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This paper presents a cascaded sliding-mode (SM) control scheme for a new pneumatic linear axis which could be seen as alternative to an electric direct linear drive. Its guided carriage is driven by a nonlinear mechanism consisting of a rocker with an antagonistic pair of pneumatic muscle actuators arranged at both sides. This innovative drive concept allows for both an increased workspace of approximately 1 m as well as higher carriage velocities of approximately 1.3 m/s as compared to a direct actuation. Modeling of the muscle-driven positioning system leads to a system of four nonlinear differential equations including polynomial approximations of the volume characteristic as well as the force characteristic of the pneumatic muscles. The differential flatness of the system is exploited in combination with SM techniques to stabilize the error dynamics in view of unmodeled dynamics. The internal pressure of each pneumatic muscle is controlled by a fast underlying control loop. Hence, the control design for the outer control loop can be simplified by considering these controlled muscle pressures as ideal control inputs. The control design of the outer control loop involves a decoupling of rocker angle as well as mean internal pressure of both pneumatic muscles as flat outputs. Additionally, model uncertainties in the equation of motion like nonlinear friction are directly counteracted by an observer-based disturbance compensation which reduces the chattering problem. Experimental results show an excellent control performance that outperforms alternative control approaches in a comparison.