Nonlinear Anti-swing Control Of An Underactuated Overhead Crane With Four Degrees Of Freedom

When an overhead crane travels, the payload would swing due to the inertia effects, resulting in inaccurately positioning, decreasing working efficiency, and affecting the service life of the overhead crane. When the girder and trolley travels at the same time, the overhead crane and payload would move in three dimensional space, and the crane has four degrees of freedom, such as the displacements of the girder and trolley and the swing angles of the girder and trolley’s moving directions of the payload. A dynamic model of overhead crane with four degrees of freedom was established when the girder and the trolley travels together, and nonlinear control theories based on sliding mode control were used to control the payload’s swing. The content of this thesis was as follows:(1) A nonlinear model of an overhead crane with the girder and trolley travelling at the same time was established from the actual structure of an overhead crane by using Lagrange Equation and the principle of virtual displacement. The model concerned the rotational inertia of the wheels, and regards the resistance of the wheels as rolling resistance. Meanwhile, an anti-skew driving force assigning law for the motors of the bridge’s both sides was proposed, neglecting the lateral displacement of the bridge.(2) A trajectory tracking anti-swing control algorithm based on hierarchical sliding mode control was provided to solve the payload’s swing problem of an overhead crane, in which a hierarchical sliding mode controller was designed to make the system’s states track the ideal trajectories, and the control system’s stability was proved by applying Lyapunov theory and Barbalat’s lemma. The simulation model was built with Level-2 M-file S-function in Simulink, and the overhead crane’s simulation model was established by using the practical parameters of a QD50x22.5 double bridge overhead crane. The simulation results showed that, the girder and trolley could reach the destination rapidly and precisely, while restricting the payload’s swing angles in a small range, and the control system’s stability was verified at the same time. The designed hierarchical sliding mode controller had nice robustness against the variation of the payload’s mass, the trolley’s mass, the rope’s length, or initial swing angles. However, the input forces of the girder and trolley which were output by the controller were chattering with high frequency, according to the simulation results.(3) Aiming at the chattering problem of the hierarchical sliding mode controller’s output, backstepping and hierarchical sliding mode control were combined to design a dynamic variable structure control law, which put the discontinuous switching control function into the first derivative of the girder and trolley’s input forces, and yielded continuous input forces, resulting in the basically eliminating of the chattering. The control system’s stability was proved theoretically and verified by simulation. Compared with the hierarchical sliding mode controller, the backstepping dynamic hierarchical sliding mode controller has the same control performance, while it weakened the chattering of the girder and trolley’s input forces effectively. Moreover, if increasing the switching gain, the system’s robustness would improve without causing the system’s chattering.(4) An experimental scheme for verifying the anti-swing control algorithm of an overhead crane was proposed. In the experimental model of an overhead crane, the driving forces were supplied by servo motors, and the displacements and the swing angles would be measured by absolute rotary encoders, while the anti-swing algorithm would control the overhead crane model in real time through MATLAB RTW and Real-Time Windows Target on a control computer.