Abstract
The dynamic characteristics of air flow in a section of ducting involve nonlinear partial differential equations in which the air pressure and weight flow vary with both space and time. Differential equations for the distributed-parameter and the lumped-parameter representations are derived. Using applicable linearizing assumptions, transfer functions are obtained for each representation. The two transfer functions are compared by applying them to a practical valve-and-ducting system selected from a control problem. Since the lumped-parameter representation is more convenient to use in controls design, a simple numerical criterion is developed to determine rapidly the conditions under which lumped representation of a distributed element is valid. Frequency-response and time-response plots for the lumped and distributed elements are included for comparison purposes.
