PID-like coupling control of underactuated overhead cranes with input constraints

A limited number of coupling-based works have been reported for stabilizing the overhead crane subject to both parametric uncertainty and input saturation. Particularly, integral action that attempts to reduce the steady-state error may fail with underactuated dynamics in the output. To mitigate these problems, this study sets a new Lyapunov function for the assignable equilibrium via an appropriate choice of tuning gains, and then produces a structurally simple controller with boundary. The proposed controller takes advantage of the coupled dissipation term and its integral action, thus achieving oscillation suppression and precision positioning regardless of input constraints and parametric uncertainties. The asymptotic stability is strictly ensured using LaSalle's invariant principle. Experiments reveal the efficiency and robustness of this method.