In this note, we address the problem of stabilization of port-Hamiltonian systems via the ubiquitous proportional-integral-derivative (PID) controller. The design is based on passivity theory, hence the first step is to identify all passive outputs of the system, which is the first contribution of the paper. Adding a PID around this signal ensures that the closed-loop system is L ₂ -stable for all positive PID gains. Global stability (and/or global attractivity) of a desired constant equilibrium is also guaranteed for a new class of systems for which a Lyapunov function can be constructed. A second contribution is to prove that this class-that is identified via some easily verifiable integrability conditions-is strictly larger than the ones previously reported in the literature. Comparisons of the proposed PID controller with control-by-interconnection passivity-based control are also discussed.

This work concerns the application of physics‐informed neural networks to the modeling and control of complex robotic systems. Achieving this goal requires extending physics‐informed neural networks to handle nonconservative effects. These learned models are proposed to combine with model‐based controllers originally developed with first‐principle models in mind. By combining standard and new techniques, precise control performance can be achieved while proving theoretical stability bounds. These validations include real‐world experiments of motion prediction with a soft robot and trajectory tracking with a Franka Emika Panda manipulator.

In this paper, we present some new results for the design of PID passivity-based controllers (PBCs) for the regulation of port-Hamiltonian (pH) systems. The main contributions are: (i) new algebraic conditions for the explicit solution of the partial differential equation required in this design; (ii) revealing the deleterious impact of the dissipation obstacle that limits the application of the standard PID-PBC to systems without pervasive dissipation; (iii) the proposal of a new PID-PBC which is generated by two passive outputs, one with relative degree zero and the other with relative degree one. The first output ensures that the PID-PBC is not hindered by the dissipation obstacle, while the relative degree of the second passive output allows the inclusion of a derivative term. Making the procedure more constructive and removing the requirement on the dissipation significantly extends the realm of application of PID-PBC. Moreover, allowing the possibility of adding a derivative term to the control, enhances its transient performance.