Retrospective Cost Adaptive Flow Control Using a Dielectric Barrier Discharge Actuator with Parameter-Dependent Modeling

Abstract

Low-Reynolds number flyers with a chord Reynolds number of 10 5 or below are sensitive to flow unsteadiness and require an effective flow control scheme to achieve stable flight performance. In this paper, unsteady aerodynamics under fluctuating free-stream conditions on an infinite wing with the SD7003 airfoil geometry at chord Reynolds number 1000 is controlled using a dielectric barrier discharge (DBD) actuator with the retrospective cost adaptive control algorithm. The control law, which requires knowledge of the first nonzero Markov parameter and nonminimum-phase zeros of the linearized flow-actuator model, adjusts control gains by minimizing a quadratic function of the retrospective performance. This paper extends previous research by addressing the lift stabilization mechanism under higher-magnitude disturbance conditions and assessing the variation of system-parameter estimates as functions of the impulse magnitude, free-stream velocity and nominal voltage. The sensitivity of the closed-loop performance to the accuracy of the parameter estimates is investigated by comparing the closed-loop performance with and without modeled parameter variations.

Nonlinearity Identification and Flow Control for Low-Reynolds Number Aerodynamics with Unsteady Free-Stream

“…. From (14), it follows that the extended control vector U'(k) can be written as (18) where American Institute of Aeronautics and Astronautics 7 (19) Next, define the retrospective performance (20) where is an optimization variable, and control matrix is given by Eq. (30) below.…”

“…The detailed mechanism causing this dependency needs further study. As an effort to incorporate the influence of disturbance on the system parameter estimates, a series of impulse tests under different actuation and flow conditions is done in the previous study 19 . Although such an approach showed the potential parametric variations according to the free-stream condition, such as the increase of the real NMP zero for a higher y-directional free-stream velocity, it lacks the effect of the unsteady processes described in the previous section.…”

“…In our previous work 19,20 , an adaptive flow control framework is introduced to mitigate the influence of moderate free-stream disturbances, around several % variations in the vertical free-stream velocity, on a wing with the SD7003 airfoil geometry at the chord Reynolds number of 1000. Assuming a linearized transfer function from the control (actuation voltage) to measurement (lift or drag) of the flow-actuator system, the system parameters required by the controller − the first nonzero Markov parameter (i.e., the initial nonzero response to an impulse) and nonminimum-phase (NMP) zeros (i.e., unstable zeros 21 ) of the linearized transfer function -are identified by using impulse response tests.…”

“…It is also shown that the system parameters are functions of the actuator location, actuation voltage, free-stream magnitude/direction, and Reynolds number, which can engender control difficulties or failure under significant flow unsteadiness. Furthermore, the scheduled variation of the system parameters based on multiple static identifications shows only a marginal improvement 19 .…”