A Swing Constraint Guaranteed MPC Algorithm for Underactuated Overhead Cranes

In practice, for an overhead crane, the payload swing needs to be kept within an acceptable domain to avoid accidents. However, as an unactuated state, the swing angle is usually very difficult to be controlled properly. Besides that, the constraints on the control input should also be carefully considered to avoid possible actuator saturation. These problems bring much challenge for control development of an underactuated crane. Motivated by this observation, a novel model predictive control (MPC) algorithm, which guarantees swing constraints theoretically and is free of actuator saturation, is proposed in this paper for a 2-D overhead crane system to achieve satisfactory performance. That is, for an overhead underactuated crane, a discrete model is first obtained by some linearization and discretization technique, based on which a novel MPC algorithm is constructed, which theoretically ensures that the payload swing is kept within the allowable range and that the control is always free of saturation. Specifically, the control input constraint is successfully addressed by solving a constrained optimization problem for the MPC method, while the kinematic equation of the crane system, which plays the role of the connection between the payload swing and the trolley movement, is utilized to convert the swing bound into some constraints on the control input so as to handle it conveniently. Both simulation and experimental results are investigated to illustrate the superior performance of the proposed method.