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

Abstract

This paper deals with modelling and control of an overhead crane with a flexible cable. The developed dynamical model includes both transverse vibrations of the flexible cable and large swing angles of cable while the trolley is moving horizontally. To carry out the modelling, Rayleigh-Ritz discretization method is used to achieve an ordinary differential equation (ODE) model for transverse deflection of the cable with finite generalized degrees of freedom. Using the Euler-Lagrange formulation, a nonlinear dynamic model of the crane system with a flexible cable is obtained. The control objective is to move the payload position to the desired point and at the same time, to reduce the payload swing and to suppress the cable's transverse vibration. To this end, a static state feedback control combined with integral error feedback is proposed. Simulations are performed using the developed nonlinear model under various conditions to illustrate the effectiveness of the proposed control system.

Tracking control design for a multi-degree underactuated flexible-cable overhead crane system with large swing angle based on singular perturbation method and an energy-shaping technique

“…In addition to the proposed control system, two other controllers, namely a linear controller based on the LQR method (Fatehi et al., 2014) and a two-time scale controller based on the approximate SP model and partial feedback linearization (ASP-PFL control) (Fatehi et al., 2015b), are applied to the flexible cable crane system. The current presented controller is different from the second controller since an exact SP model and controlled Lagrangian control (SP-CL control) are used.…”

“…The generalized coordinate, δj(t), also known as j -th vibration mode and its corresponding shape function, φj(z^) can be chosen arbitrarily but certain boundary conditions are required to be satisfied (Fatehi et al., 2014). The governing equation of the crane system's motion in a matrix form can be represented as (Fatehi et al., 2014) in which, u=Fx∈R is input controlled force and q=(x,θ,δ) T∈Rn where (x,θ)∈R2 and δ=(δ1,δ2,…,δm)∈Rm, n=m+2 is the number of DOF (i.e., n-DoF system). Matrix …”

“…The potential energy caused by the cable deflection can be rewritten as (PE)cable=12δTK(θ)δ, in which, δ∈Rm is generalized DOF of the model equation (5). Also, matrix K(θ) is defined as stiffness matrix of cable and can be written as follows (Fatehi et al., 2014) where, FP(z^)=1ℓP0P0 T and FI(z^)=1ℓ2∫P0P0 Tdz^, in which, and, K0∈<...>…”

“…One of the effective control approaches to control underactuated mechanical systems using energy-based techniques is the controlled Lagrangian method (Chang, 2010). In our previous study, a linear form of the controlled Lagrangian method was used for a crane system (Fatehi et al., 2015c).…”

“…To demonstrate the control system effectiveness, numerical simulations are performed considering an example of flexible cable crane systems with a lightweight payload. In addition to the proposed control system, two other controllers; namely, a linear controller based on the linear–quadratic regulator (LQR) method (Fatehi et al., 2014) and, a two-time scale control (TTSC) based on approximate SP model and partial feedback linearization (ASP-PFL control), (Fatehi et al., 2015b) are applied to the system for comparison. To investigate the control performance against disturbances and parameter uncertainties, a disturbance force with the amplitude of 20 N is applied to the trolley.…”