Kalman Filter for an Industrial Tower Crane Controlled in Closed-Loop with Anti-Sway Profile

Abstract

This paper presents a method for generating a velocity profile for an industrial tower crane controlled in a closed-loop anti-sway system. We obtain, as a final result of the theory developed here, the Kalman Observer for the Tower Crane System considered. In this paper, we introduce an iterative procedure for the Kalman-Bucy observer, creating a new method for controlling a Tower Crane in a closed-loop system. We introduce the use of a Kalman filter to reduce the errors introduced by both the model approximation for Anti-Sway control and, on the other hand, measurement errors due to the sensors used in the closed-loop control. Therefore, this application is characterized by the union of two fundamental factors: the control of load swing during jib rotation and the use of the Kalman filter algorithm to correct the errors obtained in closed-loop control. In this work, we describe in detail the Lagrange equations for defining the swaying effect on the jib's rotational motion and thus arrive at the iterative equations for calculating the jib's motion itself. We analyse the characteristics of the Kalman Filter in general, which, as a consequence, leads to defining the Matrix Equation of the Kalman Filter for the Jib Crane. We simulate the time evolution of the motion equations and define the input red from the input sensors randomly. We represent three Velocity Profiles: the theoretical Velocity reference profile of the Slewing, the profile of the Slewing considering both the measurement noise and the noise due to the modelling error of the phenomenon, and, finally, the profile of the Slewing output, obtained by filtering the signals through the Kalman filter. It is observed that, as the variances of the random phenomena considered decrease, an increasingly smooth trend of the profiles themselves is observed.