Feedback control has allowed great preformance improvement in many technical fields such as robotics, aerospace, telecommunication, transportation systems, manufacturing systems, and chemical processes. Recently, various attempts have been made to apply feedback control techniques to aerodynamics. This is challenging since flow can not be described by simple models. The Collaborative Center of Control Science at The Ohio State University has contributed to the advancement of the state of the art in this field with a multi-disciplinary effort to develop tools and methodologies for feedback flow control. Initially this was done by choosing as a benchmark problem the control of cavity flow resonance.

To control the cavity-flow noise, a two-dimensional synthetic-jet type actuator is used in the cavity-flow facility. This is a powerful loudspeaker connected to a converging cone ending in a slot at the beginning of the cavity. In this arrangement the waves created by the loudspeaker are directed to the position where the flow vortices are created so to control their formation.

The first attempt to control cavity flow resonance was done by using open-loop forcing. Basically I explored the effect of actuation at different frequencies and intensities. This yelded some very interesting results. For instance, actuation at 3250 Hz reduced the noise by 18 dB without introducing much noise of its own, Fig. 1 . This finding, observed also for actuation at about 3900 Hz (not presented here), inspired the design of a simple logic-based control process that automatically searches for optimal actuation conditions for reducing cavity flow resonance. This technique performed well in the experiments as it was able to find and maintain forcing frequencies that reduce cavity-flow resonance in the entire range of Mach number explored, Fig. 2 (AIAA Journal, Vol. 42, No. 9, pp. 1901-1909). Furthermore, it proved to be a powerful tool for extracting valuable information about the effect of control in a large range of forcing conditions.

With the colleagues of CCCS I also studied and tested different closed-loop linear-control techniques for reducing cavity-flow resonance. In general these controls significantly reduce the noise at the Rossiter frequency for which they are designed, but they lead to strong noise at other frequencies (see AIAA paper 2004-0573). A parallel-proportional (PP) with time delay type of control was obtained by modifying a PID controller that remedied this problem, Fig. 3. This is as effective as the open-loop method described above, but is superior as it requires less control power and is more "robust" since it works well even if some changes occur to the air flow (as shown, for instance, in Fig. 4 for the flow at Mach 0.27; see also AIAA Journal, Vol. 44, No. 5, pp. 929-938).

A the 35th AIAA Fluid Dynamics Conference and Exhibit I presented the advancements made by using a state-feedback controller based on a reduced-order model of the cavity flow (see AIAA paper 2005-5269 for more details). The method involves several successive steps.
First, Particle Image Velocimetry (PIV, see Fig. 5) is used to capture the flow over the cavity. Many of these images are processed with the Proper Orthogonal Decomposition (POD) method to approximate the temporal-spatial evolution of the flow as a combination of spatial modes (POD modes) whith amplitude modulated in time by coefficients (time coefficients). The flow quantities (for instance, the velocity) obtained using this approximation are then introduced in the Navier-Stokes equations, i.e. the equations most generally used to describe flow phenomena. These represent a good but very complex model of the flow that is not amiable for control use. However, by projecting what obtained with the previous steps onto the POD modes, a simpler model is obtained that can be used to design a controller. The model is continuously refreshed by the time coefficients which are updated from real-time pressure measurements in different locations on the side wall of the cavity (see Fig. 6) using stochastic estimation.

The model obtained with the steps above can be further simplified by linearizing it around its equilibrium point (corresponding to the mean flow, a quieter state than the resonant one) and by shifting the origin of the coordinates to this equilibrium point. Then a linear-quadratic (LQ) state-feedback controller is designed to bring and keep the system to the equilibrium point (Fig. 7). Experimental validations of such method indicate that the controller significantly reduces the resonance peak of the Mach 0.3 flow for which it was designed, see Fig. 8. The controller seems to be quite robust, as it can control the flow with some variations in the flow Mach number (see also Journal of Fluids Engineering, Vol. 129, pp. 813-824). In term of sheer noise reduction this sophisticated method is slightly less effective than the ones described above, but it actually represents a big leap forward as it is based on a model of the flow and it enables the use of modern control theory techniques to a higher degree.

Additional information on this research can be found in:

• Yuan X., Caraballo E., Little J., Debiasi M., Serrani A., Özbay H., Myatt J. H. and Samimy M., “Feedback Control Design for Subsonic Cavity Flows”, Applied and Computational Mathematics, Vol. 8, No. 1, pp. 70-91, June 2009.
• Efe M. Ö., Debiasi M., Yan P., Özbay H. and Samimy M., “Neural network-based modelling of subsonic cavity flows”, International Journal of Systems Science, Vol. 39, No. 2, pp.105-117, February 2008. [DOI: 10.1080/00207720701726188]
• Caraballo E., Little J., Debiasi M. and Samimy M., “Development and Implementation of an Experimental-Based Reduced-Order Model for Feedback Control of Subsonic Cavity Flows”, Journal of Fluids Engineering, Vol. 129, pp. 813-824, July 2007. [DOI: 10.1115/1.2742724]
• Little J., Debiasi M., Caraballo E. and Samimy M., “Effects of open-loop and closed-loop control on subsonic cavity flows”, Physics of Fluids, Vol. 19, No. 6, 065104, June 2007. [DOI: 10.1063/1.2740302]
• Samimy M., Debiasi M., Caraballo E., Serrani A., Yuan X., Little J. and Myatt J. H., “Feedback control of subsonic cavity flows using reduced-order models”, Journal of Fluid Mechanics, Vol. 579, pp. 315-346, May 2007. [DOI: 10.1017/S0022112007005204]
• Caraballo E., Little J., Debiasi M., Serrani A. and Samimy M., “Reduced Order Model for Feedback Control of Cavity Flow - The Effects of Control Input Separation”, AIAA Paper 2007-1125, 45th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 8-11 January 2007. [DOI: 10.2514/6.2007-1125]
• Debiasi M., Little J., Caraballo E., Yuan X., Serrani A., Myatt J. H. and Samimy M., “Influence of Stochastic Estimation on the Control of Subsonic Cavity Flow – A Preliminary Study”, AIAA Paper 2006-3492, 3rd AIAA Flow Control Conference, San Francisco, California, 5-8 June 2006. [DOI: 10.2514/6.2006-3492]
• Yan P., Debiasi M., Yuan X., Little J., Özbay H. and Samimy M., “Experimental Study of Linear Closed-Loop Control of Subsonic Cavity Flow”, AIAA Journal, Vol. 44, No. 5, pp. 929-938, May 2006. [DOI: 10.2514/1.14873]
• Caraballo E., Yuan X., Little J., Debiasi M., Serrani A., Myatt J. H. and Samimy M., “Further Development of Feedback Control of Cavity Flow Using Experimental Based Reduced Order Model”, AIAA Paper 2006-1405, 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 9-12 January 2006. [DOI: 10.2514/6.2006-1405]
• Little J., Debiasi M. and Samimy M., “Flow Structure in Controlled and Baseline Subsonic Cavity Flows”, AIAA Paper 2006-480, 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 9-12 January 2006. [DOI: 10.2514/6.2006-480]
• Yan P., Debiasi M., Yuan X., Caraballo E., Serrani A., Özbay H., Myatt J. H. and Samimy M., “Modeling and Feedback Control for Subsonic Cavity Flows: A Collaborative Approach”, Paper WeIB18.6, 2005 Joint CDC-ECC Conference, Seville, Spain, 12-15 December 2005. [DOI: 10.1109/CDC.2005.1583036]
• Caraballo E., Yuan X., Yan P., Debiasi M., Serrani A., Samimy M. and Myatt J. H., “Feedback Control of Cavity Flow Using Experimental Based Reduced Order Model”, AIAA Paper 2005-5269, 35th AIAA Fluid Dynamics Conference and Exhibit, Toronto, Ontario, Canada, 6-9 June 2005. [DOI: 10.2514/6.2005-5269]
• Efe M. Ö., Debiasi M., Yan P., Özbay H. and Samimy M., “Control of Subsonic Cavity Flows by Neural Networks – Analytical Models and Experimental Validation”, AIAA Paper 2005-294, 43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 10-13 January 2005. [DOI: 10.2514/6.2005-294]
• Debiasi M. and Samimy M., “Logic-Based Active Control of Subsonic Cavity-Flow Resonance”, AIAA Journal, Vol. 42, No. 9, pp. 1901-1909, September 2004. [DOI: 10.2514/1.4799]
• Debiasi M., Little J., Malone J., Samimy M., Yan P. and Özbay H., “An Experimental Study of Subsonic Cavity Flow – Physical Understanding and Control”, AIAA Paper 2004-2123, 2nd AIAA Flow Control Conference, Portland, Oregon, 28 June - 1 July 2004. [DOI: 10.2514/6.2004-2123]
• Samimy M., Debiasi M., Caraballo E., Malone J., Little J., Özbay H., Efe M. Ö., Yan P., Yuan X., DeBonis J., Myatt J. H. and Camphouse R. C., “Exploring Strategies for Closed-Loop Cavity Flow Control”, AIAA Paper 2004-576, 42nd AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 5-8 January 2004. [DOI: 10.2514/6.2004-576]
• Yan P., Debiasi M., Yuan X., Caraballo E., Efe M. Ö., Özbay H., Samimy M., DeBonis J., Camphouse R. C., Myatt J. H., Serrani A. and Malone J., “Controller Design for Active Closed-Loop Control of Cavity Flows”, AIAA Paper 2004-573, 42nd AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 5-8 January 2004. [DOI: 10.2514/6.2004-573]
• Samimy M., Debiasi M., Caraballo E., Özbay H., Efe M. Ö., Yuan X., DeBonis J. and Myatt J. H., “Development of Closed-loop Control for Cavity Flows”, AIAA Paper 2003-4258, 33rd AIAA Fluid Dynamics Conference and Exhibit, Orlando, Florida, 23-26 June 2003. [DOI: 10.2514/6.2003-4258]
• Debiasi M. and Samimy M., “An Experimental Study of the Cavity Flow for Closed-Loop Flow Control”, AIAA Paper 2003-4003, 33rd AIAA Fluid Dynamics Conference and Exhibit, Orlando, Florida, 23-26 June 2003. [DOI: 10.2514/6.2003-4003]
• Samimy M., Debiasi M., Caraballo E., Özbay H., Efe M. Ö., Yuan X., DeBonis J. and Myatt J. H., “Closed-Loop Active Flow Control – A Collaborative Approach”, AIAA Paper 2003-58, 41st AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 6-9 January 2003. [DOI: 10.2514/6.2003-58]