Loading crane plant model

The schematic diagram in Figure 17.14 shows the principle of a loading crane, which consists of a crab moving on rails. The load (freight) hangs on a rope from the crab

Figure 17.14: Schematic representation of the loading crane

such that the rope and load together can be treated as a pendulum. The load moves only in the plane that contains the direction of the rails. The force of the electrical drive, which moves the crab, is proportional to the control signal, fed into the drive system. The position of the crab and the rope (pendulum) angle are measured. The real manipulated variable to control the drive is limited to .

The plant dynamical behaviour can be described by the two coupled nonlinear differential equations

with the following parameters and variables of the crane:

The control task is to move the load from the initial position to the target position such that the load does not swing at the target position and the transition goes smoothly with a minimum of oscillations and no overshoot.