SCIENTIA SINICA Informationis, Volume 49, Issue 6: 760(2019) https://doi.org/10.1360/N112017-00202

## ${\mathcal{L}}_{1}$ adaptive control augmentation for a six-degree-of-freedom hypersonic vehicle model

• AcceptedMar 13, 2018
• PublishedJun 6, 2019
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### Abstract

In this paper, we present the design of an ${\mathcal{L}}_{1}$ adaptive control augmentation system for a six-degree-of-freedom generic hypersonic vehicle model. We focus on addressing system uncertainties, which lead to undesired performance if not properly addressed in the control design. The design begins with the development of a nonlinear dynamic inversion system as the inner-loop controller, which achieves linearization between system inputs and outputs. Linear feedback controllers are then designed as a baseline control system. In addition, the ${\mathcal{L}}_{1}$ adaptive control architecture is used to develop augmentation setups to enhance the control performance of the baseline controllers in the presence of system uncertainties and disturbances. The simulation results demonstrate that the proposed augmentation scheme improves the overall control performance and enhances the robustness of the control system.

### References

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• Figure 1

Conceptual block diagram of the proposed control scheme

• Figure 2

Reference trajectories. (a) $V_r$, (b) $\phi_r$, (c) $\theta_r$, and (d) $\psi_r$

• Figure 3

Tracking performance in test case I. (a) $V$, (b) $\phi$, (c) $\theta$, and (d) $\psi$ tracking

• Figure 4

Control inputs in test case I. (a) PLA, (b) $\delta_a$, (c) $\delta_e$, and (d) $\delta_r$

• Figure 5

Tracking performance in test case II. (a) $V$ and (b) $\phi$ tracking

• Figure 6

Tracking performance in test case II. (a) $\theta$ and (b) $\psi$ tracking

• Figure 7

Control inputs in test case II. (a) PLA and (b) $\delta_a$

• Figure 8

Control inputs in test case II. (a) $\delta_e$ and (b) $\delta_r$

• Figure 9

Tracking performance in test case IV. (a) $V$ and (b) $\phi$ tracking

• Figure 12

Control inputs in test case IV. (a) $\delta_e$ and (b) $\delta_r$

• Table 1   Simulation scenarios
 Test case Scenario rmI Nominal condition rmII Input disturbances rmIII Aerodynamic uncertainties rmIV Parametric variations rmV Reduced control functionality rmVI Combination of the uncertainties of Case II-V
• Table 2   Bounds of the uncertain aerodynamic coefficients
 Element of error vector Error bounds (3$\sigma$ limits) $\epsilon_{C_{L,\alpha}^{\alpha}}$ $\left[0.8,1.2\right]$ $\epsilon_{C_{D,\alpha}^{\alpha}}$ $\left[0.83,1.17\right]$ $\epsilon_{C_{Y,\beta}^M}$ $\left[0.85,1.15\right]$ $\epsilon_{C_{l,p}^0}$ $\left[0.6,1.4\right]$ $\epsilon_{C_{m,\alpha}^{\alpha}}$ $\left[0.83,1.075\right]$ $\epsilon_{C_{m,q}^0}$ $\left[0.6,1.4\right]$ $\epsilon_{C_{n,r}^0}$ $\left[0.6,1.4\right]$
• Table 3   Parametric variations
 Parameter Time-varying changes $m$ $m(t)=(1-\frac{\eta_{\rm~var}}{T_{\rm~sim}}t)m_0$ $I_{xx}$ $I_{xx}(t)=-7.8809\times10^{-5}m^2+25.8857m-6.9683\times10^5$ $I_{yy}$ $I_{yy}(t)=-8.289\times10^{-4}m^2+266m-7.3048\times10^6$ $I_{zz}$ $I_{zz}(t)=I_{yy}(t)$ $S$ $S(t)=\epsilon_{S}S_0$, $\epsilon_{S}\in\left[0.85,1.15\right]$ $\bar{c}$ $\bar{c}(t)=\epsilon_{\bar{c}}\bar{c}_0$, $\epsilon_{\bar{c}}\in\left[0.85,1.15\right]$ $b$ $b(t)=\epsilon_{b}b_{0}$, $\epsilon_{b}\in\left[0.85,1.15\right]$

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