An active feedback flow control theory of the axisymmetric vortex breakdown process

2015 ◽  
Vol 774 ◽  
pp. 488-528 ◽  
Author(s):  
Zvi Rusak ◽  
Joshua Granata ◽  
Shixiao Wang
Keyword(s):  
Feedback Control ◽  
Control Theory ◽  
Radial Velocity ◽  
Flow Injection ◽  
Vortex Breakdown ◽  
Flow Dynamics ◽  
Control Law ◽  
Breakdown Process ◽  
Axisymmetric Vortex ◽  
Active Feedback

An active feedback flow control theory of the axisymmetric vortex breakdown process in incompressible swirling flows in a finite-length straight circular pipe is developed. Flow injection distributed along the pipe wall is used as the controller. The flow is subjected to non-periodic inlet and outlet conditions where the inlet profiles of the axial velocity, circumferential velocity and azimuthal vorticity are prescribed, along with no radial velocity at the outlet. A long-wave asymptotic analysis at near-critical swirl ratios, which involves a rescaling of the axial distance and time, results in a model problem for the dynamics and the nonlinear control of both inviscid and high-Reynolds-number ($\mathit{Re}$) flows. The approach provides the bifurcation diagram of steady states and the stability characteristics of these states. In addition, an energy analysis of the controlled flow dynamics suggests a feedback control law that relates the flow injection to the evolving maximum radial velocity at the inlet. Computed examples of the flow dynamics based on the full Euler and Navier–Stokes formulations at various swirl levels demonstrate the evolution to near-steady breakdown states when swirl is above a critical level that depends on $\mathit{Re}$. Moreover, applying the proposed feedback control law during flow evolution shows for the first time the successful and robust elimination of the breakdown states and flow stabilization on an almost columnar state for a wide range of swirl (up to at least 30 %) above critical. The feedback control cuts the natural feed-forward mechanism of the breakdown process. Specifically, in the case of high-$\mathit{Re}$ flows, the control approach establishes a branch of columnar states for all swirl levels studied, where in the natural flow dynamics no such states exist. The present theory is limited to the control of axisymmetric flows in pipes where the wall boundary layer is thin and attached and does not interact with the flow in the bulk.

Nonlinear Control of Axisymmetric Swirling Flows in a Long Finite-Length Pipe

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
Lei Xu ◽  
Zvi Rusak ◽  
Shixiao Wang ◽  
Steve Taylor
Keyword(s):  
Reynolds Number ◽  
Feedback Control ◽  
High Reynolds Number ◽  
Vortex Breakdown ◽  
Basin Of Attraction ◽  
Swirling Flows ◽  
Active Feedback ◽  
Active Feedback Control ◽  
High Reynolds ◽  
Control Methodology

Feedback stabilization of inviscid and high Reynolds number, axisymmetric, swirling flows in a long finite-length circular pipe using active variations of pipe geometry as a function of the evolving inlet radial velocity is studied. The complicated dynamics of the natural flow requires that any theoretical model that attempts to control vortex stability must include the essential nonlinear dynamics of the perturbation modes. In addition, the control methodology must establish a stable desired state with a wide basin of attraction. The present approach is built on a weakly nonlinear model problem for the analysis of perturbation dynamics on near-critical swirling flows in a slightly area-varying, long, circular pipe with unsteady changes of wall geometry. In the natural case with no control, flows with incoming swirl ratio above a critical level are unstable and rapidly evolve to either vortex breakdown states or accelerated flow states. Following an integration of the model equation, a perturbation kinetic-energy identity is derived, and an active feedback control methodology to suppress perturbations from a desired columnar state is proposed. The stabilization of both inviscid and high-Re flows is demonstrated for a wide range of swirl ratios above the critical swirl for vortex breakdown and for large-amplitude initial perturbations. The control gain for the fastest decay of perturbations is found to be a function of the swirl level. Large gain values are required at near-critical swirl ratios while lower gains provide a successful control at swirl levels away from critical. This feedback control technique cuts the feed-forward mechanism between the inlet radial velocity and the growth of perturbation's kinetic energy in the bulk and thereby enforces the decay of perturbations and eliminates the natural explosive evolution of the vortex breakdown process. The application of this proposed robust active feedback control method establishes a branch of columnar states with a wide basin of attraction for swirl ratios up to at least 50% above the critical swirl. This study provides guidelines for future flow control simulations and experiments. However, the present methodology is limited to the control of high-Reynolds number (nearly inviscid), axisymmetric, weakly nonparallel flows in long pipes.

Tips on Stochastic Optimal Feedback Control and Bayesian Spatiotemporal Models: Applications to Robotics

2014 ◽  
Vol 137 (3) ◽  
Author(s):  
Jongeun Choi ◽  
Dejan Milutinović
Keyword(s):  
Sensor Networks ◽  
Feedback Control ◽  
Control Theory ◽  
Mobile Sensor Networks ◽  
Optimal Feedback Control ◽  
Mobile Sensor ◽  
Optimal Feedback ◽  
Spatiotemporal Models ◽  
Feedback Control Theory

This tutorial paper presents the expositions of stochastic optimal feedback control theory and Bayesian spatiotemporal models in the context of robotics applications. The presented material is self-contained so that readers can grasp the most important concepts and acquire knowledge needed to jump-start their research. To facilitate this, we provide a series of educational examples from robotics and mobile sensor networks.

Optimization approach to the constrained regulation problem for linear continuous-time fractional-order systems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Xindong Si ◽  
Hongli Yang
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
State Feedback Control ◽  
Invariant Sets ◽  
Linear Feedback ◽  
Control Law ◽  
Optimization Approach ◽  
Fractional Order Systems ◽  
Linear Feedback Control ◽  
Computational Point

AbstractThis paper deals with the Constrained Regulation Problem (CRP) for linear continuous-times fractional-order systems. The aim is to find the existence conditions of linear feedback control law for CRP of fractional-order systems and to provide numerical solving method by means of positively invariant sets. Under two different types of the initial state constraints, the algebraic condition guaranteeing the existence of linear feedback control law for CRP is obtained. Necessary and sufficient conditions for the polyhedral set to be a positive invariant set of linear fractional-order systems are presented, an optimization model and corresponding algorithm for solving linear state feedback control law are proposed based on the positive invariance of polyhedral sets. The proposed model and algorithm transform the fractional-order CRP problem into a linear programming problem which can readily solved from the computational point of view. Numerical examples illustrate the proposed results and show the effectiveness of our approach.

Feedback Control of Turbulence

1994 ◽  
Vol 47 (6S) ◽  
pp. S3-S13 ◽  
Author(s):  
Parviz Moin ◽  
Thomas Bewley
Keyword(s):  
Feedback Control ◽  
Turbulent Flows ◽  
Systems Approach ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Small Scale ◽  
Flow Equations ◽  
Active Feedback ◽  
Active Feedback Control ◽  
Mathematical Techniques

A brief review of current approaches to active feedback control of the fluctuations arising in turbulent flows is presented, emphasizing the mathematical techniques involved. Active feedback control schemes are categorized and compared by examining the extent to which they are based on the governing flow equations. These schemes are broken down into the following categories: adaptive schemes, schemes based on heuristic physical arguments, schemes based on a dynamical systems approach, and schemes based on optimal control theory applied directly to the Navier-Stokes equations. Recent advances in methods of implementing small scale flow control ideas are also reviewed.

Implications of Optimal Feedback Control Theory for Sport Coaching and Motor Learning: A Systematic Review

Motor Control ◽  
2021 ◽  
pp. 1-24
Author(s):  
Steven van Andel ◽  
Robin Pieper ◽  
Inge Werner ◽  
Felix Wachholz ◽  
Maurice Mohr ◽  
...  
Keyword(s):  
Feedback Control ◽  
Motor Learning ◽  
Control Theory ◽  
Skill Acquisition ◽  
Best Practice ◽  
Optimal Feedback Control ◽  
Optimal Feedback ◽  
Different Types ◽  
Novel Theory ◽  
Feedback Control Theory

Best practice in skill acquisition has been informed by motor control theories. The main aim of this study is to screen existing literature on a relatively novel theory, Optimal Feedback Control Theory (OFCT), and to assess how OFCT concepts can be applied in sports and motor learning research. Based on 51 included studies with on average a high methodological quality, we found that different types of training seem to appeal to different control processes within OFCT. The minimum intervention principle (founded in OFCT) was used in many of the reviewed studies, and further investigation might lead to further improvements in sport skill acquisition. However, considering the homogenous nature of the tasks included in the reviewed studies, these ideas and their generalizability should be tested in future studies.

Thermal effects on axisymmetric vortex breakdown in a spherical gap

1993 ◽  
Vol 5 (5) ◽  
pp. 1211-1223 ◽  
Author(s):  
A. Arkadyev ◽  
P. Bar‐Yoseph ◽  
A. Solan ◽  
K. G. Roesner
Keyword(s):  
Thermal Effects ◽  
Vortex Breakdown ◽  
Axisymmetric Vortex
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