Dynamic compensators for a nonlinear conservation law

Abstract

In this paper we consider the problem of designing dynamic compensators to control a class of nonlinear parabolic distributed parameter systems. We concentrate on a system with unbounded input and output operators governed by Burgers’ equation. This equation provide a one dimensional model for certain convection—diffusion phenomena. A linearized model is used to compute a robust controller (MinMax), a LQG controller and a fixed-order-finite-dimensional control law (Optimal Projection) by minimizing various energy functionals. These control laws are then applied to the nonlinear model. Different approximation schemes are used to design suboptimal active feedback controllers. This approach provides important practical information. In particular, we show how functional gains can be used to locate new sensors.

Numerical results are given to illustrate the basic ideas and to compare the various controllers.