Sensing schemes for state estimation in turbulent flows and flexible structures

摘要

We show that with a low number of sensors one can estimate, in real time, the full state of distributed parameter systems like the velocity fields of magnetohydrodynamic flows (liquid metals or plasmas in fusion) or the displacement distribution in cantilever beams (as employed in atomic force microscopy). It suffices to place the sensors at the boundary of the domain of the distributed parameter system-for example, electrodes placed at the wall of an MHD flow, or a laser sensor of the beam tip displacement. The estimation of the infinite-dimensional state of the system is performed using observers designed with the method of "backstepping" which guarantees their exponential convergence to the unsteady motion of the true system. The observer design is performed without any spatial discretization-directly on the non-reduced partial differential equation models. The observer gains do not require the solution of any high-dimensional nonlinear equations, like Riccati equations used in Kalman filters. Instead, the observer gains require the solution of a linear hyperbolic PDE, which is readily solvable both numerically and symbolically. We present simulation results that illustrate the use of our observers.