Safety-constrained position tracking of a flexible transmission system

We consider safety-constrained position tracking for a flexible transmission system consisting of a torsional shaft driven by a motor and connected to a gravitationally loaded inertia. The coupled PDE-ODE dynamics admit a semilinear formulation in which the linear input-output system is impedance passive and the gravitational torque enters as a bounded, globally Lipschitz perturbation. We establish an energy dissipation inequality for the nonlinear model and show that a position-funnel controller with supervised damping admits a unique global closed-loop trajectory. In particular, the motor-angle tracking error remains strictly inside a prescribed time-varying funnel, which can be chosen to enforce safety bounds on the motor angle.