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.
KEYWORDS: Actuators, Aerodynamics, Feedback control, Signal attenuation, 3D modeling, Solids, Acoustics, Control systems, Liquid crystal lasers, Data modeling
Blade vortex interaction (BVI) noise has been recognized as the primary determinant of the helicopter's far field acoustic signature. Given the limitations of design in eliminating this dynamic phenomenon, there exists a need for control. In this paper, we present the application, first of feedback control strategies, and then of adaptive cancellation of Leishman and Hariharan's linear aerodynamic model of a trailing edge flap. Lift fluctuations caused by vortices are taken as output disturbance. The contribution of the vortices to lift is obtained from Leishman's indicial model for gusts. The use of an active structure for actuation is assumed, and the actuator is approximated as a lag element. To design an adaptive cancellation scheme that is applicable not only to BVI but also to general problems with periodic disturbances, we start with the sensitivity method but arrive at the same scheme derived by Sacks, Bodson, and Khosla who introduced a phase advance into a pseudo-gradient scheme. We discuss stability of the scheme via averaging.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.