We present a systematic approach for determining the optimal actuator location for separation control from input–output response data, gathered from numerical simulations or physical experiments. The Eigensystem realization algorithm is used to extract state-space descriptions from the response data associated with a candidate set of actuator locations. These system realizations are then used to determine the actuator location among the set that can drive the system output to an arbitrary value with minimal control effort. The solution of the corresponding minimum energy optimal control problem is evaluated by computing the generalized output controllability Gramian. We use the method to analyze high-fidelity numerical simulation data of the lift and separation angle responses to a pulse of localized body-force actuation from six distinct locations on the upper surface of a NACA 65(1)-412 airfoil. We find that the optimal location for controlling lift is different from the optimal location for controlling separation angle. In order to explain the physical mechanisms underlying these differences, we conduct controllability analyses of the flowfield by leveraging the dynamic mode decomposition with control algorithm. These modal analyses of flowfield response data reveal that excitation of coherent structures in the wake benefits lift control, whereas excitation of coherent structures in the shear layer benefits separation angle control.
Bibliographical noteFunding Information:
This material is based upon work supported by the Air Force Office of Scientific Research under awards FA9550-16-1-0392, FA9550-17-1-0252, and FA9550-19-1-0034 monitored by Drs. Douglas R. Smith and Gregg Abate. The authors thank Dr. Kevin K. Chen for initial discussions related to optimal actuator selection.
- Dynamic mode decomposition
- Eigensystem realization algorithm
- Flow control
- Flow separation
- Lagrangian coherent structures