Design of a Robust Component-wise Sliding Mode Controller for a Two-Link Manipulator

Compared to conventional Multiple-Input Multiple-Output (MIMO) Sliding Mode Control (SMC) techniques, the component-wise SMC approach offers several advantages, including improved decoupling of system dynamics, enhanced robustness, and greater flexibility in controller design. This paper proposes a novel trajectory tracking controller for a two-link manipulator based on the component-wise sliding mode control approach. The design methodology involves determining controller gains by solving a set of inequalities. This analysis results in conditions on the system parameter uncertainties that guarantee the existence of a feasible solution to the set of inequalities. Furthermore, an algorithm is presented to determine the maximum allowable uncertainties that ensure the feasibility of the controller gains. To evaluate the performance and robustness of the proposed tracking controller, the manipulator is subjected to a series of challenging trajectories, including circular and figure-8 ones, under both nominal and maximum allowable uncertainty conditions. The proposed controller demonstrates superior performance across both circular and figure-8 trajectories, exhibiting excellent transient response and minimal steady-state error even under the maximum permissible uncertainties, which extend up to 27% in link masses. This performance is validated through a quantitative analysis that incorporates a comparative evaluation against two conventional MIMO SMC techniques. The comparison is conducted using the Integral Norm of Error (INE) to assess tracking accuracy and the Integral Norm of Control Action (INU) to evaluate the energy efficiency of the controllers. These metrics provide a comprehensive basis for analyzing both the precision and the energy consumption of the proposed control strategy in relation to established methods.