Observer-based LPV control of a nonlinear PDE

In this paper, observer-based linear parameter-varying (LPV) control of the one-dimensional nonlinear Burgers´ equation is presented. The partial differential equation is discretized using a finite difference scheme and the boundary conditions are taken as control inputs. A nonlinear high-order state space model is generated and proper orthogonal decomposition based Galerkin projection is used for model order reduction. A discrete-time quasi-LPV model that is affine in scheduling parameters is derived based on the reduced model and a polytopic dynamic output feedback LPV controller is synthesized. Since the scheduling parameters are linear combinations of system states, the synthesized output-feedback controller is converted to an observer-based state feedback controller which provides an estimate of the scheduling parameters. Simulation results demonstrate that the designed observer-based LPV controller has almost the same level of disturbance and measurement noise rejection capability compared to an output feedback LPV controller combined with a nonlinear observer. Moreover, both of the LPV controllers outperform an LQG controller based on a linearized model.