Composite optimal robust control of flexible link manipulator

Abstract

Abstract This study presents the development of a composite controller by combining the optimal robust controller(ORC) and a back-stepping controller, in presence of unmatched model uncertainty, to achieve vibration reduction and joint position tracking in a two link flexible manipulator (TLFM). The dynamics of the TLFM have been modelled using the assumed mode method, incorporating mode shapes to accurately represent the flexible links’ vibrations. Two mode shapes have been considered for each link. One source of uncertainty in the system has been identified as the payload mass. The manipulator responds differently when the payload mass connected to the end-effector is changed, demonstrating the effectiveness of the controller. The closed-loop stability is established utilizing the Lyapunov method, and trajectory convergence has been demonstrated through Barbalat’s Lemma. Unknown gains present in the controller’s formulation have been fine-tuned using the FOX optimization algorithm (FOXOA) and arithmetic optimization algorithm (AOA). The simulation results showcase the impact of both optimization techniques on the controller’s performance, validating its robustness and efficacy in the presence of uncertainties. In the simulation section, it has been found that the performance of the TLFM with FOXOA is better compared to AOA.