  In this paper, we propose several rules to tune the gains for a class of
passivity-based controllers for nonlinear mechanical systems. Such tuning rules
prescribe a desired local transient response behavior to the closed-loop
system. To establish the tuning rules, we implement a PID passivity-based
controller. Then, we linearize the closed-loop system, and we transform the
matrix of the resulting system into a class of saddle point matrices to analyze
the influence of the control gains, in terms of the oscillations and the rise
time, on the transient response of the closed-loop system. Hence, the resulting
controllers stabilize the plant and simultaneously address the performance of
the closed-loop system. Moreover, our analysis provides a clear insight into
how the kinetic energy, the potential energy, and the damping of the mechanical
system are related to its transient response, endowing in this way the tuning
rules with a physical interpretation. Additionally, we corroborate the
analytical results through the practical implementation of a controller that
stabilizes a two degrees-of-freedom (DoF) planar manipulator, where the control
gains are tuned following the proposed rules.

Systems and Control;Systems and Control