This paper addresses the control problem of a specially designed nonlinear actuator intended for use in legged robots and other related mechatronic devices. Use of this drive could considerably increase energy efficiency and the time of autonomous robot operation. Nevertheless, the highly nonlinear model of the actuator and the unavailability of part of the state for measurement pose considerable challenges to the control system design. The proposed control solution utilizes the observer-based backstepping algorithm to produce a nonlinear controller that ensures asymptotic tracking of the desired law of motion. Experimental results with friction compensation are presented to show the effectiveness and feasibility of the proposed nonlinear control method.