Control of Gantry and Tower Cranes

The main objective of this work is to design robust, fast, and practical controllers for gantry and tower cranes. The controllers are designed to transfer the load from point to point as fast as possible and, at the same time, the load swing is kept small during the transfer process and completely vanishes at the load destination. Moreover, variations of the system parameters, such as the cable length and the load weight, are also included. Practical considerations, such as the control action power, and the maximum acceleration and velocity, are taken into account. In addition, friction effects are included in the design using a friction-compensation technique.

The designed controllers are based on two approaches. In the first approach, a gain-scheduling feedback controller is designed to move the load from point to point within one oscillation cycle without inducing large swings. The settling time of the system is taken to be equal to the period of oscillation of the load. This criterion enables calculation of the controller feedback gains for varying load weight and cable length. The position references for this controller are step functions. Moreover, the position and swing controllers are treated in a unified way. In the second approach, the transfer process and the swing control are separated in the controller design. This approach requires designing two controllers independently: an anti-swing controller and a tracking controller. The objective of the anti-swing controller is to reduce the load swing. The tracking controller is responsible for making the trolley follow a reference position trajectory. We use a PD-controller for tracking, while the anti-swing controller is designed using three different methods: (a) a classical PD controller, (b) two controllers based on a delayed-feedback technique, and (c) a fuzzy logic controller that maps the delayed-feedback controller performance.

To validate the designed controllers, an experimental setup was built. Although the designed controllers work perfectly in the computer simulations, the experimental results are unacceptable due to the high friction in the system. This friction deteriorates the system response by introducing time delay, high steady-state error in the trolley and tower positions, and high residual load swings. To overcome friction in the tower-crane model, we estimate the friction, then we apply an opposite control action to cancel it. To estimate the friction force, we assume a mathematical model and estimate the model coefficients using an off-line identification technique using the method of least squares.

With friction compensation, the experimental results are in good agreement with the computer simulations. The gain-scheduling controllers transfer the load smoothly without inducing an overshoot in the trolley position. Moreover, the load can be transferred in a time near to the optimal time with small swing angles during the transfer process. With full-state feedback, the crane can reach any position in the working environment without exceeding the system power capability by controlling the forward gain in the feedback loop. For large distances, we have to decrease this gain, which in turn slows the transfer process. Therefore, this approach is more suitable for short distances. The tracking-anti-swing control approach is usually associated with overshoots in the translational and rotational motions. These overshoots increase with an increase in the maximum acceleration of the trajectories . The transfer time is longer than that obtained with the first approach. However, the crane can follow any trajectory, which makes the controller cope with obstacles in the working environment. Also, we do not need to recalculate the feedback gains for each transfer distance as in the gain-scheduling feedback controller.