Achieving accurate closed-loop position control of soft robots remains an ongoing research problem, due to the challenges posed by underactuation, elastic nonlinearities, and material creep. Although soft driving technologies relying on tendons and smart material transducers (e.g., dielectric elastomers, shape memory alloys) offer more ease of controllability compared to pneumatics, the corresponding controller design problem becomes even more challenging because of additional nonlinear effects. Those include a configuration-dependent actuation matrix, that stems from the kinematics of the actuation, and control input saturation, which is especially critical for smart material actuators. In this article, we investigate for the first time the closed-loop position control of a soft-robotic system driven by dielectric elastomer actuators. The objective is to regulate the robot state to a constant setpoint, accounting for the effects of open-loop instability, underactuation, control input saturation, and constant external disturbances. To achieve this goal, we propose a model-based feedback scheme, which combines a stabilizing energy-shaping controller with a robustifying PI-like law. After presenting the general theory, a linear matrix inequalities algorithm is proposed to practically address the controller design in spite of strong model nonlinearities. Experimental validation conducted on a prototype of the soft-robotic system confirms the effectiveness of the proposed control approach.