## 6 Experimental Verification  
We used a TFC35 electric forklift manufactured by Hefei Banyitong Science and Technology Development Co., Ltd. (Hefei, China) as the study object. The wheel speed sensor, the steering wheel sensor, the yaw rate sensor, and the roll rate sensor were installed during the experiment. The maximum wheel speed was used as the estimation of the vehicle speed. The experiment was carried out in a warehouse with 20% indoor relative humidity. The experimental environment is shown in Figure 2, and the main parameters of the forklift are shown in Table 1. The moving speed is set to 15 km/h. The external disturbance is \(H=\left[ \begin{array}{cccc}0.1&0&0&0.04\end{array} \right]^{T}\), the output disturbance is \(\theta(t)=\sin(2t)\), and the distribution matrix of sensor faults is F = C. The parameters of the ASMO are set as \(\rho_{1}(0)=\rho_{2}(0)=10\), \(\eta_{1}=\eta_{2}=-100\), \(\lambda_{1}=\lambda_{2}=0.5\). Assume that forklift sensor faults occur in different feedback channels: yaw rate sensor faults and roll rate sensor faults. The expressions are as follows:  
\[f_{s1}=\left\{ \begin{array}{ll}3,&12s\leq t<17s\\ 0,&\textit{others}\end{array} \right. \tag{46}\]  
\[f_{s2}=\left\{ \begin{array}{ll}0.2(t-10),&10s\leq t<13s\\ 0.6,&13s\leq t<15s\\ 0,&\textit{others}\end{array} \right. \tag{47}\]  
The double-lane-change (DLC) operating condition is often used to test lateral stability of vehicles. The experiment was conducted with a human operator, and the wheel angle sensor was installed to measure the steering wheel angle. The steering angle of the front wheel is shown in Figure 3. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Description** & **Values or Units** \\ \hline M & Mass of vehicle & 8720 kg \\ \(M_{\mathrm{s}}\) & Sprung mass & 7500 kg \\ \(I_{z}\) & Yaw rate of inertia around the z-axis & 3650 kg\(\cdot\)m\({}^{2}\) \\ \(I_{x}\) & Yaw rate of inertia around the x-axis & 1800 kg\(\cdot\)m\({}^{2}\) \\ \(I_{\mathrm{xz}}\) & Products of inertia around the x-axis and the z-axis & 500 kg\(\cdot\)m\({}^{2}\) \\ \(K_{\phi}\) & Total roll rate & 65,690 Nm/rad \\ \(C_{\psi}\) & Roll damping & 2100 Nm/(rad/s) \\ \(h_{l}\) & Distance from the center of gravity to the roll center & 0.3 m \\ a & Distance from the center of gravity to the rear axle & 1.2 m \\ b & Distance from the center of gravity to the front axle & 0.6 m \\ \(k_{1}\) & Corning stiffness of the front axle & 85,000 N/rad \\ \(k_{2}\) & Corning stiffness of the rear axle & 55,000 N/rad \\ \(R_{f}\) & Roll-steering parameter of the front axle & 0.07 \\ \(R_{r}\) & Roll-steering parameter of the rear axle & 0.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main parameters of the forklift. Figure 2: Experimental platform. Not considering the output disturbance, the signals of the yaw rate sensor and the roll rate sensor without faults are shown in Figure 4.  
Not considering the output disturbance, Figure 5a shows the fault reconstruction value and the fault true value of the yaw rate sensor, and Figure 5b shows values of the roll rate sensor. The observer gives the fault reconstruction value of sensors during faults and the true value of the forklift when no faults take place. To compare the effectiveness of the ASMO, an SMO proposed in [23] is also shown in this manuscript. As the parameter of the SMO is determined by the upper bound of unknown faults, the error value of the SMO reconstruction value is larger than the ASMO. It means that without knowing the upper bound of faults, the parameter of the SMO cannot be determined precisely, and the result is also not as good as the ASMO. It is clear that an ASMO can detect faults of yaw rate and roll rate sensors without knowing the upper bound of faults. Figure 4: (**a**) The yaw rate sensor signal without a fault; (**b**) The roll rate sensor signal without a fault. Figure 3: Steering wheel angle.