Tracking control for a long pneumatic transmission line

This paper presents a tracking controller for a long pneumatic transmission line modeled by a bidirectionally coupled system of partial differential equations (PDEs) and ordinary differential equations (ODEs). The feedforward part of the controller is designed by applying a flatness-based approach for hyperbolic PDEs to a second-order quasilinear model of the pneumatic system. The stabilizing feedback is derived by the application of a recently developed backstepping approach for coupled PDE-ODE systems to a different, more simple, linear model of the line. In simulations, the tracking controller is used to asymptotically stabilize a complex quasilinear third-order distributed parameter model of the pneumatic transmission line along a desired trajectory. This complex model has previously been shown to accurately reproduce the behavior of the pneumatic test bench considered.