Backstepping design of robust flatness-based tracking controllers for boundary-controlled parabolic PDEs

In this contribution the backstepping design of flatness-based tracking controllers for parabolic systems is extended by an integral action to acount for exogenous disturbances and model uncertainty. The proposed controller design only amounts to stabilizing an ODE by eigenvalue assignment and to applying the standard backstepping approach to a parabolic PDE. The robustness of the resulting disturbance rejection is demonstrated for model uncertainties, that do not destabilize the closed-loop system. Furthermore, it is shown, that the proposed design method allows the prevention of controller windup by a simple structural measure. The theoretical results are demonstrated by means of a parabolic system with spatially varying parameters.