Chaotic tip trajectory tracking and deflection suppression of a two-link flexible manipulator using second-order fast terminal SMC

The problem of chaotic tip trajectory tracking control for a planar assumed modes modelled two-link flexible manipulator is addressed. Tracking of such an apparently random-like (chaotic) desired trajectory is a challenging task. Initially, a PID-type sliding surface is designed in terms of the tip trajectory tracking error, then a second-order integral-type fast terminal sliding mode control is designed using the above-designed sliding surfaces. The desired chaotic trajectory is generated from a four-dimensional chaotic hyperjerk system. The proposed controller guarantees fast tracking performance with lower steady-state error and less control input. The model of a two-link flexible manipulator is obtained using the assumed modes method. The robustness of the proposed control method is evaluated in the presence of matched uncertainty and variability of payload. The performances of the proposed control technique are verified in terms of low tracking error and fast tip deflection suppression. The effectiveness of the proposed technique is validated using numerical simulations, and compared with the normal second-order sliding mode control (SMC) and another controller reported recently in the literature.