Air motor systems are modelled in this paper as a class of cascade connection of two non-linear affine control subsystems. The system model is discontinuous in nature, due to the discontinuity of the control volume variations in both drive and exhaust chambers. This discontinuity may present difficulties for system analysis and controller design, so an approximated continuous version of the model is derived. The model validation is conducted by the experiment and simulation. On the basis of this continuous version of system model, a servo control strategy is proposed using a deterministic control design method. Theoretical analysis shows that the desired accuracy of profile following can be guaranteed with this proposed control strategy. An example is given in the paper to demonstrate the design method.