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Pneumatic actuators are low-cost, safe, clean, and exhibit a high power to weight ratio. In this paper a new modeling approach and control law for pneumatic servo actuators are presented. The nonlinear system model is developed using a combination of mechanistic and empirical methods. The use of novel bipolynomial functions to model the valve flow rates is shown to produce a more accurate solution than prior approaches. A novel multiple-input single-output nonlinear position control law is designed using the backstepping methodology. The stability analysis includes the effects of friction modeling error and valve modeling error. Experiments are conducted with 9.5-mm bore and 6.4-mm bore pneumatic cylinders, and four low-cost two-way proportional valves. In experiments with the 9.5-mm bore cylinder and a 1.5-kg moving mass, maximum tracking errors of plusmn0.5 mm for a 1-Hz sine wave trajectory, and steady-state errors within plusmn0.05 mm for an S-curve trajectory were achieved.