Quasi-static Optimal Control Strategy of Lattice Boom Crane Based on Large-Scale Flexible Non-linear Dynamics

Lattice boom cranes are usually used to lift heavy loads with the optimized lattice structure of the boom structure. Considering the huge mass of the payload and the crane itself, the flexibility of the crane boom structure cannot be ignored. The elastic vibrations mainly accrue at the lattice boom, the luffing system, and the cables. In this paper, several flexible multibody dynamic models are established as the beam elements (spatial Timoshenko beam), the rod elements (strut tie model), and the rope elements (ideal cubic spline model). In addition, a super truss element formulation for the regular truss structure is proposed to reduce the number of degrees of freedom of the complex lattice boom components. For controlling the large-scale nonlinear dynamic system, a quasi-static optimal control strategy is designed to realize the controllable motions for the specified complex system. This method combines the static mapping relationship with the target optimal trajectory to generate the optimal trajectories of control inputs. Through the elementary motions, the dynamic calculation of the lattice boom crane is performed to simulate the lifting, the luffing, and the slewing stages. In the aspect of control, the static mapping relationship between the key state variables and the control variables is established. A specified lifting task is designed to verify the quasi-static optimal control strategy.