# Research on Backstepping Linear Active Disturbance Rejection Control of Hypersonic Vehicle
## 5 Simulation and Analysis
The curve shows that BSLADRC converges faster than PID, and it can reach the stable value for 1 s. After reaching the stable value, it can realize the stable flight of the aircraft; that is, the designed controller can accelerate the aircraft to the preset speed and then rise the aircraft to the preset altitude. But PID takes a longer time to reach steady state and has a large error, so BSLADRC has better performance and stability than PID control. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline \(k_{p}^{h}\) & 1 & \(k_{p}^{V}\) & 1 \\ \(k_{i}^{h}\) & 0.1 & \(k_{i}^{V}\) & 0.1 \\ \(k_{d}^{h}\) & 0.05 & \(k_{d}^{V}\) & 0.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: PID Controller parameters. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline \(\beta_{01}^{V}\) & 120 & \(c_{1}\) & 1 \\ \(\beta_{02}^{V}\) & 4800 & \(c_{2}\) & 1 \\ \(\beta_{01}^{V}\) & 50 & \(c_{3}\) & 2 \\ \(\beta_{02}^{V}\) & 7500 & \(c_{4}\) & 2 \\ \(\beta_{01}^{V}\) & 90 & \(c_{5}\) & 2 \\ \(\beta_{02}^{V}\) & 2700 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Controller parameters. Figure 4: Velocity tracking curve. Figure 5: Track angle tracking curve. Figure 3: Altitude tracking curve. **Example 2**. : _Considering that the hypersonic vehicle may be subjected to various unknown random disturbances in flight, they will affect the stability of the system. In order to verify the anti-jamming ability of the proposed algorithm against random disturbances, white Gaussian noise with a mean value of 0 and variance of 2.5 is used as the noise jamming of the hypersonic vehicle system in this  
Figure 8: Velocity tracking error curve. Figure 6: Angle of attack tracking curve. Figure 7: Altitude tracking error curve. simulation test. The control strategy is the same as the requirements of Example 1. Figure 9 is a Gaussian white noise curve. The controller parameters are the same as those set in Example 1. The PID controller parameter settings are the same as in Example 1._  
It can be seen that both speed and altitude can track the given speed and altitude instructions stably under the condition of interference. From the altitude tracking curves in Figure 10, it can be seen that the two controllers have reached the preset height at last, but BSLADRC obviously has a better tracking effect than PID. Before 80 s, the PID tracking effect is not as good as the BSLADRC tracking effect and has obvious error, and BSLADRC has smaller overshoot than PID, almost no overshoot and can quickly reach a stable state. From the velocity tracking curves in Figure 11, it can be seen that we can see the two controllers have reached the preset velocity at last, but BSLADRC obviously has a better tracking effect than PID. Before 90 s, the PID tracking effect is not as good as the BSLADRC tracking effect and has obvious error, and BSLADRC has smaller overshoot than PID, almost no overshoot and can quickly reach a stable state. Figure 12 shows that both controllers can finally reach a steady state, but the error of BSLADRC can converge to 0 faster. The fluctuation before 40 s of BSLADRC indicates that the aircraft will be affected by some disturbances inside the aircraft during the ascent stage, so it will lead to fluctuations. After reaching the steady state value, the stable flight of the aircraft can be realized; that is, the designed controller can make the aircraft rise to the preset altitude. However, the time for PID to reach stability is too long, and the error is also very large, and the error fluctuates between \(-5\) and 5 all the time, so BSLADRC has better performance and stability than PID control. Figure 13 shows the tracking curve of speed error.