Vibration control of underactuated mechanical systems with non-linear Euler-Lagrange control

A non-linear Euler-Lagrange (EL) controller is proposed for underactuated mechanical Euler-Lagrange systems. The rationale is that mimicking the process structure in the controller will lead to improved performance. The tuning of the controller can be rather intuitive as it can be seen as an auxiliary mechanical system that is connected to the process, also called the main system. The tuning methodology used here finds its roots in the vibration absorber technology: transfer the energy from the main to the auxiliary system and dissipate the energy in the additional structure. Energy, in the form of the Hamiltonian, is used to examine stability of the compound system using Lyapunov's direct method. To evaluate the performance of the controller, the Hamiltonian of the main system is used. A planar manipulator with two and three degrees-of-freedom (DOF) shows the effectivity of the proposed tuning method.