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Gain Scheduling Feedback Control of Tower Cranes with Friction Compensation

We have designed a controller based on gain-scheduling feedback to move a load from point to point within one oscillation cycle and 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 us to calculate the controller feedback gains for varying load weight and cable length. First, we designed the controller for gantry cranes and then extended it to tower cranes by considering the coupling between the translational and rotational motions. Numerical simulations show that the controller is effective for reducing load oscillations and transferring the load in a reasonable time compared with that of optimal control. To experimentally validate the theory, we had to compensate for friction. To this end, we estimated the friction, then applied an opposite control action to cancel it. To estimate the friction force, we assumed a mathematical model, then we estimated the model coefficients using an off-line identification technique, the least-squares method. First, the process of identification was applied to a theoretical model of a dc motor with known friction coefficients. From this example, some guidelines and rules were deduced for the choice of the least-squares parameters. Then, the friction coefficients of the gantry crane model were estimated and validated.