Upper limb exoskeletons play a crucial role in rehabilitation and assistive applications by enhancing movement capabilities for individuals with motor impairments. However, precise motion control remains a challenge due to system nonlinearities, external disturbances, and the need for robustness in dynamic environments. In this study, a modified version of the EduExo exoskeleton is developed by integrating an additional RMD-X6 servomotor to provide active shoulder flexion-extension, while retaining elbow joint actuation. The mechanical structure is modified, and its kinematic and dynamic models are derived to enable accurate physical simulation. A Sliding Mode Controller (SMC) is designed and applied to control the dual-actuated system. Unlike conventional PID control, which is limited in managing nonlinearities and external disturbances, the SMC provides high robustness and reliability. To address the inherent issue of chattering in standard SMC, a Hyperbolic tangent switching function is adopted and the controller parameters are optimized using response optimization method. The system is evaluated through Simulink-based simulations, where the controller performance is assessed under both step and circular trajectory tracking tasks. Performance metrics such as Root Mean Square Error (RMSE), settling time, and chattering are calculated. The SMC demonstrates significantly improved tracking accuracy and reduced chattering, confirming its effectiveness with approximately 20% reduction for upper limb exoskeleton control. This work demonstrates how a robust and SMC enhances the motion accuracy of a modified EduExo exoskeleton in simulation.