Distributed Feedback Control of the Benjamin-Bona-Mahony-Burgers Equation by a Reduced-Order Model

AbstractA reduced-order model for distributed feedback control of the Benjamin-Bona-Mahony-Burgers (BBMB) equation is discussed. To retain more information in our model, we first calculate the functional gain in the full-order case, and then invoke the proper orthogonal decomposition (POD) method to design a low-order controller and thereby reduce the order of the model. Numerical experiments demonstrate that a solution of the reduced-order model performs well in comparison with a solution for the full-order description.

Download Full-text

Model-Based Computation of Functional Gains for Feedback Control of Vortex Shedding

Volume 12: Mechanics of Solids, Structures and Fluids ◽

10.1115/imece2008-68950 ◽

2008 ◽

Author(s):

Imran Ahktar ◽

Jeff Borggaard ◽

John A. Burns ◽

Lizette Zietsman

Keyword(s):

Feedback Control ◽

Vortex Shedding ◽

Control Mechanism ◽

Reduced Order Model ◽

Optimal Placement ◽

Order Model ◽

Reduced Order ◽

Physical Insight ◽

Proper Orthogonal ◽

Functional Gains

Proper orthogonal decomposition (POD) is used to develop a reduced-order model of the flow past a circular cylinder. We introduce a control mechanism into the reduced-order model as a means to favorably perturb the flow to reduce vortex shedding. The feedback control for the fluid actuators is represented in terms of functional gains. These functional gains are integral kernels of the standard feedback operator and are useful in control of partial differential equations. These functional gains give us physical insight into how the control mechanism is operating. In some cases, these functional gains can provide information about the optimal placement of actuators and sensors.

Download Full-text

Reduced-Order Model of a Bladed Rotor With Geometric Mistuning

Volume 5: Turbo Expo 2007 ◽

10.1115/gt2007-27276 ◽

2007 ◽

Cited By ~ 2

Author(s):

Alok Sinha

Keyword(s):

Proper Orthogonal Decomposition ◽

Orthogonal Decomposition ◽

Reduced Order Model ◽

Order Model ◽

Reduced Order ◽

Coordinate Measurement ◽

Coordinate Measurement Machine ◽

Bladed Disk ◽

Bladed Rotor ◽

Proper Orthogonal

This paper deals with the development of an accurate reduced-order model of a bladed disk with geometric mistuning. The method is based on vibratory modes of various tuned systems and proper orthogonal decomposition of coordinate measurement machine (CMM) data on blade geometries. Results for an academic rotor are presented to establish the validity of the technique.

Download Full-text

Reduced order model-based sliding mode control of dynamic systems governed by Burgers' equation

2015 54th IEEE Conference on Decision and Control (CDC) ◽

10.1109/cdc.2015.7402490 ◽

2015 ◽

Cited By ~ 1

Author(s):

Farshid Abbasi ◽

Javad Mohammadpour

Keyword(s):

Sliding Mode Control ◽

Dynamic Systems ◽

Burgers Equation ◽

Sliding Mode ◽

Reduced Order Model ◽

Order Model ◽

Reduced Order ◽

Model Based ◽

Mode Control

Download Full-text

Thermal-electrochemical simulation of lead-acid battery using reduced-order model based on proper orthogonal decomposition for real-time monitoring purposes

Journal of Energy Storage ◽

10.1016/j.est.2021.103491 ◽

2021 ◽

Vol 44 ◽

pp. 103491

Author(s):

Amir Babak Ansari ◽

Vahid Esfahanian ◽

Farschad Torabi

Keyword(s):

Proper Orthogonal Decomposition ◽

Real Time ◽

Orthogonal Decomposition ◽

Reduced Order Model ◽

Lead Acid Battery ◽

Real Time Monitoring ◽

Order Model ◽

Reduced Order ◽

Electrochemical Simulation ◽

Proper Orthogonal

Download Full-text

Feedback Control of Cavity Flow Using Experimental Based Reduced Order Model

35th AIAA Fluid Dynamics Conference and Exhibit ◽

10.2514/6.2005-5269 ◽

2005 ◽

Cited By ~ 6

Author(s):

Edgar Caraballo ◽

X. Yuan ◽

Jesse Little ◽

Marco Debiasi ◽

P Yan ◽

...

Keyword(s):

Feedback Control ◽

Cavity Flow ◽

Reduced Order Model ◽

Order Model ◽

Reduced Order

Download Full-text

Reduced-Order Model of Unsteady Flows in a Turbomachinery Fan Modeled Using a Novel Proper Orthogonal Decomposition

Volume 2C: Turbomachinery ◽

10.1115/gt2019-90323 ◽

2019 ◽

Author(s):

Elizabeth H. Krath ◽

Forrest L. Carpenter ◽

Paul G. A. Cizmas ◽

David A. Johnston

Keyword(s):

Proper Orthogonal Decomposition ◽

Reference Conditions ◽

Stable Solution ◽

Orthogonal Decomposition ◽

Reduced Order Model ◽

Computational Time ◽

Order Model ◽

Reduced Order ◽

Proper Orthogonal ◽

Model Rotor

Abstract This paper presents a novel, more efficient reduced-order model based on the proper orthogonal decomposition (POD) for the prediction of flows in turbomachinery. To further reduce the computational time, the governing equations were written as a function of specific volume instead of density. This allowed for the pre-computation of the coefficients of the system of ordinary differential equations that describe the reduced-order model. A penalty method was developed to implement time-dependent boundary conditions and achieve a stable solution for the reduced-order model. Rotor 67 was used as a validation case for the reduced-order model, which was tested for both on- and off-reference conditions. This reduced-order model was shown to be more than 10,000 times faster than the full-order model.

Download Full-text