This study presents a hybrid control framework for the attitude regulation of a three-degree-of-freedom satellite subject to parametric uncertainties, external disturbances, actuator constraints, and implementation imperfections. The core robust controller is formulated using the Super-Twisting Algorithm, which guarantees finite-time convergence and robustness while effectively suppressing the high-frequency chattering typically associated with conventional sliding mode control. To enhance tracking precision and improve adaptability under nonlinear and uncertain conditions, deep reinforcement learning is incorporated as an adaptive compensator within the control loop. Three representative algorithms, namely Deep Deterministic Policy Gradient, Twin Delayed Deep Deterministic Policy Gradient, and Proximal Policy Optimization, are investigated and comparatively evaluated in terms of stability, convergence behavior, and control efficiency. To systematically tune the learning hyperparameters and reduce the computational burden associated with manual trial-and-error procedures, the Taguchi design of experiments method is employed to perform multi-objective optimization considering both tracking performance and control effort. The performance index is defined as a composite measure that combines time-weighted tracking error and control energy. Numerical simulations together with experimental validation on a satellite attitude simulator demonstrate that the proposed hybrid control architecture reduces settling time and control effort while improving disturbance rejection capability, without compromising stability or steady-state tracking accuracy.