Frequency domain analysis of backstepping-based disturbance rejection in a linear hyperbolic system

We perform a frequency-domain analysis of a second-order linear hyperbolic system modeling the so-called heave problem in offshore Managed Pressure Drilling (MPD) in closed loop with a backstepping controller with disturbance feedforward. A measureable disturbance enters at one boundary of the domain and the objective is to track a reference at the same boundary. Both sensing and actuation are restricted to the opposite boundary of the domain. The effect of model uncertainty on closed-loop stability and on the controller performance is investigated and compared to the performance of simpler strategies not using feedforward. The approach is directly applicable to tracking problems in other stable 2 × 2 linear hyperbolic systems controlled by backstepping.