Robust control of the trolley of a single girder overhead crane under the action of unmatched perturbations and incomplete measurement

We considered the problem of controlling an electromechanical system, which is a single-girder overhead crane trolley (mechanical subsystem) with the reduced dynamics of a DC motor (electrical subsystem). The plant operates under conditions of lack of controls, the action of parametric and external perturbations, and incomplete measurements. In this case, the perturbations acting on the mechanical subsystem are unmatched. For safe transfer of payload in these conditions, a number of solutions have been proposed. A reference trolley trajectory with an integral of the angular coordinate has been formed. The presence of the integral part leads to the damping of payload oscillations. It is shown that this part also makes it possible to suppress unmatched wind perturbations. To track the generated trajectory, a procedure for block synthesis of sigmoid fictitious controls in the mechanical subsystem and true discontinuous control in the electrical subsystem has been developed. Smooth and bounded sigmoid functions provide suppression of unmatched perturbations. These functions are implemented in the actuator and do not lead to its strong wear, which occurs during the formation of discontinuous fictitious controls. For information support of the control law, a dynamic differentiator with a sigmoid corrective action has been developed, which provides an estimate of the speed by measuring the tracking error with any given accuracy. The proposed solution will make it possible to abandon the trolley speed sensor and avoid jumps in evaluation signals. The results of numerical simulation of closed-loop systems with discontinuous and sigmoid fictitious controls are presented. They demonstrated the effectiveness of the developed approach.

overhead crane’s trolley, unmatched perturbations, parametric uncertainty, robust control, sigmoid function, dynamic differentiator