Electro-hydraulic actuators (EHAs) are increasingly used in modern industrial systems due to their compact design, energy efficiency, and high precision, offering a sustainable alternative to traditional valve-controlled hydraulic systems (VHS). However, conventional control methods such as PID and sliding mode control often fall short in ensuring robust performance in pump-driven EHA systems with rotary actuators, due to strong nonlinearities, parameter uncertainties, and unmeasurable internal states. This study introduces a novel position control method for electro-hydraulic rotary actuator systems (EHRAs) by integrating a modified backstepping algorithm, an iterative learning control (ILC) scheme, and a nonlinear state observer. The control strategy is developed based on Lyapunov stability theory to ensure robustness and convergence under varying operating conditions. A co-simulation using MATLAB/Simulink and AMESim was carried out to validate the control strategy. Quantitative results show that the proposed method achieves superior tracking accuracy with a position error below 0.5% and state estimation errors within 1% after 0.2 seconds. Simulation results indicate that the proposed control strategy maintains accurate tracking and remains stable under external disturbances. This study is the first to combine modified backstepping, ILC, and nonlinear observation for rotary EHAs. The stability of the proposed solution highlights its potential for use in high-precision motion control applications in robotics, aerospace systems, and heavy industry.