A specific challenge in robotic control applications is the identification and regulation of actuators that provide mechanical traction and motion to the robot links. The design of actuator control laws, grounded in parametric identification and experimental motor characterization, enables numerical simulations to explore diverse operating scenarios. This article presents the initial phases in the development of a robotic rehabilitation system, focused on the kinematic modeling of a parallelogram-configuration robot for upper-limb therapy, the fuzzy identification of its actuators, and their closed-loop evaluation using a fuzzy Parallel Distributed Compensation (PDC) controller with state feedback (Ackermann), whose poles are optimized via the Grey Wolf Optimizer (GWO) metaheuristic. This controller was selected for its congruence with the nonlinear universe of discourse defined by the identified model, a key feature for operation within specific functional ranges in medical applications. The simulation and hardware platform results provide evidence that fuzzy dynamic models constitute a valuable tool for application in rehabilitation systems. This work serves as a foundation for future physical implementations with the fully coupled robotic system, in order to ensure operational safety prior to the start of clinical trials.