Disturbance Observer Based Safety-Critical Model Predictive Control for Overhead Cranes

This paper investigates the problem of safety-critical model predictive control (MPC) for under-actuated overhead crane systems. In practical engineering, the payload swing angle of the overhead crane systems must be limited within an acceptable range to guarantee safety, and the trolley reach to the desired position accurately simultaneously. In addition, the payload may be disturbed by strong winds, which poses a certain threat to the safety of overhead crane operation. Considering this, a disturbance observer based safety-critical MPC algorithm using discrete-time control barrier function (CBF) is proposed, where the disturbance estimation value is embedded within the CBF to guarantee the swing angle constraints. Then the receding horizon optimization problem is formulated with the help of prediction model. Next, the optimal control input is obtained by solving the QP problem periodically. Subsequently, the stability analysis of the closed-loop system under the nominal control law is given. Finally, it is shown that the payload swing angle can be strictly limited within the safe range, and the trolley can reach the specified position under the proposed method through numerical simulations and physical experiments.