Stabilization of Mechanical Systems Using Controlled Lagrangians
Bloch, A. M., N. Leonard and J. E. Marsden
Proc. CDC, 36, 2356-2361
Abstract:
We propose an algorithmic approach to
stabilization of Lagrangian systems. The first step involves
making admissible modifications to the Lagrangian for the
uncontrolled system, thereby constructing what we call the controlled Lagrangian. The Euler-Lagrange equations derived from
the controlled Lagrangian describe the closed-loop system where
new terms are identified with control forces. Since the
controlled system is Lagrangian by construction, energy methods
can be used to find control gains that yield closed-loop
stability. The procedure is demonstrated for the problem of
stabilization of an inverted pendulum on a cart and for the
problem of stabilization of rotation of a rigid spacecraft about
its unstable intermediate axis using a single internal rotor.
Similar results hold for the dynamics of an underwater vehicle.