Partial feedback linearization for a path control in a gantry crane used in lifting machinery in civil engineering

Abstract

This paper presents an alternate form for the dynamic modelling of a mechanical system that simulates in real life a gantry crane type, using Euler Lagrange classical mechanics, which allows find the equations of motion that our model describes. In order to verify the theoretical results obtained, a comparison was made between solutions obtained by simulation in SimMechanics-Matlab and Euler Lagrange equations system, has been solved through Matlab libraries for solving equations systems of the type and order obtained. Based on the partial feedback linearization, an improved nonlinear controller is analyzed and designed for the movement of an overhead crane or industrial shed. Three control inputs composed of bridge movement forces, carriage displacement, and pendulum or load angle are used to handle the state variables consisting of bridge movement, carriage movement, load displacement, and angle of turn of the same. The objective is to bring the mass of the pendulum from one point to another with a specified distance without the oscillation from it, so that, the answer was overdamped. The asymptotic stability of Lyapunov is also studied and the control scheme is of position of the load, constituted by the non-linear feedback of the actuated and non-actuated states. To verify the quality of the control process, verify numerical simulations. The proposed controller asymptotically stabilizes all states in the system.