The paper proposes a large approach to pneumatic systems starting from the mathematical laws, written in the form of differential equations, which govern the operation of pneumatic systems and continuing with the simulation model. The concept of integrated design includes all approaches, needed for an optimal and deep system understanding, such as modeling, simulation and control. Pneumatic actuators have a nonlinear functionality because of air compressibility, the existing frictions and the valves nonlinearities. Because of these, they are used in high speed applications and simple positioning systems. Thus, the mathematical analyses of pneumatic systems have received a special attention. The differential equations were implemented in Matlab Simulink, and the model input represents the voltage on the electromagnetic valve, and the output seen on the "scope" represents the movement of the piston pneumatic axis. Some control algorithms are implemented and applied to the model and seen the basic differences.