LPV modelling and control of Burgers' equation
IFAC Proceedings Volumes (IFAC-PapersOnline) 44 (1): 5430-5435 (2011-01-01)
Contribution to Conference
Linear parameter-varying (LPV) modelling and control of a nonlinear PDE is presented in this paper. The one-dimensional viscous Burgers' 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 is used for model order reduction and the accuracy of the reduced model is verified. A discrete-time quasi- LPV model that is affine in scheduling parameters is derived based on the reduced model and a polytopic LPV controller is synthesized. A low-order functional observer is designed to estimate the scheduling parameters required for LPV controller. Simulation results demonstrate the high tracking performance and disturbance and measurement noise rejection capabilities of the designed LPV controller comparing with an LQG controller based on a linearized model. © 2011 IFAC.