Tuning rules for energy-based control methods for mechanical systems

This thesis describes several approaches for tuning the parameters of a class of passivity-based controllers for standard nonlinear mechanical systems. Particularly, we are interested in tuning controllers that preserve the mechanical system structure in the closed loop. Among these controllers, we find the well-established interconnection and damping assignment passivity-based control, the most general passivity-based control scheme that generates asymptotically stabilizing controllers for any system that can be represented in the port-Hamiltonian framework. Towards this end, first, we provide tuning rules obtained from the stabilization analysis (exponential stability and input-to-state analysis), i.e., the rate of convergence, maximum overshoot, and stability margin. Then, we linearize the system under study, which analysis leads to a set of tuning rules that prescribes the transient response behaviour in terms of performance indices such as damping ratio, rise time, or removing the overshoot. Additionally, we propose a tuning methodology to tune the gyroscopic-related parameters.
Furthermore, additional passivity-based control strategies that deal with different types of disturbances are proposed along with their associated tuning rules.
We also provide remarks on the damping phenomenon to facilitate the practical implementation of our approaches.
Moreover, all tuning rules are validated experimentally via fully-actuated and underactuated mechanical setups.