Gilead Tadmor

A hierarchy of low-dimensional models for the transient and post-transient cylinder wake

A hierarchy of low-dimensional Galerkin models is proposed for the viscous, incompressible flow around a circular cylinder building on the pioneering works of Stuart (1958), Deane et al . (1991), and Ma & Karniadakis (2002). The empirical Galerkin model is based on an eight-dimensional Karhunen–Loeve decomposition of a numerical simulation and incorporates a new ‘shift-mode’ representing the mean-field correction. The inclusion of the shift-mode significantly improves the resolution of the transient dynamics from the onset of vortex shedding to the periodic von Karman vortex street. In addition, the Reynolds-number dependence of the flow can be described with good accuracy. The inclusion of stability eigenmodes further enhances the accuracy of fluctuation dynamics. Mathematical and physical system reduction approaches lead to invariant-manifold and to mean-field models, respectively. The corresponding two-dimensional dynamical systems are further reduced to the Landau amplitude equation.

Feedback shear layer control for bluff body drag reduction

Drag reduction strategies for the turbulent flow around a D-shaped body are examined experimentally and theoretically. A reduced-order vortex model describes the interaction between the shear layer and wake dynamics and guides a path to an efficient feedback control design. The derived feedback controller desynchronizes shear-layer and wake dynamics, thus postponing vortex formation. This actuation is tested in a wind tunnel. The Reynolds number based on the height of the body ranges from 23 000 to 70 000. We achieve a 40% increase in base pressure associated with a 15% drag reduction employing zero-net-mass-flux actuation. Our controller outperforms other approaches based on open-loop forcing and extremum-seeking feedback strategies in terms of drag reduction, adaptivity, and the required actuation energy.

Design and implementation of an adaptive controller for torque ripple minimization in PM synchronous motors

This paper addresses the problem of torque ripple minimization in permanent magnet synchronous motors (PMSMs) and proposes an adaptive feedback structure as a solution. A model of PMSM that includes a torque ripple phenomenon is first developed and tested. While slightly different from the conventional one, our model is still compact and suitable for control. All parameters of the model have physical interpretation, and can either be measured directly or estimated in a numerically reliable procedure. An adaptive control algorithm is then described, enabling speed tracking while minimizing the torque ripple. Finally, the proposed algorithm is verified in simulations and implemented in a hardware setup. Experimental results show significant reduction of torque ripple (by 27 dB). Extensive analysis and simulations of hardware imposed limitations were performed as well, revealing and quantifying the issues that might affect practical ripple minimization performance.

The standard H/sub /spl infin// problem in systems with a single input delay

The standard H/sub /spl infin// problem is solved for LTI systems with a single, pure input lag. The solution is based on state-space analysis, mixing a finite-dimensional and an abstract evolution model. Utilizing the relatively simple structure of these distributed systems, the associated operator Riccati equations are reduced to a combination of two algebraic Riccati equations and one differential Riccati equation over the delay interval. The results easily extend to finite time and time-varying problems where the algebraic Riccati equations are substituted by differential Riccati equations over the process time duration.

H∞ optimal sampled-data control in continuous time systems

We consider the design of H ∞ optimal discrete-time (digital) controllers in continuous-time systems. An apparent difficulty, especially in utilizing modern transform-domain analysis in this context, stems from the absence of an appropriate (transfer function) model for the hybrid-time (discrete and continuous) closed-loop system. This difficulty is overcome through the introduction of an equivalent difference-equation model for the continuous-time system, with distributed inputs and outputs; equivalence being in the sense that the continuous-and discrete-time inputs and outputs are essentially identical. Using the interplay between the discrete and the continuous time models, solutions of the well-known purely continuous-time and purely discrete-time standard problems extend to solutions of the problem at hand. They comprise Riccati equation characterizations of feasible combinations of sampling rates and bounds on the closed-loop induced input-output norm, and parameterization of compensators. We consid...

Reduced-Order Modelling for Flow Control

The book focuses on the physical and mathematical foundations of model-based turbulence control: reduced-order modelling and control design in simulations and experiments. Leading experts provide elementary self-consistent descriptions of the main methods and outline the state of the art. Covered areas include optimization techniques, stability analysis, nonlinear reduced-order modelling, model-based control design as well as model-free and neural network approaches. The wake stabilization serves as unifying benchmark control problem.

Model-based Control of Vortex Shedding Using Low-dimensional Galerkin Models

A model-based flow control strategy is proposed for the suppression of vortex shedding behind a circular cylinder. The control design is based on a hierarchy of low-dimensional Galerkin models of the cylinder wake. These models are constructed from a Karhunen-Loeve decomposition of a simulation without actuation. The key enablers are an additional physical mode in the Karhunen-Loeve approximation and an energy-based control which respects the regime of model validity. The developed control strategy is successfully tested in direct numerical simulations. Copyright  2003 by J. Gerhard, M. Pastoor, R. King, B.R. Noack, A. Dillmann, M. Morzynski and G. Tadmor. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. ∗Research engineer. Corresponding author: phone: ++49-30-314.79574, x24100; fax: x21129; e-mail: johannes.gerhard@tu-berlin.de †Research engineer ‡Professor §Research engineer ¶Professor ‖Professor ∗∗Associate Professor

A Finite-Time Thermodynamics of Unsteady Fluid Flows

Abstract Turbulent fluid has often been conceptualized as a transient thermodynamic phase. Here, a finite-time thermodynamics (FTT) formalism is proposed to compute mean flow and fluctuation levels of unsteady incompressible flows. The proposed formalism builds upon the Galerkin model framework, which simplifies a continuum 3D fluid motion into a finite-dimensional phase-space dynamics and, subsequently, into a thermodynamics energy problem. The Galerkin model consists of a velocity field expansion in terms of flow configuration dependent modes and of a dynamical system describing the temporal evolution of the mode coefficients. Each mode is treated as one thermodynamic degree of freedom, characterized by an energy level. The dynamical system approaches local thermal equilibrium (LTE) where each mode has the same energy if it is governed only by internal (triadic) mode interactions. However, in the generic case of unsteady flows, the full system approaches only partial LTE with unequal energy levels due to strongly mode-dependent external interactions. The FTT model is first illustrated by a traveling wave governed by a 1D Burgers equation. It is then applied to two flow benchmarks: the relatively simple laminar vortex shedding, which is dominated by two eigenmodes, and the homogeneous shear turbulence, which has been modeled with 1459 modes.

Low-Dimensional Models For Feedback Flow Control. Part I: Empirical Galerkin models

A o w model which is accessible to control design must combine low dimension, robustness and a simple structure with an ample dynamic range to cover controlled transients. Key enablers are reviewed in the context of empirical Galerkin models and are exemplied for incompressible shear o ws. These enablers include ‘subgrid’ turbulence and pressure representations, hybrid models that combine multiple operating points, and actuation models. The range of model validity is identied in terms of invariant manifolds which can be exploited by observer design and has to be respected by controller design.

On torque ripple reduction in current-fed switched reluctance motors

This paper addresses a basic control issue in switched reluctance motor (SRM) drives-the production of a ripple-free torque. Simple and largely model-independent conventional supply waveforms are not able to satisfy this requirement. The goal of this paper is to improve SRM dynamical performance by compensating for motor nonlinearities, while maintaining the robustness of conventional methods. The method is based on a complete parameterization of position-dependent voltage and current profiles in ripple-free operation, and on a waveform optimization to minimize power supply requirements. Furthermore, model uncertainties are included to show that the proposed strategy consistently outperforms the conventional policy. Experimental data verifying the analytical approach are included.