This paper proposes a control strategy based on artificial neural networks (ANNs) for a positioning system with a flexible transmission element, taking into account Coulomb friction for both motor and load, and using a variable learning rate for adaptation to parameter changes and accelerate convergence. A control structure consists of a feedforward ANN that approximates the manipulator's inverse dynamical model, an ANN feedback control law, a reference model, and the adaptation process of the ANNs with a variable learning rate. A supervisor that adapts the neural network's learning rate and a rule-based supervisor for online adaptation of the parameters of the reference model are proposed to maintain the stability of the system for large variations of load parameters. Simulation results highlight the performance of the controller to compensate the nonlinear friction terms, particularly Coulomb friction, and flexibility, and its robustness to the load and drive motor inertia parameter changes. Internal stability, which is a potential problem in such a system, is also verified. The controller is suitable for DSP and very large scale integration implementation and can be used to improve static and dynamic performances of electromechanical systems.