Tuning of passivity-based controllers for mechanical systems

TL;DR

This paper presents methods for tuning passivity-based controllers in nonlinear mechanical systems, focusing on stability, overshoot reduction, and gyroscopic parameter tuning, supported by experimental validation.

Contribution

It introduces new tuning rules for stability, overshoot, rise time, and gyroscopic parameters in passivity-based controllers for mechanical systems.

Findings

Effective tuning rules for exponential stability and input-to-state stability.

Guidelines for overshoot removal and rise time control.

Experimental validation on underactuated and fully-actuated systems.

Abstract

This manuscript describes several approaches to tune the parameters of a class of passivity-based controllers for standard nonlinear mechanical systems. In particular, we are interested in controllers that preserve the mechanical system structure in 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 while prescribing the rise time. Additionally, we propose a methodology to tune the gyroscopic-related parameters. We also provide remarks on the damping phenomena to facilitate the practical implementation of our approaches. We conclude this paper with experimental results obtained from applying our tuning rules to an underactuated and a fully-actuated mechanical configuration.