Addressing Model Uncertainties and External Disturbances in Optimal Robust Control for Vibration Reduction in a Flexible Link Manipulator

A novel Optimal Robust Controller (ORC) for reducing vibration in a flexible link manipulator has been designed in this work. Compared to stiff link manipulators, flexible link manipulators have advantages, but they also have problems including link vibration, model uncertainty, and outside disruptions. The ORC aims to address these challenges and improve the positioning of the flexible links by reducing the link vibrations. Using the Assumed Mode Method (AMM), the dynamic model of a two-link flexible manipulator has been developed in order to create the ORC. With two mode shapes taken into consideration for each link, the deflection of the links has been modelled using mode shapes. The ORC has been designed to achieve robust performance in vibration reduction, even in the presence of unmatched model uncertainty. Proof of the matching condition of the uncertainty has been given, and the closed-loop stability of the resulting system has been established. The value of the uncertain parameter has been purposefully changed to illustrate the robustness of the created controller. For comparison purposes, a well-known reliable controller called the Sliding Mode Controller (SMC) has also been developed. The performance of the proposed ORC has been compared with that of the SMC in the simulation section, and the ORC is determined to be more effective at minimizing vibration.