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Paper details
Number 4 - December 2018
Volume 28 - 2018
Interconnection and damping assignment passivity-based control of an underactuated 2-DOF gyroscope
Gustavo Cordero, Víctor Santibáñez, Alejandro Dzul, Jesús Sandoval
Abstract
In this paper we present interconnection and damping assignment passivity-based control (IDA-PBC) applied to a 2 degrees
of freedom (DOFs) underactuated gyroscope. First, the equations of motion of the complete system (3-DOF) are presented
in both Lagrangian and Hamiltonian formalisms. Moreover, the conditions to reduce the system from a 3-DOF to a 2-DOF gyroscope, by using Routh’s equations of motion, are shown. Next, the solutions of the partial differential equations
involved in getting the proper controller are presented using a reduction method to handle them as ordinary differential
equations. Besides, since the gyroscope has no potential energy, it presents the inconvenience that neither the desired
potential energy function nor the desired Hamiltonian function has an isolated minimum, both being only positive semidefinite functions; however, by focusing on an open-loop nonholonomic constraint, it is possible to get the Hamiltonian of the closed-loop system as a positive definite function. Then, the Lyapunov direct method is used, in order to assure stability. Finally, by invoking LaSalle’s theorem, we arrive at the asymptotic stability of the desired equilibrium point. Experiments with an underactuated gyroscopic mechanical system show the effectiveness of the proposed scheme.
Keywords
gyroscope device, gyroscopic forces, cyclic coordinates, generalized momenta, Routh’s equations, IDA-PBC