Robust tip trajectory synchronisation between assumed modes modelled two-link flexible manipulators using second-order PID terminal SMC

Synchronisation/cooperation between manipulators is a specified emerging application in the field of robotics. However, most of the synchronisation works are reported using rigid manipulators. Flexible manipulators have their advantages over rigid manipulators and hence, the applications of flexible manipulators are more desirable. This paper takes an attempt for the robust tip trajectory synchronisation between assumed modes method modelled two-link flexible manipulators. The synchronisation is achieved between a controlled master and an identical slave manipulators. A conventional SMC is designed for the tip trajectory tracking control of the master manipulator. A second order PID terminal SMC is proposed for the synchronisation between the controlled master and an identical slave manipulators along with fast suppression of tip deflection. This control technique provides chattering free global stability of the error dynamics. The structure of the proposed controller differs from the available second order terminal SMC by enabling chattering free complete stability having no singularity problem for the synchronisation of the flexible manipulators. This superiority of the proposed technique is validated using MATLAB simulation in the presence of variable payloads and ±5% to ±30% variation in the nominal value of the parameters. The effectiveness of the proposed control technique is compared with the normal second-order SMC, and is found better in terms of low tracking error and smoother control efforts.