**6. Simulation Results**

To verify the effectiveness of the proposed approaches, we consider a 5 MW wind turbine subject to the actuator and sensor faults in the presence of disturbances and uncertainties. The model and the parameters of the wind turbine used in the simulations are taken from [4] as following:

$$\begin{aligned} \dot{x}(t) &= Ax(t) + Bu(t) + Dd(t) + M\dot{\theta}(t,y) + Ff\_a(t) \\ y(t) &= Cx(t) + F\_sf\_s(t) \\ A &= \begin{bmatrix} 0 & 1.0000 & -0.0406 & 0 & 0 \\ -88.8900 & -0.8889 & 0.0361 & 6.685c - 45 & 0 \\ 32552 & 325.2 & -13.22 & 0 & -0.1 \\ 0 & 0 & 0 & -6.6670 & 0 \\ 0 & 0 & 0 & 0 & -10 \end{bmatrix}, B = F = \begin{bmatrix} 0 & 0 \\ 0 & 0 \\ 0 & 0 \\ 10 & 0 \\ 0 & 6.6667 \end{bmatrix}, \\ \mathcal{C} = \begin{bmatrix} 0 & 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 1 & 1 & 0 & 1 \end{bmatrix}, \mathcal{M} = \begin{bmatrix} 1 \\ -0.5 \\ 1 \\ 0 \\ 0 \end{bmatrix}, F\_s = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}. \end{aligned}$$

The state and the control input vectors are denoted as

$$\begin{aligned} \boldsymbol{\mathfrak{x}}(t) &= \begin{bmatrix} \boldsymbol{\Theta}(t) & \boldsymbol{\Omega}\_{\boldsymbol{r}}(t) & \boldsymbol{\Omega}\_{\boldsymbol{\mathcal{S}}}(t) & \boldsymbol{\beta}(t) & T\_{\boldsymbol{\mathcal{S}}}(t) \end{bmatrix}^T \\ \boldsymbol{\mathfrak{u}}(t) &= \begin{bmatrix} \boldsymbol{\beta}\_{\boldsymbol{r}}(t) & T\_{\boldsymbol{\mathcal{S}},\boldsymbol{d}}(t) \end{bmatrix}^T \end{aligned}$$

where Θ(*t*) the torsion angle, Ω*r*(*t*) the rotor speed, Ω*g*(*t*) the generator speed, *β*(*t*) the pitch angle, and *Tg*(*t*) the generator torque are the state variables and *Tg*,*d*(*t*) the desired generator torque and *βr*(*t*) the pitch angle command are the control input of the wind turbine model.
