Decoupled Adaptive Neuro-Interval Type-2 Fuzzy Sliding Mode Control Applied in a 3DCrane System

Moving an object attached to a cable along a predetermined path is a very complex task when the angles of oscillation impose severe constraints. However, to minimize the swing angle, adaptive control laws are necessary, especially in case where the systems dynamics are prone to uncertainties. In this paper, we propose a decoupled adaptive neuro-interval type-2 fuzzy controller based on the sliding mode theory for the control of 3DCrane system. The considered 3DCrane system involves a plan movement in conjunction with a lifting movement. It has three control inputs only (trolley and hoisting forces) with five controlled variables (the trolley position in the XOY plane, the length of the lifting cable, and the two angles of swing). Overall, control subsystems are regarded as being decoupled interactions and that are taken as disturbances acting in the control of each individual subsystem. In the proposed approach, a conventional controller (PD) and the neuro-interval type-2 fuzzy controller are used in parallel; the PD controller ensures the asymptotic stability in compact space, the adaptation parameters of neuro-interval type-2 fuzzy inference system rules are obtained by derivation, and Lyapunov method is used to demonstrate the stability of the online learning algorithm. To validate the proposed approach, the laboratory equipment 3DCrane system is used as an experimental platform. The presented results are obtained for a trajectory tracking with a minimum of oscillations.