177 research outputs found
On the Method of Interconnection and Damping Assignment Passivity-Based Control for the Stabilization of Mechanical Systems
Interconnection and damping assignment passivity-based control (IDA-PBC) is
an excellent method to stabilize mechanical systems in the Hamiltonian
formalism. In this paper, several improvements are made on the IDA-PBC method.
The skew-symmetric interconnection submatrix in the conventional form of
IDA-PBC is shown to have some redundancy for systems with the number of degrees
of freedom greater than two, containing unnecessary components that do not
contribute to the dynamics. To completely remove this redundancy, the use of
quadratic gyroscopic forces is proposed in place of the skew-symmetric
interconnection submatrix. Reduction of the number of matching partial
differential equations in IDA-PBC and simplification of the structure of the
matching partial differential equations are achieved by eliminating the
gyroscopic force from the matching partial differential equations. In addition,
easily verifiable criteria are provided for Lyapunov/exponential
stabilizability by IDA-PBC for all linear controlled Hamiltonian systems with
arbitrary degrees of underactuation and for all nonlinear controlled
Hamiltonian systems with one degree of underactuation. A general design
procedure for IDA-PBC is given and illustrated with examples. The duality of
the new IDA-PBC method to the method of controlled Lagrangians is discussed.
This paper renders the IDA-PBC method as powerful as the controlled Lagrangian
method
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
Reduction of Controlled Lagrangian and Hamiltonian Systems with Symmetry
We develop reduction theory for controlled Lagrangian and controlled Hamiltonian systems with symmetry. Reduction theory for these systems is needed in a variety of examples, such as a spacecraft with rotors, a heavy top with rotors, and underwater vehicle dynamics. One of our main results shows the equivalence of the method of reduced controlled Lagrangian systems and that of reduced controlled Hamiltonian systems in the case of simple mechanical systems with symmetry
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