Flatness-based output feedback tracking control of a hyperbolic distributed-parameter system

The hyperbolic distributed-parameter system under consideration comprises a second-order partial differential equation that is bidirectionally coupled with a first-order ordinary differential equation. The system models the transmission at a pneumatic test bench with boundary control and collocated measurement, yet stands in place for several other lossy or loss-free transmission problems. In the paper, an observer-based output feedback tracking controller is designed using the concept of flatness. It is a design based on normal forms, as both the state feedback tracking controller and the state observer are derived using canonical coordinates, which in turn rely on special parametrizations of the system's solutions. Additionally, a new transformation between the coordinates of the so-called hyperbolic controller and observer canonical form is presented that allows for the implementation of the observer-based controller. Overall, the closed-loop system is exponentially stable. Simulation results illustrate the tracking behavior.