Flatness-based tracking control for a pneumatic system with distributed parameters

This paper considers the flatness-based tracking control design for a pneumatic system, where a tank and a proportional valve are connected via a long transmission line of approximately $20~\unit{m}$. Motivated by this test bench set-up and the aim to implement fast pressure changes in the tank, three distributed-parameter models of different complexity and physical accuracy are presented, involving linear and quasi-linear hyperbolic partial differential equations. A flatness-based state feedback control is derived based on a linear distributed-parameter model of the pneumatic system. In combination with flatness-based feedforward controllers, designed for two of the three models, tracking controllers are obtained. Based on a simulation model of the test bench, verified to match the measurement data almost perfectly, the controllers are shown to execute fast pressure changes in the tank very accurately.