Asian Journal of Control, Vol. 17, No. 2, pp. 443–458, March 2015 Published online 12 September 2014 in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/asjc.986 CONTROL OF 3D TOWER CRANE BASED ON TENSOR PRODUCT MODEL TRANSFORMATION WITH NEURAL FRICTION COMPENSATION Jadranko Matuško, Šandor Ileš, Fetah Koloni´ c, and Vinko Leši´ c ABSTRACT Fast and accurate positioning and swing minimization of heavy loads in crane manipulation are demanding and, at the same time, conficting tasks. Accurate load positioning is primarily limited by the existence of a nonlinear friction effect, especially in the low speed region. In this paper the authors propose a new control scheme for 3D tower crane, that consists of a tensor product model transformation based nonlinear feedback controller, with an additional neural network based friction compensator. Tensor product based controller is designed using linear matrix inequalities uti- lizing a parameter varying Lyapunov function. Neural network parameters adaptation law is derived using Lyapunov stability analysis. The simulation and experimental results on a 3D laboratory crane model are presented. Key Words: 3D tower crane, neural network, non-PDC control law, friction compensation, RBF network, on-line network learning. I. INTRODUCTION Cranes are widely used for heavy load transfer in modern industrial systems (transportation, construc- tion, etc). They are also becoming larger, higher and faster, requiring advanced control algorithms to meet all the requirements regarding fast and safe load transfer. Cranes usually consist of a hoisting mechanism and a trolley that moves around crane workspace. Due to a high compliance of the hoisting mech- anism, cranes are highly susceptible to the undesired oscillatory payload motion. These oscillations, can be triggered either by an external excitation at the load sus- pension point or by inertial forces due to motion of the crane. While externally induced payload oscillations are almost exclusively present in offshore cranes, oscilla- tions due to crane inertial forces are unavoidable in both off-shore and on-shore cranes. Suppression of this oscil- latory payload motion is necessary to maintain the safety of operations but also to reduce dynamic loads to the crane structure during operations. Manuscript received June 30, 2013; revised December 31, 2013; accepted February 16, 2014. The authors are with the Department of Electric Machines, Drives and Automation, Faculty of Electrical Engineering and Computing, University of Zagreb, Unska 3, Croatia. Jadranko Matuško is the corresponding author (e-mail: jadranko.matusko@ fer.hr). This work has been supported by the European Commission Seventh Frame- work Programme under grant No. 285939 (ACROSS). The additional problem, especially important when highly accurate load positioning is required, is a friction effect in the crane system. This effect degrades the sys- tem response by introducing time delay, high steady-state error in trolley and tower positions, and high residual load swings [32,33]. Early and still widely-used approaches to the crane control problem were open loop using the so-called input shaping technique [35,36]. Based on a predefned motion profle, this approach modifes the actual ref- erence applied to the crane in order to minimize the oscillations. Due to its open loop nature, this approach can be only used to suppress the oscillations induced by the crane inertial forces while those having external sources (waves, wind, etc.) remain undamped. Closed loop solutions to the crane control problem range from a simple PID control to advanced nonlin- ear control approaches, often employing artifcial intel- ligence techniques [1]. However, the most widely used approach to the crane control problem is a combina- tion of a linear controller and an adaptation mechanism. A linear quadratic controller (LQR) with a feedback gain vector as a function of the time-varying payload cable length is presented in [11,46]. A robust sliding mode based approach to the crane control problem in the case of poor information on the system dynamics or its parameters is presented in [7]. To account for the nonlinear nature of the load swinging, some authors adopted a fuzzy logic based approach [29], an adaptive fuzzy sliding mode approach [26] and a passivity based © 2014 Chinese Automatic Control Society and Wiley Publishing Asia Pty Ltd