Control of underactuated bridge cranes: A simplified IDA-PBC Approach

In this paper we present control of underactuated bridge cranes based on a simplified IDA-PBC (interconnection and damping assignment passivity based control) design. In that framework, without approximately decoupling or linearizing the complicated nonlinear model of bridge cranes, a control law is developed based on continuous-time kinetic and potential shaping by solving a set of PDEs(partial differential equations), also known as general matching conditions. The stability of the closed-loop system is proved by Lyapunov techniques and LaSalle's invariance principle. Some numerical simulation results are also provided to demonstrate the applicability of the proposed control scheme.