Adaptive time-varying super-twisting global SMC for projective synchronisation of flexible manipulator

Abstract

In this paper, a synchronisation strategy between a controlled master and three-slave two-link flexible manipulators is proposed. Two out of the three slaves are identical with the master, whereas the third one is non-identical. The master and the slave manipulators are modelled by assumed modes and lumped parameter methods, respectively. The 12 states of the master manipulator are synchronised to the 8 states of each slave manipulator. Such projective synchronisation is also not available in the literature. A global sliding mode controller is designed first for the master manipulator to track the desired trajectory. Next, the synchronisation between the master and the slaves is achieved by designing an adaptive time-varying super-twisting global sliding mode controller. The simulation results reveal that the performances of the proposed controller in terms of (i) steady-state error of synchronisation, (ii) synchronisation time and (iii) links deflection are much better than the existing controller proposed in 2016.