A reduced-order crawler crane model with active control to attenuate the transient vibrations

Abstract

The nonlinear differential equations describing the motion of a crawler crane in a plane are formulated by applying Lagrange's equation to the system kinetic energy, potential energy and virtual work. The transient response of the crane system due to the vertical drop of the suspended load is simulated by numerically integrating the equations of motion.

The crane model includes the vertical translation and rotation of the crane body, the rotation of the boom, the stretch and pendulation of the load line, and two discrete boom displacements. The model includes the effects of tilting of the crane tracks, shortening of the boom length, and loss of tension in the elastic cables.

The model has been carefully developed to include the important effects which influence the crane system motion without loosing the simplicity which allows auxiliary control systems to be added with relative ease. A hydraulic valve-controlled piston actuator is adapted to the crawler crane pendent line to reduce the boom-tip excursions which excite the motion of the suspended load. Three proportional feedback compensation techniques, which detect the error between the desired crane state and the actual crane state, are used to describe the pendent actuator's valve position.

The transient response of the system generalized coordinates for both the uncompensated crane and the compensated crane is presented subject to three sets of initial conditions and crane configurations. One controller which measures the deflection at a single point in the crane boom is able to attenuate the entire crane system response due to a 7.6 cm vertical drop of the 13,600 Kg load with only 13 Kw of hydraulic source power.