Experimental mitigation of large-amplitude transverse gusts via closed-loop pitch control

Air vehicles of all scales are susceptible to large-amplitude gusts that may lead to vehicle damage and instability. Therefore, effective physics-based control strategies and an understanding of the dominant unsteady flow physics underpinning gust encounters are desired to improve safety and reliability of flight in these conditions. To this end, this paper develops and experimentally demonstrates a proportional output-feedback lift regulation strategy based on the classical unsteady aerodynamic theories of Wagner and Küssner for wings encountering large-amplitude transverse gusts without a priori knowledge of gust strength or onset time. The tested vertical gust velocities ranged between 25% and 71% of the freestream speed. This strategy is found to successfully generalize to gusts of different strengths and directions, as well as wings at pre- and post-stall angles of attack. In addition, this paper applies dynamical systems analysis to Wagner's aerodynamic model to reveal the effect of the pitch-axis location, pitch input, and closed-loop feedback gains on the stability and robustness of the system along with the flow physics responsible. The real-time output feedback control strategy is experimentally tested in a water tow tank facility equipped with a transverse gust generator. Time-resolved force and flow-field measurements are used to discover the salient flow physics during these encounters and illustrate how closed-loop actuation mitigates their lift transients.

Figure 1

Closed-loop control diagram.

Figure 2

Sketch of a wing pitching about a point $ab$ away from the midchord.

Figure 3

Illustration of added-mass components $i$ (a) and $ii$ (b) in Eq. (2) for a pitching-up wing.

Figure 4

The influence of the control gain $k$ and the pitch axis $a$ on the location of the real part of $\text{Re}\left(s_1\right)$ pole.

Figure 5

Root locus of the system.

Figure 6

Angle of attack $\alpha$, pitch rate $\dot{\alpha }$, and lift response $C_l$ for a controlled wing starting at an initial positive angle of attack $\alpha ={20}^{\circ }$ for two different proportional gains $k$.

Figure 7

Normalized trapezoidal gust profile (solid black), the simulated normalized coefficient of lift based on Küssner's model (solid blue), and the simulated normalized coefficient of lift with closed-loop feedback control based on Küssner's and Wagner's models (dashed blue).

Figure 8

Küssner's lift response $C_L/\text{GR}$ in the frequency domain along with the amplitude ratios of the sensitivity transfer function $S$ and the complementary sensitivity transfer function $T$ at different reduced frequencies.

Figure 9

Schematic of the experimental setup.

Figure 10

Closed-loop control setup.

Figure 11

Coefficient of lift normalized by the gust ratio $C_L/\text{GR}$ of the no-control and closed-loop-control cases for various gust ratios at a reference angle of attack ${\alpha }^{\text{ref}}=0$.

Figure 12

Angle of attack $\alpha$ ( blue) and pitch rate $\dot{\alpha }$ ( red) for closed-loop control for various gust ratios at a reference angle of attack ${\alpha }^{\text{ref}}=0$.

Figure 13

(a) Lift coefficients for reference angle of attack ${\alpha }^{\text{ref}}=0^{\circ }$ and gust ratio $\text{GR}=0.50$. The velocity and vorticity fields for the no-control and control cases at $t^{*}=0.50$ (b), (f); $t^{*}=1.00$ (c), (g); $t^{*}=2.00$ (d), (h); and $t^{*}=3.00$ (e), (i); respectively.

Figure 14

A comparison of the coefficient of lift $C_L$ time histories between no control (blue) and closed-loop control (red) for $\text{GR}=0.50$ and various reference angles of attack.

Figure 15

Angle of attack $\alpha$ (blue) and pitch rate $\dot{\alpha }$ (red) for closed-loop control at $\text{GR}=0.50$ and various reference angles of attack.

Figure 16

(a) Lift coefficient for ${\alpha }^{\text{ref}}={15}^{\circ }$ and $\text{GR}=0.50$. The velocity and vorticity fields for the no-control and control cases at $t^{*}=-2.00$ (b), (g); $t^{*}=1.00$ (c), (h); $t^{*}=2.00$ (d), (i); $t^{*}=3.50$ (j), (e); and $t^{*}=7.00$ (f), (k); respectively.

Figure 17

A comparison of the lift coefficients for no-control (blue) and closed-loop control (red) at various reference angles of attack and a downward gust with $\text{GR}=0.50$.

Figure 18

Angle of attack $\alpha$ (blue) and pitch rate $\dot{\alpha }$ (red) for closed-loop control at various reference angles of attack and a downward gust with $\text{GR}=0.50$.

Figure 19

(a) Lift coefficient for ${\alpha }^{\text{ref}}={15}^{\circ }$ and a downward gust with $\text{GR}=0.50$. The velocity and vorticity fields for the no-control and control cases at $t^{*}=-2.00$ (b), (g); $t^{*}=1.00$ (c), (h); $t^{*}=2.00$ (d), (i); $t^{*}=3.50$ (e), (j); and $t^{*}=7.00$ (f), (k); respectively.

Figure 20

Lift decomposition of the uncontrolled case (a) and controlled case (b) for the ${\alpha }^{\text{ref}}=0^{\circ }$ and $\text{GR}=0.50$ case.

Figure 21

Flow-field snapshots and vorticity flux calculation boundary at $t{U}_{\infty }/c=0.75$ of the controlled case (a) and uncontrolled case (b) for reference angle of attack ${\alpha }^{\text{ref}}=0^{\circ }$ and gust ratio $\text{GR}=0.50$.

Figure 22

Schematic of circulation distribution in the flow field of a wing encountering a transverse gust.

Figure 23

A comparison of the circulatory contribution to the coefficient of lift $C_L^c$ (a) as well as the circulation in the ${\mathrm{\Gamma }}_1$ region (b) for no-control (blue) and closed-loop control (red) at a reference angle of attack ${\alpha }^{\text{ref}}=0$ and gust ratio $\text{GR}=0.50$.

Figure 24

Comparison between the circulation contained in the LEV and the circulation contained in the secondary vorticity and the boundary layer of the wing.