Cooperative control of a nonuniform gantry crane with constrained tension

In this paper, the control problem is addressed for a hybrid PDE-ODE system that describes a nonuniform gantry crane system with constrained tension. A bottom payload hangs from the top gantry by connecting a flexible cable. The flexible cable is nonuniform due to the spatiotemporally varying tension applied to the system. The control objectives are: (i) to position the payload to the desired setpoint, (ii) to regulate the transverse deflection of the flexible cable, and (iii) to keep the tension values remaining in the constrained space. Cooperative control laws are proposed and the integral-barrier Lyapunov functions are employed for stability analysis of the closed-loop system. Adaption laws are developed for handling parametric uncertainties. The bounded stability is guaranteed through rigorous analysis without any simplification of the dynamics. In the end, numerical simulations are displayed to illustrate the performance of the proposed cooperative control.