Modelling and control of overhead cranes with flexible variable-length cable by finite element method

Abstract

This work considers the modelling problem of the dynamics of overhead cranes with flexible cable and load hoisting or lowering during crane travel. The analysis includes the transverse vibrations of the flexible cable and trolley motion. A set of nonlinear ordinary differential equations governing the motion of the crane system with time-varying spatial domain is derived via the calculus of variation and Hamilton’s principle. A variable-domain finite element method is used to discretize the nonlinear system. A proportional -derivative controller is suggested to drive the crane to a desired destination. Numerical simulations are provided to show the effectiveness of the developed model and to illustrate the results.

Modelling and Control of an Overhead Crane System with a Flexible Cable and Large Swing Angle

“…The dynamic model of the crane system with flexible cable, equationn (25), which is used to simulate the system corresponds to a nonlinear under-actuated system [26,27]. The references [26,27] discuss several distinguished types of under-actuation for which the system is controllable.…”

“…In a crane system, interactive dynamics of the cable and the payload are a challenge in most applications, which demand investigation into boundary induced cable vibrations and can determine the behaviour of the crane [15]. A few studies have addressed the effects of flexibility and weight of the cable in crane systems [16][17][18][19][20][21][22][23][24][25]. They have presented planar models for an overhead crane and assumed that the cable is perfectly flexible and inextensible.…”

Fuzzy control of flexible cable overhead cranes with load hoisting

“…The equations of motion governing the dynamics of the considered crane model are derived in Moustafa et al (2004) using the Hamilton's principle and the calculus of variation. The resulting mathematical model is a set of non-linear differential equations with time-varying spatial domain and is reproduced as follows.…”

“…Many control schemes have been applied in the past to overhead cranes by using classical PD controllers (eg, Ismail, 2005;Moustafa, 1994;Moustafa and Abo-ElYazid, 1996;Moustafa and Ebied 1988;Moustafa et al, 2004;Ridout 1989). These references show that the use of PD controllers necessitates, however, the availability of an accurate mathematical model that describes the system behaviour.…”

Dynamic Response of Parallel Hoisting System under Drive Deviation between Ropes with Time-Varying Length

“…Wang et al investigated three-dimensional vibrations of an underwater geometrically nonlinear cable with a weight at the lower end [16]. Moustafa et al considered the modeling problem of the dynamics of overhead cranes with flexible cable and load hoisting or lowering during crane travel [17]. All these researches are investigated by variable-domain FEM (Vd-FEM).…”