Second order sliding mode control with proportional integral observer for wing rock

In this study, a reduced-order fast proportional integral (PI) observer with a fast convergence function based on the equivalent control notion is developed to estimate the side slip angle β. An unknown state can be discovered by forcing the PI term on the state error, which is the difference between the real and estimated states. A second order sliding mode control (SOSMC) based on a proposed nonlinear sliding manifold is designed to achieve improved transient response and control performance by robustness. The proposed sliding manifold ensures the convergence of the roll angle in finite time. To validate the assertion regarding the proposed SOSMC, classical SOSMC and proportional integral derivative (PID) SOSMC are simulated both in the absence and presence of disturbances. The simulation results show that the proposed SOSMC over-performs in terms of achieving the desired response in both cases. Additionally, a numerical analysis is also performed for both scenarios to evaluate the effectiveness of the proposed controller in terms of the power consumption of the control law and burden on the aileron control surface. Finally, Monte Carlo simulations are performed to demonstrate the robustness of the proposed controller against external disturbances.