Closed-loop control of unsteadiness over a rounded backward-facing step

2012 ◽  
Vol 703 ◽  
pp. 326-362 ◽  
Author(s):  
Alexandre Barbagallo ◽  
Gregory Dergham ◽  
Denis Sipp ◽  
Peter J. Schmid ◽  
Jean-Christophe Robinet
Keyword(s):  
Closed Loop ◽  
Random Noise ◽  
Reduced Order Model ◽  
Estimation Accuracy ◽  
Closed Loop Control ◽  
Backward Facing Step ◽  
Order Model ◽  
Loop Control ◽  
Reduced Order ◽  
And Performance

AbstractThe two-dimensional, incompressible flow over a rounded backward-facing step at Reynolds number $\mathit{Re}= 600$ is characterized by a detachment of the flow close to the step followed by a recirculation zone. Even though the flow is globally stable, perturbations are amplified as they are convected along the shear layer, and the presence of upstream random noise renders the flow unsteady, leading to a broadband spectrum of excited frequencies. This paper is aimed at suppressing this unsteadiness using a controller that converts a shear-stress measurement taken from a wall-mounted sensor into a control law that is supplied to an actuator. A comprehensive study of various components of closed-loop control design – covering sensor placement, choice and influence of the cost functional, accuracy of the reduced-order model, compensator stability and performance – shows that successful control of this flow requires a judicious balance between estimation speed and estimation accuracy, and between stability limits and performance requirements. The inherent amplification behaviour of the flow can be reduced by an order of magnitude if the above-mentioned constraints are observed. In particular, to achieve superior controller performance, the estimation sensor should be placed upstream near the actuator to ensure sufficient estimation speed. Also, if high-performance compensators are sought, a very accurate reduced-order model is required, especially for the dynamics between the actuator and the estimation sensor; otherwise, very minute errors even at low energies and high frequencies may render the large-scale compensated linearized simulation unstable. Finally, coupling the linear compensator to nonlinear simulations shows a gradual deterioration in control performance as the amplitude of the noise increases.

scholarly journals A POD-Galerkin reduced order model of a turbulent convective buoyant flow of sodium over a backward-facing step

2021 ◽  
Vol 89 ◽  
pp. 486-503 ◽  
Author(s):  
Sabrina Star ◽  
Giovanni Stabile ◽  
Gianluigi Rozza ◽  
Joris Degroote
Keyword(s):  
Reduced Order Model ◽  
Backward Facing Step ◽  
Order Model ◽  
Buoyant Flow ◽  
Reduced Order

Model Simplification and Stability Robustness With Elastic Flight Vehicles

1995 ◽  
Vol 117 (3) ◽  
pp. 336-342
Author(s):  
Brett Newman ◽  
David K. Schmidt
Keyword(s):  
Closed Loop ◽  
Order Reduction ◽  
Higher Order ◽  
Reduced Order Model ◽  
Control Law ◽  
Model Simplification ◽  
Closed Loop System ◽  
Order Model ◽  
Reduced Order ◽  
Stability Robustness

Quantitative criteria are presented for model simplification, or order reduction, such that the reduced order model may be used to synthesize and evaluate a control law, and the stability and stability robustness obtained using the reduced order model will be preserved when controlling the higher order system. The error introduced due to model simplification is treated as modeling uncertainty, and some of the results from multivariable robustness theory are brought to bear on the model simplification problem. Also, the importance of the control law itself, in meeting the modeling criteria, is underscored. A weighted balanced order reduction technique is shown to lead to results that meet the necessary criteria. The procedure is applied to an aeroelastic vehicle model, and the results are used for control law development. Critical robustness properties designed into the lower order closed-loop system are shown to be present in the higher order closed-loop system.

A Stabilization of Fixed Gain Controlled Infinite Dimensional Systems by Augmentation With Direct Adaptive Control

2017 ◽  
Author(s):  
Mark J. Balas ◽  
Susan A. Frost
Keyword(s):  
Closed Loop ◽  
Adaptive Controller ◽  
Open Loop ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
Transmission Zeros ◽  
Exponentially Stable

Linear infinite dimensional systems are described by a closed, densely defined linear operator that generates a continuous semigroup of bounded operators on a general Hilbert space of states and are controlled via a finite number of actuators and sensors. Many distributed applications are included in this formulation, such as large flexible aerospace structures, adaptive optics, diffusion reactions, smart electric power grids, and quantum information systems. We have developed the following stability result: an infinite dimensional linear system is Almost Strictly Dissipative (ASD) if and only if its high frequency gain CB is symmetric and positive definite and the open loop system is minimum phase, i.e. its transmission zeros are all exponentially stable. In this paper, we focus on infinite dimensional linear systems for which a fixed gain linear infinite or finite dimensional controller is already in place. It is usually true that fixed gain controllers are designed for particular applications but these controllers may not be able to stabilize the plant under all variations in the operating domain. Therefore we propose to augment this fixed gain controller with a relatively simple direct adaptive controller that will maintain stability of the full closed loop system over a much larger domain of operation. This can ensure that a flexible structure controller based on a reduced order model will still maintain closed-loop stability in the presence of unmodeled system dynamics. The augmentation approach is also valuable to reduce risk in loss of control situations. First we show that the transmission zeros of the augmented infinite dimensional system are the open loop plant transmission zeros and the eigenvalues (or poles) of the fixed gain controller. So when the open-loop plant transmission zeros are exponentially stable, the addition of any stable fixed gain controller does not alter the stability of the transmission zeros. Therefore the combined plant plus controller is ASD and the closed loop stability when the direct adaptive controller augments this combined system is retained. Consequently direct adaptive augmentation of controlled linear infinite dimensional systems can produce robust stabilization even when the fixed gain controller is based on approximation of the original system. These results are illustrated by application to a general infinite dimensional model described by nuclear operators with compact resolvent which are representative of distributed parameter models of mechanically flexible structures. with a reduced order model based controller and adaptive augmentation.

Characterization and Attenuation of Sandwiched Deadband Problem Using Describing Function Analysis and Application to Electrohydraulic Systems Controlled by Closed-Center Valves

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Song Liu ◽  
Bin Yao
Keyword(s):  
Closed Loop ◽  
Function Analysis ◽  
Closed Loop Control ◽  
Control Performance ◽  
Nonlinear Feedback ◽  
Describing Function ◽  
Loop Control ◽  
Actuator Dynamics ◽  
And Performance ◽  
The Stability

Unlike input deadband, the sandwiched deadband between actuator and plant dynamics is very difficult to be explicitly compensated for due to the proceeding actuator dynamics whose effect may not be negligible. The paper presents a practical way to overcome the design conservativeness of existing methods in dealing with sandwiched deadband. Specifically, a describing function based nonlinear analysis method is proposed to characterize the effect of the sandwiched deadband on the stability and performance of the overall closed-loop system. The analysis results can be used to determine the highest closed-loop bandwidth that can be achieved without inducing residual limit cycles and instability. Optimal controller parameters can then be found to maximize the achievable closed-loop control performance. The technique is applied to an electrohydraulic system controlled by closed-center valves and a nonlinear feedback controller. Simulation results showed severe oscillations as the feedback control gains are increased to the predicted threshold values. Comparative experimental results also showed the effectiveness of the proposed method in reducing the conservativeness of traditional design and the improved closed-loop control performance in implementation.

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