Modelling and energy based nonlinear control of crane lifters

A nonlinear dynamic model for a crane lifter system is derived using the Lagrangian method. The developed dynamic model has two inputs and four outputs. Several properties of the model such as passivity are presented. An energy based nonlinear control scheme is then proposed for the system. The developed scheme guarantees the asymptotic convergence of the trolley position and the hoist position to their desired values. However, the hoist and the load sway angles will either converge to zero or towards a stable trajectory. To ensure that the hoist and the load sway angles always converge to zero, a linear state feedback controller is used in conjunction with the nonlinear control scheme. The derived model and the control scheme are simulated using a digital computer; the simulation results illustrate the theoretical developments very well.