Friction electro-hydraulic load simulator (FEHLS) classified as an electro-hydraulic torque servo mechanism, encounters significant challenges in the form of parameter uncertainties, external disturbances, and unmodeled dynamics, all of which notably degrade the system's capacity for accurate tracking. This study introduces the design of a state-and-disturbance estimation observer (SDEO) aimed at approximating unobservable states and nonconforming perturbations. A specifically tailored nonlinear disturbance observer (NDO) is constructed for the purpose of estimating such mismatched disturbances. Using backstepping designed method with prescribed performance, robust disturbance rejection control (RDRC) is proposed, ingeniously integrating SDEO, NDO, and a continuous sliding mode control. The stability of the proposed RDRC is systematically scrutinized utilizing the principles of Lyapunov stability method. The practical efficacy and robustness of the devised control scheme have been convincingly validated through meticulous experimental execution and analysis.