Showing papers by "Gilead Tadmor published in 2005"

H/sup /spl infin// control and estimation with preview-part I: matrix ARE solutions in continuous time

Abstract: Preview control and fixed-lag smoothing allow a noncausal component in the controller/estimator. Time domain variational analysis is used in a reduction to an open loop differential game, leading to a complete, necessary and sufficient characterization of suboptimal values and an explicit state space design, in terms of a parameterized (nonstandard) algebraic matrix Riccati equation in a general continuous time linear system setting. The solution offers insight into the appropriate structure of the associated Hamiltonian, where the state and co-state are not the usual state of the original dynamic system and that of its adjoint. Rather, the state and co-state are selected to capture the respective lumped effects of initial data and future input selection in the allied game.

H/sup /spl infin// control and estimation with preview-part II: fixed-size ARE solutions in discrete time

Abstract: H/sup /spl infin// preview control and fixed-lag smoothing problems are solved in general discrete time linear systems, via a reduction to equivalent open-loop differential games. To prevent high order Riccati equations, found in some solutions, the state of the Hamilton-Jacobi system resides in a quotient space of an auxiliary extended state space system. The dimension of that auxiliary space is equal to the state space dimension of the original system (ignoring the delay).

Wake stabilization using POD Galerkin models with interpolated modes

Abstract: A principal challenge in the use of empirical proper orthogonal decomposition (POD) Galerkin models for feedback control design in fluid flow systems is their typical fragility and poor dynamic envelope. Closed loop performance and optimized sensor(s) location are significantly improved by use of interpolated POD modes from a succession of low dimensional models from sections of a controlled transient manifold. This strategy is demonstrated in the benchmark of stabilization of the wake flow behind a circular cylinder.

Nonlinear flow control based on a low dimensional model of fluid flow

Abstract: Nonlinear control design is shown to be a critical enabler for robust model-based suppression of a flow instability. The onset of oscillatory vortex shedding is chosen as a well investigated benchmark problem of flow control. A low-dimensional Galerkin model using a Karhunen-Loeve decomposition of the flow field is adopted from earlier studies of the authors as a control-oriented fluid flow representation. Several strategies of nonlinear controller design are employed, both, to the Galerkin model and to the flow via a direct numerical simulation of the Navier-Stokes equations (NSE). The aim is to find methods which respect the validity of low order models. Examples are formal methods such as input-output linearization, Lyapunov-based, backstepping controllers etc., and physically motivated controllers. Whereas the first test-bed is easily mastered by the formal methods, the application to the NSE is more critical, due to robustness issues.

Observers and Feedback Control for Shear Layer Vortices

Abstract: The stirring motion of shear layer vortices plays a prominent and often critical role in diverse engineering applications. Periodic zero net flow actuation is an established mechanism to effect shear layer instability and growth. Active feedback control is considered here as a means to regulate and maximize shear layer mixing: Feedback utilizes estimated vortex locations to harmonize actuation with vortex release. We propose an observer structure based on a phenomenological dynamic phasor model for the travelling waveform of sensors' readings, and illustrate its use in simulations and open and closed loop experiments with the backward facing step system, and in free shear layer simulations.

Real-Time Particle Image Velocimetry for Feedback Loops Using FPGA Implementation

Abstract: Digital Particle Image Velocimetry (PIV) is well established as a ∞uid dynamics measurement tool, being capable of non-intrusively and concurrently measuring a distributed velocity flled. Yet the intensive computational requirements of PIV limit its usage almost exclusively to ofi-line processing, analysis and modelling. This paper proposes hardware implementation of the cross-correlation algorithm as a means to make real-time PIV available for closed-loop control. This paper introduces a real-time PIV system which exploits the low-level parallelism of the cross-correlation computation by implementing it with reconflgurable hardware. The system processes 15 complete image pairs per second, which is more than 70 times speedup over a sequential software implementation. Moreover, our hardware structure can be easily expanded to a more parallel design for faster processing given su‐cient hardware resources. This design can be reused with only minor modiflcations for difierent image sizes and interrogation areas.

A method to reconstruct activation wavefronts without isotropy assumptions using a level sets approach

Abstract: We report on an investigation into using a Level Sets based method to reconstruct activation wavefronts at each time instant from measured potentials on the body surface. The potential map on the epicardium is approximated by a two level image and the inverse problem is solved by evolving a boundary, starting from an initial region, such that a filtered residual error is minimized. The advantage of this method over standard activation-based solutions is that no isotropy assumptions are required. We discuss modifications of the Level Sets method used to improve accuracy, and show the promise of this method via simulation results using recorded canine epicardial data.

Wavefront-based inverse electrocardiography using an evolving curve state vector and phenomenological propagation and potential models

Abstract: We report on an initial study of a state-space model for propagation of the activation wavefront on the heart surface. The activation wavefront was modeled as a curve evolving on the heart surface with the evolution governed by factors derived from a priori data, including anisotropy, along with study of epicardial measurements. The body-surface potential / wavefront relationship is modeled via an intermediate mapping of wavefront to epicardial potentials, again derived from data and prior physiological factors. This design avoids the over-smoothing of Tikhonov solutions and is capable of flexible inclusion of physiological information, including fiber orientation, in the model. Initial results show improvements in reconstructing activation wavefront with respect to the Tikhonov solution, especially at early activation times.