This paper deals with the robust controller design problem to regulate the position of a soft robot with elastic behavior, driven by 4 cable actuators. In this work, we first used an artificial neural network to approximate the relation between these actuators and the controlled position of the soft robot, based on which two types of robust controllers (type of integral and sliding mode) are proposed. The effectiveness and the robustness of the proposed controllers have been analyzed both for the constant and the time-varying disturbances. The performances (precision, convergence speed and robustness) of the proposed method have been validated via different experimental tests.