Closed-loop approaches to control of a wake flow modeled by the Ginzburg-Landau equation

Cohen, K., Siegel, S., McLaughlin, T., Gillies, E. and Myatt, J. (2005) Closed-loop approaches to control of a wake flow modeled by the Ginzburg-Landau equation. Computers and Fluids, 34, pp. 927-949. (doi: 10.1016/j.compfluid.2004.08.001)

Abstract

A short computational program was undertaken to evaluate the effectiveness of a closed-loop control strategy for the stabilization of an unstable bluff-body flow. In this effort, the non-linear one-dimensional Ginzburg–Landau wake model at 20% above the critical Reynolds number was studied. The numerical model, which is a non-linear partial differential equation with complex coefficients, was solved using the FEMLAB®/MATLAB® software packages and validated by comparison with published literature. At first, a model independent approach was attempted for wake suppression using feedback control. The closed-loop system was controlled using a conventional proportional-integral-derivative (PID) controller as well as a non-linear fuzzy controller. A single sensor is used for feedback, and the actuator is represented by altering the boundary conditions of the cylinder. Simulation results indicate that for a single sensor scheme, the increase in the sophistication of the control results in significantly shorter settling times. However, there is only a marginal improvement concerning the suppression of the wake at higher Reynolds numbers. The feedback control design was then augmented by switching over to a model-dependent controller. Based on computationally generated data obtained from solving the unforced wake, a low-dimensional model of the wake was developed and evaluated. The low-dimensional model of the unforced Ginzburg–Landau equation captures more than 99.8% of the kinetic energy using just two modes. Two sensors, placed in the absolutely unstable region of the wake, are used for real-time estimation of the first two modes. The estimator was developed using the linear stochastic estimation scheme. Finally, the loop is closed using a PID controller that provides the command input to the variable boundary conditions of the model. This method is relatively simple and easy to implement in a real-time scenario. The control approach, applied to the 300 node FEMLAB® model at 20% above the unforced critical Reynolds number stabilizes the entire wake. Compared to the model-independent controllers, the controller based on the low-dimensional model is far more effective in the suppression of the wake at higher Reynolds numbers. Furthermore, while the latter approach employs only the estimated temporal amplitude of the first mode of the imaginary part of the amplitude, all higher modes are stabilized. This suggests that the higher order modes are caused by a secondary instability that is suppressed once the primary instability is controlled.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Gillies, Dr Eric
• Authors: Cohen, K., Siegel, S., McLaughlin, T., Gillies, E., and Myatt, J.
• College/School: College of Science and Engineering > School of Engineering > Autonomous Systems and Connectivity
• Journal Name: Computers and Fluids
• Publisher: Elsevier
• ISSN: 0045-7930
• ISSN (Online): 1879-0747