Takagi-Sugeno Fuzzy Approach with Compressed Representation for Overhead Crane System

Abstract

This paper proposes a Takagi-Sugeno (TS) fuzzy approach for 2-dimensional of freedom overhead crane. Since this system is underactuated with nonlinear mathematical dynamic model, the requirement of achieving accurate positioning while eliminating oscillation is a challenging issue. The nonlinear sector decomposition is taken into implementation which uses the nonlinear terms in the dynamic model as scheduling variables to transform the initial system to TS representation. However, the number of TS fuzzy rules is exponential in the number of nonlinear elements in the system, leading to the increase of computational expense. Therefore, the reduced complexity method is introduced to minimize the scheduling variables in TS system. In addition, the uncertain system’s components are also taken into consideration to enhance the robust property of the system when working in practical environment. The controller is constructed based on parallel distributed compensation (PDC) approach while the linear matrix inequalities (LMIs) technique is employed to analyse the system’s stability. The effectiveness of the proposed method is demonstrated through numeral simulations.