Modeling and discretization of hydraulic actuated telescopic boom system in port-Hamiltonian formulation

The hydraulic actuated telescopic boom system is the primary operation actuator of mobile cranes and aerial platform vehicles. The purpose of this paper is to develope a unified mathematic model of such a boom system which is a multi-domain system consisting of boom structure and hydraulic drive system. The model is formulated within the port-Hamilton (PH) formalism using the definition of hydraulic system and elastic boom structure as (Stokes-) Dirac structures. The Port-Hamiltonian systems can be easily interconnected thus allowing the description of a complex system as a composition of subsystems. This property is especially useful to model a multi-domain system with energy exchanges between subsystems. Considering the boom structure as a Timoshenko beam, the luffing operation of boom system is simplified in a plane coordinate system. The Port-Hamiltonian model of the hydraulic system and the boom structure are described with details separately, a structure-preserving discretization is applied to transfer the distributed-parameter boom model into a lumped-parameter model. Then the interconnections between the subsystems are illustrated and a complete simulation including hydraulic system is accomplished in MATLAB/Simulink.