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This paper presents in detail how to model, identify, and control a 3-DOF prismatics-revolute-spherical parallel manipulator in terms of relevant parameters. A reduced model based on a set of relevant parameters is obtained following a novel approach that considers a simplified dynamic model with a physically feasible set of parameters. The proposed control system is compared with the response of a model-based control that considers the complete identification of the rigid-body dynamic parameters, friction at joints, and the inertia of the actuators. The control systems are implemented on a virtual and an actual prototype. The results show that the control scheme based on the reduced model improves the trajectory tracking precision when comparing with the control scheme based on the complete set of dynamic parameters. Moreover, the reduced model shows a significant reduction in the computational burden, allowing real-time control.