Dynamic Modeling and Transient Response of Pneumatic Transmission Pipes

The study deals with dynamic modeling and time domain simulation of pneumatic transmission pipes with a distributed parameter dissipative model that include frequency dependent viscous friction terms and heat transfer effects. The transient responses of pneumatic transmission pipes are considerably complex and difficult because the transcendent transfer functions consist of hyperbolic Bessel functions in the frequency domain. For the blocked pipes at the downstream, the pipes terminating into single valve and capacitance element pairs, transfer functions are derived, and their gain and phases are calculated theoretically. Based on the frequency responses of the theoretical transfer functions, we obtained approximated transfer functions with equal frequency responses using MATLAB. The approximated transfer functions with rational polynomials are accurate over the designated frequency ranges, and are used to analyze the time domain responses. The effects of varying parameters of the blocked pipe on the accuracy of the simulated responses are investigated.