LPV-Based Self-Adaption Integral Sliding Mode Controller With <inline-formula> <tex-math notation="LaTeX">$L_{2}$ </tex-math></inline-formula> Gain Performance for a Morphing Aircraft

Abstract

This paper designs a parameter-dependent self-adaption integral sliding mode controller which converges the system in a finite time while focusing on an uncertain linear parameter varying (LPV) model of a variant aircraft that has a large-scale variation of the sweep angle and an extension. This design promotes the robustness and L2 performance of the aircraft's speed and altitude during the variant process. According to the longitudinal nonlinear model of a morphing aircraft obtained by the KANE method, the LPV model with the stretch and the sweep angle as the time-varying parameters is derived, and then, the equivalent linear time-invariant (LTI) system is obtained by the linear fractional representation (LFR). Furthermore, the state feedback LFR-H∞ controller has deduced from the linear matrix inequality (LMI) constraints, and then, the existing conditions of the integral sliding mode are obtained from the pole assignment. There are significant uncertainties and disturbances when the linear controller acts on the nonlinear system. Therefore, an adaptive algorithm is introduced to further improve the robustness of the integral sliding mode controller. Moreover, a parameter-dependent Lyapunov function analysis shows that the designed adaptive integral sliding mode control rate can converge the LPV system trajectories to the integral sliding mode surface in a finite time. The comparative simulation results of the nonlinear model of the morphing aircraft indicate the robustness and effectiveness of this approach. The method designed in this paper can be extended to general LPV systems.

Keywords

• Morphing Aircraft
• robust control
• LPV
• integral sliding mode
• adaptive control