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The primary objective of this paper is to develop a model that accurately represents the dynamics of air flowing through the components of a pneumatic system configuration, which is common in many heavy duty vehicle applications, that eventually translates into braking force. This objective is met using the dynamic compressible airflow equations, which describe flow through an orifice. These equations are coordinated to describe the directional motion of dynamic airflow as commanded by the driver at the foot-pedal and as modified downstream by a modulator to facilitate ABS activity. The solenoid actuated relay valve also includes the motion dynamics of a piston in the existence of hysteresis and coulomb friction type built-in non-smooth nonlinearities. The adoption of an isentropic process, as opposed to the more general case of polytropic behavior, is experimentally determined to suffice for accuracy while yielding significant mathematical convenience.