical systems

SERGIO GRILLO; FELIX MACIEL; DIEGO PÉREZ

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS

WORLD SCIENTIFIC PUBL CO PTE LTD

Año: 2010 p. 857 - 886

0219-8878

The relationship between closed-loop mechanical systems (CLMS) and higher order constrained systems (HOCS) is studied. We show that second order constraints, i.e. constraints in acceleration, can be used to construct a CLMS, where control law is given by the related constraint force. As an example we show that, by means of appropriate constraints of this kind, stabilization can be achieved for the inertia wheel pendulum. We also consider the inverse problem, that is to say: can every CLMS be constructed form a HOCS, i.e. can every control law be seen as the constraint force related to a given set of constraints? We answer affirmatively this question, reflecting a deep connection between feedback systems and systems with constraints. Also, we study when these constraints can be integrated to constraints in velocities. We prove that this is possible for CLMSs constructed by means of linear methods and also by some global ones, as the kinetic shaping method with symmetry.