Energy-based Hamiltonian approach in <i>H</i>_∞ controller design for <i>n</i>-degree of freedom mechanical systems

Abstract

This paper studies the energy-based approach for ${H_\infty } $ controller design of $n $-degree of freedom mechanical systems. In this approach, the Hamiltonian function, which is the sum of kinetic and potential energies of the system, is considered as the Lyapunov function for stability analysis. The stability analysis is done based on the port-controlled Hamiltonian (PCH) model. In this regard, two theorems are given and proved that the proposed controllers lead to ${H_\infty } $ disturbance attenuation for both absolutely known system model and unknown ones with parametric uncertainties. In the case of parametric uncertainties, the energy-based controller has an adaptive approach. Performance of proposed controllers is illustrated through simulations taken on a 2-link robot manipulator system, which validate the theoretical achievements of this paper.