A pneumatic actuator with solenoid valves is a discontinuous-input system because each valve can be either in on or off state. For such an actuator, this paper proposes a sliding-mode control scheme based on an averaged continuous-input equivalent model for the open-loop system. The averaged model is obtained from the nonlinear dynamics of the open-loop discontinuous-input system undergoing pulse-width-modulation (PWM) at the input (i.e., valve open/close action). The PWM duty cycle will be regarded as a continuous input to the proposed averaged model, and thus generated by the proposed sliding-mode controller. By adjusting the PWM duty cycle, the controller switches between seven modes of operation of the open-loop system in order to select the ones with necessary and sufficient amounts of drive energy to achieve position tracking. We will show that this results in reduced position error and valve switching activity for the actuator. The proposed control scheme is experimentally used in the position control of a pneumatic actuator and the results are presented.