Tuning of Passivity-Based Controllers for Mechanical Systems

This article describes several approaches for tuning the parameters of a class of passivity-based controllers for standard nonlinear mechanical systems. In particular, we are interested in tuning controllers that preserve the mechanical system structure in the closed loop. To this end, first, we provide tuning rules for stabilization, i.e., the rate of convergence (exponential stability) and stability margin (input-to-state stability). Then, we provide guidelines to remove the overshoot. In addition, we propose a methodology to tune the gyroscopic-related parameters. We also provide remarks on the damping phenomenon to facilitate the practical implementation of our approaches. We conclude this article with experimental results obtained from applying our tuning rules to a fully actuated and an underactuated mechanical system.