16 research outputs found
Stabilization of the pendulum on a rotor arm by the method of controlled Lagrangians
Obtains feedback stabilization of an inverted pendulum on a rotor arm by the “method of controlled Lagrangians”. This approach involves modifying the Lagrangian for the uncontrolled system so that the Euler-Lagrange equations derived from the modified or “controlled” Lagrangian describe the closed-loop system. For the closed-loop equations to be consistent with available control inputs, the modifications to the Lagrangian must satisfy “matching” conditions. The pendulum on a rotor arm requires an interesting generalization of our earlier approach which was used for systems such as a pendulum on a cart
Asymptotic stabilization of the heavy top using controlled Lagrangians
In this paper we extend the previous work on the
asymptotic stabilization of pure Euler-Poincaré mechanical
systems using controlled Lagrangians to the
study of asymptotic stabilization of Euler-Poincaré mechanical
systems such as the heavy top
Asymptotic stabilization of Euler-Poincaré mechanical systems
Stabilization of mechanical control systems by the method of controlled Lagrangians
and matching is used to analyze asymptotic stabilization of systems whose
underlying dynamics are governed by the Euler-Poincar´e equations. In particular, we
analyze asymptotic stabilization of a satellite
Potential shaping and the method of controlled Lagrangians
We extend the method of controlled Lagrangians to include potential shaping for complete state-space stabilization of mechanical systems. The method of controlled Lagrangians deals with mechanical systems with symmetry and provides symmetry-preserving kinetic shaping and feedback-controlled dissipation for state-space stabilization in all but the symmetry variables. Potential shaping complements the kinetic shaping by breaking symmetry and stabilizing the remaining state variables. The approach also extends the method of controlled Lagrangians to include a class of mechanical systems without symmetry such as the inverted pendulum on a cart that travels along an incline
Potential and kinetic shaping for control of underactuated mechanical systems
This paper combines techniques of potential shaping
with those of kinetic shaping to produce some new
methods for stabilization of mechanical control systems.
As with each of the techniques themselves, our method
employs energy methods and the LaSalle invariance
principle. We give explicit criteria for asymptotic stabilization
of equilibria of mechanical systems which, in
the absence of controls, have a kinetic energy function
that is invariant under an Abelian group
Controlled Lagrangians and the stabilization of mechanical systems. II. Potential shaping
For pt.I, see ibid., vol.45, p.2253-70 (2000). We extend the method of controlled Lagrangians (CL) to include potential shaping, which achieves complete state-space asymptotic stabilization of mechanical systems. The CL method deals with mechanical systems with symmetry and provides symmetry-preserving kinetic shaping and feedback-controlled dissipation for state-space stabilization in all but the symmetry variables. Potential shaping complements the kinetic shaping by breaking symmetry and stabilizing the remaining state variables. The approach also extends the method of controlled Lagrangians to include a class of mechanical systems without symmetry such as the inverted pendulum on a cart that travels along an incline